Molecular Orbitals and Organic Chemical
Reactions
Molecular Orbitals and Organic Chemical Reactions: Reference Edition
© 2010 John Wiley & Sons, Ltd. ISBN: 978-0-470-74658-5
Ian Fleming
Molecular Orbitals and Organic
Chemical Reactions
Reference Edition
Ian Fleming
Department of Chemistry,
University of Cambridge, UK
A John Wiley and Sons, Ltd., Publication
This edition first published 2010
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Library of Congress Cataloging-in-Publication Data
Fleming, Ian, 1935–
Molecular orbitals and organic chemical reactions / Ian Fleming. — Reference ed.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-470-74658-5
1. Molecular orbitals. 2. Chemical bonds. 3. Physical organic chemistry. I. Title.
QD461.F533 2010
5470 .2—dc22
2009041770
A catalogue record for this book is available from the British Library.
978-0-470-74658-5
Set in 10/12pt Times by Integra Software Services Pvt. Ltd, Pondicherry, India
Printed and bound in Great Britain by CPI Antony Rowe, Chippenham, Wiltshire.
Contents
Preface
1
Molecular Orbital Theory
1.1 The Atomic Orbitals of a Hydrogen Atom
1.2 Molecules Made from Hydrogen Atoms
1.2.1 The H2 Molecule
1.2.2 The H3 Molecule
1.2.3 The H4 ‘Molecule’
1.3 C—H and C—C Bonds
1.3.1 The Atomic Orbitals of a Carbon Atom
1.3.2 Methane
1.3.3 Methylene
1.3.4 Hybridisation
1.3.5 C—C Bonds and Bonds: Ethane
1.3.6 C¼C Bonds: Ethylene
1.4 Conjugation—Hückel Theory
1.4.1 The Allyl System
1.4.2 Butadiene
1.4.3 Longer Conjugated Systems
1.5 Aromaticity
1.5.1 Aromatic Systems
1.5.2 Antiaromatic Systems
1.5.3 The Cyclopentadienyl Anion and Cation
1.5.4 Homoaromaticity
1.5.5 Spiro Conjugation
1.6 Strained Bonds—Cyclopropanes and Cyclobutanes
1.6.1 Cyclopropanes
1.6.2 Cyclobutanes
1.7 Heteronuclear Bonds, C—M, C—X and C=O
1.7.1 Atomic Orbital Energies and Electronegativity
1.7.2 C—X Bonds
1.7.3 C—M Bonds
1.7.4 C¼O Bonds
1.7.5 Heterocyclic Aromatic Systems
1.8 The Tau Bond Model
1.9 Spectroscopic Methods
1.9.1 Ultraviolet Spectroscopy
1.9.2 Nuclear Magnetic Resonance Spectroscopy
ix
1
1
2
2
7
9
10
10
12
13
15
18
20
23
23
29
32
34
34
37
41
42
44
46
46
48
49
49
50
56
57
59
61
61
61
62
vi
CONTENTS
1.9.3
1.9.4
2
Photoelectron Spectroscopy
Electron Spin Resonance Spectroscopy
65
66
Molecular Orbitals and the Structures of Organic Molecules
2.1 The Effects of Conjugation
2.1.1 A Notation for Substituents
2.1.2 Alkene-Stabilising Groups
2.1.3 Cation-Stabilising and Destabilising Groups
2.1.4 Anion-Stabilising and Destabilising Groups
2.1.5 Radical-Stabilising Groups
2.1.6 Energy-Raising Conjugation
2.2 Hyperconjugation— Conjugation
2.2.1 C—H and C—C Hyperconjugation
2.2.2 C—M Hyperconjugation
2.2.3 Negative Hyperconjugation
2.3 The Configurations and Conformations of Molecules
2.3.1 Restricted Rotation in -Conjugated Systems
2.3.2 Preferred Conformations from Conjugation in the
Framework
2.4 The Effect of Conjugation on Electron Distribution
2.5 Other Noncovalent Interactions
2.5.1 Inversion of Configuration in Pyramidal Structures
2.5.2 The Hydrogen Bond
2.5.3 Hypervalency
2.5.4 Polar Interactions, and van der Waals and other Weak
Interactions
69
69
69
70
76
78
81
83
85
85
92
95
100
101
3
Chemical Reactions—How Far and How Fast
3.1 Factors Affecting the Position of an Equilibrium
3.2 The Principle of Hard and Soft Acids and Bases (HSAB)
3.3 Transition Structures
3.4 The Perturbation Theory of Reactivity
3.5 The Salem-Klopman Equation
3.6 Hard and Soft Nucleophiles and Electrophiles
3.7 Other Factors Affecting Chemical Reactivity
127
127
128
135
136
138
141
143
4
Ionic Reactions—Reactivity
4.1 Single Electron Transfer (SET) in Ionic Reactions
4.2 Nucleophilicity
4.2.1 Heteroatom Nucleophiles
4.2.2 Solvent Effects
4.2.3 Alkene Nucleophiles
4.2.4 The -Effect
4.3 Ambident Nucleophiles
4.3.1 Thiocyanate Ion, Cyanide Ion and Nitrite Ion
(and the Nitronium Cation)
4.3.2 Enolate Ions
4.3.3 Allyl Anions
4.3.4 Aromatic Electrophilic Substitution
145
145
149
149
152
152
155
157
111
113
115
115
118
121
122
157
160
161
167
CONTENTS
4.4
4.5
4.6
5
6
Electrophilicity
4.4.1 Trigonal Electrophiles
4.4.2 Tetrahedral Electrophiles
4.4.3 Hard and Soft Electrophiles
Ambident Electrophiles
4.5.1 Aromatic Electrophiles
4.5.2 Aliphatic Electrophiles
Carbenes
4.6.1 Nucleophilic Carbenes
4.6.2 Electrophilic Carbenes
4.6.3 Aromatic Carbenes
4.6.4 Ambiphilic Carbenes
Ionic Reactions—Stereochemistry
5.1 The Stereochemistry of the Fundamental
Organic Reactions
5.1.1 Substitution at a Saturated Carbon
5.1.2 Elimination Reactions
5.1.3 Nucleophilic and Electrophilic Attack on a Bond
5.1.4 The Stereochemistry of Substitution at Trigonal Carbon
5.2 Diastereoselectivity
5.2.1 Nucleophilic Attack on a Double Bond with
Diastereotopic Faces
5.2.2 Nucleophilic and Electrophilic Attack on Cycloalkenes
5.2.3 Electrophilic Attack on Open-Chain Double Bonds with
Diastereotopic Faces
5.2.4 Diastereoselective Nucleophilic and Electrophilic Attack on Double
Bonds Free of Steric Effects
Thermal Pericyclic Reactions
6.1 The Four Classes of Pericyclic Reactions
6.2 Evidence for the Concertedness of Bond Making
and Breaking
6.3 Symmetry-allowed and Symmetry-forbidden Reactions
6.3.1 The Woodward-Hoffmann Rules—Class by Class
6.3.2 The Generalised Woodward-Hoffmann Rule
6.4 Explanations for the Woodward-Hoffmann Rules
6.4.1 The Aromatic Transition Structure
6.4.2 Frontier Orbitals
6.4.3 Correlation Diagrams
6.5 Secondary Effects
6.5.1 The Energies and Coefficients of the Frontier Orbitals
of Alkenes and Dienes
6.5.2 Diels-Alder Reactions
6.5.3 1,3-Dipolar Cycloadditions
6.5.4 Other Cycloadditions
6.5.5 Other Pericyclic Reactions
6.5.6 Periselectivity
6.5.7 Torquoselectivity
vii
178
178
180
182
183
183
186
199
199
200
201
203
205
207
207
210
214
222
225
226
238
241
250
253
254
256
258
258
271
286
286
287
288
295
295
298
322
338
349
355
362
viii
CONTENTS
7
Radical Reactions
7.1 Nucleophilic and Electrophilic Radicals
7.2 The Abstraction of Hydrogen and Halogen Atoms
7.2.1 The Effect of the Structure of the Radical
7.2.2 The Effect of the Structure of the Hydrogen or Halogen Source
7.3 The Addition of Radicals to Bonds
7.3.1 Attack on Substituted Alkenes
7.3.2 Attack on Substituted Aromatic Rings
7.4 Synthetic Applications of the Chemoselectivity of Radicals
7.5 Stereochemistry in some Radical Reactions
7.6 Ambident Radicals
7.6.1 Neutral Ambident Radicals
7.6.2 Charged Ambident Radicals
7.7 Radical Coupling
369
369
371
371
373
376
376
381
384
386
390
390
393
398
8
Photochemical Reactions
8.1 Photochemical Reactions in General
8.2 Photochemical Ionic Reactions
8.2.1 Aromatic Nucleophilic Substitution
8.2.2 Aromatic Electrophilic Substitution
8.2.3 Aromatic Side-chain Reactivity
8.3 Photochemical Pericyclic Reactions and Related Stepwise Reactions
8.3.1 The Photochemical Woodward-Hoffmann Rule
8.3.2 Regioselectivity of Photocycloadditions
8.3.3 Other Kinds of Selectivity in Pericyclic and Related
Photochemical Reactions
8.4 Photochemically Induced Radical Reactions
8.5 Chemiluminescence
401
401
403
403
405
406
408
408
411
430
432
437
References
439
Index
475
Preface
Molecular orbital theory is used by chemists to describe the arrangement of electrons in chemical structures.
It provides a basis for explaining the ground-state shapes of molecules and their many other properties. As a
theory of bonding it has largely replaced valence bond theory,1 but organic chemists still implicitly use
valence bond theory whenever they draw resonance structures. Unfortunately, misuse of valence bond theory
is not uncommon as this approach remains in the hands largely of the less sophisticated. Organic chemists
with a serious interest in understanding and explaining their work usually express their ideas in molecular
orbital terms, so much so that it is now an essential component of every organic chemist’s skills to have some
acquaintance with molecular orbital theory. The problem is to find a level to suit everyone. At one extreme, a
few organic chemists with high levels of mathematical skill are happy to use molecular orbital theory, and its
computationally more amenable offshoot density functional theory, much as theoreticians do. At the other
extreme are the many organic chemists with lower mathematical inclinations, who nevertheless want to
understand their reactions at some kind of physical level. It is for these people that I have written this book. In
between there are more and more experimental organic chemists carrying out calculations to support their
observations, and these people need to know some of the physical basis for what their calculations are doing.2
I have presented molecular orbital theory in a much simplified and entirely nonmathematical language.
I have simplified the treatment in order to make it accessible to every organic chemist, whether student or
research worker, whether mathematically competent or not. In order to reach such a wide audience, I have
frequently used oversimplified arguments. I trust that every student who has the aptitude will look beyond
this book for a better understanding than can be found here. Accordingly, I have provided over 1800
references to the theoretical treatments and experimental evidence, to make it possible for every reader to
go further into the subject.
Molecular orbital theory is not only a theory of bonding, it is also a theory capable of giving some insight
into the forces involved in the making and breaking of chemical bonds—the chemical reactions that are often
the focus of an organic chemist’s interest. Calculations on transition structures can be carried out with a
bewildering array of techniques requiring more or less skill, more or fewer assumptions, and greater or
smaller contributions from empirical input, but many of these fail to provide the organic chemist with
insight. He or she wants to know what the physical forces are that give the various kinds of selectivity that are
so precious in learning how to control organic reactions. The most accessible theory to give this kind of
insight is frontier orbital theory, which is based on the perturbation treatment of molecular orbital theory,
introduced by Coulson and Longuet-Higgins,3 and developed and named as frontier orbital theory by Fukui.4
Earlier theories of reactivity concentrated on the product-like character of transition structures—the concept
of localisation energy in aromatic electrophilic substitution is a well-known example. The perturbation
theory concentrates instead on the other side of the reaction coordinate. It looks at how the interaction of the
molecular orbitals of the starting materials influences the transition structure. Both influences are obviously
important, and it is therefore helpful to know about both if we want a better understanding of what factors
affect a transition structure, and hence affect chemical reactivity.
Frontier orbital theory is now widely used, with more or less appropriateness, especially by organic
chemists, not least because of the success of the predecessor to this book, Frontier Orbitals and Organic
Chemical Reactions, which survived for more than thirty years as an introduction to the subject for a high
proportion of the organic chemists trained in this period. However, there is a problem—computations show
x
PREFACE
that the frontier orbitals do not make a significantly larger contribution than the sum of all the orbitals. One
theoretician put it to me as: ‘It has no right to work as well as it does.’ The difficulty is that it works as an
explanation in many situations where nothing else is immediately compelling. In writing this book, I have
therefore emphasised more the molecular orbital basis for understanding organic chemistry, about which
there is less disquiet. Thus I have completely rewritten the earlier book, enlarging especially the chapters on
molecular orbital theory itself. I have added a chapter on the effect of orbital interactions on the structures of
organic molecules, a section on the theoretical basis for the principle of hard and soft acids and bases, and a
chapter on the stereochemistry of the fundamental organic reactions. I have introduced correlation diagrams
into the discussion of pericyclic chemistry, and a great deal more in that, the largest chapter. I have also
added a number of topics, both omissions from the earlier book and new work that has taken place in the
intervening years. I have used more words of caution in discussing frontier orbital theory itself, making it less
polemical in furthering that subject, and hoping that it might lead people to be more cautious themselves
before applying the ideas uncritically in their own work.
For all their faults and limitations, frontier orbital theory and the principle of hard and soft acids and bases
remain the most accessible approaches to understanding many aspects of reactivity. Since they fill a gap
between the chemist’s experimental results and a state of the art theoretical description of his or her
observations, they will continue to be used, until something better comes along.
In this book, there is much detailed and not always convincing material, making it less suitable as a textbook for
a lecture course; in consequence I have also written a second and shorter book on molecular orbital theory
designed specifically for students of organic chemistry, Molecular Orbitals and Organic Chemistry—The Student
Edition,5 which serves in a sense as a long awaited second edition to my earlier book. The shorter book uses a
selection of the same material as in this volume, with appropriately revised text, but dispenses with most of the
references, which can all be found here. The shorter book also has problem sets at the ends of the chapters, whereas
this book has the answers to most of them in appropriate places in the text. I hope that everyone can use whichever
volume suits them, and that even theoreticians might find unresolved problems in one or another of them.
As in the earlier book, I begin by presenting some experimental observations that chemists have wanted to
explain. None of the questions raised by these observations has a simple answer without reference to the
orbitals involved.
(i) Why does methyl tetrahydropyranyl ether largely adopt the conformation P.1, with the methoxy group
axial, whereas methoxycyclohexane adopts largely the conformation P.2 with the methoxy group
equatorial?
OMe
OMe
O
O
OMe
OMe
P.1
P.2
(ii) Reduction of butadiene P.3 with sodium in liquid ammonia gives more cis-2-butene P.4 than trans-2butene P.5, even though the trans isomer is the more stable product.
Na, NH3
P.3
+
P.4
60%
P.5
40%
(iii) Why is the inversion of configuration at nitrogen made slower if the nitrogen is in a small ring, and
slower still if it has an electronegative substituent attached to it, so that, with the benefit of both
features, an N-chloroaziridine can be separated into a pair of diastereoisomers P.6 and P.7?
PREFACE
xi
Cl
slow
N
N
Cl
P.6
P.7
(iv) Why do enolate ions P.8 react more rapidly with protons on oxygen, but with primary alkyl halides on
carbon?
H
sl ow
H
O
OH
f ast
O
OH
P.8
f ast I
Me
Me
sl ow
O
O
OMe
P.8
(v) Hydroperoxide ion P.9 is much less basic than hydroxide ion P.10. Why, then, is it so much more
nucleophilic?
N
HOO–
C
P.9
Ph
N
105 times f aster than
HO–
C
P10
Ph
(vi) Why does butadiene P.11 react with maleic anhydride P.12, but ethylene P.13 does not?
O
O
P.11
O
O
O
O
P.12
O
O
P.13
O
O
O
P.12
O
(vii) Why do Diels-Alder reactions of butadiene P.11 go so much faster when there is an electronwithdrawing group on the dienophile, as with maleic anhydride P.12, than they do with ethylene P.13?
O
O
f ast
O
P.11
P.12 O
sl ow
O
O
P.11 P.13
(viii) Why does diazomethane P.15 add to methyl acrylate P.16 to give the isomer P.17 in which the
nitrogen end of the dipole is bonded to the carbon atom bearing the methoxycarbonyl group, and not
the other way round P.14?
xii
PREFACE
N
N
N
N
CO2Me
N
CO2Me
N
CH2
CO2Me
P.14
P.15
P.16
P.17
(ix) When methyl fumarate P.18 and vinyl acetate P.19 are copolymerised with a radical initiator, why
does the polymer P.20 consist largely of alternating units?
OAc
CO2Me
CO2Me
CO2Me
CO2Me
OAc
OAc
OAc
R
+
MeO2C
CO2Me
P.19
P.18
CO2Me
CO2Me
P.20
(x) Why does the Paterno-Büchi reaction between acetone and acrylonitrile give only the isomer P.21 in
which the two ‘electrophilic’ carbon atoms become bonded?
O
(+)
CN
+
h
CN
O
(+)
P.21
In the following chapters, each of these questions, and many others, receives a simple answer. Other books
commend themselves to anyone able and willing to go further up the mathematical slopes towards a more
acceptable level of explanation—a few introductory texts take the next step up,6,7 and several others8–11 take
the story further.
I have been greatly helped by a number of chemists: first and foremost Professor Christopher LonguetHiggins, whose inspiring lectures persuaded me to take the subject seriously at a time when most organic
chemists who, like me, had little mathematics, had abandoned any hope of making sense of the subject;
secondly, and more particularly those who gave me advice for the earlier book, and who therefore made their
mark on this, namely Dr W. Carruthers, Professor R. F. Hudson, Professor A. R. Katritzky and Professor
A. J. Stone. In addition, for this book, I am indebted to Dr Jonathan Goodman for help with computer
programs, to Professor Wes Borden for some helpful discussions and collaboration on one topic, and to
Professor A. D. Buckingham for several important corrections. More than usually, I must absolve all of them
for any errors left in the book.
1
1.1
Molecular Orbital Theory
The Atomic Orbitals of a Hydrogen Atom
To understand the nature of the simplest chemical bond, that between two hydrogen atoms, we look at the
effect on the electron distribution when two atoms are held within bonding distance, but first we need a
picture of the hydrogen atoms themselves. Since a hydrogen atom consists of a proton and a single electron,
we only need a description of the spatial distribution of that electron. This is usually expressed as a wave
function , where 2dt is the probability of finding the electron in the volume dt, and the integral of 2dt
over the whole of space is 1. The wave function is the underlying mathematical description, and it may be
positive or negative; it can even be complex with a real and an imaginary part, but this will not be needed in
any of the discussion in this book. Only when squared does it correspond to anything with physical reality—
the probability of finding an electron in any given space. Quantum theory12 gives us a number of permitted
wave equations, but the only one that matters here is the lowest in energy, in which the distribution of the
electron is described as being in a 1s orbital. This is spherically symmetrical about the nucleus, with a
maximum at the centre, and falling off rapidly, so that the probability of finding the electron within a sphere
of radius 1.4 Å is 90 % and within 2 Å better than 99%. This orbital is calculated to be 13.60 eV lower in
energy than a completely separated electron and proton.
We need pictures to illustrate the electron distribution, and the most common is simply to draw a circle,
Fig. 1.1a, which can be thought of as a section through a spherical contour, within which the electron would
be found, say, 90 % of the time. This picture will suffice for most of what we need in this book, but it might be
worth looking at some others, because the circle alone disguises some features that are worth appreciating.
Thus a section showing more contours, Fig. 1.1b, has more detail. Another picture, even less amenable to a
quick drawing, is to plot the electron distribution as a section through a cloud, Fig. 1.1c, where one imagines
blinking one’s eyes a very large number of times, and plotting the points at which the electron was at each
blink. This picture contributes to the language often used, in which the electron population in a given volume
of space is referred to as the electron density.
H
0
90
1Å
(a) One contour
80 40
20 60
99
2Å
(b) Several contours
(c) An electron cloud
Fig. 1.1 The 1s atomic orbital of a hydrogen atom
Molecular Orbitals and Organic Chemical Reactions: Reference Edition
© 2010 John Wiley & Sons, Ltd. ISBN: 978-0-470-74658-5
Ian Fleming
2
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
a0
1.0
0.8
4 r 2 (r)
P
0.6
van der Waals radius
0.4
0.2
1Å
2Å
r
(a) Fraction of charge-cloud
outside a sphere of radius r
Fig. 1.2
1Å
2Å
r
(b) Radial density f or the ground
state hydrogen atom
Radial probability plots for the 1s orbital of a hydrogen atom
Taking advantage of the spherical symmetry, we can also plot the fraction of the electron population
outside a radius r against r, as in Fig. 1.2a, showing the rapid fall off of electron population with distance. The
van der Waals radius at 1.2 Å has no theoretical significance—it is an empirical measurement from solidstate structures, being one-half of the distance apart of the hydrogen atom in a C—H bond and the hydrogen
atom in the C—H bond of an adjacent molecule.13 It does not even have a fixed value, but is an average of
several measurements. Yet another way to appreciate the electron distribution is to look at the radial density,
where we plot the probability of finding the electron between one sphere of radius r and another of radius
r þ dr. This has a revealing form, Fig. 1.2b, with a maximum 0.529 Å from the nucleus, showing that, in spite
of the wave function being at a maximum at the nucleus, the chance of finding an electron precisely there is
very small. The distance 0.529 Å proves to be the same as the radius calculated for the orbit of an electron in
the early but untenable planetary model of a hydrogen atom. It is called the Bohr radius a0, and is often used
as a unit of length in molecular orbital calculations.
1.2
Molecules Made from Hydrogen Atoms
1.2.1 The H2 Molecule
To understand the bonding in a hydrogen molecule, we have to see what happens when two hydrogen atoms are
close enough for their atomic orbitals to interact. We now have two protons and two nuclei, and even with this
small a molecule we cannot expect theory to give us complete solutions. We need a description of the electron
distribution over the whole molecule—a molecular orbital. The way the problem is handled is to accept that a
first approximation has the two atoms remaining more or less unchanged, so that the description of the
molecule will resemble the sum of the two isolated atoms. Thus we combine the two atomic orbitals in a
linear combination expressed in Equation 1.1, where the function which describes the new electron distribution, the molecular orbital, is called and 1 and 2 are the atomic 1s wave functions on atoms 1 and 2.
¼ c1 1 þ c2 2
1:1
The coefficients, c1 and c2, are a measure of the contribution which the atomic orbital is making to the
molecular orbital. They are of course equal in magnitude in this case, since the two atoms are the same, but
they may be positive or negative. To obtain the electron distribution, we square the function in Equation 1.1,
which is written in two ways in Equation 1.2.
2 ¼ ðc1 1 þ c2 2 Þ2 ¼ ðc1 1 Þ2 þ ðc2 2 Þ2 þ 2c1 1 c2 2
1:2
1 MOLECULAR ORBITAL THEORY
3
Taking the expanded version, we can see that the molecular orbital 2 differs from the superposition of
the two atomic orbitals (c11)2þ(c22)2 by the term 2c11c22. Thus we have two solutions (Fig. 1.3). In
the first, both c1 and c2 are positive, with orbitals of the same sign placed next to each other; the electron
population between the two atoms is increased (shaded area), and hence the negative charge which these
electrons carry attracts the two positively charged nuclei. This results in a lowering in energy and is
illustrated in Fig. 1.3, where the horizontal line next to the drawing of this orbital is placed low on the
diagram. In the second way in which the orbitals can combine, c1 and c2 are of opposite sign, and, if there
were any electrons in this orbital, there would be a low electron population in the space between the nuclei,
since the function is changing sign. We represent the sign change by shading one of the orbitals, and we
call the plane which divides the function at the sign change a node. If there were any electrons in this
orbital, the reduced electron population between the nuclei would lead to repulsion between them; thus, if
we wanted to have electrons in this orbital and still keep the nuclei reasonably close, energy would have to
be put into the system. In summary, by making a bond between two hydrogen atoms, we create two new
orbitals, and *, which we call the molecular orbitals; the former is bonding and the latter antibonding
(an asterisk generally signifies an antibonding orbital). In the ground state of the molecule, the two
electrons will be in the orbital labelled . There is, therefore, when we make a bond, a lowering of energy
equal to twice the value of E in Fig. 1.3 (twice the value, because there are two electrons in the bonding
orbital).
*H—H
Energy
E
H
H
1 node
*
1sH
1sH
E
H—H
Fig. 1.3
HH
0 nodes
The molecular orbitals of hydrogen
The force holding the two atoms together is obviously dependent upon the extent of the overlap in the
bonding orbital. If we bring the two 1s orbitals from a position where there is essentially no overlap
at 3 Å through the bonding arrangement to superimposition, the extent of overlap steadily increases.
The mathematical description of the overlap is an integral S12 (Equation 1.3) called the overlap
integral, which, for a pair of 1s orbitals, rises from 0 at infinite separation to 1 at superimposition
(Fig. 1.4).
ð
S12 ¼ 1 2 dt
1:3
The mathematical description of the effect of overlap on the electronic energy is complex, but some of the
terminology is worth recognising, and will be used from time to time in the rest of this book. The energy E of
4
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
+1
S
0.5
HH
H H
1Å
H
2Å
r H-H
H
3Å
Fig. 1.4 The overlap integral S for two 1sH orbitals as a function of internuclear distance
an electron in a bonding molecular orbital is given by Equation 1.4 and for the antibonding molecular orbital
is given by Equation 1.5:
E¼
þ
1þS
1:4
E¼
1S
1:5
in which the symbol represents the energy of an electron in an isolated atomic orbital, and is called a
Coulomb integral. The function represented by the symbol contributes to the energy of an electron in the field
of both nuclei, and is called the resonance integral. It is roughly proportional to S, and so the overlap integral
appears in the equations twice. It is important to realise that the use of the word resonance does not imply an
oscillation, nor is it exactly the same as the ‘resonance’ of valence bond theory. In both cases the word is used
because the mathematical form of the function is similar to that for the mechanical coupling of oscillators. We
also use the words delocalised and delocalisation to describe the electron distribution enshrined in the function—unlike the words resonating and resonance, these are not misleading, and are the better words to use.
The function is a negative number, lowering the value of E in Equation 1.4 and raising it in Equation 1.5.
In this book, will not be given a sign on the diagrams on which it is used, because the sign can be
misleading. The symbol should be interpreted as ||, the positive absolute value of . Since the diagrams
are always plotted with energy upwards and almost always with the value visible, it should be obvious
which values refer to a lowering of the energy below the level, and which to raising the energy above it.
The overall effect on the energy of the hydrogen molecule relative to that of two separate hydrogen atoms
as a function of the internuclear distance is given in Fig. 1.5. If the bonding orbital is filled (Fig. 1.5a), the
energy derived from the electronic contribution (Equation 1.4) steadily falls as the two hydrogen atoms are
moved from infinity towards one another (curve A). At the same time the nuclei repel each other ever more
strongly, and the nuclear contribution to the energy goes steadily up (curve B). The sum of these two is the
familiar Morse plot (curve C) for the relationship between internuclear distance and energy, with a minimum
at the bond length. If we had filled the antibonding orbital instead (Fig. 1.5b), there would have been no
change to curve B. The electronic energy would be given by Equation 1.5 which provides only a little
shielding between the separated nuclei giving at first a small curve down for curve A, and even that would
change to a repulsion earlier than in the Morse curve. The resultant curve, C, is a steady increase in energy as
the nuclei are pushed together. The characteristic of a bonding orbital is that the nuclei are held together,
whereas the characteristic of an antibonding orbital, if it were to be filled, is that the nuclei would fly apart
unless there are enough compensating filled bonding orbitals. In hydrogen, having both orbitals occupied is
overall antibonding, and there is no possibility of compensating for a filled antibonding orbital.
1 MOLECULAR ORBITAL THEORY
5
B nuclear Coulombic repulsion
C overall
energy
E
E
B nuclear Coulombic
repulsion
0
C overall
energy
0.75Å
HH
A electronic energy
A electronic energy
H H
1Å
H
2Å
r H-H
H
3Å
(a) -Bonding orbital f illed
Fig. 1.5
H
H
1Å
2Å
H
H
r H-H
3Å
(b) -Antibonding orbital f illed
Electronic attraction, nuclear repulsion and the overall effect as a function of internuclear distance for two
1sH atoms
We can see from the form of Equations 1.4 and 1.5 that the term relates to the energy levels of the
isolated atoms labelled 1sH in Fig. 1.3, and the term to the drop in energy labelled E (and the rise labelled
E*). Equations 1.4 and 1.5 show that, since the denominator in the bonding combination is 1 þ S and the
denominator in the antibonding combination is 1 – S, the bonding orbital is not as much lowered in energy as
the antibonding is raised. In addition, putting two electrons into a bonding orbital does not achieve exactly
twice the energy-lowering of putting one electron into it. We are allowed to put two electrons into the one
orbital if they have opposite spins, but they still repel each other, because they have to share the same space;
consequently, in forcing a second electron into the orbital, we lose some of the bonding we might otherwise
have gained. For this reason too, the value of E in Fig. 1.3 is smaller than that of E*. This is why two helium
atoms do not combine to form an He2 molecule. There are four electrons in two helium atoms, two of which
would go into the -bonding orbital in an He2 molecule and two into the *-antibonding orbital. Since 2E*
is greater than 2E, we would need extra energy to keep the two helium atoms together.
Two electrons in the same orbital can keep out of each other’s way, with one electron on one side of the
orbital, while the other is on the other side most of the time, and so the energetic penalty for having a second
electron in the orbital is not large. This synchronisation of the electrons’ movements is referred to as electron
correlation. The energy-raising effect of the repulsion of one electron by the other is automatically included
in calculations based on Equations 1.4 and 1.5, but each electron is treated as having an average distribution
with respect to the other. The effect of electron correlation is often not included, without much penalty in
accuracy, but when it is included the calculation is described as being with configuration interaction, a bit of
fine tuning sometimes added to a careful calculation.
The detailed form that and take is where the mathematical complexity appears. They come from the
Schrödinger equation, and they are integrals over all coordinates, represented here simply by dt, in the form
of Equations 1.6 and 1.7:
ð
¼ 1 H1 dt
1:6
ð
¼ 1 H2 dt
1:7
6
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
where H is the energy operator known as a Hamiltonian. Even without going into this in more detail, it is
clear how the term relates to the atom, and the term to the interaction of one atom with another.
As with atomic orbitals, we need pictures to illustrate the electron distribution in the molecular orbitals. For
most purposes, the conventional drawings of the bonding and antibonding orbitals in Fig. 1.3 are clear
enough—we simply make mental reservations about what they represent. In order to be sure that we do
understand enough detail, we can look at a slice through the two atoms showing the contours (Fig. 1.6). Here we
see in the bonding orbital that the electron population close in to the nucleus is pulled in to the midpoint
between the nuclei (Fig. 1.6a), but that further out the contours are an elliptical envelope with the nuclei as the
foci. The antibonding orbital, however, still has some dense contours between the nuclei, but further out the
electron population is pushed out on the back side of each nucleus. The node is half way between the nuclei,
with the change of sign in the wave function symbolised by the shaded contours on the one side. If there were
electrons in this orbital, their distribution on the outside would pull the nuclei apart—the closer the atoms get,
the more the electrons are pushed to the outside, explaining the rise in energy of curve A in Fig. 1.5b.
(a) The σ-bonding orbital
(b) The σ*-antibonding orbital
Fig. 1.6 Contours of the wave function of the molecular orbitals of H2
We can take away the sign changes in the wave function by plotting 2 along the internuclear axis, as in
Fig. 1.7. The solid lines are the plots for the molecular orbitals, and the dashed lines are plots, for comparison,
of the undisturbed atomic orbitals 2. The electron population in the bonding orbital (Fig. 1.7a) can be seen to
be slightly contracted relative to the sum of the squares of the atomic orbitals, and the electron population
2
1
* 2H-H
2
2
2
H-H
2
1
H2
H1
(a)
bonding
H1
2
2
H2
(b) * antibonding
Fig. 1.7 Plots of the square of the wave function for the molecular orbitals of H2 (solid lines) and its component atomic
orbitals (dashed lines). [The atomic orbital plot is scaled down by a factor of 2 to allow us to compare 2 with the sum of
the atomic densities (12þ22)/2]
1 MOLECULAR ORBITAL THEORY
7
between the nuclei is increased relative to that sum, as we saw when we considered Equation 1.2. In the
antibonding orbital (Fig. 1.7b) it is the other way round, if there were electrons in the molecular orbital, the
electron population would be slightly expanded relative to a simple addition of the squares of the atomic
orbitals, and the electron population between the nuclei is correspondingly decreased.
Let us return to the coefficients c1 and c2 of Equation 1.1, which are a measure of the contribution which
each atomic orbital is making to the molecular orbital (equal in this case). When there are electrons in the
orbital, the squares of the c-values are a measure of the electron population in the neighbourhood of the atom
in question. Thus in each orbital the sum of the squares of all the c-values must equal one, since only one
electron in each spin state can be in the orbital. Since |c1| must equal |c2| in a homonuclear
p diatomic like H2,
we have defined what the values of c1 and c2 in the bonding orbital must be, namely 1/ 2 ¼ 0.707:
c1
c2
σ*
0.707
–0.707
Σc 2 = 1.000
σ
0.707
0.707
Σc 2 = 1.000
Σc 2 = 1.000
Σc 2 = 1.000
If all molecular orbitals were filled, then there would have to be one electron in each spin state on each
atom, and this gives rise to a second criterion for c-values, namely that the sum of the squares of all the cvalues on any one atom in all the molecular orbitals must also equal one. Thus the *-antibonding orbital of
hydrogen will have c-values of 0.707 and –0.707, because these values make the whole set fit both criteria.
Of course, we could have taken c1 and c2 in the antibonding orbital the other way round, giving c1 the
negative sign and c2 the positive.
This derivation of the coefficients is not strictly accurate—a proper normalisation involves the overlap
integral S, which is present with opposite sign in the bonding and the antibonding orbitals (see Equations 1.4
and 1.5). As a result the coefficients in the antibonding orbitals are actually slightly larger than those in the
bonding orbital. This subtlety need not exercise us at the level of molecular orbital theory used in this book,
and it is not a problem at all in Hückel theory, which is what we shall be using for p systems. We can,
however, recognise its importance when we see that it is another way of explaining that the degree of
antibonding from the antibonding orbital (E* in Fig. 1.3) is greater than the degree of bonding from the
bonding orbital (E).
1.2.2 The H3 Molecule
We might ask whether we can join more than two hydrogen atoms together. We shall consider first the
possibility of joining three atoms together in a triangular arrangement. It presents us for the first time with
the problem of how to account for three atoms forming bonds to each other. With three atomic orbitals
to combine, we can no longer simply draw an interaction diagram as we did in Fig. 1.3, where there were only
two atomic orbitals. One way of dealing with the problem is first to take two of them together. In this case,
we take two of the hydrogen atoms, and allow them to interact to form a hydrogen molecule, and then we
combine the and * orbitals, on the right of Fig. 1.8, with the 1s orbital of the third hydrogen atom on
the left.
We now meet an important rule: we are only allowed to combine those orbitals that have the same
symmetry with respect to all the symmetry elements present in the structure of the product and in the orbitals
of the components we are combining. This problem did not arise in forming a bond between two identical
hydrogen atoms, because they have inherently the same symmetry, but now we are combining different sets
8
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
H
A
H
H
1sH
H
H
z
H
A
*
*
H
H
1 node
H
0 nodes
2
S
H
yz
H
S
H
y
H
1
x
H
H
Fig. 1.8
yz
Interacting orbitals for H3
of orbitals with each other. The need to match, and to maintain, symmetry will become a constant refrain as the
molecules get more complex. The first task is to identify the symmetry elements, and to classify the orbitals
with respect to them. Because all the orbitals are s orbitals, there is a trivial symmetry plane in the plane of the
page, which we shall label throughout this book as the xz plane. We can ignore it, and other similar symmetry
elements, in this case. The only symmetry element that is not trivial is the plane in what we shall call the yz
plane, running from top to bottom of the page and rising vertically from it. The orbital and the 1s orbital are
symmetric with respect to this plane, but the * orbital is antisymmetric, because the component atomic
orbitals are out of phase. We therefore label the orbitals as S (symmetric) or A (antisymmetric).
The orbital and the 1s orbital are both S and they can interact in the same way as we saw in Fig. 1.3, to
create a new pair of molecular orbitals labelled 1 and 2*. The former is lowered in energy, because all the
s orbitals are of the same sign, and the latter is raised in energy, because there is a node between the top
hydrogen atom and the two bottom ones. The latter orbital is antibonding overall, because there are two
antibonding interactions between hydrogen atoms and only one bonding interaction. As it happens, its
energy is the same as that of the * orbital, but we cannot justify that fully now. In any case, the other
orbital * remains unchanged in the H3 molecule, because there is no orbital of the correct symmetry to
interact with it.
Thus we have three molecular orbitals, just as we had three atomic orbitals to make them from. Whether
we have a stable ‘molecule’ now depends upon how many electrons we have. If we have two in H3þ, in other
words a protonated hydrogen molecule, they would both go into the 1 orbital, and the molecule would have
a lower electronic energy than the separate proton and H2 molecule. If we had three electrons H3• from
combining three hydrogen atoms, we would also have a stable ‘molecule’, with two electrons in 1 and only
one in 2*, making the combination overall more bonding than antibonding. Only with four electrons in H3–
is the overall result of the interaction antibonding, because the energy-raising interaction is, as usual, greater
than the energy-lowering interaction. This device of building up the orbitals and only then feeding the
electrons in is known as the aufbau method.
We could have combined the three atoms in a straight line, pulling the two lower hydrogen atoms in
Fig. 1.8 out to lay one on each side of the upper atom. Since the symmetries do not change, the result would
have been similar (Fig. 1.9). There would be less bonding in 1 and 2*, because the overlap between the two
lower hydrogen atoms would be removed. There would also be less antibonding from the * orbital, since it
would revert to having the same energy as the two more or less independent 1s orbitals.
1 MOLECULAR ORBITAL THEORY
9
H
*
2
S
H
S
H
H
*
*
H
H
H
2
H
H
H
*
H
H
H
1
A
H
A
H
S
H
S
1
H
Fig. 1.9
H
Relative energies for the orbitals of triangular and linear H3
1.2.3 The H4 ‘Molecule’
There are even more possible ways of arranging four hydrogen atoms, but we shall limit ourselves to
tetrahedral, since we shall be using these orbitals later. This time, we combine them in pairs, as in Fig. 1.3, to
create two hydrogen molecules, and then we ask ourselves what happens to the energy when the two
hydrogen molecules are held within bonding distance, one at right angles to the other.
We can keep one pair of hydrogen atoms aligned along the x axis, on the right in Fig. 1.10, and orient the
other along the y axis, on the left of Fig. 1.10. The symmetry elements present are then the xz and yz planes.
The bonding orbital x on the right is symmetric with respect to both planes, and is labelled SS. The
antibonding orbital x* is symmetric with respect to the xz plane but antisymmetric with respect to the yz
plane, and is accordingly labelled SA. The bonding orbital y on the left is symmetric with respect to both
planes, and is also labelled SS. The antibonding orbital y* is antisymmetric with respect to the xz plane but
symmetric with respect to the yz plane, and is labelled AS. The only orbitals with the same symmetry are
therefore the two bonding orbitals, and they can interact to give a bonding combination 1 and an antibonding
combination 2*. As it happens, the latter has the same energy as the unchanged orbitals x* and y*. This is
not too difficult to understand: in the new orbitals 1 and 2*, the coefficients c, will be (ignoring the full
HH
*
*
y
H
AS
*
H
y
x
H
H
H
SA
H
*
H
H
x
H
H
x
H
*
2
H
H
SS
z
y
SS
H
y
H
1
x
H
Fig. 1.10
H
The orbitals of tetrahedral H4
10
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
treatment of normalisation) 0.5 instead of 0.707, in order that the sum of their squares shall be 1. In the
antibonding combination 2*, there are two bonding relationships between hydrogen atoms, and four antibonding relationships, giving a net value of two antibonding combinations, compared with the one in each of
theporbitals x* and y*. However the antibonding in the orbital 2* is between s orbitals with
p coefficients of
1/ 4, and two such interactions is the same as one between orbitals with coefficients of 1/ 2 (see Equation
1.3, and remember that the change in electronic energy is roughly proportional to the overlap integral S).
We now have four molecular orbitals, 1, 2*, x* and y*, one lowered in energy and one raised relative
to the energy of the orbitals of the pair of hydrogen molecules. If we have four electrons in the system, the net
result is repulsion, as usual when two filled orbitals combine with each other. Thus two H2 molecules do not
combine to form an H4 molecule. This is an important conclusion, and is true no matter what geometry we
use in the combination. It is important, because it shows us in the simplest possible case why molecules exist,
and why they largely retain their identity—when two molecules approach each other, the interaction of their
molecular orbitals usually leads to this repulsion. Overcoming the repulsion is a prerequisite for chemical
reaction and the energy needed is a major part of the activation energy.
1.3
C—H and C—C Bonds
1.3.1 The Atomic Orbitals of a Carbon Atom
Carbon has s and p orbitals, but we can immediately discount the 1s orbital as contributing to bonding,
because the two electrons in it are held so tightly in to the nucleus that there is no possibility of significant
overlap with this orbital—the electrons simply shield the nucleus, effectively giving it less of a positive
charge. We are left with four electrons in 2s and 2p orbitals to use for bonding. The 2s orbital is like the 1s
orbital in being spherically symmetrical, but it has a spherical node, with a wave function like that shown in
Fig. 1.11a, and a contour plot like that in Fig. 1.11b. The node is close to the nucleus, and overlap with the
inner sphere is never important, making the 2s orbital effectively similar to a 1s orbital. Accordingly, a 2s
orbital is usually drawn simply as a circle, as in Fig. 1.11c. The overlap integral S of a 1s orbital on hydrogen
with the outer part of the 2s orbital on carbon has a similar form to the overlap integral for two 1s orbitals in
Fig. 1.4 (except that it does not rise as high, is at a maximum at greater atomic separation, and would not
reach unity at superimposition). The 2s orbital on carbon, at –19.5 eV, is 5.9 eV lower in energy than the 1s
orbital in hydrogen. The attractive force on the 2s electrons is high because the nucleus has six protons, even
though this is offset by the greater average distance of the electrons from the nucleus and by the shielding
from the other electrons. Slater’s rules suggest that the two 1s electrons reduce the nuclear charge by 0.85
atomic charges each, and the other 2s and the two 2p electrons reduce it by 3 0.35 atomic charges, giving
the nucleus an effective charge of 3.25.
r
2Å
1
1
2Å
C
2s
(a) Wave f unction of a 2s
orbital on carbon
Fig. 1.11
(b) Contours f or the wave
f unction
(c) Conventional representation
The 2s atomic orbital on carbon
1 MOLECULAR ORBITAL THEORY
11
The 2p orbitals on carbon also have one node each, but they have a completely different shape. They point
mutually at right angles, one each along the three axes, x, y and z. A plot of the wave function for the 2px
orbital along the x axis is shown in Fig. 1.12a, and a contour plot of a slice through the orbital is shown in
Fig. 1.12b. Scale drawings of p orbitals based on the shapes defined by these functions would clutter up any
attempt to analyse their contribution to bonding, and so it is conventional to draw much narrower lobes, as in
Fig. 1.12c, and we make a mental reservation about their true size and shape. The 2p orbitals, at –10.7 eV, are
higher in energy than the 2s, because they are held on average further from the nucleus. When wave functions
for all three p orbitals, px, py and pz, are squared and added together, the overall electron probability has
spherical symmetry, just like that in the corresponding s orbital, but concentrated further from the nucleus.
Bonds to carbon will be made by overlap of s orbitals with each other, as they are in the hydrogen
molecule, of s orbitals with p orbitals, and of p orbitals with each other. The overlap integrals S between a p
orbital and an s or p orbital are dependent upon the angles at which they approach each other. The overlap
integral for a head on approach of an s orbital on hydrogen along the axis of a p orbital on carbon with a lobe
of the same sign in the wave function (Fig. 1.13a), leading to a bond, grows as the orbitals begin to overlap
(D), goes through a maximum when the nuclei are a little over 0.9 Å apart (C), falls fast as some of the s
orbital overlaps with the back lobe of the p orbital (B), and goes to zero when the s orbital is centred on the
carbon atom (A). In the last configuration, whatever bonding there would be from the overlap with the lobe
of the same sign (unshaded lobes are conventionally used to represent a positive sign in the wave function) is
exactly cancelled by overlap with the lobe (shaded) of opposite sign in the wave function. Of course this
2p
2Å
0.5
1
1Å
1
2Å
1.5Å
1.5Å
r x-axis
1Å
–0.5
(b) Contours f or the wave
f unction
(a) Wave f unction of a 2px
orbital on carbon
(c) Conventional representation
Fig. 1.12 A 2px atomic orbital on carbon
0.5
0.5
C
S
S
F
E
D
G
B
A
1Å
2Å
r C-H
(a) Overlap integral f or overlap of
a p orbital on C with an s orbital on H
Fig. 1.13
3Å
1Å
2Å
r C-C
(b) Overlap integral f or
overlap of two p orbitals on C
Overlap integrals for overlap with a p orbital on carbon
3Å
12
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
configuration is never reached, in chemistry at least, since the nuclei cannot coincide. The overlap integral
for two p orbitals approaching head-on in the bonding mode with matching signs (Fig. 1.13b) begins to grow
when the nuclei approach (G), rises to a maximum when they are about 1.5 Å apart (F), falls to zero as
overlap of the front lobes with each other is cancelled by overlap of the front lobes with the back lobes (E),
and would fall eventually to –1 at superimposition. The signs of the wave functions for the individual s and p
atomic orbitals can get confusing, which is why we adopt the convention of shaded and unshaded. The signs
will not be used in this book, except in Figs. 1.17 and 1.18, where they are effectively in equations.
In both cases, s overlapping with p and p overlapping with p, the overlap need not be perfectly head-on for
some contribution to bonding to be still possible. For imperfectly aligned orbitals, the integral is inevitably
less, because the build up of electron population between the nuclei, which is responsible for holding the
nuclei together, is correspondingly less; furthermore, since the overlapping region will also be off centre, the
nuclei are less shielded from each other. The overlap integral for a 1s orbital on hydrogen and a 2p orbital on
carbon is actually proportional to the cosine of the angle of approach , where is 0 for head-on approach
and 90 if the hydrogen atom is in the nodal plane of the p orbital.
1.3.2 Methane
In methane, there are eight valence electrons, four from the carbon and one each from the hydrogen atoms,
for which we need four molecular orbitals. We can begin by combining two hydrogen molecules into a
composite H4 unit, and then combine the orbitals of that species (Fig. 1.10) with the orbitals of the carbon
atom. It is not perhaps obvious where in space to put the four hydrogen atoms. They will repel each other, and
the furthest apart they can get is a tetrahedral arrangement. In this arrangement, it is still possible to retain
bonding interactions between the hydrogen atoms and the carbon atoms in all four orbitals, as we shall see,
and the maximum amount of total bonding is obtained with this arrangement.
We begin by classifying the orbitals with respect to the two symmetry elements, the xz plane and the yz
plane. The symmetries of the molecular orbitals of the H4 ‘molecule’ taken from Fig. 1.10 are placed on the
left in Fig. 1.14, but the energies of each are now close to the energy of an isolated 1s orbital on hydrogen,
because the four hydrogen atoms are now further apart than we imagined them to be in Fig. 1.10. The s and p
HH
*
x
H
H H
H
C
H
H H
H H
C
C
H H
H
H
H
H
y
H
SA
AS
H SS
H
SS
H
H
*
*
2
SA
AS
SS
C
2py
C 2pz
H
SS
1
H
2px
C
C
2s
H
z
H H
y
C
x
Fig. 1.14
H
H
The molecular orbitals of methane constructed from the interaction of the orbitals of tetrahedral H4 and a
carbon atom
1 MOLECULAR ORBITAL THEORY
13
orbitals on the single carbon atom are shown on the right. There are two SS orbitals on each side, but the overlap
integral for the interaction of the 2s orbital on carbon with the 2* orbital is zero—there is as much bonding with
the lower lobes as there is antibonding with the upper lobes. This interaction leads nowhere. We therefore have
four interactions, leading to four bonding molecular orbitals (shown in Fig. 1.14) and four antibonding (not
shown). One is lower in energy than the others, because it uses overlap from the 2s orbital on carbon, which is
lower in energy than the 2p orbitals. The other three orbitals are actually equal in energy, just like the component
orbitals on each side, and the four orbitals are all we need to accommodate the eight valence electrons. There will
be, higher in energy, a corresponding set of antibonding orbitals, which we shall not be concerned with for now.
In this picture, the force holding any one of the hydrogen atoms bonded to the carbon is derived from more
than one molecular orbital. The two hydrogen atoms drawn below the carbon atom in Fig. 1.14 have bonding
from the low energy orbital made up of the overlap of all the s orbitals, and further bonding from the orbitals,
drawn on the upper left and upper right, made up from overlap of the 1s orbital on the hydrogen with the 2pz and
2px orbitals on carbon. These two hydrogen atoms are in the node of the 2py orbital, and there is no bonding to
them from the molecular orbital in the centre of the top row. However, the hydrogens drawn above the carbon
atom, one in front of the plane of the page and one behind, are bonded by contributions from the overlap of their
1s orbitals with the 2s, 2py and 2pz orbitals of the carbon atom, but not with the 2px orbital.
Fig. 1.14 uses the conventional representations of the atomic orbitals, revealing which atomic orbitals
contribute to each of the molecular orbitals, but they do not give an accurate picture of the resulting electron
distribution. A better picture can be found in Jorgensen’s and Salem’s pioneering book, The Organic
Chemist’s Book of Orbitals,14 which is also available as a CD.15 There are also several computer programs
which allow you easily to construct more realistic pictures. The pictures in Fig. 1.15 come from one of these,
Jaguar, and show the four filled orbitals of methane. The wire mesh drawn to represent the outline of each
molecular orbital shows one of the contours of the wave function, with the signs symbolised by light and
heavier shading. It is easy to see what the component s and p orbitals must have been, and for comparison the
four orbitals are laid out here in the same way as those in Fig. 1.14.
Fig. 1.15
One contour of the wave function for the four filled molecular orbitals of methane
1.3.3 Methylene
Methylene, CH2, is not a molecule that we can isolate, but it is a well known reactive intermediate with a bent
H—C—H structure, and in that sense is a ‘stable’ molecule. Although more simple than methane, it brings us
for the first time to another feature of orbital interactions which we need to understand. We take the orbitals
14
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
of a hydrogen molecule from Fig. 1.3 and place them on the left of Fig. 1.16, except that again the atoms are
further apart, so that the bonding and antibonding combination have relatively little difference in energy. On
the right are the atomic orbitals of carbon. In this case we have three symmetry elements: (i) the xz plane,
bisecting all three atoms; (ii) the yz plane, bisecting the carbon atom, and through which the hydrogen atoms
reflect each other; and (iii) a two-fold rotation axis along the z coordinate, bisecting the H—C—H angle. The
two orbitals, HH and *HH in Fig. 1.16, are SSS and SAA with respect to these symmetry elements, and
the atomic orbitals of carbon are SSS, SSS, ASA and SAA. Thus there are two orbitals on the right and one on
the left with SSS symmetry, and the overlap integral is positive for the interactions of the HH and both the 2s
and 2pz orbitals, so that we cannot have as simple a way of creating a picture as we did with methane, where
one of the possible interactions had a zero overlap integral.
In more detail, we have three molecular orbitals to create from three atomic orbitals, and the linear
combination is Equation 1.8, like Equation 1.1 but with three terms:
¼ c1 1 þ c2 2 þ c3 3
1:8
Because of symmetry, |c1| must equal |c3|, but |c2| can be different. On account of the energy difference, it
only makes a small contribution to the lowest-energy orbital, as shown in Fig. 1.17, where there is a small
p lobe, in phase, buried inside the s orbital s. It would show in a full contour diagram, but does not intrude in
a simple picture like that in Fig. 1.16. The second molecular orbital up in energy created from this
interaction, the z orbital, is a mix of the HH orbital, the 2s orbital on carbon, out of phase, and the 2pz
orbital, in phase, which has the effect of boosting the upper lobe, and reducing the lower lobe. There is then a
third orbital higher in energy, shown in Fig. 1.17 but not in Fig. 1.16, antibonding overall, with both the 2s
and 2pz orbitals out of phase with the HH orbital. Thus, we have created three molecular orbitals from three
atomic orbitals.
Returning to Fig. 1.16, the other interaction, between the *HH orbital and its SAA counterpart, the 2px
orbital, gives a bonding combination x and an antibonding combination (not shown). Finally, the remaining
p orbital, 2py with no orbital of matching symmetry to interact with, remains unchanged, and, as it happens,
unoccupied.
If we had used the linear arrangement H—C—H, the x orbital would have had a lower energy, because the
overlap integral, with perfect head-on overlap ( ¼ 0), would be larger, but the z orbital would have made
no contribution to bonding, since the H atoms would have been in the node of the p orbital. This orbital would
C
2py
SAA
ASA
SSS
H
H
antibonding
bonding
*HH
H
H
HH
H
H
H
C
x
H
H
SSS
y
C
2s
C
s
Fig. 1.16
2py
z
C
H
x
C
C 2pz
SAA
SSS
z
2px
C
H
H
The molecular orbitals of methylene constructed from the interaction of the orbitals of H2 and a carbon atom
1 MOLECULAR ORBITAL THEORY
H
H
15
+
C
+
H
H
–2s
HH
H
H
+
–2s
HH
H
HH
Fig. 1.17
C
H
+
C
2s
*z
C
C
2pz
+
C
–2pz
+
–2pz
z
C
H
H
C
C
H
s
H
Interactions of a 2s and 2pz orbital on carbon with the HH orbital with the same symmetry
simply have been a new orbital on carbon, half way between the s and p orbitals, making no contribution to
bonding, and the overall lowering in energy would be less than for the bent structure.
We do not actually need to combine the orbitals of the two hydrogen atoms before we start. All we need to
see is that the combinations of all the available s and p orbitals leading to the picture in Fig. 1.16 will account
for the bent configuration which has the lowest energy. Needless to say, a full calculation, optimising the
bonding, comes to the same conclusion. Methylene is a bent molecule, with a filled orbital of p character,
labelled z, bulging out in the same plane as the three atoms. The orbital s made up largely from the s
orbitals is lowest in energy, both because the component atomic orbitals start off with lower energy, and
because their combination is inherently head-on. An empty py orbital is left unused, and this will be the
lowest in energy of the unfilled orbitals—it is nonbonding and therefore lower in energy than the various
antibonding orbitals created, but not illustrated, by the orbital interactions shown in Fig. 1.16.
1.3.4 Hybridisation
One difficulty with these pictures, explaining the bonding in methane and in methylene, is that there is no
single orbital which we can associate with the C—H bond. To avoid this inconvenience, chemists often use
Pauling’s idea of hybridisation; that is, they mix together the atomic orbitals of the carbon atom, adding the s
and p orbitals together in various proportions, to produce a set of hybrids, before using them to make the
molecular orbitals. We began to do this in the account of the orbitals of methylene, but the difference now is
that we do all the mixing of the carbon-based orbitals first, before combining them with anything else.
Thus one-half of the 2s orbital on carbon can be mixed with one-half of the 2px orbital on carbon, with its
wave function in each of the two possible orientations, to create a degenerate pair of hybrid orbitals, called sp
hybrids, leaving the 2py and 2pz orbitals unused (Fig. 1.18, top). The 2s orbital on carbon can also be mixed
with the 2px and 2pz orbitals, taking one-third of the 2s orbital in each case successively with one-half of the
2px and one-sixth of the 2pz in two combinations to create two hybrids, and with the remaining two-thirds of
the 2pz orbital to make the third hybrid. This set is called sp2 (Fig. 1.18, centre); it leaves the 2py orbital
unused at right angles to the plane of the page. The three hybrid orbitals lie in the plane of the page at angles
of 120 to each other, and are used to describe the bonding in trigonal carbon compounds. For tetrahedral
carbon, the mixing is one-quarter of the 2s orbital with one-half of the 2px and one-quarter of the 2pz orbital,
in two combinations, to make one pair of hybrids, and one quarter of the 2s orbital with one-half of the 2py
and one-quarter of the 2pz orbital, also in two combinations, to make the other pair of hybrids, with the set of
four called sp3 hybrids (Fig. 1.18, bottom).
16
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
√ 2 2s
1
√ 2 2s
1
+
+
√ 2 –2px
1
√ 2 2px
1
=
sp hybrid
=
sp hybrid
√ 3 2s
+
√ 2 –2px
+
√6 2pz
=
sp2 hybrid
√ 3 2s
+
√2 2px
+
√6 2pz
1
=
sp2 hybrid
+
√ 3 –2pz
=
sp2 hybrid
1
1
1
1
√13 2s
1
2
√ 4 2s
1
+
√2 –2px
+
√ 4 –2pz
=
sp3 hybrid
√ 14 2s
+
√12 2px
+
√ 4 –2pz
=
sp3 hybrid
√ 14 2s
+
√ 12 –2py
+
√ 41 2pz
=
(large lobe in front of the
plane of the page, and
small lobe behind)
√
+
√
+
√
=
(large lobe behind the
plane of the page, and
small lobe in front)
1
4 2s
1
1
2 2py
1
1
Fig. 1.18
1
4 2pz
sp3 hybrid
sp3 hybrid
Hybrid orbitals
The conventional representations of hybrid orbitals used in Fig. 1.18 are just as misleading as the conventional representations of the p orbitals from which they are derived. A more accurate picture of the sp3 hybrid
is given by the contours of the wave function in Fig. 1.19. Because of the presence of the inner sphere in the
2s orbital (Fig. 1.11a), the nucleus is actually inside the back lobe, and a small proportion of the front
lobe reaches behind the nucleus. This follows from the way a hybrid is constructed by adding one-quarter of
the wave function of the s orbital (Fig. 1.11a) and three-quarters in total of the wave functions of the p orbitals
(Fig. 1.12a). As usual, we draw the conventional hybrids relatively thin, and make the mental reservation that
they are fatter than they are usually drawn.
=0.1
=0.2
=0.3
=0.4
2Å
Fig. 1.19
1
1
2Å
A section through an sp3 hybrid on carbon
1 MOLECULAR ORBITAL THEORY
17
The interaction of the 1s orbital of a hydrogen atom with an sp3 hybrid on carbon can be used in the usual
way to create a CH bonding orbital and a *CH antibonding orbital (Fig. 1.20). Four of the bonding orbitals,
each with two electrons in it, one from each of the four hybrids, point towards the corners of a regular
tetrahedron, and give rise to the familiar picture for the bonds in methane shown in Fig. 1.21a.
*C—H
H
H
sp3C
1sH
C—H
Fig. 1.20
H
Bonding and antibonding orbitals of a C—H bond
H H
H H
H
H
(a) The sp3 hybrids on carbon overlapping with
the s orbitals of hydrogen
Fig. 1.21
H
H
(b) Conventional bonds
Methane built up using sp3 hybridised orbitals
This picture has the advantage over that in Fig. 1.14 that the C—H bonds do have a direct relationship with
the lines drawn on the conventional structure (Fig. 1.21b). The bonds drawn in Fig. 1.14 do not represent
anything material but without them the picture would be hard to interpret. The two descriptions of the overall
wave function for methane are in fact identical; hybridisation involves the same approximations, and the
taking of s and p orbitals in various proportions and various combinations, as those used to arrive at the
picture in Fig. 1.14. For many purposes it is wise to avoid localising the electrons in the bonds, and to use
pictures like Fig. 1.14. This is what most theoreticians do when they deal with organic molecules, and it is
what the computer programs will produce. It is also, in most respects, a more realistic model. Measurements
of ionisation potentials, for example, show that there are two energy levels from which electrons may be
removed; this is immediately easy to understand in Fig. 1.14, where there are filled orbitals of different
energy, but the picture of four identical bonds from Fig. 1.20 hides this information.
For other purposes, however, it is undoubtedly helpful to take advantage of the simple picture provided by
the hybridisation model, even though hybridisation is an extra concept to learn. It immediately reveals, for
example, that all four bonds are equal. It can be used whenever it offers a simplification to an argument as we
shall find later in this book, but it is good practice to avoid it wherever possible. In particular, the common
18
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
practice of referring to a molecule or an atom as ‘rehybridising’ is not good usage—the rehybridisation in
question is in our picture, not in the molecule. It is likewise poor (but unfortunately common) practice to
refer to atoms as being sp3, sp2 or sp hybridised. Again the atoms themselves are not, in a sense, hybridised, it
is we who have chosen to picture them that way. It is better in such circumstances to refer to the atoms as
being tetrahedral, trigonal, or digonal, as appropriate, and allow for the fact that the bonds around carbon
(and other) atoms may not have exactly any of those geometries.
1.3.5 C—C s Bonds and p Bonds: Ethane
With a total of fourteen valence electrons to accommodate in molecular orbitals, ethane presents a more
complicated picture, and we now meet a C—C bond. We will not go into the full picture—finding the
symmetry elements and identifying which atomic orbitals mix to set up the molecular orbitals. It is easy
enough to see the various combinations of the 1s orbitals on the hydrogen atoms and the 2s, 2px, 2py and 2pz
orbitals on the two carbon atoms giving the set of seven bonding molecular orbitals in Fig. 1.22.
H
H
H
C
H
*z′
C
H
H
H
bonding
H
H
H
H
H
H
H
H
H
H
H
H
H
C
H
H
C
C
z
H
H
2 nodes
H
H
H
H
y′
x
H
C
C
H
C
H
C
H
C
H
H
H
z′
C
H
H
H
C
3 nodes
H
*x
C
H
H
H
H
H
*y′
C
H
C
antibonding
H
C
H
H
C
H
H
H
C
H
y
H
1 node
s′
H
H
H
C
H
H
C
H
s
0 nodes
H
Fig. 1.22 The bonding orbitals and three antibonding orbitals of ethane
There is of course a corresponding picture using sp3 hybrids, but the following account shows how easy it is to
avoid them. We shall concentrate for the moment on those orbitals which give rise to the force holding the two
carbon atoms together; between them they make up the C—C bond. The molecular orbitals (s and s0 ), made up
1 MOLECULAR ORBITAL THEORY
19
largely from 2s orbitals on carbon, are very like the orbitals in hydrogen, in that the region of overlap is directly on
a line between the carbon nuclei; as before, they are called orbitals. The bonding in the lower one is very strong,
but it is somewhat offset by the antibonding (as far as the C—C bond is concerned) in the upper one. They are both
strongly bonding with respect to the C—H bonds. There is actually a little of the 2px orbital mixed in with this
orbital, just as we saw in Fig. 1.17 with a 2pz orbital, but most of the 2px orbital contributes to the molecular orbital
x, which is also in character, and very strong as far as the C—C bond is concerned. This orbital has a little of the
2s orbital mixed in, resulting in the asymmetric extension of the lobes between the two carbon nuclei and a
reduction in size of the outer lobes. This time, its antibonding counterpart (*x) is not involved in the total bonding
of ethane, nor is it bonding overall. It is in fact the lowest-energy antibonding orbital.
In the molecular orbitals using the 2py and 2pz orbitals of carbon, the lobes of the atomic orbitals overlap
sideways on. This is the distinctive feature of what is called p bonding, although it may be unfamiliar to meet this
type of bonding in ethane. Nevertheless, let us see where it takes us. The conventional way of drawing a p orbital
(Fig. 1.12c) is designed to give elegant and uncluttered drawings, like those in Fig. 1.22, and is used throughout this
book for that reason. A better picture as we have already seen, and which we keep as a mental reservation when
confronted with the conventional drawings, is the contour diagram (Fig. 1.12b). With these pictures in mind, the
overlap sideways-on can be seen to lead to an enhanced electron population between the nuclei. However, since it is
no longer directly on a line between the nuclei, it does not hold the carbon nuclei together as strongly as a -bonding
orbital. The overlap integral S for two p orbitals with a dihedral angle of zero has the form shown in Fig. 1.23, where
it can be compared with the corresponding overlap integral taken from Fig. 1.13b. Whereas the overlap integral
goes through a maximum at about 1.5 Å and then falls rapidly to a value of –1, the p overlap integral rises more
slowly but reaches unity at superimposition. Since C—C single bonds are typically about 1.54 Å long, the overlap
integral at this distance for p bonding is a little less than half that for bonding. p Bonds are therefore much weaker.
1
p p
S
0.5
p p
1Å
2Å
r C-C
3Å
–0.5
–1
Fig. 1.23
Comparison of overlap integrals for p and bonding of p orbitals on C
Returning to the molecular orbitals in ethane made from the 2py and 2pz orbitals, we see that they again fall in
pairs, a bonding pair (py and pz) and (as far as C—C bonding is concerned, but not overall) an antibonding pair
(py0 and pz0 ). These orbitals have the wrong symmetry to have any of the 2s orbital mixed in with them. The
electron population in the four orbitals (py, pz, py0 and pz0 ) is higher in the vicinity of the hydrogen atoms than in
the vicinity of the carbon atoms, and these orbitals mainly contribute to the strength of the C—H bonds, towards
which all four orbitals are bonding. The amount both of bonding and antibonding that they contribute to the
C—C bond is small, with the bonding and antibonding combinations more or less cancelling each other out.
Thus the orbital (x) is the most important single orbital making up the C—C bond. We can construct for it an
interaction diagram (Fig. 1.24), just as we did for the H—H bond in Fig. 1.3. The other major contribution to C—C
bonding comes from the fact that s is more C—C bonding than s0 is C—C antibonding, as already mentioned.
20
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
*
x
E
*
px
px
E
x
Fig. 1.24
A major part of the C—C bond of ethane
Had we used the concept of hybridisation, the C—C bond would, of course, simply have been seen as
coming from the bonding overlap of sp3 hybridised orbitals on carbon with each other, and the overall picture
for the C—C bond would have looked very similar to x in Fig. 1.24, except that it would have used different
proportions of s and p orbitals, and would have been labelled sp3. For simplicity, we shall often discuss the
orbitals of bonds as though they could be localised into bonding and antibonding orbitals like x and x*.
We shall not often need to refer to the full set of orbitals, except when they become important for one reason
or another. Any property we may in future attribute to the bonding and antibonding orbitals of a bond, as
though there were just one such pair, can always be found in the full set of all the bonding orbitals, or they can
be found in the interaction of appropriately hybridised orbitals.
1.3.6 C=C p Bonds: Ethylene
The orbitals of ethylene are made up from the 1s orbitals of the four hydrogen atoms and the 2s, 2px, 2py and 2pz
orbitals of the two carbon atoms (Fig. 1.25). One group, made up from the 1s orbitals on hydrogen and the 2s, 2px
and 2py orbitals on carbon, is substantially bonding, which causes the orbitals to be relatively low in energy.
These five orbitals with ten of the electrons make up what we call the framework. Standing out, higher in
energy than the -framework orbitals, is a filled orbital made up entirely from the 2pz orbitals of the carbon atom
overlapping in a p bond. This time, the p orbital is localised on the carbon atoms with no mixing in of the 1s
orbitals on the hydrogen atoms, which all sit in the nodal plane of the pz orbital. The bonding in this orbital gives
greater strength to the C—C bonding in ethylene than the p orbitals give to the C—C bonding in ethane, which is
one reason why we talk of ethylene as having a double bond. Nevertheless, the C—C bonding in the framework is greater than the p bonding from overlap of the two pz orbitals. This is because, other things being
equal, p overlap is inherently less effective in lowering the energy than overlap. Thus in the interaction
diagram for a p bond (Fig. 1.26), the drop in energy Ep from p bonding is less than E in Fig. 1.24 for comparable
bonding, and this follows from the larger overlap integral for approach than for p approach (Fig. 1.23).
Similarly, Ep* in Fig. 1.26 is less than E* in Fig. 1.24. Another consequence of having an orbital localised
on two atoms is that the equation for the linear combination of atomic orbitals contains only two terms
(Equation 1.1), and the c-values are again 0.707 in the bonding orbital and 0.707 and –0.707 in the
antibonding orbital. In simple Hückel theory, the energy of the p orbital on carbon is given the value ,
which is used as a reference point from which to measure rises and drops in energy, and will be especially
useful when we come to deal with other elements. The value of Ep in Fig. 1.26 is given the symbol , and is
also used as a reference with which to compare the degree of bonding in other p-bonding systems. To give a
sense of scale, its value for ethylene is approximately 140 kJ mol–1 (¼ 1.45 eV ¼ 33 kcal mol–1). In other
words the total p bonding in ethylene is 280 kJ mol–1, since there are two electrons in the bonding orbital.
1 MOLECULAR ORBITAL THEORY
21
H
H
C
C
H
H
z
H
H
C
C
H
H
z
*
antibonding
bonding
C
C
H
H
y'
H
H
H
H
C
C
H
H
x
y
H
H
C
C
H
H
s'
H
H
Fig. 1.25
H
H
C
C
the bonding orbitals of
the framework
H
H
C
C
H
H
s
The bonding orbitals and one antibonding orbital of ethylene
*
E
*
pz
pz
E
Fig. 1.26
A C¼C p bond
This separation of the framework and the p bond is the essence of Hückel theory. Because the p bond in
ethylene in this treatment is self-contained, free of any complications from involvement with the hydrogen
atoms, we may treat the electrons in it in the same way as we do for the fundamental quantum mechanical
picture of an electron in a box. We look at each molecular wave function as one of a series of sine waves. In
these simple molecules we only have the two energy levels, and so we only need to draw an analogy between
them and the two lowest levels for the electron in the box. The convention is to draw the limits of the box one
bond length out from the atoms at the end of the conjugated system, and then inscribe sine waves so that a node
always comes at the edge of the box. With two orbitals to consider for the p bond of ethylene, we only need the
180 sine curve for p and the 360 sine curve for p*. These curves can be inscribed over the orbitals as they are
on the left of Fig. 1.27, and we can see on the right how the vertical lines above and below the atoms duplicate
the pattern of the coefficients, with both c1 and c2 positive in the p orbital, and c1 positive and c2 negative in p*.
The drawings of the p orbitals in Figs. 1.26 and 1.27 have the usual problem of being schematic. A better
picture as we have already seen, and which we keep as a mental reservation when confronted with the
22
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
*
c1
c2
c1
Fig. 1.27
c2
The p orbitals of ethylene and the electron in the box
conventional drawings, is the contour diagram (Fig. 1.12b). A better sense of the overlap from two side-byside p orbitals is given in Fig. 1.28, where we see more clearly that in the bonding combination, even
sideways-on, there is enhanced electron population between the nuclei, but that it is no longer directly on a
line between the nuclei. The wire-mesh diagrams in Fig. 1.29, illustrate the shapes of the p and p* orbitals
even better, with some sense of their 3D character.
Fig. 1.28
Fig. 1.29
A section through the contours of the p and p* wave functions of ethylene
Wire-mesh outlines of one contour of the p and p* wave functions of ethylene
1 MOLECULAR ORBITAL THEORY
1.4
23
Conjugation—Hückel Theory16,17
The interaction of atomic orbitals giving rise to molecular orbitals is the simplest type of conjugation. Thus
in ethylene the two p orbitals can be described as being conjugated with each other to make the p bond. The
simplest extension to make longer conjugated systems is to add one p orbital at a time to the p bond to make
successively the p components of the allyl system with three carbon atoms, of butadiene with four, of the
pentadienyl system with five, and so on. Hückel theory applies, because in each case we separate completely
the p system from the framework, and we can continue to use the electron-in-the-box model.
1.4.1 The Allyl System
The members of the allyl system are reactive intermediates rather than stable molecules, and there are three
of them: the allyl cation 1.1, the allyl radical 1.2 and the allyl anion 1.3. They have the same framework and
the same p orbitals, but different numbers of electrons in the p system.
2
1
3
1.1
1.2
1.3
It is necessary to make a mental reservation about the diagrams 1.1–1.3, so commonly used by organic
chemists. These diagrams are localised structures that seem to imply that C-1 has the positive charge (an
empty p orbital), the odd electron (a half-filled p orbital) or the negative charge (a filled p orbital),
respectively, and that C-2 and C-3 are in a double bond in each case. However, we could have drawn the
cation 1.1, redrawn as 1.4a, equally well the other way round as 1.4b, and the curly arrow symbolism shows
how the two drawings are interconvertible. This device is at the heart of valence bond theory. For now we
need only to recognise that these two drawings are representations of the same species—there is no reaction
connecting them, although many people sooner or later fall into the trap of thinking that ‘resonance’ like 1.4a
! 1.4b is a step in a reaction sequence. The double-headed arrow interconnecting them is a useful signal;
this symbol should be used only for interconnecting ‘resonance structures’ and never to represent an
equilibrium There are corresponding pairs of drawings for the radical 1.5a and 1.5b and for the anion 1.6a
and 1.6b.
1.4a
1.4b
1.4c
1.5a
1.5b
1.5c
1.6a
1.6b
1.6c
One way of avoiding these misleading structures is to draw the allyl cation, radical or anion as in 1.4c, 1.5c and
1.6c, respectively, illustrating the delocalisation of the p orbitals with a dashed line, and placing the positive or
negative charge in the middle. The trouble with these drawings is that they are hard to use clearly with curly
arrows in mechanistic schemes, and they do not show that the positive charge in the cation, the odd electron in
the radical or the negative charge in the anion are largely concentrated on C-1 and C-3, the very feature that the
drawings 1.4a and 1.4b, 1.5a and 1.5b and 1.6a and 1.6b illustrate so well. We shall see that the drawings with
24
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
apparently localised charges 1.4a, 1.4b, 1.5a and 1.5b and 1.6a and 1.6b illustrate not only the overall p
electron distribution but also the important frontier orbital. It is probably better in most situations to use one of
the localised drawings rather than any of the ‘molecular orbital’ versions 1.4c, 1.5c or 1.6c, and then make the
necessary mental reservation that each of the localised drawings implies the other.
H
H
C
H
C
C
H
H
1.7
The allyl cation, radical and anion have the same framework 1.7, with 14 bonding molecular orbitals
filled with 28 electrons made by mixing the 1s orbitals of the five hydrogen atoms either with the sp2 hybrids
or with the 2s, 2px and 2py orbitals of the three carbon atoms. The allyl systems are bent not linear, but we
shall treat them as linear to simplify the discussion. The x, y and z coordinates have to be redefined as local x,
y and z coordinates, different at each atom, in order to make this simplification, but this leads to no
complications in the general story.
As with ethylene, we keep the framework separate from the p system, which is made up from the three pz
orbitals on the carbon atoms that were not used in making the framework. The linear combination of these
orbitals takes the form of Equation 1.9, with three terms, creating a pattern of three molecular orbitals, 1, 2 and
3*, that bear some resemblance to the set we saw in Section 1.3.3 for methylene. In the allyl cation there are two
electrons left to go into the p system after filling the framework (and in the radical, three, and in the anion, four).
¼c1 1 þ c2 2 þ c3 3
1:9
We can derive a picture of these orbitals using the electron in the box, recognising that we now have three
orbitals and therefore three energy levels. If the lowest energy orbital is, as usual, to have no nodes (except
the inevitable one in the plane of the molecule), and the next one up one node, we now need an orbital with
two nodes. We therefore construct a diagram like that of Fig. 1.27, but with one more turn of the sine curve, to
include that for 540, the next one up in energy that fulfils the criterion that there are nodes at the edges of the
box, one bond length out, as well as the two inside (Fig. 1.30).
The lowest-energy orbital, 1, has bonding across the whole conjugated system, with the electrons
concentrated in the middle. Because of the bonding, this orbital will be lower in energy than an isolated p
*
c1
3
0.500
c1
–0.707
c3
c2
0.500
c2
–0.707
2
c3
0.707
c1
c2
c3
1
0.500
Fig. 1.30
0.707
The p orbitals of the allyl system
0.500
1 MOLECULAR ORBITAL THEORY
25
orbital. The next orbital up in energy 2, is different from those we have met so far. Its symmetry demands
that the node be in the middle; but this time the centre of the conjugated system is occupied by an atom and
not by a bond. Having a node in the middle meansphaving a zero coefficient c2 on C-2, and hence the
coefficients on C-l and C-3 in this orbital must be –1/ 2, if, squared and summed, they are to equal one. The
atomic orbitals in 2 are so far apart in space that their repulsive interaction does not, to a first approximation,
raise the energy of this molecular orbital relative to that of an isolated p orbital. In consequence, whether
filled or not, it does not contribute to the overall bonding. If the sum of the squares
p of the three orbitals on C-2
is also to equal one, then the coefficients on C-2 in 1 and 3* must also be –1/ 2. Finally, since symmetry
requires that the coefficients onpC-1 and C-3 in 1 and 3* have the same absolute magnitude, and the sum of
their squares must equal 1–(1/ 2)2, we can deduce the unique set of c-values shown in Fig. 1.30. A pattern
present in the allyl system because of its symmetry is seen with other symmetrical conjugated systems: the |c|
values are reflected across a mirror plane placed horizontally, half way up the set of orbitals, between 1 and
3*, and also across a mirror plane placed vertically, through C-2. It is only necessary therefore to calculate
four of the nine numbers in Fig. 1.30, and deduce the rest from the symmetry.
In this picture of the bonding, we get no immediate appreciation of the energies of these orbitals relative to
those of ethylene. The nonbonding orbital 2 is clearly on the level, that of a p orbital on carbon, and 1 is
lowered by the extra p bonding and 3* is raised. To assess the energies, there is a simple geometrical device
that works for linear conjugated systems. The conjugated system, including the dummy atoms at the ends of
the sine curves, is inscribed vertically inside a circle of radius 2, following the convention that one p bond in
ethylene defines . This is shown for ethylene and the allyl system in Fig. 1.31, where the dummy atoms are
marked as dots at the top and bottom of the circle. The energies E of the p orbitals can then be calculated
using Equation 1.10:
E ¼ 2 cos
kp
nþ1
1:10
where k is the number of the atom along the sequence of n atoms. This is simply an expression based on the
trigonometry of Fig. 1.31, where, for example, the p orbital of ethylene is placed on the first atom (k ¼ 1) of
the sequence of two (n ¼ 2) reading anticlockwise from the bottom. Thus the energies of the p orbitals in the
allyl system are 1.414 below the level and 1.414 above the level.
3
*
2
*
3
1.414
2
/3
1.414
1
1
0
ethylene
Fig. 1.31
the allyl system
Energies of p molecular orbitals in ethylene and the allyl system
We can gain further insight by building the picture of the p orbitals of the allyl system in another way.
Instead of mixing together three p orbitals on carbon, we can combine two of them in a p bond first, as in
Fig. 1.26, and then work out the consequences of having a third p orbital held within bonding distance of
26
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
the C¼C p bond. Although Fig. 1.26, and all the interaction diagrams for single bonds, illustrated the
bonding orbital as less bonding than the antibonding orbital is antibonding, this detail confuses the simple
picture for conjugated systems that we want to build up here, and is left out of the discussion. We have to
consider the effect of the p orbital, on the right of Fig. 1.32 on both the p and p* orbitals of ethylene on the
left. If we look only at the interaction with the p orbital, we can expect to create two new orbitals in much
the same way as we saw when the two 2pz orbitals of carbon were allowed to interact in the formation of
the p bond of Fig. 1.26. One orbital 1 will be lowered in energy and the other x raised. Similarly if we
look only at its interaction with the p* orbital, we can expect to create two new orbitals, one lowered in
energy y and one raised 3*. We cannot create four orbitals from three, because we cannot use the p
orbital separately twice.
*
3
*
x
pC
y
1
Fig. 1.32
A p orbital interacting independently with p and p* orbitals. (No attempt is made to represent the relative
sizes of the atomic orbitals)
We can see in Fig. 1.32 that the orbital 1 has been created by mixing the p orbital with the p orbital in a
bonding sense, with the signs of the wave function of the two adjacent atomic orbitals matching. We can also
see that the orbital 3* has been created by mixing the p orbital with the p* orbital in an antibonding sense,
with the signs of the wave functions unmatched. The third orbital that we are seeking, 2 in Fig. 1.33, is a
combination created by mixing the p orbital with the p orbital in an antibonding sense and with the p* orbital
in a bonding sense. We do not get the two orbitals, x and y in Fig. 1.32, but something half way between,
namely 2 in Fig. 1.33. By adding x and y in this way, the atomic orbitals drawn to the left of the energy
levels labelled x and y in Fig. 1.32 cancel each other out on C-2 and reinforce each other on C-1 and C-3,
thereby creating the molecular orbital 2 in Fig. 1.33.
We have of course arrived at the same picture for the molecular orbitals as that created from mixing the
three separate p orbitals in Fig. 1.30. As before, the atomic orbitals in 2 are far enough apart in space for the
molecular orbital 2 to have the same energy as the isolated p orbital in Fig. 1.33. It is a nonbonding
molecular orbital (NBMO), as distinct from a bonding ( 1) or an antibonding ( 3*) orbital. Again we see for
the allyl cation, radical and anion, that, as a result of the overlap in 1, the overall p energy of the allyl system
has dropped relative to the sum of the energies of an isolated p orbital and of ethylene by 2E, which we know
from Fig. 1.31 is 2 0.414 or something of the order of 116 kJ mol–1 of extra p bonding relative to that in
1 MOLECULAR ORBITAL THEORY
27
*
3
*
pC
2
E
1
Fig. 1.33
The allyl system by interaction of a p orbital with p and p* orbitals
ethylene. In the radical and anion, where 2 has either one or two electrons, and 3* is still empty, the energy
drop is still 2E, because p and 2 are essentially on the same level. (It is not uncommon to express these drops
in energy as a ‘gain’ in energy—in this sense, the gain is understood to be to us, or to the outside world, and
hence means a loss of energy in the system and stronger bonding.)
It is worth considering at this stage what the overall p electron distribution will be in this conjugated
system. The electron population in any molecular orbital is derived from the square of the atomic orbital
functions, so that the sine waves describing the coefficients in Fig. 1.34a are squared to describe the electron
distribution in Fig. 1.34b. The p electron population in the molecule as a whole is then obtained by adding up
the electron populations, allowing for the number of electrons in each orbital, for all the filled p molecular
orbitals. Looking only at the p system, we can see that the overall p electron distribution for the cation is
–0.707
*
*2
3
3
0.500
0.500
–0.707
2
0.707
0.25
2
2
0.50
0.50
0
0.25
0.50
0.25
0.50
2
1
1
0.500
0.707
0.500
(a) Wave f unctions
Fig. 1.34
0.25
(b) Electron populations f or one electron
Wave functions and electron population for the allyl orbitals
28
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
derived from the squares of the coefficients in 1 alone, since this is the only populated p orbital. Roughly
speaking, there is half an electron (2 0.52) on each of C-1 and C-3, and one electron (2 0.7072) on
C-2. This is illustrated graphically in Fig. 1.35a. Since the nucleus has a charge of þ1, the excess charge on
C-1 and C-3 is þ0.5, in other words the electron deficiency in the cation is concentrated at the two ends.
2
2
1
2
0.50
(a)
1.0
2
1
2
2
0.50
1.50
electron population in the allyl cation
Fig. 1.35
+2
(b)
1.0
1.50
electron population in the allyl anion
Total p electron populations in the allyl cation and anion
For the anion, the p electron population is derived by adding up the squares of the coefficients in both 1
and 2. Since there are two electrons in both orbitals, there are 1.5 electrons (2 0.52 þ 2 0.7072)
roughly centred on each of C-1 and each of C-3, and one electron (2 0.7072) centred on C-2. This is
illustrated graphically in Fig. 1.35b. Subtracting the charge of the nucleus then gives the excess charge as
–0.5 on C-1 and C-3, in other words the electron excess in the anion is concentrated at the two ends. Thus the
drawings of the allyl cation 1.4a and 1.4b illustrate the overall p electron population, and the corresponding
drawings for the anion 1.6a and 1.6b do the same for that species.
As we shall see later, the most important orbitals with respect to reactivity are the highest occupied
molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). These are the frontier
orbitals. For the allyl cation, the HOMO is 1, and the LUMO is 2. For the allyl anion, the HOMO is 2, and
the LUMO is 3*. The drawings of the allyl cation 1.4a and 1.4b emphasise not only the overall p electron
population but even better emphasise the electron distribution in the LUMO. Similarly, the drawings of the
allyl anion 1.6a and 1.6b emphasise the HOMO for that species. It is significant that it is the LUMO of the
cation and the HOMO of the anion that will prove to be the more important frontier orbital in each case. In
radicals, the most important orbital is the singly occupied molecular orbital (SOMO). For the allyl radical
this is the half-filled orbital 2. Once again, the drawings 1.5a and 1.5b emphasise the distribution of the odd
electron in this orbital.
One final detail with respect to this, the most important orbital, is that it is not quite perfectly nonbonding.
Although C-1 and C-3 are separated in space, they do interact slightly in 2, as can be seen in the wire-mesh
drawing of the nonlinear allyl system in Fig. 1.36, where the perspective allows one to see that the right hand
ψ1
ψ2
Fig. 1.36
ψ 3*
The p molecular orbitals of the allyl system
1 MOLECULAR ORBITAL THEORY
29
lobes, which are somewhat closer to the viewer, are just perceptibly repelled by the left hand lobes, and that
neither of the atomic orbitals on C-1 and C-3 in 2 is a straightforwardly symmetrical p orbital. This orbital
does not therefore have exactly the same energy as an isolated p orbital—it is slightly higher in energy.
1.4.2 Butadiene
The next step up in complexity comes with four p orbitals conjugated together, with butadiene 1.8 as the parent
member. As usual there is a framework 1.9, which can be constructed from the 1s orbitals of the six
hydrogen atoms and either the sp2 hybrids of the four carbon atoms or the separate 2s, 2px and 2py orbitals. The
framework has 18 bonding molecular orbitals filled with 36 electrons. Again we have two ways by which we
may deduce the electron distribution in the p system, made up from the four pz orbitals and holding the
remaining four electrons. Starting with the electron in the box with four p orbitals, we can construct Fig. 1.37,
which shows the four wave functions, inside which the p orbitals are placed at the appropriate regular intervals.
4
2
H
H
1
3
C
C
H
1,
C
H
H
1.9
1.8
We get a new set of orbitals,
H
C
2,
3*,
and
4*,
each described by Equation 1.11 with four terms:
¼ c1 1 þ c2 2 þ c3 3 þ c4 4
0.371
3 nodes
1:11
–0.600 0.600
–0.371
*
4
0.600
0.600
–0.371 –0.371
2 nodes
*
LUMO
3
0.600
1 node
–0.600
HOMO
2
0.371
0 nodes
0.371 –0.371
0.600 0.600
0.371
1
Fig. 1.37
p Molecular orbitals of butadiene
30
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
The lowest-energy orbital 1 has all the c-values positive, and hence bonding is at its best. The nexthighest energy level has one node, between C-2 and C-3; in other words, c1 and c2 are positive and c3 and c4
are negative. There is therefore bonding between C-l and C-2 and between C-3 and C-4, but not between C-2
and C-3. With two bonding and one antibonding interaction, this orbital is also overall bonding. Thus the
lowest-energy orbital of butadiene, 1, reasonably enough, has a high population of electrons in the middle,
but in the next orbital up, 2, because of the repulsion between the wave functions of opposite sign on C-2
and C-3, the electron population is concentrated at the ends of the conjugated system. Overall, summing the
squares of the coefficients of the filled orbitals, 1 and 2, the p electrons are, at this level of approximation,
evenly spread over all four carbon atoms of the conjugated system.
We can easily give numerical values to these coefficients, using the convention that the edge of the box is
drawn one bond length out from the terminal carbon atoms. Treating the conjugated system as being linear,
the coefficients are proportional to the sine of the angle, as defined by the position of the atom within the sine
curve. The algebraic expression for this idea in the general case, and illustrated in Fig. 1.37 for the specific
case of butadiene, with the atomic orbitals inscribed within the sine curves, is Equation 1.12:
rffiffiffiffiffiffiffiffiffiffiffiffiffi
2
rjp
cjr ¼
sin
1:12
nþ1
nþ1
giving the coefficient cjr for atom j in molecular orbital r of a conjugated system of n atoms (so that j and
r ¼ 1, 2, 3, . . . , n). The expression in front of the sine function is the normalisation factor to make the squares
of the coefficients add up to one. Thus, taking 2 for butadiene (r ¼ 2, n ¼ 4 and the sine curve is a full 2p):
the normalisation factor for n ¼ 4 is 0.632, the angle for the first atom (j ¼ 1) is 2p/5, the sine of which is
0.951, and the coefficient c1 is the product 0.632 0.951 ¼ 0.600. Similarly, c2 is 0.371, c3 is –0.371 and c4
is –0.600.
Large lists of coefficients for conjugated systems, some as easily calculated as butadiene above, some
more complicated, have been published.18 As with the allyl system, other patterns are also present because of
the symmetry of the molecule: for alternant conjugated systems (those having no odd-membered rings), the
|c| values are reflected across a mirror plane placed horizontally, half way between 2 and 3*, and also
across a mirror plane placed vertically, half way between C-2 and C-3. It is only necessary therefore to
calculate four of the 16 numbers in Fig. 1.37, and deduce the rest from the symmetry.
Alternatively, we can set up the conjugated system of butadiene by looking at the consequences of
allowing two isolated p bonds to interact, as they will if they are held within bonding distance. It is perhaps a
little easier to see on this diagram the pattern of raised and lowered energy levels relative to those of the p
bonds from which they are derived. Let us first look at the consequence of allowing the orbitals close in
energy to interact, which they will do strongly (Fig. 1.38). (For a brief account of how the energy difference
between interacting orbitals affects the extent of their interaction, see the discussion of Equations 1.13 and
1.14 on p. 54.) The interactions of p with p and of p* with p* on the left create a new set of orbitals, a- d*.
This is not the whole story, because we must also allow for the weaker interaction, shown on the right, of the
orbitals further apart in energy, p with p*, which on their own would create another set of orbitals, w- z*.
Mixing these two sets together, and allowing for the greater contribution from the stronger interactions, we
get the set of orbitals (Fig. 1.39), matching those we saw in Fig. 1.37. Thus, to take just the filled orbitals, we
see that 1 is derived by the interaction of p with p in a bonding sense ( a), lowering the energy of 1 below
that of the p orbital, and by the interaction of p with p* in a bonding sense ( w), also lowering the energy
below that of the p orbital. Since the former is a strong interaction and the latter weak, the net effect is to
lower the energy of 1 below the p level, but by a little more than the amount ( in simple Hückel theory,
illustrated as Ep in Fig. 1.26) that a p orbital is lowered below the p level (the dashed line in Figs. 1.31, 1.32
and 1.33, called in simple Hückel theory) in making the p bond of ethylene. However, 2 is derived from
the interaction of p with p in an antibonding sense ( b), raising the energy above that of the p orbital, and by
the interaction of p* with p in a bonding sense ( x), lowering it again. Since the former is a strong interaction
1 MOLECULAR ORBITAL THEORY
31
*
d
*
*
y
*
z
*
*
c
b
w
a
Fig. 1.38
x
Primary interactions of the p molecular orbitals of two molecules of ethylene. (No attempt is made to
represent the relative sizes of the atomic orbitals)
and the latter weak, the net effect is to raise the energy of 2 above the p level, but not by as much as a p*
orbital is raised above the p level in making the p bond of ethylene. Yet another way of looking at this system
is to say that the orbitals 1 and 2 and the orbitals 3* and 4* mutually repel each other.
We are now in a position to explain the well-known property that conjugated systems are often, but not
always, lower in energy than unconjugated systems. It comes about because 1 is lowered in energy more
than 2 is raised (E1 in Fig. 1.39 is larger than E2). The energy (E1) given out in forming 1 comes from the
*
4
*
*
* LUMO
3
2
HOMO
E2
E1
1
Fig. 1.39
Energies of the p molecular orbitals of ethylene and butadiene by orbital interaction
32
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
overlap between the atomic orbitals on C-2 and C-3; this overlap did not exist in the isolated p bonds. It is
particularly effective in lowering the energy of 1, because the coefficients on C-2 and C-3 are large. By
contrast, the increase in energy of 2, caused by the repulsion between the orbitals on C-2 and C-3, is not as
great, because the coefficients on these atoms are smaller in 2. Thus the energy lost from the system in
forming 1 is greater than the energy needed to form 2, and the overall p energy of the ground state of the
system ( 12 22) is lower. We can of course see the same pattern, and attach some very approximate numbers,
using the geometrical analogy. This is illustrated in Fig. 1.40, which shows that 2 is raised above p by
0.382 and 1 is lowered below p by 0.618. The overall lowering in energy for the extra conjugation is
therefore (2 0.618 þ 2 1.618) – 4 ¼ 0.472 or about 66 kJ mol–1.
*
4
*
*
3
0.618
2
1.618
1
ethylene
Fig. 1.40
butadiene
Energies of the p molecular orbitals of ethylene and butadiene by geometry
Before we leave butadiene, it is instructive to look at the same p orbitals in wire-mesh diagrams (Fig. 1.41) to
reveal more accurately what the electron distribution in the p molecular orbitals looks like. In the allyl system
and in butadiene, we have seen more than one filled and more than one empty orbital in the same molecule. The
framework, of course, with its strong bonds, has several other filled orbitals lying lower in energy than either
1 or 2, but we do not usually pay much attention to them when we are thinking of reactivity, simply because
they lie so much lower in energy. In fact, we shall be paying special attention to the filled molecular orbital
which is highest in energy ( 2, the HOMO) and to the unoccupied orbital of lowest energy ( 3*, the LUMO).
ψ1
Fig. 1.41
ψ2
ψ 3*
ψ 4*
The p molecular orbitals of butadiene in the s-trans conformation
1.4.3 Longer Conjugated Systems
In extending our understanding to the longer linear conjugated systems, we need not go through all the arguments
again. The methods are essentially the same. The energies and coefficients of the p molecular orbitals for all six
systems from an isolated p orbital up to hexatriene are summarised in Fig. 1.42. The viewpoint in this drawing is
directly above the p orbitals, which appear therefore to be circular. This is a common simplification, rarely likely
to lead to confusion between a p orbital and an s orbital, and we shall use it through much of this book.
1.00
1
1
0.707
0.618
0.618
0.500 1.618
–0.707
C
0.500
1.618
0.371
0.600
0.600
0.371
0.600
0.371
–0.371
0.600
0.600
–0.371
–0.371
–0.600
0.371
–0.600
0.600
–0.371
1.732
1
1
1.732
0.288
0.500
0.576
0.500
0.288
0.500
0.500
0.576
0.576
–0.576
–0.500
–0.500
0.500
0.288
0.288
–0.500
0.576
–0.500
–0.500
0.500
–0.500
1.802
1.247
0.445
0.445
1.247
1.802
0.232
0.418
0.521
0.521
0.418
0.232
0.418
0.521
0.232
–0.232
–0.521
–0.418
The energies and coefficients of the p molecular orbitals of the smaller conjugated systems
0.500
0.707
0.500
Fig. 1.42
0.707 0.707 1.414
–0.707 0.707
1.414
–0.707
C
0.521
0.232
0.521
–0.232
–0.418
–0.418
0.418
0.232
–0.521
–0.418
0.232
0.521
0.418
0.232
–0.418
0.521
–0.521
0.418
–0.232
–0.521
0.232
0.232
–0.521
0.418
34
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
The longer the conjugated system, the lower the energy of 1, but each successive drop in energy is less than
it was for the system with one fewer atoms, with a limit at infinite length of 2. Among the even-atom species,
the longer the conjugated system, the higher the energy of the HOMO, and the lower the energy of the LUMO,
with the energy gap becoming ever smaller. With a narrow HOMO—LUMO gap, polyenes allow the easy
promotion of an electron from the HOMO to the LUMO, and the longer the conjugated system, the easier it is,
making the absorption of UV and visible light ever less energetic. Most organic chemists will be happy with
this picture, and most of the consequences in organic chemistry can be left at this level of understanding.
At the extreme of an infinite polyene, however, simple Hückel theory reduces the HOMO—LUMO gap to
zero, since the secants in diagrams like Fig. 1.40, would become infinitely small as they moved to the perimeter
of the circle. Such a polyene would have equal bond lengths between each pair of carbon atoms, there would be
no gap between the HOMO and the LUMO, and it would be a metallic conductor. This is not what happens—
long polyenes, like polyacetylene, have alternating double (or triple) and single bonds, and their interconversion, which is the equivalent of the movement of current along the chain, requires energy. The theoretical
description of this modification to simple Hückel theory is known by physicists as a Peierls distortion. It has its
counterpart for chemists in the Jahn-Teller distortion seen, for example, in cyclobutadiene, which distorts to
have alternating double and single bonds, avoiding the degenerate orbitals and equal bond lengths of square
cyclobutadiene (see Section 1.5.2). The simple Hückel picture is evidently wrong at this extreme of very long
conjugated systems. One way of appreciating what is happening is to think of the HOMO and the LUMO
interacting more strongly when they are close in energy, just as the filled and unfilled orbitals of butadiene repel
each other (Fig. 1.39), but more so. The residual gap, corresponding approximately to what is called by
physicists the ‘band-gap energy’, is amenable to tuning, by attaching suitable substituents, just like any other
HOMO—LUMO gap. Tailoring it has proved to be a basis for tuning the properties of optical devices.19
The process by which alternating double and single bonds might exchange places is strictly forbidden by
symmetry, but occurs in practice, because the mismatch in symmetry of adjacent elements is disrupted by having
an atom lacking an electron or carrying an extra electron in the chain.20 Thus an ‘infinite’ polyene can have long
stretches of alternating single and double bonds interrupted by a length of conjugated p orbitals resembling a
conjugated cation, radical or anion. Such ‘defects’ are chains of conjugated atoms, but like the chain of the
polyene itself, the feature of equal bond lengths does not stretch infinitely along the whole ‘molecule’, as simple
Hückel theory would suggest. It is limited in what physicists call ‘solitons’. In the soliton, there is no bond
alternation at its centre, but bond alternation appears at greater distances out from its centre. Solitons provide a
mechanism for electrical conduction along the chain, which is described as being ‘doped’. Unfortunately, the
physicists’ nomenclature in the polymer area departs from that of the organic chemist, with expressions like
‘tight binding model’ meaning much the same as the LCAO approximation, ‘band structure’ for the stack of
orbitals, ‘band gap’ for the HOMO—LUMO gap, ‘valence band’ for the HOMO, ‘Fermi energy’ meaning
roughly the same as the energy of the HOMO, and the ‘conduction band’ meaning roughly the same as the
LUMO. The physical events are of course similar, and the comparisons have been elegantly discussed.21 Such a
breakdown in Hückel theory is not normally encountered in organic chemistry, where delocalisation can be
expected to stretch undeterred by the length of the conjugated systems in what we might call ordinary molecules.
1.5
Aromaticity22
1.5.1 Aromatic Systems
One of the most striking properties of conjugated organic molecules is the special stability found in the group
of molecules called aromatic, with benzene 1.10 as the parent member and the longest established example.
Hückel predicted that benzene was by no means alone, and that cyclic conjugated polyenes would have
exceptionally low energy if the total number of p electrons could be described as a number of the form
(4n þ 2), where n is an integer. Other 6p-electron cyclic systems such as the cyclopentadienyl anion 1.11 and
the cycloheptatrienyl cation 1.12 belong in this category. The cyclopropenyl cation 1.13 (n ¼ 0),
1 MOLECULAR ORBITAL THEORY
35
[14]annulene 1.14 (n ¼ 3), [18]annulene 1.15 (n ¼ 4) and many other systems have been added over the
years.23 Where does this special stability come from?
1.10
1.11
1.12
1.13
1.14
1.15
We can approach this question in much the same way as we approached the derivation of the molecular
orbitals of conjugated systems. We begin with a framework containing the C—C and C—H bonds. We
must then deduce the nodal properties of the p molecular orbitals created from six p orbitals in a ring. They
are all shown both in elevation and in plan in Fig. 1.43. The lowest-energy orbital 1 has no node as usual, but
because the conjugated system goes round the ring instead of spilling out at the ends of the molecule, as it did
–0.408
0.577
0.408
0.408
–0.408
–0.408
–0.289
–0.289
–0.289
–0.289
0.500
–0.500
–0.500
0.500
0.500
–0.500
0.500
–0.500
0.408
0.577
*
6
*
*
4
5
2
0.577
3
1
0.289
0.289
–0.289
–0.289
0.408
–0.577
0.408
0.408
0.408
0.408
0.408
Fig. 1.43
The p molecular orbitals of benzene
36
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
with the linear conjugated systems, the coefficients on all six atoms are equal. The other special feature is
that there are two orbitals having the same energy with one node 2 and 3, because they can be created in
two symmetrical ways, one with the node horizontal 2 and one with it vertical 3. Similarly, there are two
orbitals, 4* and 5*, with the same energy having two nodes. Finally there is the one orbital, 6*, with three
nodes.
The size of the coefficients can be deduced from the position of the atoms within the sine curves, in the
usual way. They support the assumption from symmetry that the amount of bonding in 2 equals that in 3.
Thus the allyl-like overlap in the two halves of 2 has bonding between a large (–0.577) and two small
(–0.289) lobes, whereas the antibonding interaction is between the two small lobes. The result is actually a
lowering of energy for this orbital equal to that of the p bond in ethylene (). In 3 there is bonding between
lobes of intermediate size (–0.500) and the interaction across the ring between the lobes of opposite sign is,
like 2 in the allyl system, nonbonding rather than antibonding. Overlap between the p orbitals in ethylene
(c ¼ 0.707) gives rise to a lowering of energy () worth one full p bond. Overlap between two lobes of the
same sign in 3 with coefficients of –0.50 gives rise to half a p bond (0.7072 ¼ 0.500), and two such
interactions comes again to one full p bond. The fully bonding overlap of the six orbitals (c ¼ 0.408) in 1
gives rise to two p bond’s worth of bonding. The total of p bonding is thus 2 4, which is two more units
than three isolated p bonds. Benzene is also lowered in p energy by more than the amount for three linearly
conjugated p bonds: taking the numbers for hexatriene from Fig. 1.40, the total of p bonding is 2 (1.802
þ 1.247 þ 0.445) ¼ 7. The extra p bonding is the special feature of aromatic systems.
The energies of the molecular orbitals can also be deduced by the same device, used for linear
conjugated systems, of inscribing the conjugated system inside a circle of radius 2. There is no need
for dummy atoms, since the sine curves go right round the ring, and the picture is therefore that shown in
Fig. 1.44.
*
6
*
*
4
5
2
2
3
1
Fig. 1.44 The energies of the p molecular orbitals of benzene
It is also possible to find the source of aromatic stabilisation by looking at an interaction diagram. For
benzene 1.10, one way is to start with hexatriene 1.16, and examine the effect of bringing the ends of the
conjugated system, C-1 and C-6, within bonding distance (Fig. 1.45). Since we are only looking at the p
energy, we ignore the C—H bonds, and the fact that to carry out this ‘reaction’ we would have to break two of
them and make a C—C bond in their place. In 1 and 3 the atomic orbitals on C-1 and C-6 have the same
sign on the top surface. Bringing them within bonding distance will increase the amount of p bonding, and
lower the energy of 1 and 3 in going from hexatriene to benzene. In 2 however, the signs of the atomic
orbitals on C-1 and C-6 are opposite to each other on the top surface, and bringing them within bonding
distance will be antibonding, raising the energy of 2 in going from hexatriene to benzene. The overall result
is two drops in energy to one rise, and hence a lowering of p energy overall.
1 MOLECULAR ORBITAL THEORY
37
6
1
1.16
1.10
–0.521
3
0.445
–0.521
1
2
3
0.418
–0.418
0.232
0.232
Fig. 1.45
2
1
1.247
1.802
2
1
The drop in p energy in going from hexatriene to benzene
However, the ups and downs are not all equal as Fig. 1.45, which is drawn to scale, shows. The net lowering
in p energy, relative to hexatriene, is actually only one value, as we deduced above, not two. It is barely
legitimate, but there is some accounting for this difference—the overlap raising the energy of 2 and
lowering the energy of 3 is between orbitals with large coefficients, more or less cancelling one another
out; however, the overlap between C-1 and C-6 in 1 is between orbitals with a small coefficient, making that
drop close to 0.5 as shown in Fig. 1.45.
One of the most striking artifacts of aromaticity, in addition to the lowering in energy, is the diamagnetic
anisotropy, which is characteristic of these rings. Although known long before NMR spectroscopy was
introduced into organic chemistry, its most obvious manifestation is in the downfield shift experienced by
protons on aromatic rings, and perhaps even more vividly by the upfield shift of protons on the inside of the large
aromatic annulenes. The theory24,25 is beyond the scope of this book, but it is associated with the system of p
molecular orbitals, and can perhaps be most simply appreciated from the idea that the movement of electrons
round aromatic rings is free, like that in a conducting wire, as epitomised by the equal C—C bond lengths.
Like the conjugation in polyenes that we saw earlier, aromaticity does not stretch to infinitely conjugated
cyclic systems, even when they do have (4nþ2) electrons. Just as long polyenes do not approach a state with
equal bond lengths as the number of conjugated double bonds increases, the (4nþ2) rule of aromaticity
breaks down, with bond alternation setting in when n reaches a large number. It is not yet clear what that
number is with neither theory nor experiment having proved decisive. Early predictions26 that the largest
possible aromatic system would be [22] or [26]annulene were too pessimistic, and aromaticity, using the
ring-current criterion, probably peters out between [34] and [38]annulene.27
1.5.2 Antiaromatic Systems
A molecule with 4n p electrons in the ring, with the molecular orbitals made up from 4n p orbitals, does not
show this extra stabilisation. Molecules in this class that have been studied include cyclobutadiene 1.17
38
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
(n ¼ 1), the cyclopentadienyl cation 1.18, the cycloheptrienyl anion 1.19, cyclooctatetraene 1.20 and
pentalene 1.21 (n ¼ 2), [12]annulene 1.22 (n ¼ 3) and [16]annulene 1.23 (n ¼ 4).
We can see this most easily by looking at the molecular orbitals of square cyclobutadiene in
Fig. 1.46. As usual, the lowest energy orbital 1 has no nodes, and, as with benzene and because of
the symmetry, there are two exactly equivalent orbitals, 2 and 3, with one node. The bonding in 1
is between atomic orbitals with coefficients of 0.500, not only between C-1 and C-2, but also between
C-2 and C-3, between C-3 and C-4 and between C-4 and C-1. If the overlap in 3 of benzene, which
also has coefficients of 0.500, gives an energy-lowering of 1, then the overlap in 3 of cyclobutadiene should give twice as much energy-lowering, since there are twice as many bonding interactions
(this makes an assumption that the p orbitals are held at the same distance by the framework in
both cases). In contrast, the bonding interactions both in 2 and 3 are exactly matched by the
antibonding interactions, and there is no lowering of the energy below the line () representing the
energy of a p atomic orbital on carbon. The molecular orbitals 2 and 3 are therefore nonbonding
orbitals, and the net lowering in energy for the p bonding in cyclobutadiene is only 2 2. The
energies of the four p orbitals are again those we could have deduced from the model inscribing the
conjugated system in a circle, with the point of the square at the bottom. The total p stabilisation of
2 2 is no better than having two isolated p bonds—there is therefore no special extra stabilisation
from the cyclic conjugation relative to two isolated p bonds. There is however less stabilisation than
that found in a pair of conjugated double bonds—the overall p bonding in butadiene, taking values
from Fig. 1.40, is 2 (1.618 þ 0.618) ¼ 4.472 and the overall p bonding in cyclobutadiene is only
2 2 making it less stable by 0.472.
0.500
–0.500
–0.500
0.500
*
4
2
3
2
0.500
0.500
–0.500
–0.500
Fig. 1.46
1
0.500
0.500
0.500
0.500
0.500
–0.500
0.500
–0.500
The p molecular orbitals of cyclobutadiene
1 MOLECULAR ORBITAL THEORY
1.17
1.18
39
1.19
1.20
1.21
1.22
1.23
We can reach a similar conclusion from an interaction diagram, by looking at the effect of changing
butadiene 1.24 into cyclobutadiene 1.25 (Fig. 1.47). This time there is one drop in p energy and one rise,
and no net stabilisation from the cyclic conjugation. As with benzene, we can see that the drop is actually less
(from overlap of orbitals with a small coefficient) than the rise (from overlap of orbitals with a large
coefficient). Thus cyclobutadiene is less stabilised than butadiene.
1.25
1.24
2
–0.600
2
0.618
1
1.618
0.600
0.371
0.371
Fig. 1.47
2
1
No change in p energy in going from butadiene to cyclobutadiene
There is much evidence that cyclic conjugated systems of 4n electrons show no special stability.
Cyclobutadiene dimerises at extraordinarily low temperatures (>35K).28 Cyclooctatetraene is not planar,
and behaves like an alkene and not at all like benzene.29 When it is forced to be planar, as in pentalene, it
becomes unstable to dimerisation even at 0 C.30 [12]Annulene and [16]annulene are unstable with respect
to electrocyclic reactions, which take place below 0 C.31 In fact, all these systems appear on the whole to
be significantly higher in energy and more reactive than might be expected, and there has been much
speculation that they are not only lacking in extra stabilisation, but are actually destabilised. They have
been called ‘antiaromatic’32 as distinct from nonaromatic. The problem with this concept is what to make
the comparisons with. We can see from the arguments above that we can account for the destabilisation
40
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
relative to conjugated p bonds—linear conjugation is more energy-lowering than the cyclic conjugation of
4n electrons, which goes some way to setting the concept of antiaromaticity on a physical basis. This
argument applies to the thermodynamics of the system, which indirectly affects the reactivity. That 4n
systems are unusually reactive is also explicable with an argument based on the frontier orbitals, as we
shall see later—the HOMO is unusually high in energy for a neutral molecule, at the nonbonding level
for cyclobutadiene and the other uncharged cyclic hydrocarbons 1.18–1.23, significantly above the level
of the HOMO of the linear conjugated hydrocarbons, and at the same time the LUMO is correspondingly
low in energy.
The prediction from the argument in Fig. 1.46 is that square cyclobutadiene ought to be a diradical with
one electron in each of 2 and 3, on the grounds that putting a second electron into an occupied orbital is not
as energy-lowering as putting the first electron into that orbital (see Section 1.2). This is not borne out by
experiment, which has shown that cyclobutadiene is rectangular with alternating double and single bonds
and shows no electron spin resonance (ESR) signal.33
We can easily explain why the rectangular structure is lower in energy than the square. So far, we have made
all p bonds contribute equally one -value to every p bond. The difference in -values, and hence in the
strengths of p bonds, as a function of how closely the p orbitals are held, can be dealt with by defining a
standard 0 value for a C¼C double bond and applying a correction parameter k, just as we shall in Equation
1.16 for the effect of changing from a C¼C double bond to a C¼X double bond. Some values of k for different
distances r can be seen in Table 1.1,34 which was calculated with 0 based on an aromatic double bond, rather
than the double bond of ethylene, and by assuming that is proportional to the overlap integral S.
Table 1.1 Variation of the correction factor k with distance r
r (Å)
k
r (Å)
k
1.20
1.33
1.35
1.397
1.38
1.11
1.09
1.00
1.45
1.48
1.54
0.91
0.87
0.78
In the rectangular structure of cyclobutadiene, the symmetry is lowered, and the molecular orbitals
corresponding to 2 and 3 are no longer equal in energy (Fig. 1.48). The overall bonding in 1 is more
or less the same as in the square structure—C-1 and C-2 (and C-3 and C-4) move closer together in 1, and
the level of bonding is actually increased by about as much as the level of bonding is decreased in moving the
C-1
C-2
0.500
–0.500
0.500
–0.500
*
3
0.500
0.500
2
–0.500
–0.500
C-4
Fig. 1.48
C-3
0.500
0.500
0.500
0.500
1
The three lowest-energy p molecular orbitals of rectangular cyclobutadiene
1 MOLECULAR ORBITAL THEORY
41
other pairs apart. In the other filled orbital, 2, the same distortion, separating the pair (C-1 from C-4 and C-2
from C-3) will reduce the amount of p antibonding between them, and hence lower the energy. The
corresponding argument on 3 will lead to its being raised in energy, and becoming an antibonding orbital.
With one p orbital raised in energy and the other lowered, the overall p energy will be much the same, and the
four electrons then go into the two bonding orbitals. This is known as a Jahn-Teller distortion, and can be
expected to be a factor whenever a HOMO and a LUMO are very close in energy,35 as we have already seen
with very long conjugated systems in Section 1.4.3. The square structure will be the transition structure for
the interconversion of the one rectangular form into the other, a reaction that can be expected to be fairly
easy, but to have a discernible energy barrier. Proper molecular orbital calculations support this conclusion.36 We must be careful in arguments like this, based only on the p system, not to get too carried away. We
have not allowed for distortions in the framework in going from the square to the rectangular structure, and
this can have a substantial effect.
1.5.3 The Cyclopentadienyl Anion and Cation
A slightly different case is provided by the cyclopentadienyl anion and cation. The device of inscribing the
pentagon in a circle sets up the molecular orbitals in Fig. 1.49. The total of p bonding energy is
2 3.236 ¼ 6.472 for the anion, in which there are two electrons in 1, two electrons in 2, and two
electrons in 3. The anion is clearly aromatic, since the open-chain analogue, the pentadienyl anion has only
2 2.732 ¼ 5.464 worth of p bonding (Fig. 1.40), the extra stabilisation being close to 1, and closely
similar to the extent by which benzene is lower in energy than its open-chain analogue, hexatriene. The
cyclopentadienyl anion 1.11, a 4nþ2 system, is well known to be exceptionally stabilised, with the pKa of
cyclopentadiene at 16 being strikingly low for a hydrocarbon. The cation, however, has p-bonding energy of
2 2.618 ¼ 5.236, whereas its open-chain analogue, the pentadienyl cation, in which there are two
electrons in 1 and two electrons in 2, has more p bonding, specifically 2 2.732 ¼ 5.464. The
cyclopentadienyl cation 1.18, a 4n system, can be expected to be thermodynamically high in energy overall
and therefore difficult to make, and so it is known to be. The cyclopentadienyl cation is not formed from its
iodide by solvolysis under conditions where even the unconjugated cyclopentyl iodide ionises easily.37 In
addition, the cyclopentadienyl cation ought to be especially electrophilic for kinetic reasons, since the energy
of the LUMO is actually below the level. It is also known to be a diradical in the ground state.38 The
fluorenyl cation, the dibenz analogue of the cyclopentadienyl cation, however, does not appear to be
significantly higher in energy than might be expected of a doubly benzylic cation held coplanar.39
0.20
0.60
4*
5*
–0.51
–0.37
4*
1.618
0.63
*
5
0.37
–0.60
0.618
2
0.20
3
2
0.63
0.60
2
1
3
0.45
1
Fig. 1.49
The energies and coefficients of the p molecular orbitals of the cyclopentadienyl system
42
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
A striking difference between all the aromatic and all the antiaromatic systems is the energy difference
between the HOMO and the LUMO. The aromatic systems have a substantial gap between the frontier
orbitals, and the antiaromatic systems a zero gap in simple Hückel theory or a small gap if the Jahn-Teller
distortion is allowed for. The difference in energy between the HOMO and the LUMO correlates with the
hardness of these hydrocarbons as nucleophiles, and with some measures of aromaticity.40 For example,
in antiaromatic rings with 4n electrons, there is a paramagnetic ring current, which is a manifestation of
orbital effects, just like the diamagnetic ring currents from aromatic rings. The protons at the perimeter of
a 4n annulene, when it is stable enough for measurements to be made, are at high field, and protons on the
inside of the ring are at low field. The slow interconversion of the double and single bonds in antiaromatic systems means that there is no free movement of the electrons round the ring, and so any
diamagnetic anisotropy is muted. At the same time, the near degeneracy of the HOMO and the LUMO
in the 4n annulenes allows a low-energy one-electron transition between them with a magnetic moment
perpendicular to the ring, whereas the aromatic systems, with a much larger energy gap between the
highest filled and lowest unfilled orbitals do not have this pathway.41 Single electrons are associated with
induced paramagnetic fields, as seen in the ESR spectra of odd electron systems.
1.5.4 Homoaromaticity42
The concept of aromaticity can be extended to systems in which the conjugated system is interrupted, by a
methylene group, or other insulating structural feature, provided that the overlap between the p orbitals of
the conjugated systems can still take place through space across the interruption. When such overlap has
energy-lowering consequences, evident in the properties of the molecule, the phenomenon is called
homoaromaticity. Examples are the homocyclopropenyl cation 1.26, the trishomocyclopropenyl cation
1.27, the bishomocyclopentadienyl anion 1.28 and the homocycloheptatrienyl cation 1.29. Each of these
species shows evidence of transannular overlap, illustrated, and emphasised with a bold line on the
orbitals, in the drawings 1.26b, 1.27b, 1.28b and 1.29b. The same species can be drawn without orbitals
in localised structures 1.26a, 1.27a, 1.28a and 1.29a and with the drawings 1.26c, 1.27c, 1.28c and 1.29c
showing the delocalisation. For simplicity, the orbital drawings do not illustrate the whole set of p
molecular orbitals, which simply resemble in each case the p orbitals of the corresponding aromatic
system.
However, homoaromaticity appears to be absent in homobenzene (cycloheptatriene) 1.30a and in
trishomobenzene (triquinacene) 1.31a, even though transannular overlap looks feasible. In both cases,
the conventional structures 1.30a and 1.30c, and 1.31a and 1.31c are lower in energy than the homoaromatic structures 1.30b and 1.31b, which appear to be close to the transition structures for the
interconversion.
H
H
H
H
H
1.26a
1.26b
1.26c
1.27a
H
1.27b
H
1.28a
1.28b
1.28c
1.29a
H
1.29b
1.27c
H
1.29c
1 MOLECULAR ORBITAL THEORY
43
Homoantiaromaticity is even less commonly invoked. Homocyclobutadiene 1.32b and the homocyclopentadienyl cation 1.33b are close to the transition structures for the interconversion of cyclopentadiene
1.32a and bicyclo[2.1.0]pentene 1.32c and of the cyclohexatrienyl cation 1.33a and the bicyclo[3.1.0]hexenyl cation 1.33c. However, homoantiaromaticity does show up in these cases, in the sense that, unlike the
interconversions in 1.30 and 1.31, neither of these interconversions is rapid.
H
H
1.30b
1.30a
1.30c
1.31b
1.31a
1.31c
H
H
H
H
1.32b
1.32a
1.33b
1.32c
1.33a
1.33c
We evidently have three situations, summarised in Fig. 1.50. In Fig. 1.50a, the homoaromatic structures
1.26c–1.29c, however they may be drawn, are at an energy minimum relative to the hypothetical localised
structures 126a–129a, and there is an energy E associated with the cyclic delocalisation. In Fig. 1.50b, we
have the localised structures 1.30a and c or 1.31a and c at minima, with the potentially homoaromatic
systems 1.30b or 1.31b near or at the top of a shallow curve. Finally with the homoantiaromatic systems, the
transition structures 1.32b or 1.33b are evidently high in energy with a greatly enlarged DE, the activation
energy for the interconversion of the localised structures. We shall see this again in Chapter 6 with
electrocyclic interconversions—those with aromatic transition structures like 1.30b and 1.31b are ‘allowed’,
and those with antiaromatic transition structures like 1.32b and 1.33b are ‘forbidden’.
The concept of homoaromaticity and homoantiaromaticity is sound. The nature of the overlap in
the aromatic and antiaromatic systems is not dependent upon the atoms being directly bonded by the
framework. The framework in an aromatic system has the effect of holding the p orbitals close,
44
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
1.32b,1.33b
1.26a-1.29a
1.30b,1.31b
E
E
E
1.32c,1.33c
1.30c,1.31c
1.26c-1.29c
(a) Homoaromatic systems
Fig. 1.50
1.32a,1.33a
1.30a,1.31a
(b) Potentially homoaromatic
systems
(c) Homoantiaromatic
systems
Relative energies of some localised, homoaromatic and homoantiaromatic structures
making the p overlap strong in consequence. Separating the p orbitals by a methylene group, or any
other insulating group, will usually weaken such overlap, and often cause it to be stronger on one
surface than the other, but it does not necessarily remove it completely. In favourable cases it can be
strong, and lead to noticeable effects. The factors affecting when it is and is not strong have been
discussed.43
1.5.5 Spiro Conjugation
In addition to and p overlap, p orbitals can overlap in another way, even less effective in lowering the
energy, but still detectable. If one conjugated system is held at right angles to another in a spiro structure,
with the drawing 1.34 representing the general case and hydrocarbons 1.35 and 1.36 two representative
examples, the p orbitals of one can overlap with the p orbitals of the other, as symbolised by the bold lines on
the front lobes in the drawing 1.34. The overlap integral will be small, but if the symmetry matches, the
interaction of the molecular orbitals can lead to new orbitals, raised or lowered in energy in the usual way. If
the symmetry is not appropriate, the overlap will simply have no effect.
1.34
1.35
1.36
Take spiroheptatriene 1.35, with the unperturbed orbitals of each component shown on the left and right in
Fig. 1.51. The only orbitals that can interact are 2 on the left and p* on the right; all the others having the
wrong symmetry. For example, the interaction of the top lobes of 1 on the left and the upper p orbital of the
p orbital on the right, one in front and one behind, have one in phase and one out of phase, exactly cancelling
each other out; similarly with the front p lobes on the right and the upper and lower lobes of the front-right p
orbital of 1 on the left.
The two orbitals that do interact, 2 and p*, which have the same symmetry, create the usual pair of new
orbitals, one raised and one lowered. Since there are only two electrons to go into the new orbitals, the overall
energy of the conjugated system is lowered. The effect, DEs, is small, both because of the poor overlap, and
because the two orbitals interacting are far apart in energy, which we shall see later is an important factor.
Nevertheless, it is a general conclusion that if the total number of p electrons is a (4nþ2) number, the spiro
system is stabilised, leading to the concept of spiroaromaticity.
1 MOLECULAR ORBITAL THEORY
45
*
4
*
*
3
Es
2
1
1.35
Fig. 1.51
p Molecular orbitals of the ‘aromatic’ spiroheptatriene
There is equally a phenomenon of spiroantiaromaticity when the total number of p electrons is a 4n
number, as in spirononatetraene 1.36 (Fig. 1.52). Here the only orbitals with the right symmetry to
interact productively are the 2 orbitals on each side (ignoring the interaction of the unfilled 4*
orbitals with each other, which has no effect on the energy because there are no electrons in these
*
4
*
*
3
4
*
3
Es*
2
2
Es
1
1
1.36
Fig. 1.52
p Molecular orbitals of the ‘antiaromatic’ spirononatetraene
46
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
orbitals). They lead to the usual two new orbitals, but since there are four electrons to go into them,
the net effect is to raise the overall energy, with the bonding combination lowered in energy DEs less
than the antibonding combination is raised DEs*. The splitting of the energy levels (DEs þ DEs*) has
been measured to be 1.2 eV, and this molecule does show exceptional reactivity, in agreement with
the increase in overall energy and the raising of the energy of the HOMO.44
1.6
Strained s Bonds—Cyclopropanes and Cyclobutanes
As we have just seen, it is possible to have some bonding even when the overlap is neither strictly head-on
nor sideways-on. It is easily possible to retain much more of the bonding when the orbitals are rather better
aligned than those in spiro-conjugated systems, as is the case in several strained molecules, epitomised by
cyclopropane.
1.6.1 Cyclopropanes
There are several ways to describe the bonds in cyclopropane. The most simple is to identify the C—H
bonds as coming from the straightforward sp3 hybrids on the carbon atoms and the 1s orbitals on the
hydrogen atoms 1.37 in the usual way, and the C—C bonds as coming from the remaining sp3 hybrids
imperfectly aligned 1.38. In more detail, these orbitals ought to be mixed in bonding and antibonding
combinations to create the full set of molecular orbitals, but even without doing so we can see that C—C
bonding is somewhere between bonding (head-on overlap) and p bonding (sideways-on overlap). We can
expect these bonds to have some of the character of each, which fits in with the general perception that
cyclopropanes can be helpfully compared with alkenes in their reactivity and in their power to enter into
conjugation. Thus cyclopropane 1.40 is much less reactive than ethylene 1.39 towards electrophiles like
bromine, but it is much more reactive than ethane 1.41. Conjugation of a double bond or an aromatic ring
with a cyclopropyl substituent is similar to conjugation with an alkene, but less effective in most cases.
However, conjugation between a cyclopropane and an empty p orbital on carbon is more effective in
stabilising the cyclopropylmethyl cation than conjugation with a double bond is in the allyl cation (see p. 88).
H
H
H
H
HH
H
H
H
H
1.37
Br
1.39
1.38
Br
Br
Br
f ast
H
H
Br
Br
Br
Br
no reaction
Br
1.40
slow
Br
1.41
Another way of understanding the C—C bonding, known as the Walsh description, emphasises the
capacity of a cyclopropyl substituent to enter into p bonding. In this picture, which is like the picture of
the bonding in ethane without using hybridisation (Fig. 1.22), the six C—H bonds are largely made up from
the s orbitals on hydrogen and the s, px and pz orbitals on carbon, with the x, y and z axes redefined at each
corner to be local x, y and z coordinates. The picture of C—H bonding can be simplified by choosing sp
1 MOLECULAR ORBITAL THEORY
47
hybridisation from the combination of the 2s and 2px orbitals, and using the three sp hybrids with the large
lobes pointing outside the ring and the three pz orbitals to make up the CH bonding orbitals (Fig. 1.53).
Some of these orbitals contribute to C—C bonding, notably the CH,pCC orbital, but the major contributors
are the overlap of the three sp hybrids with the large lobes pointing into the ring, which produce one
bonding combination CC, and the three py orbitals, which combine to produce a pair of bonding orbitals
pCC, each with one node, and with coefficients to make the overall bonding between each of the C—C
bonds equal.
H
H
H
H
H
H
CC
py
H
H
H
H
CC
H
H
H
H
H
py
H
H
H
CH
H
H
CH
H
H
H
H
H
H
H
CC
H
H
H
H
H
H
CH, CC
H
H
H
H
H
H
H
H
H
CH
H
H
CH
H
H
H
H
H
H
H
CH
H
H
Fig. 1.53
H
A simplified version of the occupied Walsh orbitals of cyclopropane
The advantage of this picture is that it shows directly the high degree of p bonding in the C—C bonds, and
gives directly a high-energy filled p orbital, the pCC orbital at the top right, largely concentrated on C-1, and
with the right symmetry for overlap with other conjugated systems, as we shall see in Section 2.2.1.
A remarkable property of cyclopropanes is that they are magnetically anisotropic, rather like benzene—
but with the protons coming into resonance in their NMR spectra at unusually high field, typically 1 ppm
upfield of the protons of an open-chain methylene group. For 1H NMR spectroscopy, this is quite a large
effect, and it is also strikingly in the opposite direction from that expected by the usual analogy drawn
between a cyclopropane and an alkene. The anisotropy45 is most likely a consequence of the presence of
overlap from three sets of orbitals having a total of six electrons in them. These could be seen as the 1s sp3
orbitals contributing to the C—H bonds 1.37, which we could have mixed to get a set of orbitals resembling
48
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
the p orbitals of benzene. Alternatively, turning to Fig. 1.53, the pair of CH orbitals just below the highest
occupied orbitals, together with the CH,pCC orbital, clearly have the same nodal pattern as the filled p
orbitals of benzene (Fig. 1.43), and the pattern is repeated in the three filled orbitals of lowest energy. This
pattern of orbitals is associated, as with benzene, with the capacity to support a ring current, but, in contrast to
benzene, the derived field places the protons in cyclopropanes in the region experiencing a reduced magnetic
field 1.42.
The same explanation, although we shall not show the molecular orbitals, has been advanced to account
for the small difference in chemical shift between the axial and equatorial protons in cyclohexanes,
detectable in cyclohexane itself by freezing out at –100 C the otherwise rapid interconversion of the two
chair conformations.46 The axial protons come into resonance upfield at d1.1 and the equatorial protons
downfield at d1.6. It is possible that the three axial C—H bonds on each side overlap in a p sense to create a
trishomoaromatic system, with a diamagnetic ring current which places the axial protons in the reduced
magnetic field 1.43, and the equatorial protons in the enhanced magnetic field 1.44.
0.3
applied
field
H
H
1.1
1.6
H
H
H
H
H
H
H
H
H
H
H
1.42
H
H
H
H
H
1.43
1.44
1.6.2 Cyclobutanes
It is not necessary to go through the whole exercise of setting up the molecular orbitals of cyclobutanes,
which show many of the same features as cyclopropanes, only less so. Cyclobutanes also show enhanced
reactivity over simple alkanes, but they are less reactive towards electrophiles, and cyclobutyl groups are less
effective as stabilising substituents on electron-deficient centres than cyclopropyl groups.
The most striking difference, however, is that the protons in cyclobutanes come into resonance in their
1
H NMR spectra downfield of the protons from comparable methylene groups in open-chain compounds.47
The effect is not large, typically only about 0.5 ppm, with cyclobutane itself, for example, at d1.96 in
contrast to the average of the cyclohexane signals at d1.44. In a cyclobutane, four sets of C—H bonds are
conjugated, and the pattern of orbitals will be similar to those of cyclobutadiene (Fig. 1.46). Again there
will be two sets, and the top two of each set will be degenerate. The ring current is therefore in the opposite
direction, adding to the applied field at the centre of the ring, and the protons experience an enhanced field
1.45. The effect may be rather less in cyclobutanes than in cyclopropanes, because the cyclobutane ring is
flexible, allowing the ring to buckle from the planar structure 1.45, and the C—H bonds thereby avoid the
full eclipsing interactions inevitable in cyclopropanes, and compensated there by the aromaticity they
create.
applied
field
H
H
H
H
H
H
H
1.45
H
1 MOLECULAR ORBITAL THEORY
1.7
49
Heteronuclear Bonds, C—M, C—X and C=O
So far, we have been concentrating on symmetrical bonds between identical atoms (homonuclear bonds) and on
bonds between carbon and hydrogen. The important interaction diagrams were constructed by combining atomic
orbitals of more or less equal energy, and the coefficients, c1 and c2, in the molecular orbitals were therefore more
or less equal in magnitude. It is true that C—H bonds, both in the picture without hybridisation (Fig. 1.14) and in
the picture with hybridisation (Fig. 1.20), involve the overlap of atomic orbitals of different elements, but the
difference in electronegativity, and hence in the energy of the atomic orbitals of these two elements, was not
significant at the level of discussion used in the earlier part of this chapter. In other cases where we have seen
orbitals of different energy interacting, we have either ignored the consequences, because it did not make any
significant difference to the discussion at that point, or we have deferred discussion until now. The interaction of
orbitals of different energy is inescapable when we come to consider molecules, like methyl chloride and
methyllithium, with single bonds to other elements, and molecules with double bonds to electronegative
elements like oxygen. As we have mentioned in passing, atomic orbitals of different energy interact to lower
(and raise) the energy of the resultant molecular orbitals less than orbitals of comparable energy.
1.7.1 Atomic Orbital Energies and Electronegativity
There are two standard ways of assessing the relative energies of the orbitals of different elements. One is to use
one or another of the empirical scales of electronegativity. Pauling’s, which is probably the most commonly
used, is empirically derived from the differences in dissociation energy for the molecules XX, YY and XY.
Several refinements of Pauling’s scale have been made since it first appeared in 1932, and other scales have been
suggested too. A good recent one, similar to but improving upon Pauling’s, is Allen’s,48 drawn to scale in
Fig. 1.54, along with values assigned by Mullay49 to the carbon atoms in methyl, vinyl and ethynyl groups.
H and First Row
0.91
1.58
2.05
2.30
2.54
Hybrids on C
0.87
Na
1.29
Mg
1.61
Al
1.92
Si
sp3
2.25
P
2
2.59
S
2.87
Cl
Li
Be
B
H
C
3.07
N
3.61
O
4.19
F
Fig. 1.54
2.3
2.6
3.1
Second Row
sp
Third Row
0.73
K
1.03
Ca
1.76
Ga
1.99
2.21
2.42
2.69
Ge
As
Se
Br
Fourth Row
0.71
0.96
Rb
Sr
1.66
1.82
1.98
2.16
2.36
In
Sn
Sb
Te
I
sp
Allen electronegativity values and Pauling-based values for carbon hybrids
In spite of the widespread use of electronegativity as a unifying concept in organic chemistry, the electronegativity of an element is almost never included in the periodic table. Redressing this deficiency, Allen
strikingly showed his electronegativity scale as the third dimension of the periodic table, and his vivid picture
is adapted here as Fig. 1.55.
50
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
F
O
N
Cl
H
Se
P
B
I
As
Si
Al
Be
Br
S
C
Te
Ge
Sb
Sn
Ga
In
Mg
Li
Ca
Na
Sr
K
Rb
Fig. 1.55
Electronegativity as the third dimension of the periodic table (adapted with permission from L. C. Allen,
J. Am. Chem. Soc., 1989, 111, 9003. Copyright 1989 American Chemical Society)
An alternative and more direct way of getting a feel for the relative energies of atomic orbitals is to take them
from calculations, reproduced to scale for the first and second row elements in Fig. 1.56.50 The soundness of
these energies is backed up by measurements of the ionisation potentials (IPs), which measure the energy
needed to remove an electron from the element. These calculations rank the elements in much the same order,
although with a couple of explicable anomalies, which need not concern us here. This figure separates the s and
the p orbitals, but we can easily calculate the relative energies of hybrid orbitals on any of the elements from
group three to group eighteen. The ranking of the hybrids for carbon, nitrogen, oxygen and fluorine is given in
Fig. 1.57 on the same scale and with the s and p orbital energies carried over for comparison.
The two pictures, the empirical values of Fig. 1.54 and the calculated values of Fig. 1.56, show that the
relative positions of the elements on these scales are essentially the same. However, the electronegativity
scale shows the methyl, vinyl and ethynyl groups below that for the 1s orbital on hydrogen, whereas the
atomic orbital energies place hydrogen in the middle of the range for the different kinds of carbon. This
uncertainty provides fuel for debate about which way C—H bonds are polarised, and about whether a C—H
bond or a C—C bond is the better electron donor, but the main conclusion is that the energies of the atomic
orbitals for C and H are very comparable, and the bond between them is not strongly polarised.
1.7.2 C—X s Bonds
We are now ready to construct an interaction diagram for a bond made by the overlap of atomic orbitals with
different energies. Let us take a C—Cl bond, in which the chlorine atom is the more electronegative
element. Other things being equal, the energy of an electron in an atomic orbital on an electronegative
element is lower than that of an electron on a less electronegative element (Fig. 1.56).
As usual, we can tackle the problem with or without using the concept of hybridisation. The C—X bond in
a molecule such as methyl chloride, like the C—C bond in ethane (Fig. 1.22), has several orbitals contributing
1 MOLECULAR ORBITAL THEORY
H
Li
p
s
51
B
Be
O
N
C
Na
F
–5.4
p
–6.0 p –5.7
s
–5.2
s
s
–9.4
p
s
Al
Mg
P
Si
S
Cl
–3.5
p
–12.9
p
p
–11.3
–15.9
–9.8
p
s
p
–19.4
–7.8
p
s
–14.7
s
p –6.0
–10.7
–13.6
s
–7.6
p
–15.0
–18.6
s
–20.9
–25.6
s
s
–13.7
–18.4
s
s
–11.7
–25.3
–32.4
s
–40.1
Fig. 1.56 Valence atomic orbital energies in eV (1 eV ¼ 96.5 kJ mol–1 ¼ 23 kcal mol–1)
H
–13.6
C
1s
N
–10.7
–12.9
–13.6
–15.1
p
sp3
sp2
sp
–19.4
s
O
–12.9
p
–16.1
–17.1
–19.3
sp3
sp2
sp
–25.6
s
–15.9
p
–20.0
–21.4
sp3
sp2
–24.2
sp
–32.4
Fig. 1.57
F
–18.6
p
–24.4
–25.8
sp3
sp2
–29.4
sp
–40.1
s
s
Atomic orbital energies for hybrid orbitals in eV
to the force which keeps the two atoms bonded to each other; but, just as we could abstract one of the
important pair of atomic orbitals of ethane and make a typical interaction diagram for it (Fig. 1.24), so can we
now take the corresponding pair of orbitals from the set making up a C—Cl bond.
The important thing for the moment is the comparison between the C—C orbitals and the corresponding
C—Cl orbitals. What we learn about the properties of C—Cl bonds by looking at this one orbital will be the
same as we would have learned, at much greater length, from the set as a whole. Alternatively, we can use an
interaction diagram for an sp3 hybrid on carbon and an sp3 hybrid on chlorine, and compare the result with
52
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
the corresponding interaction of two sp3 hybrids on carbon. Both pictures will be very similar, and we can
learn the same lesson from either.
In making a covalent bond between carbon and chlorine from the 2px orbital on carbon and the 3px orbital
on chlorine, we have an interaction (Fig. 1.58) between orbitals of unequal energy (–10.7 eV for C and –13.7
eV for Cl, from Fig. 1.56). The interaction diagram in Fig. 1.58 could equally have been drawn using sp3
hybrids on carbon and chlorine in place of the p orbitals. The hybrids have lower energies (–12.9 eV for
carbon and –16.6 eV for chlorine), because they have some s character, and the difference in energy between
them is greater, but the rest of the story and our conclusions will be unchanged. Alternatively we could use
Allen’s electronegativities, which effectively take the involvement of s orbitals in hybrids into account.
*C—Cl
px
EC
Cl
Ei
Cl
px
ECl
C—Cl
Cl
Fig. 1.58 A major part of the C—Cl bond
On account of the loss of symmetry, the chlorine atom has a larger share of the total electron population. In
other words, the coefficient on chlorine for the bonding orbital, CCl is larger than that on carbon. It follows
from the requirement that the sum of the squares of all the c-values on any one atom in all the molecular
orbitals must equal one, that the coefficients in the corresponding antibonding orbital, *CCl must reverse
this situation: the one on carbon will have to be larger than the one on chlorine.
What we have done in Fig. 1.58 is to take the lower-energy atomic orbital on the right and mix in with it, in
a bonding sense, some of the character of the higher-energy orbital on the left. This creates the new bonding
molecular orbital, which naturally resembles the atomic orbital nearer to it in energy more than the one
further away. We have also taken the higher-energy orbital and mixed in with it, in an antibonding sense,
some of the character of the lower-energy orbital. This produces the antibonding molecular orbital, which
more resembles the atomic orbital nearer it in energy. When the coefficients are unequal, the overlap of a
small lobe with a larger lobe does not lower the energy of the bonding molecular orbital as much as the
overlap of two atomic orbitals of more equal size. ECl in Fig. 1.58, is not as large as E in Fig. 1.24.
Using this interaction, and others taking account of the same factors, we can set up a set of filled orbitals
for methyl chloride, represented schematically in Fig. 1.59a, along with the lowest of the unoccupied
orbitals. As with other multi-atom molecules, several orbitals contribute to C—Cl bonding, with more
bonding than antibonding from the overlap of the s orbitals, but probably nearly equal bonding and
antibonding from the orbitals having p bonding between the carbon and the chlorine. The same degree of
bonding can be arrived at by using the hybrid orbitals shown in Fig. 1.59b, where all of the C—Cl bonding
comes from the sp3 hybrids.
We might be tempted at this stage to say that we have a weaker bond than we had for a C—C bond, but we
must be careful in defining what we mean by a weaker bond in this context. Tables of bond strengths give the
C—Cl bond a strength, depending upon the rest of the structure, of something like 352 kJ mol–1 (84 kcal mol–1),
whereas a comparable C—C bond strength is a little lower at 347 kJ mol–1 (83 kcal mol–1). Only part of the
1 MOLECULAR ORBITAL THEORY
53
H
H
LUMO
C
Cl
C
Cl
3
sp *CCl H
H
H
*CCl
H
H
Cl
C
LUMO
H
C
Cl
C
H
H
H
H
H
Cl
CCl
H
H
Cl
C
Cl
H
C
H
H
H
C
H
Cl
sp3CCl
H
H
H
H
H
H
H
C
C
H
Cl
Cl
H
(b) the sp3-hybridised orbitals
of the C—Cl bond
H
(a) without using hybridisation
Fig. 1.59 The filled molecular orbitals and the lowest unfilled molecular orbital of methyl chloride
C—Cl bond strength represented by these numbers comes from the purely covalent bonding given by 2ECl in
Fig. 1.58. The other part of the strength of the C—Cl bond comes from the electrostatic attraction between the
high electron population on the chlorine atom and the relatively exposed carbon nucleus.
We usually say that the bond is polarised, or that it has ionic character. This energy is related to the value Ei
in Fig. 1.58, as we can readily see by using an extreme example: suppose that the energies of the interacting
orbitals are very far apart (Fig. 1.60, where the isolated orbitals are the 3s orbital on Na and a 2p orbital on F,
with energies of –5.2 and –18.6 eV); the overlap will be negligible, and the new molecule will now have
almost entirely isolated orbitals in which the higher-energy orbital has given up its electron to the lowerenergy orbital. In other words, we shall have a pair of ions. There will be no covalent bonding to speak of, and
Na
Na 3s
Ei
F
Fig. 1.60
2p F
A much oversimplified ionic bond
54
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
the drop in energy in going from the pair of radicals to the cation plus anion is now Ei in Fig. 1.60, which, we
can see, is indeed related to Ei in Fig. 1.58.
The C—Cl bond is strong, if we try to break it homolytically to get a pair of radicals, and a comparable
—
C C bond is marginally easier to break this way. This is what the numbers 352 and 347 kJ mol–1 refer to. In
other words, EC þ ECl in Fig. 1.58 is evidently greater than 2E in Fig. 1.24. However, it is very much easier
to break a C—Cl bond heterolytically to the cation (on carbon) and the anion (on chlorine) than to cleave a
C—C bond this way. In other words, 2ECl in Fig. 1.58 is less than 2E in Fig. 1.24.
The important thing to remember is that when two orbitals of unequal energy interact, the lowering in
energy is less than when two orbitals of very similar energy interact. Conversely, when it comes to
transferring an electron, the ideal situation has the electron in a high-energy orbital being delivered to the
‘hole’ in a low-energy orbital.
In a little more detail, the extent of the energy lowering ECl is a function not only of the difference in
energy Ei between the interacting orbitals, but also of the overlap integral S. The overlap integrals for
forming a C—N, a C—O or a C—F bond are essentially, at least in the region for the normal internuclear
distances and outwards, parallel to the overlap integral for the formation of a C—C bond (Figs. 1.13b and
1.23b), but displaced successively by about 0.2 Å to shorter internuclear distances for each element. This is
because the orbitals of the first-row elements have similar shapes, but the electrons are held more tightly in to
the nucleus of the more electronegative elements, and the more electronegative they are the tighter they are
held. This simply means that the atoms must be a little closer together to benefit from the overlap. We have
already seen that when orbitals of identical energy interact, the energy lowering is roughly proportional to S
(see p. 4). When they are significantly different in energy, however, it is roughly proportional to S2. They are
also, as we have seen above, inversely proportional to the energy difference Ei. The equations for the
energies of the lowered and raised orbitals in Fig. 1.58, ECCl and E*CCl, respectively, take the form shown in
Equations 1.13 and 1.14.
ECCl ¼ EpCl þ
ð CCl EpCl SCCl Þ 2
EpCl –EpC
1:13
ECCl ¼ EpC þ
ð CCl EpC SCCl Þ 2
EpC –EpCl
1:14
Clearly a full expression for the overall electronic energy is a complex one if it is to take account of the
changes between these expressions and those in Equations 1.4 and 1.5 for the energies when the interacting
orbitals are degenerate.
A picture of the electron distribution in the orbitals between carbon and chlorine is revealed in the wiremesh diagrams in Fig. 1.61, which show one contour of the CCl and *CCl orbitals of methyl chloride.
Comparing these with the schematic version in Fig. 1.58, we can see better how the back lobe on carbon in
CCl overlaps with the s orbitals on the hydrogen atoms, and that the front lobe in *CCl wraps back behind
σ CCl
Fig. 1.61
σ *CCl
The major C—Cl bonding orbital and the LUMO for methyl chloride
1 MOLECULAR ORBITAL THEORY
55
the carbon atom to include a little overlap to the s orbitals of the hydrogen atoms. We need to remove an
oversimplification and delve a little more into detail in order to see how this comes about.
The pictures in Fig. 1.59a are shown as though the lowest-energy orbitals were made up from the
interaction only of s orbitals with each other. Likewise the next higher orbitals are made up only of the
interactions of p orbitals on the carbon and chlorine, and necessarily s orbitals on hydrogen. These
interactions are certainly the most important, and the simplification works, because the s orbitals on carbon
and chlorine are closer in energy to each other than they are to each other’s p orbitals, and vice versa, as
shown in Fig. 1.62a. However, the direct interactions of s with s and p with p are only a first-order treatment,
and a second-order treatment has to consider that the s orbital on carbon can interact quite strongly with the
px orbital on chlorine, and there will even be a small interaction from the px orbital on carbon and the s orbital
on chlorine. This complication is similar to something we saw earlier with methylene, with the allyl system
and with butadiene (Figs. 1.16. 1.32 and 1.38), where we used the device for constructing molecular orbitals,
first looking at the strong interaction of orbitals close in energy, and then modified the result by allowing for
the weaker interactions of orbitals further apart in energy. The true mixing of orbitals for methyl chloride
would still leave the lowest energy orbital looking largely like the mix of s with s, but there would be a
contribution with some p character, in inverse proportion to the energy difference between the s and p
orbitals. It is the presence of some p character in the orbitals contributing to the *CCl orbital in Fig. 1.61 that
allows the outer counters to reach round behind the carbon atom. We saw the same feature earlier in the
picture of an sp3 hybrid (Fig. 1.19), where the cause was essentially the same—the mixing of s and p orbitals
in optimum proportions for lowering the overall energy.
The problem of identifying sensible mixes of orbitals would have been much more acute had we used
methyl fluoride instead of methyl chloride. With methyl fluoride, the 2s orbital on carbon is almost identical
in energy with the 2p orbitals on fluorine, as shown in Fig. 1.62b. The 2px orbital from that element and the 2s
orbital on carbon have the right symmetry, and their interaction would provide the single strongest
contribution to C—F bonding. Continuing from here to make a full set of the molecular orbitals for methyl
fluoride, mixing in a small contribution from the p orbital on carbon, for example, would not have made as
tidy and understandable a picture as the one for methyl chloride in Fig. 1.59. Most strikingly, the lowestenergy orbital would be an almost pure, undisturbed s orbital on fluorine, and there would be
correspondingly little of this orbital to mix in with the others.
–3.5 p
Li
–5.4 s
Li
pC –10.7
pC –10.7
pC –10.7
–13.7 p
Cl
sC –19.4
sC –19.4
–18.6 p
F
sC –19.4
–25.3 s
Cl
–40.1 s
F
(a) Methyl chloride
(b) Methyl f luoride
(c) Methyllithium
Fig. 1.62 Some of the major interactions contributing to C—Cl bonding for MeCl, to C—F bonding for MeF, and to
C—Li bonding for MeLi
56
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
1.7.3 C—M s Bonds
When the bond from carbon is to a relatively electropositive element like lithium, the same problems
can arise—with methyllithium the most strongly interacting orbitals contributing to the C—Li bond
(Fig. 1.62c) are the 2s orbital on lithium and the 2px orbital on carbon. The pictorial set of molecular
orbitals therefore is not one in which you can see immediately which atomic orbitals make the major
contribution to which molecular orbitals. The interaction between a 2s orbital on lithium and a 2px
orbital on carbon has the form shown in Fig. 1.63. The energy of the lithium 2s orbital is –5.4 eV,
making the carbon atom, with a 2p orbital at –10.7 eV, the more electronegative atom. The bonding
orbital LiC is polarised towards carbon, and the antibonding *LiC towards lithium. Organic chemists
often refer to organolithium compounds as anions. Although there evidently is some justification for
this way of thinking, it is as well to bear in mind that they are usually highly polarised covalent
molecules. Furthermore, they are rarely monomeric, almost always existing as oligomers, in which
the lithium is coordinated to more than one carbon atom, making the molecular orbital description
below severely over-simplified
*LiC
Li
Li
sLi
px
LiC
Fig. 1.63
Li
A contributory part of the Li—C bond
The filled and one of the unfilled orbitals for monomeric methyllithium are shown in Fig. 1.64. The lowest
energy orbital is made up largely from the 2s orbital on carbon and the 1s orbitals on hydrogen, with only a
little mixing in of the 2s orbital of lithium and even less of the 2p. The next two up in energy are largely p
mixes of the 2pz and 2py orbitals on carbon with a little of the 2pz and 2py on lithium, and, as usual, the 1s
orbitals on hydrogen. The 2pz and 2py orbitals on lithium have a zero overlap integral with the 2s orbital on
carbon, and this interaction, although between orbitals close in energy (Fig. 1.62c), makes no contribution.
Then come the two orbitals we have seen in Fig. 1.63: the 2px orbital on carbon interacting productively with
the 2s orbital on lithium, giving rise to the highest of the occupied orbitals CLi, which has mixed in with it
the usual 1s orbitals on hydrogen and a contribution from the 2px orbital on lithium, symbolised here by the
displacement of the orbital on lithium towards the carbon. The next orbital up in energy, the lowest of the
unfilled orbitals, is its counterpart *CLi, largely a mix of the 2s and the 2px orbital of lithium, symbolised
again by the displacement of the orbital on lithium away from the carbon, with a little of the 2px orbital of
carbon out of phase.
A picture of the electron distribution in the frontier orbitals between carbon and lithium is revealed in the
wire-mesh diagrams in Fig. 1.65, which show one contour of the CLi and *CLi orbitals of methyllithium,
unrealistically monomeric and in the gas phase. Comparing these with the schematic version in Fig. 1.64, we
can see better how the s and px orbitals on lithium mix to boost the electron population between the nuclei in
CLi, and to minimise it in *CLi. The HOMO, CLi, is used on the cover of this book.
1 MOLECULAR ORBITAL THEORY
57
H
H
H
C
LUMO
H
*CLi
3
Li
C
sp *CLi
Li
H
H
H
H
H
C
H
H
Li
CLi
H
C
H
C
H
H
HOMO
H
Li
H
Li
sp3CLi
C
Li
H
H
H
C
Li
H
(a) without using hybridisation
Fig. 1.64
(b) the sp3-hybridised orbitals of
the C—Li bond
The filled and one of the unfilled molecular orbitals of methyllithium
σ CLi
Fig. 1.65
σ *CLi
The HOMO and LUMO for methyllithium
1.7.4 C=O p Bonds
Setting up the molecular orbitals of a C¼O p bond is relatively straightforward, because the p orbitals in the
p system in Hückel theory are free from the complicating effect of having to mix in contributions from
s orbitals. The px orbital on oxygen is placed in Fig. 1.66 at a level somewhat more than 1 below that of the
px orbital on carbon, although not to scale. The energy of a p orbital on oxygen is –15.9 eV and that on carbon
–10.7 eV (Fig. 1.56). As with p bonds in general, the raising of the p* and lowering of the p orbitals above
and below the atomic p orbitals is less than it was for a C—O bond, and less than the corresponding p bond
between two carbon atoms. Both the pC¼O and the p*C¼O orbitals are now lower in energy than the pC¼C and
p*C¼C orbitals, respectively, of ethylene, which by definition are 1 above and 1 below the level.
The polarisation of the carbonyl group is away from carbon towards oxygen in the bonding orbital,
and in the opposite direction in the antibonding orbital, as usual. The wire-mesh pictures in Fig. 1.67
show more realistically an outer contour of these two orbitals in formaldehyde, and the plots in Fig.
1.68 show the electron distribution in more detail. Note that in these pictures it appears that the p
electron population in the bonding orbital is nearly equal on oxygen and on carbon. This is not the
case, as shown by the extra contour around the oxygen atom in the plot in Fig. 1.68. The electron
58
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
1
O
LUMO
*C=O
pC
1
pO
O
HOMO
Fig. 1.66
π
Fig. 1.67
C=O
A C¼O p bond
π*
Wire-mesh plot of the p and p* orbitals of formaldehyde
π
Fig. 1.68
O
π*
Electron population contours for the p and p* orbitals of formaldehyde
1 MOLECULAR ORBITAL THEORY
59
distribution around the oxygen atom is simply more compact, as a consequence of the higher nuclear
charge on that atom. This is another way in which the conventional lobes as drawn in Fig. 1.66 are
misleading.
There is no set of fundamentally sound values for and to use in Hückel calculations with heteroatoms.
Everything is relative and approximate. The values for energies and coefficients that come from simple
calculations on molecules with heteroatoms must be taken only as a guide and not as gospel. In simple
Hückel theory, the value of to use in a calculation is adjusted for the element in question X from the
reference value for carbon 0 by Equation 1.15. Likewise, the value for the C¼C bond in ethylene 0 is
adjusted for C¼X by Equation 1.16.
X ¼0 þ hX 0
1:15
CX ¼kCX 0
1:16
The adjustment parameters h and k take into account the trends in Figs. 1.54–1.56 and the changes in the
overlap integrals for making C—X bonds discussed on p. 54, but are not quantitatively related to those
numbers. Instead, values of h for some common elements and of k for the corresponding C¼X p bonds
(Table 1.2) have been recommended for use in Equations 1.15 and 1.16.51 They are only useful to see trends.
Table 1.2
Parameters for simple Hückel calculations for p bonds with heteroatoms
Element
B
C
N
C
N
N
O
C
N
h
k
Element
–0.45
0.73
0
1
Si
0.51
1.02
P
1.37
0.89
P
0.97
1.06
S
O
Si
P
P
S
h
k
0
0.75
0.19
0.77
0.75
0.76
0.46
0.81
O
O
2.09
0.66
S
S
1.11
0.69
F
F
2.71
0.52
Cl
Cl
1.48
0.62
As with single bonds to electronegative heteroatoms, it is easier to break a C¼O bond heterolytically and a
C¼C bond homolytically. Some reminders of a common pattern in chemical reactivity may perhaps bring a
sense of reality to what must seem, so far, an abstract discussion: nucleophiles readily attack a carbonyl
group but not an isolated C¼C double bond; however, radicals readily attack C¼C double bonds, and,
although they can attack carbonyl groups, they do so less readily.
1.7.5 Heterocyclic Aromatic Systems
The concept of aromaticity is not restricted to hydrocarbons. Heterocyclic systems, whether of the pyrrole
type 1.46 with trigonal nitrogen in place of one of the C¼C double bonds, or of the pyridine type 1.47 with a
60
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
trigonal nitrogen in place of a carbon atom, are well known. The p orbitals of pyrrole are like those of the
cyclopentadienyl anion, and those of pyridine like benzene, but skewed by the presence of the electronegative heteroatom. The energies and coefficients of heteroatom-containing systems like these cannot be
worked out with the simple devices that work for linear and monocyclic conjugated hydrocarbons. The
numbers in Fig. 1.69 are the results of simple Hückel calculations using parameters like those in Table 1.2 for
equations like Equations 1.15 and 1.16, and some trends can be seen. The overall p energy is lowered by the
cyclic conjugation. The lowest-energy orbital 1 is always polarised towards the electronegative atom, and
the next orbital up in energy 2 (and the highest unoccupied orbital) is polarised the other way. This
polarisation is more pronounced in the pyridinium cation 1.48, where the protonated nitrogen is effectively a
more electronegative atom. In the pyridine orbitals, the HOMO is actually localised as the nonbonding lone
pair of electrons on nitrogen, and the degeneracy of 2 and 3, and of the corresponding antibonding orbitals,
is removed, but not by much. The orbitals with nodes through the heteroatoms are identical in energy and
coefficients with those of the corresponding hydrocarbon. The orbitals 3 and 5* in pyrrole, with a node
through the nitrogen atom, are identical to 2 and 4* in butadiene, and 3 and 5* in pyridine and its cation
are identical to 3 and 5* in benzene.
N
H
N
1.47
1.46
N
H
1.48
–0.45
–0.48
0.45
0.44
–0.38
–0.60
*
6
*
5
4*
1.62
1.93
–0.39
0.32
–0.25
N
H
*
5
0.57
–0.49
N
4*
1.00
0.57
1.00
N
H
0.58
3
2
0.5
N
–0.50
0.50
1.00
N
1
2.30
1.32
N
0.65
0.41
2.11
N
0.34
0.43
H
–0.08
–0.57
2.28
1
–0.52
0.26
0.36
N
H
0.29
0.42
N
0.52
Fig. 1.69
0.63
2
1
0.33
N
H
3
–0.19
H
N
H
0.50
0.60
1.17
–0.56
0.42
1.00
N
N
H
0.20
0.35
–0.58
1.00
0.70
–0.37
n
0.60
4*
–0.24
0.55
0.62
5*
N
0.37
N
H
0.50
0.50
0.84
H
2
*
0.26
1.90
6
0.37
1.30
3
N
0.41
0.65
N
H
p Molecular orbitals of pyrrole, pyridine and the pyridinium ion. (Calculated using h¼1 and k¼1 for pyrrole,
h¼0.5 and k¼1 for pyridine, and h¼1 and k¼1 for the pyridinium cation)
1 MOLECULAR ORBITAL THEORY
1.8
61
The Tau Bond Model
The Hückel version of molecular orbital theory, separating the and p systems, is not the only way of
accounting for the bonding in alkenes. Pauling showed that it is possible to explain the electron distribution
in alkenes and conjugated polyenes using only sp3-hybridised carbon atoms. For ethylene, for example,
instead of having sp2-hybridised carbons involved in full bonding, and p orbitals involved in a pure p bond,
two sp3 hybrids can overlap in something between and p bonding 1.49. The overall distribution of electrons
in this model is exactly the same as the combination of and p bonding in the conventional Hückel picture
(Fig. 1.25). In practice, this model, usually drawn with curved lines called t bonds 1.50,52 has found few
adherents, and the insights it gives have not proved as useful as the Hückel model. For example, the t bonds
between C-1 and C-2 and between C-3 and C-4 in butadiene 1.51 are not so obviously conjugated as the p
bonds in the Hückel picture in Fig. 1.37. It is useful, however, to recognise that it is perfectly legitimate, and
that on occasion it might have some virtues, not present in the Hückel model, especially in trying to explain
some aspects of stereochemistry.
H
H
H
H
H
H
H
H
1.50
1.49
H
H
1
H
3
2
H
4
H
H
1.51
1.9
Spectroscopic Methods
A number of physical methods have found support in molecular orbital theory, or have provided evidence
that the deductions of molecular orbital theory have some experimental basis. Electron affinities measured
typically from polarographic reduction potentials correlate moderately well with the calculated energies of
the LUMO of conjugated systems. Ionisation potentials can be measured in a number of ways, and the results
correlate moderately well with the calculated energies of the HOMO of conjugated systems.53 Several other
measurements, like the energies of conjugated systems, bond lengths, and energy barriers to rotation, can be
explained by molecular orbital theory, and will appear in the normal course of events in the next chapter. A
few other techniques, dealt with here, have helped directly in our understanding of molecular orbital theory,
and we shall use evidence from them in the analysis of chemical structure and reactivity in later chapters.
1.9.1 Ultraviolet Spectroscopy
When light of an appropriate energy interacts with an organic compound, an electron can be promoted from a
low-lying orbital to a higher energy orbital, with the lowest-energy transition being from the HOMO to the
LUMO. Selection rules govern which transitions are allowed and which are forbidden. One rule states that
electron spin may not change, and another that the orbitals should not be orthogonal. The remaining selection rule
is based on the symmetries of the pair of orbitals involved. In most cases, the rules are too complicated to be made
simple here.54 Group theory is exceptionally powerful in identifying which transitions are allowed, and it is one of
the first applications of group theory that a chemist pursuing a more thorough understanding comes across. One
case, however, is easy—that for molecules which only have a centre of symmetry, like s-trans butadiene 1.8. The
62
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
allowed transitions for these molecules are between orbitals that are symmetric and antisymmetric with respect to
the centre of symmetry. Thus the HOMO, 2, is symmetric with respect to the centre of symmetry half way
between C-2 and C-3, and the LUMO, 3*, is antisymmetric (Fig. 1.37). Accordingly, this transition is allowed
and is indeed strong, as is the corresponding transition for each of the longer linear polyenes.
Data for this the longest wavelength p!p* transition are available for ethylene,55 where the problem is pulling
out the true maximum from a broad band in the vacuum UV, and for a long list of the lower polyenes, where the
maximum is easy to measure in the UV region when methyl or other alkyl groups are present at the termini to
stabilise the polyenes against electrocyclisation and polymerisation. Fig. 1.70 is a plot of the experimentally
determined56 values of lmax for the longest wavelength absorption for a range of such polyenes R(CH¼CH)nR,
converted to frequency units, against (ELUMO – EHOMO) in units calculated using Equation 1.17:
DE¼4 sin
p
2ð2n þ 1Þ
1:17
which is simply derived from the geometry of figures like Figs. 1.31 and 1.39. The correlation is astonishingly good—in view of the simplifications made in Hückel theory, and in view of the fact that most
transitions, following the Frank-Condon principle, are not even between states of comparable vibrational
energy. Nevertheless, Fig. 1.70 is a reassuring indication that the simple picture we have been using is not
without foundation, and that it works quite well for relative energies. Similarly impressive correlations can
be made using aromatic systems, and even for ,-unsaturated carbonyl systems. It is not however a good
measure of absolute energies, and the energy of the p!p* transition measured by UV cannot be used directly
as a measure of the energy difference between the HOMO and the LUMO. This can be seen from that fact
that the line in Fig. 1.70 does not go through the origin, as Hückel theory would predict, but intersects the
ordinate at 15 500 cm–1, corresponding to an energy of 185 kJ mol–1 (44 kcal mol–1).
60,000
50,000
max
40,000
(nm)
162.5
227
274
310
342
380
401
411
426
n
1
2
3
4
5
6
7
8
9
max
max
(cm–1)
61, 500
44, 000
36, 400
32, 300
29, 200
26, 300
24, 900
24, 300
23, 500
E( )
2.00
1.24
0.89
0.69
0.57
0.48
0.42
0.37
0.33
30,000
20,000
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
E LUMO – E HOMO
Fig. 1.70
Frequency of first p!p* transitions of some representative polyenes R(CH¼CH)nR plotted against (ELUMO –
EHOMO) calculated using Equation 1.17
1.9.2 Nuclear Magnetic Resonance Spectroscopy
Chemical shift is substantially determined by the electron population surrounding the nucleus in question
and shielding it from the applied field. Chemical shifts, and 13C chemical shifts in particular, are therefore
used to probe the total electron population. The chemical shift range with protons is so small that aromatic
ring currents and other anisotropic influences make such measurements using proton spectra unreliable.
1 MOLECULAR ORBITAL THEORY
63
Coupling constants J measure the efficiency with which spin information from one nucleus is transmitted
to another. This is not usually mediated through space, but by interaction with the electrons in intervening
orbitals. Transmission of information about the magnetic orientation of one nucleus to another is dependent
upon how well the orbitals containing those electrons overlap, as well as by the number of intervening
orbitals. In a crude approximation, the number of intervening orbital interactions affects both the sign and the
magnitude of the coupling constant.
Coupling constants can be either positive or negative. Although this does not affect the appearance of the 1HNMR spectrum, it does change the way in which structural variations affect the magnitude of the coupling
constant. To understand why coupling constants can be positive or negative, we need to look into the energetics
of coupling. In hydrogen itself, H2, there are three arrangements with different energies: the lowest energy with
the nuclear spins of both nuclei H and H0 aligned, the highest with both opposed, and in between two ways equal
in energy with the alignments opposite to each other (Fig. 1.71a, where upward-pointing arrows indicate nuclear
magnets in their low-energy orientation with respect to the applied magnetic field, downward-pointing arrows
indicate nuclear magnets in their high-energy orientation with respect to the magnetic field, and levels of higher
energy are indicated by vertical upward displacement). The transitions which the instrument measures are those
in which the alignment of one of the nuclei changes from the N state (the high-energy orientation, aligned with
the applied magnetic field) to the N state (the low-energy orientation, aligned in opposition to the applied
magnetic field). There are four such transitions labelled W in Fig. 1.71a, and all of them equal in magnitude. The
receiving coils detect only the one signal, and the spectrum shows one line and hence no apparent coupling.
H H'
W1
A X
W A1
W 1'
H H'
A X
W X1
H H'
W 2'
W2
H H'
A X
(a) H—H'
Fig. 1.71
W X2
A X
W A2
(b) A—X not coupled
Energy levels of atomic nuclei showing no coupling
If now we look at two different atoms A and X, we have the same set-up, but this time the two energy levels in
the middle are of different energy, one with A aligned and the other with X aligned (Fig. 1.71b). ‘A’ might be
a 13C, and ‘X’ a 1H atom, but the general picture is the same for all AX systems. If there is no coupling
(J ¼ 0), as when the nuclei are far apart, the AX energy level will be as much above the mid-point as the
energy level for the AX nucleus is below it. There will again be four transitions, two equal for the A
nucleus, labelled WA, and two equal for the X nucleus, labelled WX, giving rise to one line from each.
If, however, the two nuclei are directly bonded, they will affect each other. The A spin will be opposed to
the spin of one of the intervening electrons in an s orbital (only s orbitals have an electron population at the
nucleus); that electron is paired with the other bonding s electron. In the lowest energy arrangement of the
system, both the A and X nuclei are spin-paired with the bonding electrons with which they interact most
strongly (as in Fig. 1.72c). As a result, the A and the X nuclei will be opposed in the lowest energy
arrangement. Conversely, the system will be higher in energy when these spins are aligned. Thus, the two
energy levels in which the A and X nuclei have parallel spins will be raised and the two energy levels in
which they are opposed will be lowered (Fig. 1.72b). Thus, there are now four new energy levels, four
different transitions, WA1 and WA2, and WX1 and WX2, and four lines in the AX spectrum. The A signal is a
64
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
doublet and the X signal is a doublet, with the same separation between the lines, because (WA1 –
WA2) ¼ (WX1 – WX2) ¼ JAX. Thus, the extent of the raising and lowering of each of the energy levels is
JAX/4. More complicated versions of this kind of diagram, more complicated than can be explained here, are
needed to analyse spin interactions for nuclei with values of I 6¼ ½, for systems more complicated than AX,
and even more complicated ones to make sense of those spectra that are not first order.
J/4
A X
W A1
W X1
A X
J/4
A
X
W X2
A X
A X
J/4
(a) A—X not coupled
Fig. 1.72
W A2
J/4
(b) A—X positively coupled
(c) Transmission of inf ormation
about nuclear spin in directly
bonded nuclei through the s electrons
Energy levels of atomic nuclei without (a) and with the capacity to show coupling (b)
If instead of being directly bonded, the A and X nuclei are separated by two bonds, the transmission of
information through the s electrons leads the two nuclei to be parallel in the low-energy arrangement, in
contrast to the high-energy arrangement of Fig. 1.72. The model that illustrates this point is given in
Fig. 1.73c, and implies that the nuclei will be antiparallel in the high-energy arrangement. Now the energy
levels will have the lowest and highest energy levels lowered by the interaction of the two spins, and the
levels in between raised (Fig. 1.73b). If the coupling constant is the same as that in Fig. 1.72, the two
transitions for the A nucleus, WA1 and WA2, are of the same magnitude as before but have changed places,
and similarly for WX1 and WX2. The appearance of the spectrum will not have changed, but the coupling
constant J is negative in sign. In general, although not always, one-bond couplings 1J and three-bond
couplings 3J are positive in sign, and two- and four-bond couplings 2J and 4J are negative in sign.
A X
J/4
J/4
A X
J/4
A X
A X
C
W X1
A
W X2
X
W A2
J/4
(a) A—X not coupled
Fig. 1.73
W A1
(b) A—X negatively coupled
(c) Transmission of inf ormation
about nuclear spin in geminally
bonded nuclei through the s electrons
Energy levels of atomic nuclei with the capacity to show coupling through two bonds
The connection between spin-spin coupling and orbital involvement can be found in several familiar
situations. Thus, the 1J values for 1H—13C coupling are correlated with the degree of s character at carbon
1.52–1.54. More subtly the 1H—13C coupling constant is a measure of the C—H bond length, with the axial
protons in cyclohexanes having a slightly smaller value (122 Hz) than the equatorial protons (126 Hz),57 a
phenomenon known as the Perlin effect.58 The explanation is found in the hyperconjugation of the antiperiplanar axial-to-axial C—H bonds on neighbouring atoms (see p. 85). The coupling between geminal
1 MOLECULAR ORBITAL THEORY
65
protons is negative but larger in absolute magnitude when both C—H bonds are conjugated to the same p
bond 1.55 than when they are not 1.56.
1
J 125 Hz
H
H
H
1
H
H
H
1.54
H
H
H
H
2
J –14.9 Hz
H
J 249 Hz
H
H
1.53
1.52
1
J 156 Hz
H
H
2
J –12 Hz
H
H
1.55
1.56
Strong coupling from anti-periplanar and syn-coplanar vicinal hydrogen atoms 1.57 and 1.59, and virtually
zero coupling with orthogonal C—H bonds 1.58 (the Karplus equation), is a consequence of the conjugation
of the bonds with each other.59 Coupling constants are usually larger when the intervening bond is a p bond,
with the trans and cis 3J coupling in alkenes typically 15 and 10 Hz for the same 180 and 0 dihedral angles.
Longer-range coupling is most noticeable when one or more of the intervening bonds is a p bond, most
strikingly demonstrated by 5J values as high as 8–10 Hz in 1,4-cyclohexadienes 1.60. When there are no p
bonds, the strongest long range coupling is found when the intervening bonds are oriented and held rigidly
for efficient conjugation with 4J W-coupling 1.61 and 1.62.
H
3
H
3
J 9-13 Hz
J ~0 Hz
H
H
H
3
J ~10 Hz
H
1.57
1.58
H
H
Ph
H
5
J 9 Hz
1.59
J 1-2 Hz
1.61
5
J 1-1.5 Hz
H
1.60
H
4
H
H
1.62
1.9.3 Photoelectron Spectroscopy
Photoelectron spectroscopy60 (PES) measures, in a rather direct way, the energies of filled orbitals, and
overcomes the problem that UV spectroscopy does not give good absolute values for the energies of
molecular orbitals. The values obtained by this technique for the energies of the HOMO of some simple
molecules are collected in Table 1.3. Here we can see how the change from a simple double bond (entry 6) to
a conjugated double bond (entry 10) raises the energy of the HOMO. Similarly, we can see how the change
from a simple carbonyl group (entry 8) to an amide (entry 14) also raises the HOMO energy, just as it ought
to, by analogy with the allyl anion (Fig. 1.33), with which an amide is isoelectronic. We can also see that the
interaction between a C¼C bond (p energy –10.5 eV) and a C¼O bond (p energy –14.1 eV) gives rise to a
HOMO of lower energy (–10.9 eV, entry 16) than when two C¼C bonds are conjugated (–9.1 eV, entry 10).
Finally, we can see that the more electronegative an atom, the lower is the energy of its HOMO (entries
1 to 5). All these observations confirm that the theoretical treatment we have been using, and will be
extending in the following chapters, is supported by some experimental evidence.
66
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
Table 1.3 Energies of HOMOs of some simple molecules from PES (1 eV ¼ 96.5 kJ
mol–1 ¼ 23 kcal mol–1)
Entry
Type of orbital
Energy (eV)
n
n
n
n
n
π
π
n
π
ψ2
ψ1
ψ2
n
π
n
π
π
–9.9
–10.48
–10.85
–12.6
–12.8
–10.51
–11.4
–10.88
–14.09
–9.1
–11.4 or –12.2
–10.17
–10.13
–10.5
–10.1
–10.9
–8.9
18
π
–9.25
19
π
–9.3
n
–10.5
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Molecule
:PH3
:SH2
:NH3
:OH2
:ClH
CH2=CH2
HC≡CH
:O=CH2
CH2=CH-CH=CH2
HC≡C-C≡CH
H2NCH=O:
CH2=CH-CH=O
O
N
20
1.9.4 Electron Spin Resonance Spectroscopy
A final technique which both confirms some of our deductions and provides useful quantitative data for frontier
orbital analysis is ESR spectroscopy.61 This technique detects the odd electron in radicals; the interaction of the
spin of the electron with the magnetic nuclei (1H, 13C, etc.) gives rise to splitting of the resonance signal, and
the degree of splitting is proportional to the electron population at the nucleus. Since we already know that the
coefficients of the atomic orbitals, c, are directly related to the electron population, we can expect there to be a
simple relationship between these coefficients and the observed coupling constants. This proves to be quite a
good approximation. The nucleus most often used is 1H, and the coefficient of the atomic orbital which is
measured in this way is that on the carbon atom to which the hydrogen atom in question is bonded.
The McConnell equation (Equation 1.18) expresses the relationship of the observed coupling constant
(aH) to the unpaired spin population on the adjacent carbon atom (C) The constant Q is different from one
situation to another, but when an electron in a pz orbital on a trigonal carbon atom couples to an adjacent
hydrogen, it is about –24 G. Applied to aromatic hydrocarbons, where it is particularly easy to generate
radical cations and anions, there proves to be a good correlation between coupling constants and the
calculated coefficients in the HOMO and LUMO, respectively.62
aH ¼ Q H
CH C
1:18
1 MOLECULAR ORBITAL THEORY
67
However, the relationship between coupling constant and electron population is not quite as simple as this. Thus,
although p orbitals on carbon have zero electron population at the nucleus, coupling is nevertheless observed;
similarly, in the allyl radical 1.63, which ought to have zero odd-electron population at the central carbon atom,
coupling to a neighbouring hydrogen nucleus is again observed. This latter coupling turns out to be opposite in
sign to the usual coupling, and hence has given rise to the concept of ‘negative spin density’. Nevertheless the
technique has provided some evidence that our deductions about the coefficients of certain molecular orbitals
have some basis in fact as well as in theory: the allyl radical does have most of its odd-electron population at C-l
and C-3; and several other examples will come up later in this book. We merely have to remember to be cautious
with evidence of this kind; at the very least, the observation of negative spin density should remind us that the
Hückel theory of conjugated systems (the theory we have been using) is a simplification of the truth.
The standard ways of generating radicals for ESR measurements involve adding an electron to a molecule
or taking one away. In the former case the odd electron is fed into what was the LUMO, and in the latter case
the odd electron is left in the HOMO. Since these are the orbitals which appear to be the most important in
determining chemical reactivity, it is particularly fortunate that ESR spectroscopy should occasionally give
us access to their coefficients.
Here is a selection of some of the more important conjugated radicals and radical ions, to some of which
we shall refer in later chapters. They all show how the patterns of molecular orbitals deduced in this chapter
are supported by ESR measurements. The numbers are the coupling constants |aH| in gauss.
CH2 16.4
H 4.1
13.9 H
H
14.8 H
H
1.63
O
H 5.1
H 6.7
H 1.8
H 1.9
H 6.1
H 10.2
1.64
H 3.75
CH3 0.8
H 6.9
CH3 5.1
H 5.5
H 1.5
1.8 H
1.68
H 5.3
H 5.0
H 1.8
H 3.5
CH3
H 1.1
1.69
6.5 H
H 1.9
1.72
CH3 2.0
H 6.9
H 7.7
1.67
1.71
NO2
H 5.1 H3C
H 0.6
1.66
1.65
H 3.9
1.70
5.3 H
H 3.1
H 1.5
H 1.4
1.73
H 2.7
1.74
2
Molecular Orbitals and the Structures of
Organic Molecules
Chapter 1 established the fundamentals of molecular orbital theory, and especially of the Hückel method for
handling conjugated systems. This chapter uses the language those ideas were presented in to explain some of
the better known structural features of organic molecules. It is largely concerned with the ground state and the
thermodynamic properties of molecules, not with kinetics and how molecules behave in chemical reactions,
which is reserved for the rest of the book. It is important to realise that conjugation, for example, may, and
usually does, make a molecule thermodynamically more stable than an unconjugated one, but it does not follow
that conjugated systems are less reactive. Indeed, they are often more reactive or, we might say, kinetically less
stable. Organic chemists use ‘stable’ and ‘stability’ without always identifying which meaning they are
assuming. In this chapter we shall look at thermodynamic stability, and reserve reactivity for later chapters.
2.1
The Effects of p Conjugation
We saw in Chapter 1 that the p conjugation in the allyl system and in butadiene is energy-lowering, with the
total p energy of a conjugated system lower than the sum of the energies of the isolated components. We have
also seen even better energy lowering when the conjugation is within a ring of 4nþ2 p electrons. We must
now look at the effect a substituent has on thermodynamic stability and polarisation when it is attached, and
hence conjugated with, the p or p orbitals of simple systems like alkenes, carbocations, radicals and anions.
The effects on energy can, of course, be estimated computationally using more or fewer assumptions and
approximations, as we have already seen with some simple systems. Alternatively, in some cases, the
information is available from an experimental measurement like the heat of combustion or of hydrogenation.
However, these aids are not always to hand. Furthermore, a computation does not necessarily make
immediate chemical sense, and an experimental measurement still needs an explanation. The discussion in
the following pages shows that we can work out the effects of substituents in an easy, nonmathematical way,
both on the overall energy, and on the energy and polarisation of the frontier orbitals. Although the procedure
used is legitimate (and works), it is perhaps worth bearing in mind that it does not resemble the method used
by theoreticians in proper calculations.
2.1.1 A Notation for Substituents
Before we discuss the effects of substituents on the energies and coefficients of conjugated systems, it will be
convenient to have at our disposal a notation for the various types of substituents which we shall come across.
There are three common types, which we shall designate with the letters C-, Z- and X- (Fig. 2.1), each of
Molecular Orbitals and Organic Chemical Reactions: Reference Edition
© 2010 John Wiley & Sons, Ltd. ISBN: 978-0-470-74658-5
Ian Fleming
70
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
C
stands f or
or
OMe
R
Z
or
stands f or
O
O
or
C
or
metal
OMe
X
donors or
acceptors
and
neutral
etc.
N
or
stands f or
or
Fig. 2.1
CH3
or
NO2
e.g.
NMe2
etc.
SiMe3
BR2
etc.
etc.
acceptors
and
acceptors
acceptors
but
donors
donors
but
acceptors
donors
but
neutral
Definitions and character of substituents
which modifies the reactivity of conjugated systems in a different way. This classification, which was first
introduced by Houk,63 is used throughout this book.
C-Substituents are simple conjugated systems of carbon atoms, like vinyl or phenyl. They may be p donors or
p acceptors, depending upon what they are conjugated with, responding to and stabilising electron demand or
electron excess, as appropriate. Their effect on the framework is small, because the point of attachment is a
carbon atom, and C—C single bonds are not strongly polarised.
Z-Substituents are conjugated systems which are also electron withdrawing, like formyl, acetyl, cyano, nitro,
sulfonyl and carboxy. They withdraw electrons from double bonds that they are conjugated with, and, since most
of them have electronegative heteroatoms, they are also weakly electron withdrawing by an inductive effect within
the framework. Such substituents are therefore strong p acceptors and usually weak, but occasionally, strong acceptors, especially for substituents like nitro and sulfonyl, where an electronegative heteroatom is the point of
attachment. There is another group of p electron-withdrawing substituents, which are slightly different from the Zsubstituents listed above. Metals, and metalloids like the silyl group, are p acceptors (Section 2.2.3.2) but, because
metals are more electropositive than carbon, they are donors. These substituents have not been given a separate
symbol, but their effect on the p system is more often than not what we shall be interested in, and they are included
among the group labelled Z.
X-Substituents are typically electronegative heteroatoms like nitrogen, oxygen or sulfur which carry a lone
pair of electrons. They donate their lone pairs to a p system, and those based on electronegative heteroatoms
withdraw electrons from the framework. They are therefore p donors and acceptors, exactly the opposite
of the metals and metalloids. We usually include simple alkyl groups in the category of X-substituents,
because they are able, by overlap of the C—H (or C—C) bonds with the p system ( conjugation or
hyperconjugation, Section 2.2) to supply electrons to a conjugated system. Alkyl groups are therefore
p donors, but they are largely neutral with respect to the framework. The electronegative halogen atoms
are anomalous; technically they are X-substituents, but their effect in the p system is weak, because the lone
pairs of electrons are so tightly held, and they are strong acceptors.
2.1.2 Alkene-Stabilising Groups
2.1.2.1 C-Substituents. We saw in Chapter 1 with butadiene (Fig. 1.39) that a simple double bond, the
most simple of the C-substituents, lowers the total p energy when it is conjugated to another double bond to
2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES
71
make butadiene. We can see the same thing with styrene, but the picture is a little more complicated, because
we need to see how a substituent attached to a benzene ring affects the energies and coefficients of each of the
p orbitals. We shall return to this problem later when we consider the effect of having Z- and X-substituents
conjugated with the p orbitals of benzene.
The filled and the lowest of the unfilled p molecular orbitals for styrene (actually calculated for simplicity
for a hypothetical linear structure) are shown in Fig. 2.2. The lowest-energy orbital 1 is largely the same as
1 in benzene (Fig. 1.43) with a small addition from the p orbital of the ethylene component in phase and
with a correspondingly small drop in energy, because the orbitals that we are mixing here are far apart in
energy. With the ethylene attached to the large coefficient in 2 of benzene, the interaction in the bonding
sense is strong because these two orbitals are similar in energy. The node shifts up, as drawn, to pass through
the two ortho carbons, making this orbital close to the sum of two allyl fragments. As a result, it is
significantly lowered in energy relative to 2 in benzene. The 4 orbital in styrene, higher in energy, is
made up from the same two components, p in ethylene and 2 of benzene, combined in an antibonding sense.
We see 2 lowered in energy and 4 raised in energy, in much the same way as 1 and 2 in butadiene are
lowered and raised, respectively, relative to the energies of the p orbitals of ethylene. In contrast, the ethylene
attached to the node in 3 in benzene has no effect, and the orbital 3 in linear styrene is identical to 3 in
benzene. The net effect among the filled orbitals is to lift the degeneracy of 2 and 3 in benzene, lowering
the energy of the one and leaving the other unchanged, and raising the energy and polarising the orbital 4
which most closely resembles the p orbital of ethylene. The total p stabilisation in styrene is 2 5.21,
whereas the total p stabilisation for the separate components benzene and ethylene is 2 5.0. The lowest
of the unfilled orbitals is largely made up from the p* orbital of ethylene combined in a bonding sense with
the 4* orbital of benzene, lowering its energy. The p* orbital of ethylene can have no effect on the 5*
orbital of benzene, because it would be at a node, and that orbital (not illustrated) would be the same as the
5* orbital of benzene.
This exercise shows that the effect on the energy of the p molecular orbitals of adding simple
conjugation in the form of a p bond or of a benzene ring is very similar—a C-substituent lowers the
–0.39
0.60
–0.33
LUMO
0.66
*
5
0.31
0.13
–0.39
0.39
0.60
–0.33
0.66
HOMO
4
–0.31
0.13
0.35
0.50
0
0
0.39
1.00
0.50
3
0.35
1.41
0
2
0.31
0
0.14
–0.35
0.51
–0.50
2.14
0.39
1
0.33
0.31
Fig. 2.2
The filled p molecular orbitals and the LUMO of styrene
72
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
overall p energy, it raises the energy of the HOMO (from 1 below the level in ethylene to 0.62 below
it in butadiene and 0.66 in styrene), and it lowers the energy of the LUMO (from 1 in ethylene to 0.62
in butadiene and 0.66 in styrene). Similarly with the coefficients—the terminal carbon atom in the sidechain, both in the HOMO and in the LUMO has a larger coefficient than the internal atom. Thus a
benzene ring has a similar effect as a substituent to that of a simple double bond, but to a somewhat lesser
degree.
2.1.2.2 Z-Substituents. As an example of the simplest possible Z-substituent, we need to work out the
p molecular orbitals of acrolein 2.1. A simple Hückel calculation gives the picture in Fig. 2.3, which is what
we want, but a derivation like this gives us no insight.
0.66
*
0.23
O
1.53
4
–0.43
O
–0.58
0.43
–0.23
2.1
LUMO
*
O
0.35
3
0.66
–0.58
–0.58
0.58
O
HOMO
O
1.00
2
0
2.2
0.58
0.66
0.43
1.88
O
1
0.23
Fig. 2.3
0.58
The p molecular orbitals of acrolein. (These energies and coefficients were calculated using h ¼ 1 and k ¼ 1)
Dealing first with the energies, let us instead consider the p structure of acrolein. If we ignore the fact that
one of the atoms is an oxygen atom and not a carbon atom, we shall simply have the orbitals of butadiene.
Obviously we cannot ignore the oxygen atom. One way to take it into consideration is to regard the
carbonyl group as a kind of carbonium ion, highly stabilised by an oxyanion substituent 2.2. Normally we
do not draw it this way, because such good stabilisation is better expressed by drawing the molecule (as in
2.1) with a full p bond between the oxygen atom and the carbon atom. The truth is somewhere in between,
and organic chemists usually make a mental reservation about the meaning of such drawings as 2.1 and
2.2. We make the mental reservation that the butadiene-like system, implied by the drawing of a localised
structure 2.1, is only one extreme approximation of the true orbital picture for acrolein. The other extreme
approximation is an allyl cation, substituted by a noninteracting oxyanion, as implied by the localised
drawing 2.2.
The energies for the molecular orbitals for these two extremes are shown in Fig. 2.4 with the allyl cation
and the separate oxyanion on the left and butadiene on the right. The energies of the p* and p orbitals of
ethylene are placed for reference as dashed lines 1 above and below, respectively. The true orbital energy
for the orbitals of acrolein must be in between those of the corresponding orbitals of the allyl cation and
2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES
73
1.618
*
4
1.414
*
*
4
3
1
0.618
LUMO
*
3
LUMO
2
HOMO
*
3
LUMO
2
0.618
HOMO
1.414
HOMO
1
2
1.618
1
1
1
O
O =
O
2.2
Fig. 2.4
2.1
Z
2.3
The energies of the p orbitals of acrolein 2.1 as a weighted sum of the p orbitals of an oxyanion-substituted
allyl cation 2.2 and butadiene 2.3
butadiene. We can perhaps expect the true structure to be more like the butadiene system than the allyl cation
system (for the same reason that we prefer to draw it as 2.1 rather than 2.2). What we immediately learn from
Fig. 2.4 is that the effect of mixing in some allyl cation like nature to the butadiene orbitals is to lower the
energy of each of the molecular orbitals relative to those of butadiene. We can also see that the effect of
having a Z-substituent conjugated with the double bond of ethylene is, as usual with conjugation, to lower the
energy of the system overall, with 1 and 2 together having more p bonding than the separate orbitals of
ethylene and a carbonyl group. The energy of the HOMO of acrolein, 2, is, however, little changed from
that of the p orbital of ethylene. Also, because it is butadiene-like, the HOMO and the LUMO will be closer
in energy than they are in ethylene—the LUMO will have been lowered in energy relative to that of ethylene
and the HOMO will be very similar in energy. What we have done is to superimpose the orbitals of an allyl
cation on those of butadiene, and, with suitable weighting, to add the two together. This device does not give
us the whole picture of Fig. 2.3, but it does give us some sense of how the p orbitals can reasonably be
expected to have the energies shown there.
We can use the same ideas to deduce the pattern, but not the actual values, of the coefficients. We have
again a contribution from the allyl-cation-like nature of acrolein and from its butadiene-like nature. The
coefficients of the allyl cation orbitals and the oxyanion p orbital are on the left of Fig. 2.5, and the
coefficients of the butadiene orbitals in the middle. The coefficients on each atom and in each molecular
orbital of acrolein can then be expected to be somewhere in between the corresponding coefficients in the
two components. The average of the two components is given on the right in Fig. 2.5, these representing a
simple unweighted sum. These numbers are not coefficients, because they have not been arrived at with
legitimate algebra, and, squared and summed, they do not, of course, add up either horizontally or vertically
to one. They are however similar in their general pattern to those obtained by calculation in Fig. 2.3, and this
74
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
–0.707
–0.600
0.371
0.500
0.707
–0.371
0.500
–0.30
O
=
0.600
0.69
0.30
O
=
0.371
0.19
0.600
2
0.06
0.55
0.371
+
1.000
–0.54
0.54
–0.371
*
3
–0.600
0.600
O
O
0.65
+
0.500
0.30
–0.19
0.371
HOMO
0.55
=
0.600
–0.707
*
4
0.600
+
0.707
O
0.44
0.600
–0.371
LUMO
–0.19
=
+
0.500
–0.65
–0.371
1
0.30
1
O
2.2
Fig. 2.5
=
+
2
Z
2.3
Crude estimates of the coefficients of the p orbitals of a Z-substituted alkene as an arbitrarily unweighted
average of the coefficients of an allyl cation 2.2 and butadiene 2.3
similarity gives us some reason to believe that this way of deducing the relative magnitudes of the
coefficients is legitimate.
To take the LUMO of a Z-substituted alkene ( 3*) as an example, the carbon atom C-1 with the
Z-substituent on it has a zero coefficient on the corresponding atom in the allyl cation and a small coefficient
in butadiene (–0.371). The coefficient on C-1 in the LUMO of a Z-substituted alkene is therefore likely to be
very small (–0.19 in Fig. 2.5, and –0.23 in Fig. 2.3). In contrast, the carbon atom C-2 has large coefficients
both in the allyl cation (0.707) and in butadiene (0.60). The coefficient on C-2 in the LUMO of a
Z-substituted alkene is therefore large (0.65 in Fig. 2.5, and 0.66 in Fig. 2.3).
If we turn now to the HOMO of acrolein ( 2) and look at C-1, the allyl cation has a very large coefficient
(0.707) on the central atom, but butadiene has a small coefficient on the corresponding atom (0.371). The two
effects therefore act in opposite directions—the conjugation causing a reduction in the coefficient on the
carbon atom carrying the formyl group, and the allyl-cation-like contribution causing an increase in this
coefficient. The result is a medium-sized coefficient (0.54 in Fig. 2.5, and 0.58 in Fig. 2.3). For C-2, it is the
allyl cation that has the smaller coefficient (0.500) and the butadiene the larger (0.600). The combination is
again a medium-sized coefficient (0.55 in Fig. 2.5, and 0.58 in Fig. 2.3). We have already seen that acrolein
is probably better represented by the drawing 2.1 than by the drawing 2.2, from which we may guess that it is
the butadiene-like character which makes the greater contribution to the HOMO. If this is the case, acrolein
will have its HOMO coefficients polarised in the same way as those of butadiene, but to a lesser extent (as
indeed they are in Fig. 2.5). (Epiotis64 actually came to the opposite conclusion for acrylonitrile i.e. Z ¼ CN;
his calculation was a legitimate one, not the crude approximation used here, but in effect it had evidently
given greater weight to the allyl cation-like nature of the system. This shows that the situation is delicately
balanced. It may well be that some Z-substituents do give the opposite polarisation in the HOMO to that
shown in Fig. 2.5.)
2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES
75
2.1.2.3 X-Substituents. In an X-substituted alkene like methyl vinyl ether 2.4, we have a lone pair of
electrons brought into conjugation with the double bond. We can deduce the pattern of molecular orbitals by
an interaction diagram Fig. 2.6 resembling that for the allyl anion 1.6 in Fig. 1.33. The earliest example in
which the idea of comparing a heteroatom-substituted system with the corresponding hydrocarbon anion as
an extreme version, is found in Zimmerman’s use of the benzyl anion as a model for anisole.65 The difference
is that the lone pair on oxygen, being on an electronegative element, is lower in energy than that on carbon.
This lowers the energy of all the orbitals 1– 3* relative to their counterparts in the allyl system. However
the orbital 1 is created by the interaction of the lone-pair orbital on the oxygen atom, labelled n, in a bonding
sense with both p and p*, strongly with the former and weakly with the latter, because of the greater
separation of energy of the interacting orbitals. In contrast, 2 is derived by the weak interaction of n with p*
in a bonding sense, and strongly with p in an antibonding sense. As a result 1 is lowered in energy more than
2 is raised, and the overall energy is lowered relative to the energy of the separate orbitals of the p bond and
the lone pair. We saw the same pattern in the interaction of the orbitals of butadiene from two separate
p bonds (Fig. 1.39). As usual, conjugation has lowered the overall energy. The net p stabilisation has been
measured crudely by comparing the heats of hydrogenation of ethylene and ethyl vinyl ether as 25 kJ mol1
(6 kcal mol1).66 We should also note that both the HOMO and the LUMO of an X-substituted alkene are
raised in energy relative to the HOMO and LUMO of ethylene, with the HOMO raised more than the LUMO.
*
LUMO
1
*
LUMO
3
2
HOMO
HOMO
n
1
1
OMe
=
X
OMe
2.4
Fig. 2.6
Energies of the p orbitals of an X-substituted alkene
In order to deduce the coefficients for an X-substituted alkene, we adopt the idea that at one extreme, the lone
pair on the oxygen atom is fully and equally involved in the overlap with the p bond, so that the orbitals will
be those of an allyl anion 2.5. At the other extreme, to make allowance for the fact that the lone pair on an
electronegative atom like oxygen is not as effective a donor as a filled p orbital on carbon, it is an alkene with
no participation from the lone pair on the oxygen atom, together with the isolated lone pair. Thus we add a bit
of allyl anion-like character, on the left in Fig. 2.7, to the unperturbed alkene, in the centre of Fig. 2.7. The
average of the two components is printed on the right in Fig. 2.7, these representing a simple unweighted
sum. As with the Z-substituted alkene, these numbers are not coefficients, because they have not been arrived
76
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
–0.60
–0.707
LUMO
=
+
0.500
*
3
0.25
0.50
0.500
0.500
X
0.25
=
+
HOMO
0.707
0.500
–0.707
X
0.60
0.707
0.35
+
0.500
2
–0.35
O
=
X
0.25
0.500
1
0.75
1.000
1
=
+
2
X
—OMe
2.5
Fig. 2.7 Crude estimates of the coefficients of the p orbitals of an X-substituted alkene as an arbitrarily unweighted
average of the coefficients of an allyl anion 2.5 and an alkene
at with legitimate algebra, and, squared and summed, they do not add up either horizontally or vertically to
one. However illegitimate, they match the pattern of large, medium and small coefficients obtained from a
simple Hückel calculation. The lowest-energy orbital 1 has a large contribution from the lone pair added to
the lowest-energy orbital of the allyl anion, creating an orbital strongly polarised towards the X-substituent.
For the HOMO, the unperturbed alkene has (necessarily) equal coefficients on each atom, and the allyl anion
has a zero coefficient on the atom bearing the X-substituent. The result of mixing these two is 2, a relatively
strongly polarised orbital as far as the coefficients on C-1 and C-2 are concerned. For the LUMO, the
unperturbed alkene again has equal coefficients, but the allyl anion has a larger coefficient on the carbon
atom carrying the X-substituent than on the other one. The result is 3*, an orbital mildly polarised in the
opposite direction.
Thus any of the three types of substituent, C, Z or X, is overall energy-lowering in the p orbitals of an
alkene. Where pathways exist, we can therefore expect C¼C double bonds to move into conjugation with
any of these substituents. We can also expect that there will be some regioselectivity to their reactions,
because their frontier orbitals are polarised, a topic to which we shall return in later chapters.
2.1.3 Cation-Stabilising and Destabilising Groups67
2.1.3.1 C- and X-Substituents. A molecule having an empty p orbital on carbon, and therefore carrying a
positive charge, will be lowered overall in energy by p conjugation with a C-substituent. We have seen this
already, from the opposite direction, when we moved from the orbitals of an alkene to those of an allyl cation
in Fig. 1.33. Similarly, the effect of an X-substituent is even more stabilising, as we saw in considering the
orbitals of a carbonyl group in Fig. 1.66, which could equally well have been drawn with two electrons in the
pO orbital and none in the pC. The weakest kind of X-substituent is an alkyl group, to which we shall return
while discussing the stabilisation of cations by hyperconjugation in Section 2.2.
Further manifestations of stabilisation by the overlap of a filled with an unfilled orbital are the effects of
X-substituents on an empty p orbital on a metal. Thus trimethylborate 2.6 is much less Lewis acidic than
boron halides 2.7, because the oxygen lone pairs overlap more efficiently with the empty p orbital on the
2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES
77
boron.68 When X is fluorine, the energy match with the empty orbital on the boron is worse than for oxygen,
because fluorine is so much more electronegative, and when X is any of the other halogens, the p orbitals are
spread too far out from the nucleus for good p overlap with a first-row element.
MeO
B
OMe
OMe
X
2.6
B
X
X
2.7
2.1.3.2 Z-Substituents. The effect of a Z-substituent on a neighbouring carbocation is not so straightforward. Fig. 2.8 shows the interaction between the orbitals of a carbonyl group and an empty p orbital on carbon.
The set of p orbitals in the middle is quantitatively different but otherwise essentially the same as the set of
orbitals in the middle of Fig. 2.6, which was arrived at by an alternative sequence. There are, however, two fewer
electrons to go into the p system this time. We deduce that there is an overall lowering of p energy, because 1 is
lower in energy than the pC¼O orbital as a result of the interaction with the empty p orbital, pC. However, this
lowering is not large, because this interaction is between an orbital at the level and a p orbital, pC¼O, low in
energy (Fig. 1.66). The overall lowering in p energy is not therefore as great as the corresponding lowering in
energy in 1 of the allyl cation (E in Fig. 1.33). We might notice at this stage that 2 is lowered in energy,
whereas it was not lowered at all in the allyl cation. The reason is that this orbital is made up by interaction of the
p orbital with the p orbital of the carbonyl group in an antibonding sense and with the p* orbital in a bonding
sense, as with the allyl cation. Since both the p and p* orbitals are lower in energy in a carbonyl group than in an
alkene, the antibonding contribution to 2 is weakened and the bonding contribution strengthened.
*
3
*C=O
pC
LUMO
2
C=O
HOMO
O
Fig. 2.8
1
O
The p orbitals of a carbocation conjugated to a Z-substituent
It is well known, however, that a carbonyl group does not appear to be a stabilising influence on a
carbocation, and yet we have just deduced that it is stabilised in the p system. In the first place, much of
78
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
the evidence for its high energy comes from its high reactivity, that is its kinetic properties, and not its
thermodynamic. Nevertheless there is evidence that it is thermodynamically destabilised.
The most obvious factor that we have left out in the argument above is the Coulombic effect of the
partially ionic character of both the and the p bond of a carbonyl group. The polarisation of both bonds
towards the oxygen atom (Fig. 1.66) places a significant positive charge on the carbonyl carbon atom,
immediately adjacent to the full positive charge on the nucleus of the carbon atom carrying the empty
p orbital. This is energy-raising, because the now relatively exposed nuclei repel each other. We thus have a
small energy-lowering contribution from the p overlap, but an energy-raising contribution from an adverse
Coulombic effect.69 Evidently the latter wins. For the first time, we see that conjugation cannot always
be relied upon to lower the overall energy.
2.1.4 Anion-Stabilising and Destabilising Groups70
Organic chemists use the word anion, and especially the word carbanion, loosely, as mentioned already on
p. 56. The ‘anions’ are either trigonal carbons carrying substantial excess negative charge, such as enolate
ions, or compounds with carbon-metal (C—M) bonds. In enolate ions, the orbital of what we are calling an
anion would correspond to the p orbital on the terminal carbon in 2 of an X-substituted alkene
(Section 2.1.2.3), which has a large coefficient on C-2 (Fig. 2.7). In compounds containing a C—M bond,
the orbital of the anion is the bonding orbital LiC in Fig. 1.63, which also has a large coefficient on carbon.
Thus, C-2 of an enolate and a C—M bond have similar features to a genuine carbanion, and it is not altogether
unreasonable to call them carbanions.
2.1.4.1 C-Substituents. The orbitals for the interactions of C-, Z- and X-substituents with a filled
p orbital on carbon are the same as those we have just used for their interaction with an empty p orbital,
but with two more electrons to feed into the resultant p orbitals. The interaction of a C-substituent with a
filled p orbital gives us the orbitals of an allyl anion, and these are just as p-stabilised as the allyl cation
(Fig 1.33). The p stabilisation by a C-substituent of an enolate ion or of a C—M bond would be similar, but
made a little more complicated by having to bring in more orbitals.
2.1.4.2 Z-Substituents. Even better, conjugation of a filled p orbital with a Z-substituent gives us the
same orbitals as in Fig. 2.8, but now 2 is filled, and, since it is lowered in energy by the interaction below the
level of 2 of the allyl anion, the level, the overall p energy is lower still. The extra pair of electrons means
that a partial positive charge is no longer adjacent to an unshielded nucleus, and the nuclei are no longer as
exposed to Coulombic repulsion. This is the p system for an enolate ion, to which we shall return when we
consider the polarisation of the orbitals, and again for the ambident nucleophilicity of this important system.
The special kind of Z-substituent (see p. 70) that is seen with metals is even more straightforwardly
stabilising of an anion. The orbital interaction is that of an empty p orbital on the metal with the filled
p orbital of the anion. It is the same story, but looked at from the opposite direction, as the overlap of an
X-substituent with the empty p orbital of a metal as seen in the boron compounds 2.6 and 2.7. An example of
anion stabilisation is the ease with which 9-methyl-9-BBN 2.8 can be deprotonated to give the organolithium
compound 2.10.71 The special feature of this system is that the base 2.9 is strong enough to remove a proton,
but too hindered to bond directly as a ligand on the metal, which would otherwise be the preferred reaction.
As usual the ‘anion’ is in fact a LiC bond but the polarisation of the filled orbital is towards carbon, making it
anion-like.
+
B
2.8
N
Li
2.9
B
2.10
Li
2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES
79
A related explanation applies to the well known stabilisation of carbanions by a neighbouring sulfur,
phosphorus or silicon group. Using a filled orbital on carbon as the generalised picture for such ‘anions’
as C—M bonds or enolate ions, the main stabilisation comes from overlap of the filled orbital of the anion
with the *YR orbital 2.11,72 and is at a maximum when the orbitals are anti-periplanar, accounting for the
exceptional ease with which the anion 2.12 can be prepared by removing the bridgehead proton.73 The effect
in the p system is strong enough, even for a donor like a trimethylsilyl group, counter-intuitively to be
stabilising of an anion. In the simplest case, trimethylsilylmethyllithium 2.13 can be prepared from tetramethylsilane and butyl-lithium, showing that the silyl substituent is more stabilising than the propyl
substituent in butyllithium.
Li
R
S
*YR
S
S
Si
Li
Y
2.11 Y = Si, P or S
2.12
2.13
The interaction diagram is that in Fig. 2.9, illustrating overlap between a bond and a p orbital, which is
called conjugation, and to which we shall return in Section 2.2. The bonding interaction between a first-row
atom R and a second-row atom Y is inherently less energy-lowering for the YR orbital and less energyraising for the *YR orbital than it would be if Y were the corresponding first-row element—the overlap
integrals are smaller because of the long bond lengths.74 Consequently, the energy of the YR orbital is
relatively high, and the *YR orbital is relatively low. The overall stabilisation represented by E is
substantial, because of the strong bonding interaction of the high level YR orbital and the pC orbital.
However, in a sense more important, the relatively low energy of the *YR orbital makes the interaction
between it and the pC orbital keep the energy of the 2 orbital relatively low. It may be above or below the level, depending upon the element Y, and the nature of the substituents R, but it will not be raised high in
energy overcoming the lowering in energy E. The sulfur and the phosphorus have the added advantage
of being (mild) -withdrawing groups. The silicon, however, even though it is a donor, has the advantage
*
3
R
R
*YR
Y
Y
R
Y
pC
2
R
R
YR
Y
E
Y
1
Fig. 2.9
The stabilisation of an anion by adjacent sulfur, phosphorus and silicon groups
80
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
of having the Si—R bonds more polarised from silicon towards the R group. If R is hydrogen or a carbon
group, they are the electronegative elements in this context, making the coefficient on silicon large in the
antibonding orbital *SiH and therefore more effective in lowering the energy of the 2 orbital.
Anion stabilisation by second-row elements has hitherto, and most simply, been accounted for by
invoking overlap of the filled p orbital of the anion with an empty d orbital on the sulfur, phosphorus or
silicon. This is unmistakably stabilising, as usual with the overlap of a filled with an unfilled orbital of any
kind, but the contribution it makes is unlikely to be significant, because the 3d orbitals on these second-row
elements and a 2p orbital on carbon are much too far apart in energy75 and too ill-matched in size to have a
significant interaction. Anion stabilisation by sulfur, phosphorus and silicon appears to be better accounted
for by the arguments expressed in Fig. 2.9, which has largely, but not entirely,76 replaced that using the
overlap with the empty d orbitals.
A lone pair on an electronegative element can take the place of the carbanion in this argument, and overlap
with an appropriately electron-withdrawing bond can be similarly p-stabilising. Trisilylamine 2.14, unlike
trimethylamine, is planar,77 with a trigonal nitrogen atom, probably largely as a result of the overlap of the
nitrogen lone pair with the Si—H orbitals, which are polarised from silicon towards the hydrogen. As a result
of the involvement of the lone pair in this conjugation, silylamines are much weaker bases than ammonia.78
Silyl ethers 2.15 are similarly less effective as Lewis bases than other ethers,79 and they show wide angles for the two bonds to the oxygen atom. The extent of the interaction of the oxygen lone pair with *SiX in a
range of silyl ethers 2.15, detected by a shortening of the Si—O bond length d, correlates with the extent to
which the Si—O—C bond approaches linearity, reaching 180° for hexaphenyldisiloxane 2.16, and the
explanation can be found in orbital interactions related to those described above. 80,81
d
H
*SiH
Si
N
H
H
2.14
SiH3
SiH3
X3Si
O R
2.15
Ph3Si
O
SiPh3
2.16
2.1.4.3 X-Substituents. We have seen that sulfur- and phosphorus-based groups like phenylthio or
diphenylphosphinyl are X-substituents that are anion-stabilising, but they are exceptional. X-Substituents
are usually p-destabilising rather than stabilising. The interaction of a lone pair of electrons on an oxygen
atom, as a model for an X-substituent, and a filled p orbital on carbon create the p orbitals of the carbonyl
group (Fig. 1.66) but with two electrons in p*CO. Since this interaction is the interaction only of atomic
orbitals, the overall effect is a rise in energy, because p*CO is raised more in energy than pCO is lowered. In
practice, although this effect in the p system must be present, electronegative elements usually stabilise an
adjacent ‘anionic’ carbon. The reason is two-fold. In the first place, there is a Coulombic effect working in
the framework against the effect in the p system. The Coulombic effect is energy-lowering for an anion,
because X-substituents based on electronegative heteroatoms are acceptors. We see this conspicuously in
the ease with which a base can remove the proton from chloroform. In the second place, we do not usually
have an anion—what we have is a C—M bond. The repulsive interaction of a lone pair on an X-substituent and
the orbital is energy-raising. However, when the atom is a metal, it changes the story, because it has empty
orbitals that can accept coordination from the lone pairs of the electronegative heteroatom. This coordination
may be directly within the molecule, but is more often present in an aggregate, and it is always powerfully
energy-lowering, making any effect on the p overlap much less important.
The one X-substituent that probably does destabilise an anion is an alkyl group. An alkyl group, although
classified as an X-substituent, is not a acceptor, nor does it have much of a capacity to coordinate to a metal.
Its destabilising effect is by conjugation, which is discussed in Section 2.2.1.
2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES
81
2.1.5 Radical-Stabilising Groups82
2.1.5.1 C-, Z- and X-Substituents. All three kinds of substituent stabilise radicals. A C-substituent gives
the orbitals of the allyl radical, which is just as stabilised as it was for the cation and anion (Fig. 1.33). A
Z-substituent gives the same orbitals as those in Fig. 2.8, but with one electron in 2, leading to an overall
drop in p energy and a reduction in the amount of Coulombic repulsion that destabilised cations. Finally an
X-substituent gives the orbitals of the carbonyl group (Fig. 1.66) but with one electron in p*CO. With two
drops in energy from the doubly filled orbital pCO matched by only one rise in energy from the singly
occupied p*CO, the overall effect is a drop in energy. The three types of radical are summarised and placed on
the same energy scale in Fig. 2.10, which also draws attention to the singly occupied molecular orbital
(SOMO), the frontier orbital of a radical.
*
3
*
O
3
1
1
*C=O
O SOMO
SOMO
2
O SOMO
2
1
1
1
O
O
O
C
Fig. 2.10
O
C=O
1
Z
X
Energies and coefficients of the p orbitals of C-, Z- and X-substituted radicals
The overall stabilisation by an X-substituent83 accounts for the ease with which such radicals as 2.17 and
2.18 are generated in the peroxidation of amines and ethers, and why such radicals as 2.19 are long-lived.
O
N
2.17
N
O
O
2.18
2.19
Since both electron-donating and electron-withdrawing groups stabilise radicals, Hammett plots for radicalforming reactions using , ands þ values are poor, because these parameters emphasise the capacity to
82
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
stabilise charge. To solve this problem, independent of the polar character of radical reactions (Chapter 7), a
special scale has been constructed using hyperfine coupling constants with the benzylic hydrogens in
substituted benzyl radicals to establish the values. The numbers are all small, but all kinds of parasubstituents give positive values, denoting stabilisation, with the unusual exception of fluorine (–0.11).
Some examples are: Ac 0.066, CN 0.043, tBu 0.036, MeO 0.034, Cl 0.017, Me 0.015, SOMe 0.006, OAc
0.001, CF3 0.001 and, by definition, H 0.84
2.1.5.2 Captodative Stabilisation.85 A special case is a radical that has both an X- and a Z-substituent,
either directly attached to a radical centre as in the radical 2.20 or conjugated to it through a p system, as in
the long-lived radicals 2.21–2.24. Radicals with this feature are called captodative,86 the capto referring to
the Z-substituent (electron capture) and the dative to the X-substituent. Such systems have also been called
merostabilised.87 Since both types of substituent can stabilise a radical, it is reasonable that both together can
continue to stabilise a radical. We can see how this might be in Fig. 2.11, where the filled orbitals of a
Z-substituted radical on the right are taken from Fig. 2.10 and an arbitrary lone pair is placed on the left. The
interaction of these two systems creates the set of orbitals in the centre.
O–
Me
CO2Me
CN
t
N
SBut
BuS
N
Me
CN
O
2.20
CN
N
Et
2.21
2.22
CN
2.23
O2N
NPh2
NO2
2.24
There is a rise in energy in creating 3, but there is only one electron in this orbital. There is a small drop in
energy in creating 2 and a more significant drop in energy in creating 1, both of which have two electrons
in them. Overall the energy has dropped, and the radical as a whole is lower in p energy than the separate
components.
Another way of looking at the whole set of orbitals is to recognise that the captodative system consists
minimally of four atoms, each with a p orbital, with the two at each end electronegative, and with a total of
five electrons in the p system. An O—C—C—O arrangement is the paradigm. We can set up such a system in a
different way from that in Fig. 2.11 by joining two carbonyl groups together by their carbon atoms, and
feeding five electrons into the resultant p orbitals, which would resemble the p orbitals of butadiene, but all
3
2
1
2
1
X
1
X
Fig. 2.11
Z
Z
The effect of bringing an X-substituent into conjugation with a Z-substituted radical
2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES
83
lower in energy because of the presence of the electronegative atoms and with one electron in 3*. The result
is of course the same as in Fig. 2.11, with 3 coming out as an essentially nonbonding orbital somewhere near
the level.
Yet another way to appreciate this outcome is to think of the ultimate captodative system as being a radical
flanked on one side by the simplest possible donor, a filled p orbital on carbon, and on the other by the
simplest possible acceptor, an empty p orbital on carbon. This system is of course the allyl radical, which has
its SOMO, 2 in this case, precisely at the level.
However, it is not obvious whether captodative substitution is actually better at lowering the overall
energy than having two Z- or two X-substituents. Several calculations have been carried out and much
experimental evidence has been accumulated, but the point has still not been resolved. What is clear is that
captodative substitution is not inherently worse in stabilising a radical than two like substituents, and if there
is a specific captodative effect, it is small, never more than about 25 kJ mol1 (6 kcal mol1). The kind of
experimental evidence that seems to imply special stabilisation to captodative radicals is the ease of the
reversible C—C fragmentation of the diaminosuccinate 2.25, in which the rate implies that the captodative
radical 2.26 is some 17 kJ mol1 (4 kcal mol1) lower in energy than might be expected by adding together
the stabilising effects of each of the substituents.88
Me2N
NMe2
Me2N
NMe2
+
EtO2C
CO2Et
EtO2C
2.25
CO2Et
2.26
Another piece of evidence comes from measurements of the rate of rotation about the C-2 to C-3 bond of a
range of allyl radicals 2.27. At the point of highest energy in the rotation, the radical will lose its allylic
character (Section 2.3.1.5), and be stabilised only by the substituents R1 and R2. The captodative radical with
R1 ¼ OMe and R2 ¼ CN had the lowest activation energy, some 12 kJ mol1 (2.9 kcal mol1) lower than the
sum of the substituent effects would have suggested, and with the radicals with R1 ¼ R2 ¼ OMe and
R1 ¼ R2 ¼ CN having activation energies some 24 kJ mol1 (5.7 kcal mol1) higher in energy.89
R2
R1
2.27a
R1
R2
2.27b
What does seem to be clear is that neither two donors nor two acceptors have quite twice the stabilising effect
on a radical of one, but one of each does have something close to an additive effect. In this formulation at
least, the captodative effect does appear to be real.
2.1.6 Energy-Raising Conjugation
We saw above that not all conjugation is energy-lowering—an empty p orbital conjugated to a Z-substituent
(Section 2.1.3), and a filled p orbital conjugated with an X-substituent (Section 2.1.4) were both energyraising. In the former case, the system is usually stabilised in the p system, but Coulombic effects make it
overall destabilising. In the latter, the repulsive effect of two filled orbitals inherently destabilise the
p system (E2 > E1 in Fig. 2.12), but other factors such as coordination within dimers, sometimes lead to
overall stabilisation. Examples of the repulsive interaction of two filled p orbitals where there are no
mitigating factors are the conformations adopted by hydrogen peroxide 2.28 and hydrazine 2.29. The
84
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
2
HOMO
E2
X
X
E1
1
X
X
X
X
The p interaction of two X-substituents
Fig. 2.12
overlap is avoided by twisting about the X—X bond, so that the two lone pairs are as little in conjugation as
possible.
O
H
H
N
O
H N
H
H
2.28
2.29
H
Two further examples of energy-raising conjugation are related to the orbitals we saw in Fig. 2.11. Two
carbonyl groups in conjugation can be viewed as a carbocation conjugated to a Z-substituent. We used the
idea earlier of a carbonyl group as having some of the character of a carbocation, since the p bond is polarised
towards the oxygen atom. If such a group is conjugated to a carbonyl group, the p molecular orbitals will be
those of Fig. 2.11, but with no electrons in 3. As with a carbocation in Fig. 2.8, the presence of the
Z-substituent is probably p-stabilising, with 1 in Fig. 2.11 falling in energy more than 2 rises, but there will
be a Coulombic repulsion between the two carbon atoms, both of which bear a partial positive charge.
Evidence for the consequent high energy comes from the extent to which -diketones like
1,2-cyclohexanedione 2.30 have the enol 2.31 as the stable tautomer, and evidence for the p stabilisation
can be found in such molecules as glyoxal 2.32, where the carbonyl groups stay in conjugation rather than
twisting. Twisting would do nothing to relieve the Coulombic repulsion, but it would remove the
p conjugation. The s-trans conformation is favoured, because the relatively large partial negative charges
on the oxygen atoms repel each other.
O
O
O
OH
H
O
2.32
2.30
O
O
H
O
2.33
2.31
A second system is essentially the same, but with two more electrons—the enediolate ion 2.33 has the
p molecular orbitals of butadiene, lowered by the presence of the two electronegative atoms, but with two
electrons in 3*. However one thinks of it, it is a p system higher in energy than the separated components.
We have seen therefore that both the diketone and the enediolate are destabilised systems, but that the
2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES
85
radical, with one electron more than the diketone and one fewer than the dienolate, may even be especially
well stabilised. A manifestation of this situation is the use of enediolates and related systems like metol anion
2.34 as photographic developers, where their role is to transfer one electron to the silver cation.90 Another
familiar example is the ease with which hydroquinone anions 2.35 are oxidised to the captodative quinhydrone radical anion 2.21, and quinones 2.36 are reduced to the same species.
O
NHMe
2.34
2.2
O
O
O
–e, –H+
–e
+e, +H+
+e
OH
O
O
2.35
2.21
2.36
Hyperconjugation—s Conjugation91
Conjugation has largely been discussed so far as taking place between p orbitals in a p system. However, it is
just as reasonable to consider the conjugation of bonds with each other or of bonds with p orbitals. It is
usual to look at hybridised orbitals for the bonds. In the simplest possible case, ethane, the p bonding from
the pz components in Fig. 1.22 would be subsumed into the sp3 hybrids of the C—H bonds and into their
conjugation with each other.
The overlap of bonds with bonds or p orbitals is called hyperconjugation, a serious misnomer, because
hyperconjugation, far from being especially strong, as the prefix hyper implies, is usually a feeble level of
conjugation compared with the kind of p conjugation that we have seen so far. Another term that is
sometimes used is conjugation, on the grounds that it is conjugation of a bond with something else,
but this is not satisfactory either, since the overlap is p in nature not . Yet another term that is used is vertical
stabilisation,92 which is not a misnomer, but is not usefully specific about its nature. Perhaps for these
reasons, the word hyperconjugation appears to survive, and probably cannot be dislodged. Although present
in all compounds having interacting bonds, it is most significant when it is energy-lowering.
2.2.1 C—H and C—C Hyperconjugation
2.2.1.1 Hyperconjugation of C—H Bonds with C—H Bonds. Using hybridised orbitals for C—H bonds,
and mixing them in the usual way to show conjugation, creates the molecular orbitals of Fig. 2.13, which is
set up for the anti-periplanar interaction. There is an equivalent set of orbitals interacting in a syn-coplanar
arrangement, the relative merits of which are discussed on pp. 98–100.
The major interactions are between the C—H orbitals close in energy, namely with , and * with *.
The and * orbitals of the C—H bond are so far apart in energy that the effect of mixing in the interaction of
with * will be small, and the overall result can reasonably be expected to be energy-raising overall
(E2 > E1). This is a useful lesson. The interaction of two filled orbitals is only energy lowering when there is
an additional contribution from a bonding interaction with an empty orbital close enough in energy and with
the right symmetry, as in the lowering in energy of both 1 and 2 in butadiene by the bonding contribution
from the p with p* interactions (Figs. 1.38 and 1.39), in contrast to the situation here, where the orbitals are
too far apart in energy.
The interactions of all the -bond orbitals with each other in larger molecules than ethane affect the overall
electron distribution and energy, but sometimes a particularly strong interaction stands out, and can be
invoked to explain a molecular property. This is the explanation93 for the Perlin effect mentioned on p. 64, in
which the 1H-13C coupling constants reveal that the axial C—H bonds in cyclohexanes are slight longer than
the equatorial C—H bonds. Of all the -bond interactions, that between the anti-periplanar axial C—Hs on
86
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
H
(
*
1– 2)
H
H
*
*
H
1
2
H
*
(
1+ 2)
(
1– 2)
H
H
H
E2
H
1
2
H
E1
H
(
1+ 2)
H
Fig. 2.13
Hyperconjugation of one C—H bond with another
adjacent atoms, the bold lines in the drawing 2.37, are the most powerful. As we can see in Fig. 2.13, this is
overall energy-raising, and the effect is to stretch these C—H bonds as a result of their overall weakening.
Evidently the geometrically similar anti-periplanar overlap of the equatorial C—H bonds with the neighbouring C—C bonds, the bold lines in the drawing 2.38, is less powerful, a feature that contributes to the idea that
C—H hyperconjugation is stronger than C—C hyperconjugation.
2.2.1.2 Hyperconjugation of C—H Bonds with Lone Pairs. Overlap between a filled p orbital and the
orbitals of a C—H bond is similarly energy-raising overall. A C—H bond anti-periplanar to a filled p orbital
is weakened 2.39, and the bond length increased. The hydrogen atom is potentially a hydride leaving group,
and -hydride delivery is well known with alkyl Grignard and lithium reagents, which are often called
anions. The same overlap explains94 the weakening of C—H bonds conjugated to anti-periplanar nitrogen
lone pairs, as seen in the lower C—H stretching frequency in the infrared spectra for compounds like the
amine 2.40, which gives what are called Bohlmann bands, typically at 2700–2800 cm1, instead of at the
more usual frequency 2800–2900 cm1 for a more tightly held C—H bond.95
H
H
H
H
N
H
H
H
H
H
2.37
2.38
2.39
H
2.40
H
2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES
87
2.2.1.3 Stabilisation of Alkyl Cations by Hyperconjugation. The effects of conjugation of one bond
with another are buried in the framework, and their consequences, being the sums of several such
interactions, are not particularly obvious except in minor features of bonding such as those discussed
above. Hyperconjugation is much more evident in the stabilisation given to an empty p orbital on carbon
by a neighbouring alkyl group, and to which the word is most frequently applied. It is well known that alkyl
substituents stabilise carbocations. Fig. 2.14 shows the interaction of the orbitals of the C—H bond on the
left with the empty p orbital on the right. The net result is the lowering of the overall energy by an amount 2E.
The interaction in Fig. 2.14 is similar to that shown in Fig. 1.33 for the allyl cation, except that it is a bond
instead of a p bond interacting with the empty p orbital. Because the CH orbital in Fig. 2.14 is lower in
energy than the p orbital in Fig. 1.33, the hyperconjugative interaction with the empty p orbital is less
effective, and the overall drop in energy 2E is less than it was for simple p conjugation.
*
H
3
H
*
CH
2
H
pC
H
CH
E
H
1
Fig. 2.14 Interaction of the orbitals of a C—H bond with an empty p orbital on carbon
As usual, hybridisation, although a convenient device, is unnecessary—the energy-lowering could equally
well have been explained using the pz orbital on carbon, with the most significant interaction illustrated on
the left in Fig. 2.15. Indeed, this provides a more simple way to appreciate that the lowest-energy
conformation of the cation is not overwhelmingly that in which one of the bonds is aligned to overlap
with the empty p orbital. Because the two p-type orbitals, pz and py, have the same energy, the interactions in
the two conformations shown in Fig. 2.15 are, to a first approximation, equal (EA ¼ EB). We can expect that
the barrier to rotation about the C—C bond of the ethyl cation will be small. Although intuitively reasonable,
it is not so easy to set up an interaction diagram using hybridisation to show that the energy-lowering effect of
the imperfectly lined up overlap of two C—H orbitals with the empty p orbital is the same as the perfectly
lined up overlap of one.
Whereas the interaction of a C—H bond with another C—H bond is energy-raising (Fig. 2.13), the
interaction of a C—H bond with a bond to an electronegative element is energy-lowering. The shift in
electron population towards the electronegative element gives the carbon atom of the bond some of the
character of a carbocation. As a result the hyperconjugation is more like the interaction of a C—H bond with
an empty p orbital, and is both energy-lowering and more powerful. The effect can be seen in the lengthening
of C—H bonds involved in such hyperconjugation, as in the 1,3-dioxan 2.41. In contrast to cyclohexanes,
88
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
H
H
H
H
H
C
H
C
C
H
pz
pyH
C
H
H
z
EA
H
H
y
C
C
EB
H
H
H
H
C
H
H
(a) Conf ormation A
(b) Conf ormation B
Fig. 2.15
H
C
H
Orbital interactions stabilising two conformations of the ethyl cation
which have the axial C—H bonds longer than the equatorial, the equatorial C—H bond at C-5 in 1,3-dioxan is
longer than the axial C—H bond. The reason is that the conjugation between the equatorial bond and the C—O
bond anti-periplanar to it, emphasised with the bold lines, is now stronger.93 This is known as the reverse
Perlin effect.
H
lengthened
5
O
O
H
2.41
The overlap and its consequences, as illustrated in Figs. 2.14 and 2.15, could equally well have been
drawn with C—C bonds in place of the C—H bonds. The energies of C—C and C—H bonding and
antibonding orbitals are similar to each other, and the value of E will be similar. Indeed it is still a
matter of debate, both in theory and in interpreting experimental results, whether C—H or C—C bonds are
more effective as p-donor substituents, a topic we shall return to in Chapter 5. What is clear is that alkyl
groups in general are effectively p-electron donors, in much the same way as, but to a lesser extent than, a
double bond or a lone pair. We have already used this fact in classifying an alkyl group as an
X-substituent (Fig. 2.1).
One case where C—C bonds are exceptionally effective in hyperconjugation is in the stabilisation
provided by a cyclopropyl substituent to an empty p orbital. The cyclopropylmethyl cation is actually better
stabilised than an allyl cation, as judged by the 41 times more rapid solvolysis in a good ionising solvent of
cyclopropylmethyl chloride 2.42 than of crotyl chloride 2.43.96
Cl
H2O, EtOH
OEt
Cl
50°
2.42
k1 (rel) 41
H2O, EtOH
OEt
50°
2.43
k1 (rel) 1
In this case, hyperconjugation appears, unusually, to be better than p conjugation. This can be explained
using the Walsh orbitals of a cyclopropane (Fig. 1.53), where one of the degenerate pair of highest occupied
orbitals is a py orbital with a large coefficient on carbon which can orient itself in such a way as to stabilise an
empty p orbital on a neighbouring atom 2.44a, seen from a different perspective in 2.44b. This is like
2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES
89
conjugation with a full p orbital, and is therefore more effective in lowering the p energy than conjugation
with a p bond is in the allyl cation (Fig. 1.33). The other high-energy filled orbital in the Walsh diagram has
the wrong symmetry for overlap with the neighbouring p orbital, and has no effect on its energy one way or
the other. If the carbonyl group is thought of as a highly stabilised carbocation, this picture 2.44 is supported
experimentally by the preferred conformation in many systems,97 as can be seen in the two most populated
conformations adopted by cyclopropane carboxaldehyde 2.45a and 2.45b.98
H
H
H
H
=
H
H
H
H
H
H
O
H
O
H
H
H
2.44a
2.44b
2.45a
2.45b
As usually defined, hyperconjugation implies no change in the shape of the molecule caused by the extra
overlap, as illustrated in Fig. 2.14. However, the extra bonding in 1 between the C—H bond and the
p orbital ought to have the effect of shortening the C—C bond and lengthening the C—H bond (or C—C
bond if that is involved), and there is experimental evidence from X-ray crystal structures that this does
indeed happen.99 Thus the bicyclo[2.2.1]heptyl cation 2.46 shows shortening of the three C—C bonds to
the cationic centre relative to a typical bond between a tetrahedral and a trigonal carbon (1.522 Å), and
lengthening of the bond between C-1 and C-6 relative to a typical bond between two tetrahedral carbons
(1.538 Å).100 This shows the effects expected from the hyperconjugative overlap shown with bold lines on
the drawing 2.47.
H
–0.011Å
6
1 2
H
+0.172Å
–0.113Å
–0.046Å
2.46
2.47
Hyperconjugation has had a chequered history. The valence-bond representation of it has misled many
people. It was proposed in the 1930s, although not named as such, as an explanation for the BakerNathan order (Me > Et > Pri > But) of apparent electron-releasing ability of alkyl groups.101 Today, the
Baker-Nathan order is almost always better explained by steric hindrance to solvation rather than by
C—H hyperconjugation being more effective than C—C hyperconjugation: tert-butyl compounds are not
as well solvated as methyl, and the device of placing the alkyl group para to the site of reaction does not,
as it was supposed to, remove it from solvation sites. For this reason, hyperconjugation was quite widely
discredited in the 1950s.102 Today, it enjoys a more soundly based popularity. Formulated in molecular
orbital terms, as Mulliken did when he first used the word,103 and especially as used to explain the
electron-donating effects of alkyl groups, hyperconjugation is widely accepted. It is better to think of an
alkyl group as contributing its electrons by hyperconjugative p overlap than by an inductive effect in the
framework. An alkyl group is not a donor, unless the atom to which it is bonded is significantly
more electronegative than tetrahedral carbon, and, in any case, donation is not obviously able to
influence the thermodynamic and kinetic properties of a p system. The capacity of a methyl group to be
either a donor or an acceptor,104 depending upon what it is bonded to, has been a source of much
unnecessary confusion.
90
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
attraction
narrows the
angle
H
attraction shortens
the C—C bond
2.48
H
H
H
2.49a
2.49b
2.49c
2.2.1.4 Bridging in Carbocations. Hyperconjugative overlap ought also to reduce the H—C—C angle ,
because there is now extra bonding between the hydrogen atom and the empty p orbital 2.48. Since 1
resembles more the CH orbital that it is close to in energy, the p orbital will have a small coefficient, and
this effect may not be large. However, there is the possibility that the attraction builds up, until the
hydrogen atom sits halfway between the two carbon atoms 2.49. The bonding in this structure 2.49a can be
represented with hybridisation as two half filled orbitals made up from sp3 hybrids and the 1s orbital of
hydrogen 2.49b, or without hybridisation as largely made up by the interaction of the empty 1s orbital of an
isolated proton with both lobes of the p bond of ethylene 2.49c. The bonding, however it is described, is the
same, and similar in nature to that of other two-electron, two-bond bridged systems, such as those in
diborane. This structure may be the minimum in the energy profile, as it is in diborane, or it may be a
maximum, in which case it is the transition structure for the [1,2]-shift of the hydrogen or carbon atom
from one carbon to the next.
Although tertiary cations like 2.46 are well established not to have bridged structures, it is not easy to
discover whether hyperconjugation, with the minimum movement of the atoms, or the full bridged structure
is the lower in energy for secondary cations. In the 1960s, a large amount of effort went into trying to solve
experimentally the problem of the nonclassical ion, as it was called, using more complex systems than the
ethyl cation, and with carbon as the bridging group.105 No easy answers were forthcoming, and theoretical
calculations also gave conflicting or ambiguous answers, one of many problems being that calculations on
ions in the gas phase inherently favour bridged structures, because bridged structures spread the charge more
effectively when there is no solvent to help. The present state of opinion probably favours structures like 2.48
without bridging for almost every alkyl cation except the most simple, the ethyl cation itself, which is only
found in the gas phase.106 The bridged structure 2.49 is therefore a low-energy transition structure for a [1,2]hydride shift, and, with carbon in the bridge, the transition structure for the Wagner-Meerwein type of
cationic rearrangement.
Successive [1,2]-shifts of this kind are so easy in cyclopropylmethyl cations 2.50 ! 2.51 ! 2.52 ! 2.53,
etc., that each of the three carbons carrying two hydrogen atoms can take up the place of the others, and
experimentally each has been found to have an equal probability of capturing whatever nucleophile is
supplied.97 The other carbon, carrying just one hydrogen, is the only one that is different, but it too can
capture a nucleophile to give cyclobutyl products 2.56. This has led to much conjecture about the low-energy
structure of such cations, suggesting that the picture 2.44 is inadequate. Another aspect of this intriguing
system is the possibility occasionally seen in substituted examples, in which the nucleophile is captured at
one of the bridging methylene carbons to give 3-butenyl products 2.55 rather than cyclopropylmethyl
products like 2.54 and 2.57. It is tempting to identify the bridged structure 2.51, which may or may not be
a minimum, as the source of these products, since the picture 2.51 is the structure of a 3-butenyl cation with
the empty p orbital coordinated to the p bond. However, this picture lacks the right symmetry to make all the
methylenes identical, and an alternative 2.58, with the single carbon sitting above the middle of a trimethylene fragment is needed to do that. This picture is not, in fact, supported by any evidence, and a better
structure, as judged by subtle NMR experiments, resembles a carbene sitting above the p orbitals of an allyl
2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES
91
cation 2.59.107 This picture is not far from that shown in 2.44, as long as we allow for the incompleteness of
that picture, which only illustrates the major source of stabilisation for the carbocation, and accept that rapid
interconversions make all the methylene carbons equivalent.
H
H
H
H
2.50
2.51
2.52
2.53
Nu
Nu
Nu
Nu
2.54
2.55
2.56
H
H
C
H
C
H
CH
C
H
H
2.57
C H
H
H
H
C
C
C
H
H
H
2.58
2.59
2.2.1.5 Stabilisation of a p Bond by Hyperconjugation. Hyperconjugation has also been used to explain
another well-known thermodynamic property—that alkenes prefer to be more rather than less substituted
by alkyl groups. An alkene like 2-methyl-1-butene 2.60 undergoes easy protonation in acid to give the
t-amyl cation 2.61, which can lose a proton to give 2-methyl-2-butene 2.62. The ease of the reaction is
explained by the hyperconjugative stabilisation given to the intermediate tertiary cation 2.61, as
discussed in Section 2.2.1.3 above. What is not so obvious is why the more-substituted alkene 2.62 is
lower in energy then the less-substituted alkene 2.60, which it certainly is, because the equilibrium lies
well to the right. Heats of hydrogenation of alkenes provide quantitative evidence of the greater
thermodynamic stability of the more substituted alkenes, with the attachment of one or more alkyl
group more or less additively increasing the heat of hydrogenation of an alkene by about 10 kJ mol1
(2.4 kcal mol1).108
H
2.60
–H
2.61
2.62
One factor appears to be the hyperconjugative stabilisation of the C¼C p bond by the alkyl groups. Fig. 2.16
shows the interaction of the orbitals of a bond with the orbitals of a p bond. Two p bonds interacting are
overall energy-lowering, as we saw in Fig. 1.39 for butadiene. However, two bonds interacting are overall
energy-raising, as we saw in Fig. 2.13 for ethane. Hyperconjugation of a bond with a p bond could go either
way, and evidently it falls on the side of being energy-lowering. The -bonding orbital and the
92
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
H
H
*
4
*
H
*
*
3
H
2
E2
H
H
E1
Fig. 2.16
1
Hyperconjugative stabilisation of a C¼C p bond
p*-antibonding orbital are perhaps just close enough for them to mix in a bonding sense effectively to lower
the energies of 1 and 2, and thereby to make the drop in energy E1 a little greater than the rise in energy E2.
2.2.2 C—M Hyperconjugation
In Fig. 2.14, the stabilising effect of the hyperconjugation was quite small, because the energy gap between
the -bonding orbital and the empty p orbital on carbon was large. A bond closer in energy to the empty p
orbital should have a larger interaction and be more stabilising. This is the case when the bond is between a
metal and carbon. A metal is inherently more electropositive than carbon (to an organic chemist anything
more electropositive than carbon can be regarded as a metal). A metal and a carbon atom will have an
interaction diagram like that of the C—O bond in Fig. 1.35, except that the carbon will be the electronegative atom and the metal will take the place of the carbon. Fig. 2.17 shows the energies of the bonding and
antibonding orbitals from carbon to an electropositive element M on the left and to an electronegative
element X on the right.
Transferring the orbitals for a C—M bond on the left in Fig. 2.17 to an interaction diagram like that of
Fig. 2.14, leads to Fig. 2.18 as a description of a -metalloethyl cation 2.63. With the CM bonding orbital
higher in energy than the bonding CH orbital, the interaction with the empty p orbital on carbon will be
stronger than it was for C—H, and the drop in energy E will be greater. Such cations are well stabilised by
hyperconjugation.
Metal-stabilised cations can be expected to adopt and retain the conformation 2.63. The alternative
conformation 2.64, with the empty p orbital at right angles to the M—C bond, is not stabilised any better
than it is by an alkyl group, because the M—C bond is in the node of the empty p orbital and there will be no
interaction between them. Since rotation would have to go through this conformation, there must be a barrier.
The stabilisation seen in Fig. 2.18 is enhanced by the polarisation of the M—C bond. The coefficients in the
CM orbital are large on the carbon atom and small on the metal atom, just as the coefficients of the C—X (or
C—O) bonding orbital are large on the X (or O) atom and small on the carbon atom (Figs. 1.59 and 2.19). The
bonding interaction of the CM orbital with the empty p orbital will therefore be greater than it was for the
corresponding overlap of the CH orbital in Fig. 2.14, where the coefficient on the carbon atom was smaller,
being more or less equal on both atoms. Thus we have a more favourable energy match and a more
favourable coefficient for the overlap of the M—C bond than for the H—C bond.
2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES
M
M
2.63
M
93
C
2.64
*CM
*CX
C
X
pM
M
pC
C
pX
M
C
CM
CX
Fig. 2.17
X
X
C
-Bonding and antibonding orbitals from carbon to an electropositive element M and to an electronegative
element X
M
M
*
3
*CM
C
C
M
C
2
pC
M
M
CM
C
E
1
Fig. 2.18
C
Interaction of the orbitals of a carbon-metal bond with an empty p orbital on carbon
94
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
The degree of this stabilisation is of course dependent upon what the metal is.109 In practice, cations with
this general structure have been investigated using barely metallic metals, like silicon, because the more
familiar and substantially metallic elements are too reactive. Even a trimethylsilyl group as the atom M in a
cation 2.65 is lost too easily for the cation itself to be studied directly,110,111 with essentially only one
sighting, and that in a heavily hindered case.112 Nevertheless, it is clear from much evidence that silyl groups
are substantially stabilising of cations.113 The Si—C bond is aligned with the empty p orbital,114,115 and
rotation about the C—C bond is dramatically slowed down so that cations of the general structure 2.65 are
configurationally stable during most reactions.
Me3
Si
Me3Si
2.65
2.66
The question of bridging also arises here, since the lowest energy structure might be the bridged cation 2.66.
Experimental evidence on -silylethyl cations is somewhat inconclusive,116 but is perhaps moving towards
the belief that the hyperconjugation model is more likely to be true than the bridging model for most
cations.112 Calculations in simple systems indicate that only the least substituted cation, the trimethylsilylethyl cation itself, might be bridged, and that applies only to the vapour phase, which is likely to emphasise
bridging, since no solvent influences can provide stabilisation to the localised cation.117 The structure 2.65
with hyperconjugation is probably the better description of all the more substituted -silicon-stabilised
cations.
A complementary observation is seen when a silyl group is conjugated to a carbonyl group in an acylsilane
2.69, which is yellow in colour because of the exceptionally long wavelength of the n!p* transition in the
UV spectrum. The n!p* transition is the promotion of one of the electrons of the lone pair on the carbonyl
oxygen, labelled nO into the p* orbital of the carbonyl group (Fig. 2.19). Two effects contribute to the long
wavelength of this transition in the acylsilane. The Si—C bond from the silicon atom to the carbonyl carbon is
conjugated with the anti-periplanar lone pair on the oxygen atom. This conjugation is like that in Fig. 2.18,
1
*C=O
*C=O
*C=O
n→ *
max
n→ *
270 nm
max
n→ *
298 nm
max
380 nm
nO
1
nO
nO
C=O
C=O
O
O
C=O
O
SiMe3
2.68
2.67
Fig. 2.19
n!p* transitions of ketones
2.69
2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES
95
but with pC replaced by the lower-energy nO orbital of the lone pair. Thus the lone pair is raised in energy, just
as 2 is raised, but this time it is filled. At the same time the Si—C bonds between the silicon atom and the
methyl substituents are polarised as in Fig. 2.18 with the electron distribution moved away from the silicon
and spread out into the methyl groups. A trimethylsilyl group is a Z-substituent, as we saw on pp. 78–80 of
that special kind that does not include a contribution from having a p bond, and it lowers the energy of the p*
orbital. The combination of the raised nO orbital and the lowered p* orbital decreases the frequency and
hence increases the wavelength of the transition from 270 nm for acetone 2.67 to 380 nm for acetyltrimethylsilane 2.69. The conjugation from a C-substituent, as with the ,-unsaturated ketone 2.68, lowers the
p* orbital more than the conjugation with the silyl group lowers it, but leaves the energy of the nO orbital
essentially unchanged. The n!p* wavelength is raised relative to that of acetone, but the effect is smaller.118
2.2.3 Negative Hyperconjugation119
2.2.3.1 Negative Hyperconjugation with a Cation. If instead of a metal, the carbon is bonded to an
electronegative element, the interaction diagram corresponding to Fig. 2.18 changes to that of Fig. 2.20. The
orbitals of the X—C bond, taken from Fig. 2.17, are now lower in energy than the corresponding C—H
orbitals. The interaction of CX with the p orbital will now have little energy-lowering effect on 1, because
the orbitals are so far apart in energy. There is therefore little p stabilisation afforded to a cation in the
conformation 2.70, and in addition there will be the usual strong inductive electron withdrawal destabilising
it in the framework. The alternative conformation 2.71 possesses the greater degree of hyperconjugative
stabilisation, as long as the other substituents on the carbon atom are not as electronegative as X, and will be
preferred, but the inductive withdrawal will still make it a relatively high-energy cation. A trifluoromethyl
group, for which the two conformations would be essentially equivalent, is well known to be a powerful
destabilising influence on a carbocation.69
X
X
2.70
2.71
X
*
3
X
*CX
C
C
X
pC
E
C
2
X
X
CX
C
Fig. 2.20
1
C
Interaction of the orbitals of a bond between carbon and an electronegative element X with a p orbital
on carbon
96
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
2.2.3.2 Negative Hyperconjugation with an Anion. However, if it is a carbanion that is conjugated to
the X—C bond, the p orbital is filled. The orbital 2 in Fig. 2.19 is lowered in energy significantly by an
amount E as a consequence of the orbital *CX being so much closer in energy to the p orbital than either of
the orbitals *CM in Fig. 2.18 or *CH in Fig. 2.14. Since 2 is filled, there is a drop in energy E, which the
cation does not benefit from. As a consequence of the hyperconjugation, the conformation 2.72 is now
stabilised more than the alternative 2.73. Furthermore, the large coefficient on carbon in the *CX orbital
makes its overlap with the filled p orbital even more bonding than without the electronegative element X, and
the small coefficient on carbon in the CX orbital makes its overlap with the filled p orbital even less
antibonding, both factors further contributing to E, the lowering in energy of the 2 orbital. This type of
hyperconjugation is sometimes called ‘negative’ hyperconjugation, because it is conjugation with a negative
charge, but it is another serious misnomer, since energy-lowering is usually regarded as a positive outcome.
X
X
2.72
2.73
This phenomenon is not usually seen with carbanions themselves. Even if it were, simple carbanions would
not be trigonal as they are shown in Fig. 2.20 and in the drawings 2.72 and 2.73. The picture in Fig. 2.20 is
simply the paradigm for the more general structures, like organolithium compounds, which are called anions.
The well-known electron-withdrawing power of the trifluoromethyl group is at least partly, and perhaps
wholly, explained by negative hyperconjugation,120 as is the capacity of an o-fluoro group to induce
metallation of a benzene ring.121 Another manifestation of negative hyperconjugation is the capacity
of neighbouring silicon-, phosphorus- and sulfur-based groups to stabilise anions, already covered in
Section 2.1.4.2.
2.2.3.3 The Anomeric Effect.122 A lone pair on an electronegative element conjugated to a C—X bond,
in which X is an electronegative element, is a special category of negative hyperconjugation. The bestknown illustration of this anomeric effect, as it is called,123 is in the equilibrium position for the methyl
glucosides 2.74 and 2.75, where it has long been known that, when equilibration is possible, as it is here, the
diastereoisomer with the axial methoxy group 2.75 is the lower in energy, in spite of the usual observation
that the lowest-energy conformation of six-membered rings has substituents equatorial.124
HO
HO
HO
HCl, MeOH
O
OMe
OH
2.74
HO
HO
HO
O
HO
OMe
2.75
Although several factors are at work, the generally accepted explanation for this phenomenon is principally
associated with negative hyperconjugation, similar to the stabilisation of a carbanion discussed in the
preceding section, but with the lone pair on the ring oxygen atom taking the place of pC. Lone pairs are
given the letter n as a distinctive label. Thus the anomeric effect is a consequence of the overlap of the
nonbonding lone pair nO with the low-lying * orbitals of the exocyclic C—O bond 2.76, superimposed, of
course, on all the usual interactions of filled orbitals with filled orbitals.125 The lone pairs on oxygen can be
described as being in two sp3 hybrids. Only when the exocyclic C—O bond is axial are its orbitals able to
overlap well with the axial sp3 hybrid lone pair on the ring oxygen 2.76. Alternatively, without using
hybridisation, it is the nonbonding pz lone pair that overlaps better with an axial C—O bond.
2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES
97
nO
O
H
*
OMe
2.76
At the same time, the methyl group on the exocyclic oxygen adopts a conformation in which it sits gauche to
the ring oxygen atom, as a consequence of the lone pair on the exocyclic oxygen atom being conjugated antiperiplanar with the * orbital of the endocyclic C—O bond 2.77. This is perhaps a little clearer in the
Newman projection from above 2.78. The preference for the gauche orientation is called the exo anomeric
effect. The exo anomeric effect operates even with those tetrahydropyrans that have equatorial substituents
at the anomeric centre—although the endocyclic oxygen cannot indulge in an anomeric interaction, the
exocyclic oxygen can 2.79 (¼ 2.80).
O
O
*
H
=
Me
O
*
O
O
H
H
O Me
2.78
=
O
H
nO
nO
2.77
Me
Me
2.79
2.80
The anomeric effect can be seen in many systems with the features RO—C—X, most of which adopt a
conformation with the R group gauche to the X group rather than anti, as one might have expected. This is the
generalised anomeric effect, and it has many manifestations, such as the preferred conformations for
fluoromethanol 2.81 and methoxymethyl chloride 2.82. Nor is it confined to oxygen lone pairs. The preferred
conformation for the diazaacetal 2.83 has one of the alkyl groups axial in order that the lone pair on that
nitrogen can be conjugated with the C—N bond. The optimum anomeric effect in this system would have
both alkyl groups axial, but this conformation would have a 1,3-diaxial interaction between the alkyl groups,
and this steric repulsion, not surprisingly, overrides the anomeric effect.
H
H
F
N
O
H
2.81
R
H
Me
Cl
O
N
H
2.82
2.83
R
Bond lengths are also affected, just as they are in the other examples of conjugation involving bonds. When
the two heteroatoms are different 2.84, with one lone pair on a less electronegative atom like oxygen and the
other on a more electronegative element like a halogen, bond shortening is more noticeable in the O—C bond,
and the C—X bond is increased in length. The anomeric effect between nO and *CX increases the p bonding
in the C—O bond but, because it mixes in an antibonding orbital between the C atom and the halogen, that
bond is weakened and made longer. The anomeric effect of nX with *CO is less, because *CX is lower in
energy than *CO and nO is higher in energy than nX, making the energy match better between nO and *CX.
Thus the consequence of a lop-sided anomeric effect is overall to weaken the C—X bond—as the electron
population is increased on the carbon atom, the X atom moves away.
98
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
increased bonding,
bond-shortening
decreased bonding,
bond-lengthening
1.382Å
1.394Å
4
nO
O
*CX
O
3
O
1
X
1.819Å
Cl
O
Cl
O
2
1.425Å
1.781Å
1.432Å
2.85
2.84
2.86
This is dependent upon the geometry, as seen in the structure of cis-1,1-dichlorodioxan 2.85.126 The length
of the equatorial C—Cl bond is the same as that in methyl chloride, because it is oriented at an angle giving
little conjugation with the lone pairs on the neighbouring O-1. In contrast, the axial C—Cl bond is lined up
for an anomeric effect with the axial lone pair on O-4, and it is longer. At the same time, the bond between
O-4 and C-3 is shortened, whereas the bond between O-1 and C-2 is close to that for the C—O bond in a
normal ether.
In symmetrical systems, anomeric effects are acting in both directions, but it is clear that bond-shortening
from the anomeric effect in the one direction is stronger than the bond-lengthening in the other, in line with
the overall stabilisation provided by the anomeric effect. Thus, with dimethoxymethane 2.86,127 the central
pair of C—O bonds are equal in length and both are shorter than normal because of the anomeric effects,
while the other pair of C—O bonds, the O—Me groups, have normal C—O bond lengths.
1.326Å
1.358Å
1.385Å
HH
F
F
H
2.87
1.317Å
HH
FH
F
F
2.88
FF
F
F
2.89
F
2.90
Similarly, the fluoromethanes have F—C bonds that shorten128 as the number of fluorines increases from one
in 2.87 to four in 2.90, and the number of generalised anomeric effects accumulates. The bond-strengthening
represented by these bond-shortenings contributes to the reduced reactivity towards nucleophilic substitution
seen in polyhalogenated alkanes.
If the axial exocyclic oxygen-based group in a tetrahydropyran 2.76 is a better leaving group than
methoxy, the anomeric effect between the ring oxygen and the substituent is increased. A better leaving
group like phenoxy effectively has a more electronegative oxygen. The anomeric effect shortens the
endocyclic bond, and lengthens the exocyclic bond. Using X-ray crystallographic data, Kirby has shown
that there is a linear correlation between the pKa of a range of exocyclic groups OR and the length of either
the endocyclic or the exocyclic C—O bond. He finds that the better the leaving group (the lower the pKa of
RO–), the shorter the endocyclic and the longer the exocyclic bond, providing a quantitative demonstration of
the anomeric effect. Since the pKas also correlate with the rates with which the acetals undergo solvolytic
cleavage of the exocyclic bond, he has produced a true structure–reactivity correlation, and a series of stills
from a movie for the early stages of the reaction.129
2.2.3.4 Syn-coplanar and Anti-periplanar Overlap. In the discussion about the anomeric effect, the
lone pair has been oriented, without comment, anti to the C—X bond. The lone pair and the C—X bond are
able to overlap in this orientation 2.91 since they are coplanar, but at first sight they could equally easily
have overlapped had they been syn 2.92. Undoubtedly, coplanarity is the single most important constraint
for good overlap, but what about the choice between syn and anti? One answer, immediately apparent even
in these simplified drawings, is that the syn arrangement 2.92 carries with it at least one eclipsing
2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES
99
interaction with the substituent R, whereas the anti arrangement 2.91 has all substituents and lone pairs
staggered. The eclipsed arrangement is not even a minimum, but a transition structure for rotation about
the O—C bond.
gauche
nO
*
=
O
=
O
*
R
X
X
nO
R
R
R
X
X
eclipsed
eclipsed
2.91
2.92
This simple difference alone accounts for why anti arrangements, both in anomeric effects and in
-eliminations (to be discussed in Chapter 4), are so common. However, this is not the whole story,
because there are systems where this factor is not present, and yet there is still a preference for anti
anomeric effects (and anti eliminations). Thus the tricyclic skeleton of the acetal 2.93 rigidly locks the
exocyclic group OR syn to one oxygen lone pair in the ring and more or less orthogonal to the other. As a
result it still shows an anomeric effect, but it is smaller than the corresponding anti anomeric effect found
in simple tetrahydropyrans—the reactivity towards exocyclic bond cleavage and the bond length of the
exocyclic C—O bond still correlate with the pKa of the OR group, but the slopes are not as steep.130
OR
O
=
O
H
H
OR
2.93
A tempting way to explain the inherent preference for anti over syn arrangements is to picture the
antibonding hybridised orbitals with the large lobes behind the bond instead of between the atoms. Thus
we might redraw the *CX orbital in 2.91 as 2.94, and 2.92 as 2.95. Intuitively, this seems to make sense—the
orbitals of opposite sign in their atomic wave functions will repel each other. Many organic chemists
succumb to this temptation, for, having chosen this picture, we see that there appears to be much better
overlap with the nO orbital in the anti arrangement 2.94—the large lobes are close and on the same side. In the
corresponding syn arrangement with this way of drawing the antibonding orbital 2.95, the large lobes are on
opposite sides and the overlap is ‘obviously’ less.
nO
X
nO
O
ant i
*
R
*
O
syn
R
X
2.94
2.95
Unfortunately it is illegitimate. When we mix two atomic orbitals, the bonding orbital with an attendant drop
in energy is paired with an antibonding orbital with its corresponding rise in energy, and a mathematical
formulation determines the sizes of the lobes in each. One cannot arbitrarily move the lobes in and out,
100
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
however commonly you may come across this device in your reading. A truer picture can be seen in the wiremesh drawing of the LUMO of methyl chloride in Fig. 1.61, where the *CCl orbital shows that both
the inside lobe and the outside are large, and not at all like the lobes in the drawings 2.94 and 2.95, where the
difference between them is much too exaggerated.
We are left therefore with the problem of accounting for the preference for anti overlap. The confusion
is partly an artifact of the use of hybridisation. Various attempts by theoretical chemists show how
buried in subtle balances, and how far from straightforward, the preference for anti overlap may
be.131,132 Perhaps the most simple explanation is a more careful use of pictures like those in 2.94 and
2.95, but drawing them 2.96 and 2.97 with somewhat more realistic hybrid orbitals. The anti arrangement still has good bonding overlap, but in the syn arrangement, there are both attractions and repulsions
between the nO orbital and *CX orbital.133 Furthermore, the anti arrangement keeps the centres of
negative charge as far apart as they can be. There is more discussion on this topic in the section on
-elimination in Chapter 5.
repulsion
nO
X
nO
O
ant i
*
R
*
O
syn
R
X
2.96
2.3
2.97
The Configurations and Conformations of Molecules
Defining the terms configuration and conformation poses a problem, because there is no sharp
boundary between them. Eliel discusses this point authoritatively,134 but all we need here is some
sense that conformational changes are usually those that can take place rapidly at room temperature or
below, making the isolation of separate conformers difficult, and configurational changes have energy
barriers high enough to make it possible to isolate configurational isomers. In the discussion that
follows we shall cross the borderline from time to time—conformational barriers can rise above those
that can be crossed at room temperature, and configurational barriers like double bond geometries can
become so low that they are easily crossed, but the ambiguity is usually not serious. Although it is good
practice to keep the two words distinct in your mind, it is wise not to get too fixated on which word is
being used.
Conjugation, whether it is in the p system or in the system, is one of the factors responsible both for the
configurations that molecules preserve and the conformations that molecules adopt. The energy-lowering
induced by p conjugation usually has the effect of making the planar arrangement with the maximum of
p overlap the lowest in energy, and imparting a barrier to rotation about any single bonds separating the
elements of conjugation. At one extreme is benzene with its perfectly flat ring and no C—C single bonds.
At the other extreme, is the preferred conformation for dimethoxymethane 2.86 stemming from the anomeric
effect, a p effect embedded in a molecule with nothing but single bonds. Energy-raising conjugation has the
opposite effect, as we have already seen in such examples as the orthogonal relationships of the lone pairs in
hydrogen peroxide 2.28 and hydrazine 2.29, to which we could add two other examples. The twisted
conformation 2.98 for a sulfonium ylid simultaneously stabilises the carbanion by negative hyperconjugation with the neighbouring S—Me bonds and avoids the overlap with the lone pair on sulfur.135 The buckling
of cyclooctatetraene 2.99, with a clear separation into double and single bonds, allows it, amongst other
things, to avoid the consequences of an antiaromatic conjugated system. We shall now look at some more
general examples.
2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES
S
= Ar
S
101
Ar
2.98
2.99
2.3.1 Restricted Rotation in p-Conjugated Systems
2.3.1.1 One p Bond. It hardly needs saying that a p bond is not usually free to rotate. The p energy 2Ep that
we saw in Fig 1.26 (˜280 kJ mol1) would be lost at the transition structure for rotation about the C—C bond,
which would have the two p orbitals orthogonal. This value is higher than the energy normally available for a
chemical reaction. For rotation about a p bond to become easy in the ground state, either the transition
structures like diradical 2.101 or the zwitterion 2.102 must be stabilised or the planar structure 2.100 must be
destabilised.
A
D
C
B
B
A
2.101
D
C
2.100
A
B
D
C
2.103
A
D
C
B
2.102
An experimental value for the activation barrier for the isomerisation of cis-2-butene 2.104 is 259 kJ mol1
(62 kcal mol1). Phenyl groups stabilise radical centres, and the barrier to rotation in stilbenes 2.105 is
correspondingly reduced from that in 2-butene to 179 kJ mol1 (43 kcal mol1). Steric interaction between
the cis-vicinal substituents raises the energy of the planar structure, and contributes to lowering the barrier to
rotation. In a fairly extreme example, the bifluorenylidene 2.106 benefits from both effects, and the barrier
falls to 95 kJ mol1 (23 kcal mol1).136
259 kJ mol–1
179 kJ mol–1
Ph
2.104
95 kJ mol–1
Ph
2.105
Pri
Pri
2.106
Alternatively, the substituents A and B may stabilise a cationic centre on one side and the substituents C and
D an anionic centre on the other 2.102. Alkenes having donor substituents at one end and acceptors at the
other are called ‘push-pull’ alkenes, and the barriers to rotation are indeed lowered,137 with the enamine
system of the alkene 2.107 having a barrier of 66 kJ mol1 (16 kcal mol1).138 More subtly, the substituents
in the allene 2.108 enable the phenyl and the methyl groups to exchange places rapidly, with coalescence of
102
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
the signals from the trimethylsilyl groups in the 1H-NMR spectrum at –90 °C.139 The two trimethylsilyl
groups stabilise a cation on the central carbon atom (see p. 94) of the allene, and the empty orbitals on the
boron atoms stabilise an anion on the carbon atom adjacent to them (p. 78). There are more examples on
pp. 109–111.
66 kJ mol–1
36 kJ mol–1
Ar
CO2Me
Me2N
CO2Me
2.107
B
Me3Si
Me3Si
B
Me
Ph
Ar
2.108
Photochemical excitation, however, takes one electron from the p orbital and promotes it to the p*. The
p energy now is (Ep – Ep*), removing the energetic benefit of conjugation, and making the conformation
2.101, with the two p orbitals orthogonal, the lowest in energy. Initially, the excited state must be in the high
energy, planar conformation 2.100, but if the photochemically excited molecule has a long enough lifetime,
the conformation will change to that with the lower energy 2.101. Later, when the electron in the p* orbital
returns to the p orbital, the molecule will return to the planar arrangement 2.100 or 2.103. This is the pathway
for cis–trans isomerisation of alkenes induced by irradiation.
2.3.1.2 Allyl and Related Systems. It is not quite so obvious that the allyl conjugated system is also more
or less configurationally stable, whether it is the cation, the radical or the anion. The drawing of a bond in
the localised structure 2.109a disguises the p bonding present between C-1 and C-2. The pair of structures
2.109a and 2.109b, of course, reveal that this is not the case, and C-1 and C-2 are just as strongly p-bonded as
C-2 and C-3.
2
3
2
1
2.109a
3
1
2.109b
It is even more impressively evident in the molecular orbitals of the allyl system (Fig. 1.33), where the lowest
filled orbital, 1, has p bonding across the whole conjugated system, and the only other orbital, the
nonbonding 2, makes no contribution to p bonding whether it is empty or filled. The total p-bonding
energy for all three allyl systems (Fig. 1.31) is 2 1.414. If rotation were to take place about the bond
between C-1 and C-2, the transition structure would have a full p bond between C-2 and C-3 and an
orthogonal p orbital on C-1. The difference in p energy between the conjugated allyl system (2 1.414)
and this transition structure with a full p bond (2) is therefore 2 0.414, or about 116 kJ mol1 (28 kcal
mol1), making the p bond strength between C-1 and C-2 nearly half that of a simple p bond, quite large
enough to restrict rotation under normal conditions. This is of course a very approximate calculation, which
has been stigmatised as ‘little more than a mnemonic’.140 Nevertheless, higher levels of calculation show
that a substantial barrier is present, but reveal that the cation, radical and anion are not in detail the
same—the unsubstituted cation is calculated to have a rotation barrier in the gas phase of 140 kJ mol1
(33.5 kcal mol1), the radical a barrier of 63 kJ mol1 (15 kcal mol1) and the anion a barrier of 85 kJ mol1
(20 kcal mol1).140 The lower barrier in the radical may be associated with the difficulty of localising charge
on a carbon atom in the transition structure for rotation in either of the ions. In solution, solvation by a
notional polar solvent lowers the numbers for the cation and anion to 115 and 70 kJ mol1 (27.5 and 17
kcal mol1), still large enough to retain configurational identity under normal conditions. 1,3-Disubstituted
2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES
103
allyl systems therefore have three configurations, usually called W-shaped 2.110, sickle-shaped 2.111, and
U-shaped 2.112, which do not easily interconvert by rotation about the C—C bonds.
W-shaped
sickle-shaped
U-shaped
2.110
2.111
2.112
Alternatively, interconversion between the stereoisomeric allyl cations can take place by capture of a
nucleophile at either end, followed by rotation about the more or less normal single bond, and then
regeneration of the cation by ionisation. Interconversion between the corresponding anions can take place
similarly by coordination (1) to a metal at one end or the other. Because of the availability of these
pathways, experimental measurements of the barrier to rotation have confirmed that it is less than the very
approximate theoretical value of 116 kJ mol1 (28 kcal mol1). Furthermore, measurements have generally
been made on significantly more substituted systems. Such substitution can stabilise the filled, half-filled or
empty p orbital, or the double bond, even when these components are no longer conjugated, and so
appropriate substituents lower the barrier to rotation.
In one of the most simple cases, with a methyl group at C-1 and C-3, the U-shaped cation 2.112 generated
in a superacid medium was converted into the sickle-shaped cation 2.111 with a half-life of about 10 min at
10 °C, and the cation 2.111 into the W-shaped cation 2.110 with the same half-life at 35 °C. These
correspond to enthalpies of activation of 74 and 101 kJ mol1 (18 and 24 kcal mol1), respectively. This
measurement only sets lower limits to the rotation barrier of an allyl cation, because it is not known whether
rotation takes place in the cations themselves or in the corresponding allyl chlorides with which they could be
in equilibrium.141 The barrier in cations is also much affected by solvation and by the degree of substitution
at the termini, since the transition structure for rotation draws on such stabilisation more strongly than the
delocalised allyl cation does.
R
R
2.113
2.114
Allyl radicals like 2.113 can also retain their configuration before being trapped by a reagent, but rotation giving
the isomer 2.114 can take place. Free energies of activation of 66 kJ mol1 (16 kcal mol1) (R ¼ D)142 and 60 kJ
mol1 (14 kcal mol1) (R ¼ Me)143 have been measured for this process, close to the calculated value.
For the allyl anion itself, a good measurement is not really possible, because the free anion is not an
accessible intermediate in solution—it is usually coordinated to a metal. If the coordination to the metal is 1
it will weaken the p bonding relative to the free anion, and if it is 3 it will strengthen it. The measured barrier
is therefore dependent upon the metal counterion, but values of 45, 70, and 76 kJ mol1 (11, 17, and 18 kcal
mol1) have been measured for allyl-lithium, potassium and caesium, respectively, with the last of these
presumably a lower limit for the true barrier in a free allyl anion.144 One system free of this complication has
been thoroughly studied: the azomethine ylids 2.115 and 2.116 are isoelectronic with an allyl anion, but do
not have metal counterions. The free energy barrier to the conversion of the isomer 2.115 into the isomer
2.116 is 85 kJ mol1 (20.3 kcal mol1) and for the reverse reaction it is 84 kJ mol1 (20.1 kcal mol1), there
being little difference in energy (1 kJ mol1) between the two isomers.145 Note that the ester groups greatly
stabilise the anionic charge at C-1 and C-3, making rotation about the bond between C-1 and C-2 (or between
C-2 and C-3) much easier than it would be in the free allyl anion.
104
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
CO2Me
Ar N
MeO2C
120°
MeO2C
Ar N
MeO2C
Ar = p-MeOC6H4-
2.115
2.116
A number of related conjugated systems of three p orbitals show the same restricted rotation, although
not to the same degree. Amides 2.117 typically have a barrier to rotation about the C—N bond of 80–90
kJ mol1 (19–21.5 kcal mol1), they have nearly trigonal nitrogen atoms, in contrast to amines, which
have nearly tetrahedral nitrogen atoms, and the C—N bond is shortened because of the extra bonding
provided by the p overlap between the nitrogen lone pair and the p bond of the carbonyl group.146 The
barrier to rotation is particularly easy to measure in this case, because rotation can be detected in the
NMR spectra. The two methyl groups of an N,N-dimethylamide show separate N-methyl signals at room
temperature, and heating causes the two signals to coalesce. The comparatively rigid and planar
conformation present in the amide system has profound consequences on the conformations of peptides
and proteins.
The other systems, esters 2.118,147 enamines 2.119,148 and enol ethers 2.120,149,150 similarly have
restricted rotation about the bond drawn as a single bond but the barrier is successively lower in each as
the degree of p bonding becomes less and less, and the degree of p bonding localised at the double bond
increases. This localisation also affects the lone pair, so that enamines, unlike amides, do not have a
trigonal nitrogen atom, but a somewhat pyramidalised one,151 with the lone pair tilted slightly away
from the vertical, relieving some of the eclipsing suffered by the alkyl substituents on the nitrogen
atom.
80-90 kJ mol–1
N
O
2.117
40-50 kJ mol–1
O
2.118
O
15-25 kJ mol–1
N
10-16 kJ mol–1
O
2.119
2.120
The asymmetry in these systems explains why the degree of p bonding differs on each side of the
central atom. The allyl anion, with a plane of symmetry through the central atom, has a node at that
atom in 2, and this orbital makes no contribution to p bonding. Amides, esters, enamines, enol ethers
and enolate ions do not have a node precisely on the central atom, and so 2 does make a contribution
to p bonding. Taking planar N,N-dimethylvinylamine and the enolate of acetaldehyde as examples,
simple Hückel calculations give the p orbitals in Fig. 2.21, which includes the allyl anion for
comparison. These are specific cases of X-substituted alkenes that we saw earlier in Figs. 2.6 and
2.7, and the enolate ion is also a specific example with the same set of orbitals as the more generalised
cation shown in Fig. 2.8.
While the overlap between the atomic orbitals on the N or the O and the adjacent C are strongly
bonding in 1, they are antibonding in 2. However, both 1 and 2 contribute to p bonding between the
two carbon atoms, and enamines and enolate ions have very restricted rotation there. This is one reason
why it is usually wise to draw enolate ions with the charge on oxygen 2.121a rather than as carbonylstabilised carbanions 2.121b—not only is more of the total charge on oxygen, but the degree of
2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES
0.500
–0.707
0.500
–0.70
0.65
–0.70
200
0.21
3*
170
*
N
0.707
3
0.69
0.19
140
O
*
3
–0.707
0
2
0.64
–0.61
0.500
105
0.707
0.37
88
–0.41
N
0.500
0.59
0.70
120
2
O
200
0.54
1
0.56
2
0.90
0.38
280
0.41
N
0.17
1
O
330
1
N
O
Fig. 2.21
p Orbital energies and coefficients from simple Hückel calculations of the allyl anion, enamine and enolate
ion (orbital energies in kJ mol1 relative to )
p bonding is better illustrated this way. As we shall see later, the carbanion drawing 2.121b reveals the
nature of the HOMO ( 2).
O
2.121a
O
2.121b
One remaining detail to be explained is the relative energy of the two planar conformations available in
some of these systems. Thus monosubstituted amides adopt the s-trans (Z) conformation 2.122a rather
than the s-cis (E) 2.122b,152 esters similarly adopt the conformation 2.123a rather than 2.123b,153 and
even enol ethers adopt the conformation 2.124a rather than 2.124b. Within each pair, the difference in
energy [5–25 kJ mol1 (1.2 6 kcal mol1) at room temperature] is usually too large to detect the minor
conformer directly, but the energy needed to interconvert them is low, making it impossible to isolate the
conformers. The explanation for the conformational preference is most straightforward in the case of
esters. The s-trans conformation 2.123a benefits from the anti orientation of the carbon chains R1 and R2.
In other words, the alkyl chain R1 is effectively a larger substituent than the carbonyl oxygen, and the
ester alkyl group R2 prefers to be anti to it. This is certainly not the whole story, because formate esters,
with R1 only a hydrogen atom, ought to be the other way round, and they are not. There must be a
stereoelectronic component as well, which is identifiable as the generalised anomeric effect (Section
2.2.3.3) involving energy-lowering overlap of a p orbital on one electronegative atom with * for a bond
from carbon to another electronegative atom. In the s-trans conformation 2.123a, a lone pair on the
oxygen atom is oriented anti to the C—O single bond of the carbonyl group, but in the s-cis conformation
2.123b it is syn.154 This is partly responsible for the relatively high reactivity of the smaller-ring lactones
compared with open-chain esters, since these lactones are forced to adopt the high-energy s-cis
conformation.
106
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
H
R1
N
R1
O
R2 N H
O
R2
2.122a
2.122b
R1
O
O R2
R1
R2 O
2.123a
O
2.123b
R1
O R2
R1
R2 O
2.124a
2.124b
The explanation for the preferred conformation of enol ethers 2.120 is probably similar, with * for the C—C
p bond lower in energy than * for the other C—C or C—H bond leading to R1, making the p orbital on
oxygen align itself anti to the p bond. This preference is much less than with esters—the difference in energy
between the two conformations 2.124 is only about 5 kJ mol1 (1.2 kcal mol1),155 whereas with esters 2.123
it is probably 20 kJ mol1 (6 kcal mol1) or more.156 All these effects can be overridden by steric effects
from large substituents, so that enol ethers with substituents cis to the oxygen atom no longer adopt the s-cis
conformation.
The explanation for why amides prefer to adopt the conformation 2.122a with the N—H bond anti to the
carbonyl group is less certain. The carbon chains are still anti, and that may well be the major effect. In
most proteins and peptides, the NH is involved in hydrogen bonding, and that will make some contribution.
It is tempting to see in this system evidence for hyperconjugation from the H—N bond, anti to * for the
C—O bond, being better than hyperconjugation from the alkyl group R2, but this is probably quite a
minor factor.
2.3.1.3 Dienes. In order to maintain the maximum level of p bonding, butadiene is planar, with the
orbitals shown in Fig. 1.37. We estimated there that the conjugation between the two p bonds lowered the
energy by about 66 kJ mol1 (16 kcal mol1). We can see it in another way by noting that the p bonding in 1
between the p orbitals on C-2 and C-3 is between large lobes (c2 ¼ c3 ¼ 0.600), and the antibonding
interaction in 2 is between small lobes (|c1| ¼ |c2| ¼ 0.371). The planar conformations are called s-trans
2.125 and s-cis 2.126, where the letter s denotes a conformation about a single bond. Experimentally, the
activation energy for rotation about the bond between C-2 and C-3 is approximately 28 kJ mol1 (6.7 kcal
mol1) going from s-trans to s-cis, and 16 kJ mol1 (3.8 kcal mol1) going from s-cis to s-trans,157 low
enough for rotation to take place rapidly at room temperature, but different enough to ensure that most of the
molecules will be in the s-trans conformation. Since the difference in energy between these two conformations is 12 kJ mol1 (2.9 kcal mol1) in favour of the s-trans, making the population of the s-cis conformation
at room temperature about 1%.
s-trans
1
2
3
s-cis
4
100
1
2.125
1
4
H
H
2.126
2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES
107
There are two reasons for the preference for the s-trans conformation. The more obvious is that the hydrogen
atoms at C-1 and C-4 which are cis to the other double bond are sterically quite close in the s-cis
conformation 2.126, and repel each other. However, the difference in energy between cis- and trans-2butene, which have similar, although not the same, differences in steric compression, is only about 4 kJ
mol1 (1 kcal mol1). Another reason can be found in the p system (exaggerated in Fig. 2.22), where the
p orbitals on C-1 and C-4 are closer in space in the s-cis conformation than they are in the s-trans, and all
the other orbital interactions, C-1 with C-2, C-1 with C-3, and their symmetry counterparts, are all equal in
the two conformations. The lobes on C-1 and C-4 in 1 are small and bonding, but this attractive overlap is
more than offset by the antibonding interaction between the large lobes in 2, making the overall interaction
repulsive (DE2 > DE1).158
LUMO
*
3
Etrans
HOMO
Ecis
bonding
2
E2
antibonding
E1
1
bonding
Fig. 2.22
Differences in p orbital energies for s-trans and s-cis butadiene
This perception also provides a simple explanation for an otherwise puzzling observation in UV spectroscopy. Dienes constrained to adopt an s-cis conformation by being endocyclic in a six-membered ring,
absorb UV light at a longer wavelength than open-chain dienes with a comparable degree of substitution.
Woodward’s rules for UV absorption in dienes give a base value for s-trans dienes of 214 nm and for s-cis
dienes of 253 nm. This absorption is a measure of the gap in energy between 2 and 3*. If we look again at
Fig. 2.22, we can see that whereas 2 is raised in energy in the s-cis conformation relative to the s-trans, 3*
will be lowered in energy, making the energy gap Ecis less than Etrans.
Another otherwise puzzling result can be explained in a similar way. Reduction of butadiene with sodium
in liquid ammonia159 or in an amine160 gives more cis-2-butene Z-2.131 than trans-2-butene E-2.131,
typically in a ratio of about 60:40. Since the trans-2-butene is the lower in energy, by about 4 kJ mol1
(1 kcal mol1), this is certainly counterthermodynamic. To explain this result we first have to know at what
stage the geometry became fixed, and then determine why the kinetics favoured the formation of the cis
product. By looking at the orbitals of the starting materials and each of the likely intermediates
2.127 2.130, we can work out that the stereochemistry is probably determined in the first step, the addition
of the first electron to the diene system. The diene conformations are present in a ratio of about 99:1. The first
intermediate will be the radical anions 2.127, which will have the extra electron in 3*. This increases the
degree of p bonding between C-2 and C-3, and so rotation is less likely at this stage than it was in the diene.
The next step is either the addition of a second electron to give the dianions 2.128 or protonation to give the
108
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
allyl radicals 2.129, with the next step in either case being the formation of the allyl anions 2.130.161 With an
extra electron in 3*, the dianions have even stronger bonding between C-2 and C-3, and so do the allyl
radicals and anions, as already discussed in Section 2.3.1.2. Finally, protonation of the allyl anions is
evidently selective for the terminus C-1, giving the 2-butenes 2.131, which no longer have any possibility
of rotation between C-2 and C-3. Thus the degree of p bonding between C-2 and C-3 increases at each step as
the reaction proceeds, and it seems likely that the excess of cis-2-butene Z-2.131 in the mixture is caused by
the s-cis diene 2.126 accepting the first electron more easily than the more abundant s-trans diene 2.120. This
is plausible, since we have already deduced that 3* in the diene which accepts this electron is lower in
energy in the s-cis conformation.
+H
+e
+e
+H
E-2.128
+H
slow
2.125
+e
E-2.127
E-2.130
E-2.131
E-2.129
1
99
+H
+e
2
+e
fast
2.126
1
Z-2.128
3
+H
+H
+e
Z-2.127
Z-2.130
Z-2.131
Z-2.129
The overall conclusion here is that cis-2-butene is formed selectively from the s-cis conformation of the
diene, in spite of the mixture being rich in the s-trans. This shows that chemical reactions cannot safely be
used, as they have been,162 to estimate the proportions of the conformations present at equilibrium.
Although less plausible, there is one final observation that might be explained by the attractive interaction
in 3* between the ends of a conjugated system of four p orbitals. 1-Substituted allyl-metal species are
surprisingly a little more stable in the sickle-shaped configuration 2.132 than in the W-configuration
2.133,163 in contrast to butadiene, which is more stable in the s-trans conformation. The C—H bond of the
cis methyl group is conjugated with the p orbitals of the allyl anion, and as such will have orbitals that
resemble those of butadiene, but with two extra electrons. There could therefore be a net attractive force
between the methyl group and C-3, in spite of the expected steric repulsion. This observation has received a
lot of attention, and much more sophisticated theoretical treatment than this.164
1.7-13.4 kJ mol–1
R
3
2.132
1
R
2.133
2.3.1.4 Enones. Simple ,-unsaturated carbonyl compounds also show thermodynamically a preference
for the s-trans conformation. Acrolein has a smaller difference in energy than butadiene between the s-trans
2.134a and s-cis 2.134b conformations of 7 kJ mol1 (1.7 kcal mol1), but a similar barrier to rotation of
2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES
109
about 28 and 21 kJ mol1 (6.7 and 5 kcal mol1), depending upon which direction the barrier is approached
from.165 Methyl acrylate 2.135 has an even smaller difference in energy of 1.3 kJ mol1 (0.3 kcal mol1),
and a somewhat smaller barrier to rotation [approximately 16 kJ mol1 (3.8 kcal mol1) from either
direction].166 These successively smaller differences in energy look like steric effects, since the oxygen of
the carbonyl group in acrolein is smaller than the methylene group in butadiene, and the methoxy substituent
in methyl acrylate is larger than the hydrogen in acrolein. However, methyl vinyl ketone 2.136, with an
energy difference of 2.4 kJ mol1 (0.6 kcal mol1) in favour of the s-trans conformation, is rather more
s-trans 2.136a than methyl acrylate,167,168 yet the methyl group can usually be counted on to be more
sterically demanding than a methoxy group. This implies that some conjugation effects are present that
override the steric effects to some extent. However, steric effects do come into play when there are
-substituents cis to the carbonyl group. Mesityl oxide 2.137 is variously estimated to be 95% or 72% in
the s-cis form 2.137b,167,168 which obviously benefits from the smaller steric interaction from the cis C-3
methyl group with the oxygen atom in the s-cis conformation than with the methyl group of the ketone in the
s-trans conformation 2.137a. Steric effects also come into play when there is a C-2 substituent, which
increases the proportion of s-trans conformer.
O
95
5
H
2.134a
O
O
OMe
2.134b
O
73
7
2.136a
H
28 or 5
72 or 95
2.137a
O
2.135b
O
O
OMe
37
2.135a
3
2.136b
63
3
O
2.137b
By analogy with butadiene, we might expect an aptitude kinetically for reaction in the s-cis conformation.
This has barely been looked at; lithium in ammonia reduction of various ,-unsaturated ketones gives
mixtures of the E- and Z-enolates possibly reflecting the proportions of the s-trans and s-cis conformers,
respectively, in the starting material as well as their relative reactivity with respect to accepting an electron.
There is, however, some evidence that the proportion of Z-enolate is a little higher than the proportion of s-cis
conformer.169
2.3.1.5 Lowering the Energy of the Transition Structure for Rotation. With longer conjugated
systems the p stabilisation increases in the usual way, but each increment makes a smaller and smaller
difference. In the transition structure for rotation, the full p stabilisation is divided into two, with each
part having a shorter conjugated system. As a result, the barrier to rotation about the internal double bonds
goes down as conjugated systems get longer. With polyenes, the barrier does appear to drop, although
there is always ambiguity about the mechanism of isomerisation with such reactive compounds.
Carotenoids, for example, having eleven double bonds conjugated together, are notoriously susceptible
to cis-trans isomerisation, but it does seem likely that some of them are simply thermally induced
rotations.170
Moving on to the weaker p bonding in allyl systems, we deduced in Section 2.3.1.2 that the simple Hückel
barrier to rotation is 0.828. By the same type of calculation we can estimate the barrier in the pentadienyl
system: the full degree of p stabilisation (Fig. 1.42) is 2 þ (2 1.73) ¼ 5.46; the p stabilisation of the
separate components for rotation between C-2 and C-3 is the sum of the energy of a p bond (2) and of an
allyl system (2 1.414), which comes to 4.82, and so the difference is now only 0.64. The experimental
110
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
value in simple allyl systems is only a little above that which can be crossed at the normal temperatures of
chemical reactions, and so we can expect that the longer conjugated systems with an odd number of atoms
will rarely have stable configurations.
This effect is supplemented by terminal electronegative substituents, which increase the overall electron
population at the extremities of the conjugated system, and reduce the effectiveness of overlap in the carbon
chain in between. Thus the system of five conjugated p orbitals present in an alkene with an X-substituent at
one end and a Z-substituent at the other (a ‘push-pull’ alkene, see p. 101), will have molecular orbitals related
to the pentadienyl anion (Fig. 1.42). The nitroenamine 2.138, which has one of the best donors and one of the
best acceptors, although drawn with a full double bond between C-2 and C-3, has much weaker p bonding
between these atoms than that drawing implies, just as the enamine 2.107 did. Rotation about this bond is
actually fast enough to make isolation of individual geometrical isomers impossible.171 The individual
isomers in systems like this can sometimes be detected in the NMR spectra, where another consequence of
the reduced double bond character between C-2 and C-3 is seen in the low coupling constant (10.5 Hz)
between the trans-disposed protons.172
<80 kJ mol–1
N
O
3
N
1
2
N
N
O
2.139
<40 kJ mol–1
NO2
N
N
O
2.138
O
N
O O
N
H
2.141
H
2.140
Another way of looking at the ease of rotation between C-2 and C-3 and the restriction between N-1 and C-2
is with the resonance structure 2.139, which has the effect of expressing the reduction in double bond
character and the stabilisation of the cationic and anionic components, at C-2 and C-3, respectively, in the
transition structure for rotation. However, it is important to recognise the difference between the resonance
structure 2.139 and the transition structure for rotation 2.140. The difference is that overlap of orbitals
expressed as resonance cannot have any change in the position of the atoms, and it is correctly symbolised
with the double-headed arrow. Rotation does have a change in the position of the atoms, and it is a ‘reaction’,
symbolised with conventional reaction arrows. The cation-stabilising group at one end and the anionstabilising group at the other stabilise the intermediate components, which are no longer conjugated in the
transition structure 2.140. Such contributions to lowering the energy barrier will come from any stabilisation
of the intermediate components in the transition structure—cation-stabilising, radical-stabilising or anionstabilising, as appropriate—they will all lower the barrier, as we have seen for the radical in Section 2.2.5 and
for the anion in Section 2.3.1.2. Increasing the stabilisation of the cationic centre in the transition structure,
by having two donor substituents, as in the enediamine 2.141, causes the two N-methyl groups to be
coincident in the NMR spectrum even at 63°C, because rotation about the formal C¼C double bond is
fast on the NMR timescale.173
At the same time, rotation about the formally single bond between N-1 and C-2 in these compounds is
more restricted than drawing a single bond implies, just as it was with amides and with the enamine 2.107.
The two N-methyl groups in both enamines 2.107 and 2.138 have different chemical shifts and coalescence
measurements show that the free energy of activation for rotation is 56 kJ mol1 (13 kcal mol1) for the
former and 69 kJ mol1 (16.5 kcal mol1) for the latter, which indicates that the degree of p bonding there
2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES
111
and between C-2 and C-3 must be comparable in both cases.174 Decreasing the stabilisation of the anionic
centre in the transition structure with a less powerful acceptor than a nitro group, as in the ester 2.142, lowers
the barrier to rotation about the N—C bond from 69 kJ mol1 to 58 kJ mol1 (14 kcal mol1).
69 kJ mol–1
56 kJ mol–1
58 kJ mol–1
67 kJ mol–1
CO2Me
N
CO2Me
N
N
O
O
N
O
2.107
OMe
2.138
O
N
OMe
2.142
2.143
Extended conjugation through double bonds illustrates the principle of vinylogy, a word made up by
combining vinyl and analogy. Vinylogous conjugated systems often have similar properties, both in the
ground state and in reactivity, to the parent systems. The conjugated system of 2.142, for example, is that of a
vinylogous carbamate, in which the restricted rotation about the N—C bond, 58 kJ mol1 (14 kcal mol1) is
similar to but smaller than that of the corresponding carbamate 2.143, 67 kJ mol1 (16 kcal mol1).175 This
illustrates again the lowering in the degree of p bonding between neighbouring atoms as the conjugated
system gets longer.
Another way in which the barrier to rotation about a single bond is lowered is when conjugation is not
energy lowering (Section 2.1.6). Whereas the barrier to rotation about the C—O bond of anisole 2.144 is close
to 25 kJ mol1 (6 kcal mol1), because the lone pair on the oxygen has net p bonding with the benzene ring in
the same way as it has with ethylene in methyl vinyl ether 2.124, the barrier disappears in p-dimethoxybenzene 2.145. Conjugation between the lone pairs on the two oxygen atoms is not energy lowering.176
In contrast, the barrier substantially increases when the lone pair is conjugated through the benzene ring to an
empty p orbital 2.146.177
25 kJ mol–1
O
~0 kJ mol–1
O
2.144
44 kJ mol–1
O
O
2.145
2.146
2.3.2 Preferred Conformations from Conjugation in the s Framework
We have already seen in Section 2.2.3.3 how conformation can be affected by anomeric interactions, which
can lead electronegative substituents to be axial at the 2-position in tetrahydropyranyl rings, and sometimes
cause a chain of atoms to adopt a seemingly more hindered gauche conformation 2.81–2.83, 2.85 and 2.86
rather than the more usual zigzag arrangement. Similar hyperconjugative interactions in neutral molecules
between two bonds, one a donor and the other a acceptor, can lead them to adopt conformations in
which the stereoelectronic effect overrides the purely steric effect.
1,2-Difluoroethane might be expected to adopt the zigzag conformation 2.147, both because the dipoles
from the C—F bonds will be opposed, and because the two larger groups will be further apart. However, it
does not—it adopts the conformation 2.148 instead, with an enthalpy advantage of 2.5–3.8 kJ mol1 (0.6–0.9
kcal mol1) as well as a small favourable entropy factor, since there are two gauche conformations and only
one anti.178 The enthalpy advantage in this conformation stems from the anti-periplanar conjugation of the
112
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
C—H bonds with the vicinal C—F bonds. Hyperconjugation will be energy-lowering with an interaction
diagram like that in Fig. 2.14, but with the low-lying antibonding orbital *CF taking the place of the empty
pC orbital. It is the same interaction of orbitals that we saw in the C—H bond lengthening in the 1,3-dioxan
2.41. A similar explanation accounts for the fact that cis-difluoroethene 2.150 is lower in energy than its
trans isomer 2.149, in contrast to most other alkenes.179 Although less powerful, the effect is still evident
in other dihaloethanes, in other 1,2-disubstituted alkanes like dimethoxyethane, and in the helical
conformation of polyoxyethylene -(CH2CH2O)n-, which contrasts with the zigzag conformation of
polyethylene.
HH
F
HH
H
H
F
H
H
F
HH
F
FH
F
H
F
F
2.148
2.147
2.149
2.150
The same type of overlap can take place through a double bond to give a vinylogous version. In the
conformation 2.151 of an allylic ether, the C—O bond is conjugated with the p bond, but in the conformation
2.152 the C—H bond is conjugated with the p bond and the C—O bond is not. Which of these is preferred is
dependent upon the electronic nature of the substituent Y at the other end of the double bond. When the
substituent Y is an alkyl group (a p donor by hyperconjugation) the preferred conformation is 2.151, because
there is then an energy-lowering interaction, conjugated through the double bond, with the C—O bond (a p
acceptor). When the substituent Y is a carbonyl or nitrile group (a p acceptor), the preferred conformation is
2.152, because this avoids the energy raising conjugation through the double bond of one p acceptor with
another.180,181 This type of allylic ether is one of the most important examples of a stereogenic centre
adjacent to a double bond affecting which surface of the double bond is the less hindered, and hence the more
reactive.
R
Y
H
H
Y
OR
RO
R
2.151
2.152
preferred for Y = alkyl
preferred for Y = CO2Et or C≡N
With a more powerful donor like an Si—C bond, the preference for the donor and the acceptor bonds to be
anti can be seen in cyclohexyl esters carrying a silyl group. The equilibrium proportion of the alcohol is in
favour of the normal diequatorial isomer 2.153 (R ¼ H), but with esters (R ¼ acyl) the equilibrium shifts to
favour the diaxial conformation 2.154. Furthermore, the equilibrium constant correlates with how good the
carboxylate ion is as a leaving group (pKa of RO drops).182
OR
OR
SiMe3
SiMe3
2.153
2.154
preferred for R = H
preferred for R = acyl
2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES
2.4
113
The Effect of Conjugation on Electron Distribution
Conjugation affects not only the energies and conformations of organic molecules but also the distribution of
the electrons. This has consequences on where the sites of highest charge are located, and on the polarities of
molecules as manifest in such properties as the sites of ambident reactivity, dipole moments and the patterns
in which they stack in crystals.
We are already familiar with the stabilising effect of an electronegative substituent conjugated with an
empty p orbital (see p. 58). The carbonyl group is polarised so that the carbon atom carries substantial
positive charge, as symbolised in Fig. 1.66 by the small p orbital on the carbon atom in the HOMO.
Conversely, the oxygen atom carries a substantial negative charge, and carbonyl compounds have a strong
dipole. This shift in the electron population is often illustrated with resonance structures like 2.155 and 2.156
which show the oxygen carrying negative charge.
An imine shows a similar polarity to that in a carbonyl group, but reduced because nitrogen is less
electronegative than oxygen. However, in an iminium ion, in which the molecule as a whole carries a
positive charge, the effect is enhanced, and iminium ions are more reactive electrophiles than the
corresponding aldehyde or ketone. However, expressing this idea with resonance structures like
2.157 and 2.158 can be misleading. The impression is given that the nitrogen atom is positively
charged in the one, and not carrying charge in the other, in contrast to the negative charge inoffensively written on the corresponding resonance structure 2.156 for a ketone. The nitrogen atom in the
imminium ion is negatively charged throughout, not only in the p system but in the framework
as well.
O
2.155
O
2.156
N
2.157
N
2.158
Organic chemists, using resonance structures, are meticulous about keeping track of charge, illustrating it with strict adherence to Lewis structures and carefully placing a formal charge on an atom
whenever appropriate. The convention has the charge on the nitrogen in this case, because of the
consumption of the lone pair on the nitrogen in forming the fourth bond when an imine is changed into
an iminium ion. The positive charge is drawn on the nitrogen atom as a formality —it is a kind of bookkeeping. In fact, the electron deficiency is spread elsewhere —to the adjacent carbon atom, as illustrated in the resonance structure 2.158, and relayed by conjugation onto the hydrogen and carbon
atoms joined to that carbon and to the nitrogen atom itself. The electron population on the electronegative atom is high, and not low as the drawing 2.157 implies. The sum of the coefficients in the
filled p orbitals on the nitrogen atom in pyridine 1.47 in Fig. 1.69 is smaller than the sum of the
coefficients on the nitrogen atom in the pyridinium ion 1.48, in which the nitrogen is drawn, as usual,
with a positive charge which it does not carry. There is nothing wrong with this formalism —drawing
these structures is unavoidable if curly arrows are to be used to show where the electrons are coming
from and moving to in the course of a reaction —but it can certainly be misleading about the actual
electron distribution.
If the carbonyl group is conjugated with a p bond, as in ,-unsaturated ketones, the fraction of positive
charge on the carbon atom is shared with the p bond, and the carbon becomes partly cationic in nature, as
symbolised in Figs. 2.3 and 2.4 by the relatively small p orbitals on the carbon atom in 1 and 2 of acrolein
as a model for a Z-substituted alkene. Looking again at those pictures, it is clear that the sum of the
coefficients of the filled p orbitals on the carbonyl carbon is smaller than the sum at the carbon, and that
114
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
the p electron deficiency is therefore greater at the carbonyl carbon. We shall return to this picture when we
discuss ambident electrophilicity in Chapter 4 in Section 4.5.2.
Enol ethers, and even more powerfully enolate ions, have an oxygen lone pair conjugated to a p bond,
with the result that the total p electron population at C-2 is high, as illustrated in Fig. 2.7 for an enol ether
and in Fig. 2.21 for an enolate ion. It is not, however, higher than the total p electron population on the
oxygen atoms, which remain the sites of highest electron population. This sharing of the electrons is often
illustrated with resonance structures such as 2.121 for an enolate ion and 2.159 for an enol ether. The
drawings 2.121a and 2.159a remind us that there is a substantial p bond from C-1 to C-2, but the drawings
2.121b and 2.159b illustrate the increase in the electron population on C-2. Nevertheless, the oxygen atom
is not positively charged in an enol ether as the drawing 2.159b seems to imply. The electron deficiency is
taken up by the substituents on C-1 and on the oxygen atom. Although an increase in electron population is
spread to C-2, the electrons remain substantially on the oxygen atom itself, as befits an electronegative
element. We shall return to the enolate ion when we discuss ambident nucleophilicity in Chapter 4 in
Section 4.3.2.
MeO
MeO
2
2.159a
1
2
2.159b
Experimental evidence for the shift in electron population when an X-substituent is attached to a double bond
is found in the chemical shifts of protons on C-2 in enol ethers, and even more conspicuously in the NMR
spectra of enamines. Thus, the proton on C-3 in the enamine 2.161 comes into resonance at higher field than
the corresponding proton in phenalene 2.160, because the increased electron population on C-3 shields the
adjacent proton. The corresponding proton in the ammonium salt 2.162 is at unusually low field, first of all
because there is no lone pair conjugated with the double bond, but also because the ammonium ion
inductively withdraws the electrons from the p bond, demonstrably leaving H-3 relatively exposed.183
Again, the ammonium ion, although positively charged overall has most of the charge on the p-bonded
carbons, on their substituents, and especially on the hydrogen atoms of the methyl groups, not on the nitrogen
atom, on which it is formally placed.
H
H
3
6.49
3
5.70
2.160
H
NMe
3
NMe2
7.10
2.161
2.162
A striking illustration of how misleading it is to place the positive charge on the electronegative atom in
drawings like 2.159b, 2.157 and 2.162, is provided by the standard explanation found in many textbooks for
why the dipole of pyrrole 2.163 points from the nitrogen atom towards the carbon atoms of the ring, whereas
the dipole for furan 2.164 is in the other direction. The standard explanation is that the overlap illustrated by
the resonance structures 2.163b and 2.163c moves the electron population onto the carbon atoms and leaves
the nitrogen positively charged. Furan with a more electronegative heteroatom is not so strongly polarised.
This cannot be the reason, because the resonance structures 2.163b and 2.163c illustrate the electron
distribution in only one of the p orbitals, the highest in energy 3 in Fig. 1.69. The overall negative charge
2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES
115
on the nitrogen is higher than on carbon if we sum the coefficients for the three filled p orbitals, and the same
pattern must hold in the framework. It is not permissible when explaining a physical property of a whole
molecule to use only one of the orbitals—it is like confusing thermodynamic with kinetic effects—that one
orbital, the HOMO, appears to have a profound effect on the kinetics, but is not adequate to explain a
thermodynamic property.
N
H
2.163a
N
H
N
H
O
2.163b
2.163c
2.164
The explanation for the unexpected direction of the dipole is that pyrrole has an N—H bond, strongly
polarised towards the nitrogen and furan does not have a substituent on the oxygen atom. Calculations
support this picture, and reveal that the dipole moments in these systems are all lower than their
saturated counterparts as a result of the overlap in the p system.184 The overlap illustrated by the
curly arrows does move charge towards the carbon atoms, but not powerfully enough to overcome the
usual pattern, that the electronegative atom carries more of the negative charge than the carbon and
hydrogen atoms.
2.5
Other Noncovalent Interactions185
We began in Chapter 1 by considering the strongest forces involved in bonding, the covalent bonds
themselves, and worked our way down from the strongest bonds to the weakest p bonds. In this Chapter,
we have looked at the weaker p interactions of covalent bonds with each other and with p orbitals, and
have come down to a level at which they provide only a delicate balance affecting the shapes molecules
choose to adopt. There are a few other forces at work, both within a molecule and affecting how one
molecule can interact with another, which also stem from the electron distribution. Weak though some of
them are, these forces have profound consequences not only on the shape a molecule adopts, but also on
the degree and sites of solvation, on intermolecular forces affecting the bulk properties of polymers and
controlling crystal packing, on intramolecular forces affecting protein folding, and on molecular recognition in such important pairings as those between an enzyme and its substrate, and between a receptor
and its agonist.
2.5.1 Inversion of Configuration in Pyramidal Structures
Amines are pyramidal in structure, but if the nitrogen atom carries three different substituents it cannot
be resolved into a pair of enantiomers, because of the rapid inversion of configuration 2.165a ! 2.165b,
which has an energy barrier of the order of 24 kJ mol1 (6 kcal mol1).186 In contrast, the corresponding
phosphines are easily resolved, and are configurationally highly stable with respect to the inversion
2.166a ! 2.166b, which probably has a barrier of at least 140 kJ mol1 (34 kcal mol1).187 The
inversion of configuration at nitrogen is made slower if the nitrogen is in a small ring, and slower still
if it has an electronegative substituent attached to it. With the benefit of both features, an N-chloroaziridine can be separated into a pair of diastereoisomers 2.167a and 2.167b.188 In contrast to amines,
imines, which have trigonal nitrogen atoms, are configurationally stable with respect to cis–trans
isomerisation 2.168a ! 2.168b by way of inversion at nitrogen, as well as by restricted rotation about
the p bond.
116
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
fast
N
slow
P
N
P
24 kJ mol–1
2.165a
140 kJ mol–1
2.165b
2.166a
2.166b
Cl
N
Cl
slow
N
N
N
>100 kJ mol–1
2.167a
2.167b
2.168a
2.168b
All these properties can be understood by considering the molecular orbitals involved in the inversion
process.189 The method is to start with the orbitals of the planar arrangement, and look for interactions that
encourage pyramidalisation. For ammonia and phosphine the three occupied orbitals and the lowest unoccupied orbital are shown in Fig. 2.23. In both cases, the pyramidal arrangement, which keeps the electron
populations as far apart as possible, is the stable conformation. The HOMO and the LUMO are orthogonal in
the planar arrangement, and there is no Jahn-Teller distortion (see pp. 34 and 41). In the pyramidal arrangement, with the hydrogen atoms moved down (or up), the HOMO and LUMO are no longer orthogonal, and
Jahn-Teller distortion occurs, lowering the energy of the HOMO and raising the energy of the LUMO. The
lower energy of the HOMO lowers the overall energy of the molecule from that of the planar arrangement. The
closer in energy the HOMO and the LUMO, the more strongly they interact. The HOMO energy is largely that
of a p orbital on nitrogen or phosphorus, and the latter is higher in energy, since nitrogen is the more
electronegative. Bonding between one of these elements and hydrogen will lead to a larger split between
the and the * orbital with nitrogen than with phosphorus, because the energy match is closer. In consequence
the LUMO, which is a * orbital, is relatively lower in energy for phosphine than for ammonia. With the
HOMO higher in energy and the LUMO lower in energy for phosphorus than for nitrogen, the Jahn-Teller
distortion is stronger in phosphines. It follows that losing that stabilisation by passing through the planar
arrangement is energetically more costly for phosphorus than for nitrogen. The larger the HOMO–LUMO
interaction in the planar configuration the more favourable is it for the hydrogen atoms to be out of the plane,
and phosphines do indeed have a smaller H—P—H bond angle than the H—N—H angle in ammonia.
Carbanions are tetrahedral, and inversion of configuration can be expected to be easy—since the LUMOs,
the *CH orbitals, are high in energy, the HOMO–LUMO gap is not small as it is in a phosphine. However,
carbanions in the form of compounds containing C—Li bonds can often be configurationally stable by virtue
of the bond, which would have to be broken to allow inversion.
If two of the hydrogen atoms in Fig. 2.23a are brought closer together, in imitation of having the atom A in
a small ring, the LUMO energy will be lowered as the bonding between the hydrogen atoms increases. There
will be no effect on the HOMO, which does not involve the hydrogen atoms, and so the HOMO–LUMO gap
will be reduced, thus explaining why a small ring stabilises the tetrahedral geometry. Similarly, replacing
one of the hydrogen atoms with an electronegative element will lower the energy of the LUMO, and leave the
HOMO largely unaffected. Any p contribution from the lone pair on the electronegative element will be
small, and will raise the energy of the HOMO a little. Aziridines like 2.167 and cyclopropyl lithium reagents
are notably more configurationally stable than their open-chain counterparts.
The highest filled and the two lowest unfilled molecular orbitals of a linear methyleneimine are shown in
Fig. 2.24. The HOMO is largely the lone pair, but the LUMO p*CN offers no opportunity for bending at the
nitrogen atom to have any effect. However, the next orbital up in energy *CN, called the NLUMO, while
orthogonal to the HOMO in the linear structure, can mix with it if the N—H bond bends. Mixing in the
NLUMO with the HOMO lowers the energy of the latter, and therefore lowers the energy overall. The vinyl
2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES
A
H
H
H
H
H
H
A
H
H
A
HOMO
H
H
A
A
H
H
H
A
* LUMO
H
H
A
A
H
H
LUMO
H
H
HOMO
A
H
A
H
(a) planar
Fig. 2.23
H
H
H
H
H
117
H
H
H
H
(b) pyramidal
Filled molecular orbitals and the lowest unfilled of planar ammonia and phosphine
H
H
H
H
N
Fig. 2.24
N
H
NLUMO
LUMO
H
H
H
H
H
N
N
H
HOMO
H
Highest filled and lowest unfilled orbitals of linear methyleneimine
anion and protonated formaldehyde are isoelectronic with this system, but the HOMO–NLUMO gap will be
larger the more electronegative the element carrying the lone pair. Vinyl anions can be expected to be
configurationally stable, as indeed vinyl Grignard and lithium reagents are, but protonated carbonyl groups
will be less so. When the nitrogen of the imine carries another electronegative atom, as it does in oximes and
hydrazones, a kind of effect comes into play, the HOMO–NLUMO gap is reduced, the interaction is made
stronger on bending, and the bent structure is even lower in energy relative to the linear than it was for the
simple imine.
The same considerations apply to radicals,190 except that inversion is more favourable than it was with
anions and lone-pair bearing atoms, because pyramidalisation with one electron in the HOMO only
contributes half the stabilisation imparted by having two electrons. EPR spectroscopy allows the rates of
inversion to be measured, and it has been found that, although the methyl radical itself is essentially planar,
any substitution, but especially with electronegative elements or by incorporation into a small ring, increases
the degree of pyramidalisation, and the barrier to inversion. In general, even though most substituted
118
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
carbon-based radicals are pyramidal, their configurations are rapidly lost by inversion through a planar
transition structure. The methyl groups in the tert-butyl radical, for example, are 10° out of plane, and the
barrier for inversion is only about 2 kJ mol1 (0.5 kcal mol1). However, as with anions and lone-pair
bearing systems, a radical based on an element lower in the periodic table, like phosphorus, silicon or tin, can
be stable enough to retain its configuration through a chemical reaction, as the radical 2.170 does in the
halogenation of the enantiomerically enriched silane 2.169. The product is the enantiomerically enriched
chloride 2.171 with retention of configuration.191 A comparable reaction on carbon would have given
racemic product.
Me
(PhCOO)2
Si H
Np
Ph
Me
Np
Ph
2.169
Me
CCl4
Si
Si Cl
Np
Ph
2.170
2.171
2.5.2 The Hydrogen Bond192
2.5.2.1 X—H . . . X Bonds. The traditional hydrogen bond is found when a hydrogen atom bonded to
one electronegative atom is close to another electronegative atom. It is found at its strongest and most
simple in the HF2 ion, which has been estimated to have in the gas phase an energy below that of the
separate components of no less than 167 kJ mol1 (39 kcal mol1), and at its most famous in the strong
AT and GC pairing of bases in the double helical structure of DNA. The pattern of filled molecular
orbitals in the HF2 system, shown in Fig. 2.25, resembles that of the allyl anion—a low-energy orbital
with no nodes, and a nonbonding orbital with a node at the central atom. The node at the hydrogen atom
leaves it with no interactions with the two fluorine atoms, which are far enough apart to be essentially
nonbonding. For this arrangement to be stabilised, 1 and 2 must together be lower in energy than the
corresponding orbitals in the separate components HF and F. Electronegative elements will lead to high
electron populations on the atoms at the two ends of the three-atom system, incidentally making it
exceptionally difficult to locate the hydrogen atoms by X-ray crystallography, and leading to the very low
field at which they come into resonance in 1H-NMR spectra. More importantly, with respect to the energy
of the system, electronegative elements have compact orbitals in 2, making residual repulsion between
them lower. This orbital picture also explains why a linear array is best; any bending decreases the
bonding in 1 and increases the antibonding in 2. With other atoms, inherently less electronegative than
fluorine, hydrogen bonding becomes weaker: in water it is estimated to be 22 kJ mol1 (5 kcal mol1) and
the intramolecular hydrogen bond in the enol of a -dicarbonyl compound is in the range 33–57 kJ mol1
(8–14 kcal mol1).
Fig. 2.25
F
H
F
3
F
H
F
2
F
H
F
1
*
The molecular orbitals of the symmetrical hydrogen bonds in HF2
2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES
119
The same set of orbitals applies to such other forms of strong hydrogen bonding as the bridged B—H—B
bonds in diborane 2.172193 and the bridged C—H—C bond in the cyclodecyl cation 2.173,194 except that in
these systems there are only two electrons to be fed into the three-atom orbitals, leaving 2 empty. Since high
electronegativity for the two atoms at the ends principally exerts its effect in keeping 2 as little antibonding
as possible, high electronegativity is no longer a requirement when 2 is empty.
H B
H
H
H
B
H
H
H
H
2.172
2.173
An alternative perception for the nature of conventional hydrogen bonding, not in conflict with the molecular
orbital picture, is that it stems from a Coulombic attraction between the negative charge of the lone pairs of
the one electronegative element, and the partial positive charge left on the hydrogen atom by the polarisation
of the bond towards the other electronegative element. In this picture, we also see that a hydrogen bond
resembles the transition structure for proton transfer between basic sites. This is perhaps the best way to
explain why hydrogen bonding towards the fluorine atom of an F—C bond is extraordinarily weak.195
Although highly charged, the fluorine atoms are not basic, and are not available for attracting a proton.
2.5.2.2 C—H. . .X Bonds. When the hydrogen atom is attached to carbon, it still has an attractive
interaction with lone pairs on electronegative elements, but the degree of hydrogen bonding is much
smaller than with conventional hydrogen bonds, probably never more than about 17 kJ mol1 (4 kcal
mol1), and usually much less. These kinds of hydrogen bonds manifest themselves in small shifts in
spectroscopic properties,196,197 such as a lowering by anything up to 100 cm1 in the C—H stretching
frequency in their infrared spectra,198 in small downfield shifts of protons when the 1H-NMR spectra are
taken in oxygen-containing solvents, and in preferred conformations, such as that for propanal 2.187a, and
as seen within many structures derived from X-ray crystallographic data.199 The strength of this kind of
hydrogen bond correlates with the acidity of the C—H bond,197,200 in line with the picture of hydrogen
bonding as a model for proton transfer. Thus the hydrogen atoms on haloforms, on acetylenes, on
methylene groups between two electron-withdrawing groups, on aldehydes and on alkenes are the ones
most often involved in C—H. . .O hydrogen bonds. Knowledge of when these hydrogen bonds might be
strong has made it possible to design pairs of compounds that crystallise together, like the 2:1 combination
2.174 of trinitrobenzene and dibenzylidenecyclo-pentanone, and has provided a basis for crystal engineering and supramolecular design.
O
N
O
O
H
O
H
H
H
O
O
H
H
O
H
N
O
H
N
H
N
H
O
N
O
O
O
N B O
H
O2S
O
O
H
H
N
O
2.175
2.174
120
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
One of the most striking manifestations of the importance of C—H. . .X hydrogen bonds is in the way they
affect the conformations adopted in transition structures, where small energy differences can have a large
effect. Conspicuously, the capacity of the hydrogen atom in an aldehyde to be a relatively good hydrogenbond donor, considering that it is attached to a carbon atom, has played a major role in understanding how
chiral catalysts work.201 One example is the structure deduced for the complex 2.175 between benzaldehyde and Kiyooka’s oxazaborolidine, which induces high enantiocontrol in Mukaiyama aldol reactions.
The carbonyl oxygen is coordinated to the boron, and the weak hydrogen bond—the dashed line—is just
strong enough to hold the si face of the aldehyde, the front face as drawn here, exposed to the attack of
nucleophiles.
2.5.2.3 X—H . . . p Bonds. Similarly weak hydrogen bonds can also be formed from protons bound to
electronegative elements coordinating to the p orbitals of C¼C p bonds. The strength, estimated to be
anything up 17 kJ mol1 (4 kcal mol1), is clearly strong enough to be important in interactions like that
of a drug with its receptor in biological systems.202 The effect is seen in lower frequency O—H
stretching in the infrared spectra of alcohols, correlating with how closely the hydrogen atom sits to
a double bond or an aromatic ring,203 and most dramatically in the upfield shift of 1.5 ppm for the
phenolic OH proton when the spectrum is taken for a solution approaching infinite dilution in benzene
rather than in carbon tetrachloride.204 The large shift is not so much a measure of the strength of the
O—H. . .p hydrogen bond, as a consequence of the proton sitting in the shielding region of the ring
current 2.176.
2.5.2.4 C—H . . . p Bonds. Even weaker hydrogen bonds, rarely responsible for stabilisation of more
than 4 kJ mol1 (1 kcal mol 1), can be detected between C—H bonds and C¼C p bonds.205 These
interactions are again seen in some packing arrangements in X-ray crystal structures, in small changes
in infrared stretching frequencies, and most dramatically in some noticeable upfield shifts in the
1
H-NMR spectra when changing the solvent from carbon tetrachloride or chloroform to benzene or
toluene. On the whole, the larger shifts in the NMR spectra are seen with the more acidic C —H bonds,
with chloroform for example showing a shift of 1.35 ppm at infinite dilution, because of the formation
of a bond to the centre of the p system 2.177. 206 It has been suggested that an ammonium salt can
interact with aromatic rings 2.178 by C —H. . .p hydrogen bonding, and thereby explain how the
charged ammonium neurotransmitter from acetylcholine can be recognised at its aromatic-rich
receptor site, in spite of the ionic nature of the one component and the hydrophobic nature of the
other.207
Ph
O
1.5 ppm
upfield
Cl
Cl 1.35 ppm
C Cl upfield
H
H
2.176
2.177
N
H
H
H
2.178
It might perhaps be argued that hydrogen bonding may not be the best way to describe this attraction.
Because H—C bonds made up from the 1s orbitals on hydrogen and the 2px and 2py orbitals on carbon are
overall polarised towards carbon, the hydrogen atoms on the periphery of p systems are overall positively
charged, and the centre of the p system is negatively charged. The attraction of the one for the other is then
seen as simply electrostatic. One might equally argue that all kinds of hydrogen bonding can best be thought
of as simply electrostatic, and that arguments over what to call the attraction are only about what to call it and
not about its fundamental nature.
2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES
121
Weak C—H. . .p interactions may also be responsible for such unexpected observations as the preference
for a gauche interaction between the tert-butyl and phenyl groups in the sulfoxide 2.179a rather than the
more obvious anti-periplanar arrangement 2.179b of the two largest groups,208 for the cyclohexanone 2.180
to have the phenyl group axial,209 where it can bond to the hydrogen atoms of the methyl group, rather than
equatorial, as would be expected for a group with a higher A-value (2.8) than that of a methyl group (1.7), and
for the frequent occurrence in crystal structures and in host–guest interactions of arrangements of aromatic
rings in which the C—Hs of one aromatic ring point at the plane of the ring of another 2.181,210 in contrast to
p stacking that is so often invoked (Section 2.5.4).
H-bonded?
H-bonded?
Me
H
O
S
S
H
O
H
H
H
H-bonded?
O
H
H
Me
2.179a
2.179b
2.180
2.181
It might be thought that feeble hydrogen bonding of this kind was of little significance, but its effect is
magnified when it contributes to small energy differences in transition structures, where arguments about
preferred conformations influenced even by such small effects as C—H. . .p hydrogen bonding and other
weak interactions are often called upon.211 An energy difference of 4 kJ mol1 (1 kcal mol1) in two
transition structures derived from the same starting materials gives a product ratio of 83:17 at room
temperature. Ratios of this kind are commonplace in organic reactions, where small energy differences
determine the sense and degree of stereo and other kinds of selectivity.
2.5.3 Hypervalency
There are many well known molecules which clearly have more than the complete octet of electrons
found in traditional Lewis structures. These include such molecules as PF5, SF4, PhICl2, and XeF2, such
ions as SiF5 and PCl6, and transition structures like those involved in S N2 reactions at carbon and
silicon, and any of the elements below them and to the right of them in the periodic table. Such
molecules have been called hypervalent,212 and have been said to have expanded valence shells.
Hypervalent molecules almost always have a high proportion of electronegative elements among
their ligands.
The standard method of explaining how such molecules can be stable is to invoke the interaction of a
filled p or hybrid orbital on one of the ligands with an empty d orbital on the central element. This
immediately explains why the stable hypervalent molecules are all found with elements in the second row
or below, where d orbitals are available, and not in the first, where they are not. The d orbitals can be
combined with the s and p orbitals in any combination to give a bewildering array of hybrid orbitals to use
for this kind of bonding.
Like any interaction of filled with unfilled orbitals, interactions with empty d orbitals are bound to be
stabilising. The problem, as we have already seen earlier in explaining why a silyl, phosphenyl, or sulfenyl
group is p-withdrawing, is that d orbitals are too high in energy relative to the p orbitals for their
interaction to have much effect. It is better to see hypervalent bonding as the consequence of orbital
interactions like those involved in hydrogen bonding.213 Essentially, the central atom Y is seen as involved
in normal bonding to n2 of its ligands. In addition, a p orbital on each of the two remaining ligands
X together with an unused p orbital on the central element Y interact to create a set of three molecular
122
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
*
X
Y
X
3
X
Y
X
2
X
Y
X
1
Fig. 2.26 The key molecular orbitals of hypervalent bonding
orbitals as shown in Fig. 2.26. For the system to be overall bonding, it is necessary for 2 to be largely
nonbonding, which it will be if the ligands are kept well apart, and are electronegative elements, just as
they are in hydrogen bonding.
Thus a pentacovalent phosphorus compound will have the three least electronegative ligands in the plane
of a trigonal bipyramid 2.182, with bonds formed from the 3s and the 3px and 3py orbitals, and the two most
electronegative ligands disposed linearly at the apices, with bonds formed from the two lower orbitals in
Fig. 2.26. Furthermore, the more electronegative ligands will also carry more negative charge, and will repel
each other most thoroughly if they are both apical. In consequence of both orbital and charge effects, the
apical bonds are weaker than the basal, and these are well known214 to be the ones that break during
reactions. It follows that they are also the ones that are formed most easily in the reverse of those reactions,
and apical attack is indeed normally observed.
Nu (–)
X
R
P
X
2.182
R
R
R
C R
R
X (–)
2.183
Nu
R
Si R
R
X
2.184
The same pattern is seen in the transition structures 2.183 for the SN2 reaction at carbon, which will have five
ligands around the central atom. Apical entry of a nucleophile and apical departure will give the lowestenergy transition structure, and hence explain the overall inversion of configuration. Changing to silicon,
what was a transition structure with carbon can be an intermediate with a lifetime 2.184, because the bonds
are so much longer and 2 is that much less antibonding. We shall return to this subject when we discuss the
stereochemistry of nucleophilic substitution in Chapter 5.
2.5.4 Polar Interactions, and van der Waals and other Weak
Interactions
2.5.4.1 Coulombic Forces. If two molecules, or two parts of one molecule, have charges or dipoles, the
sites of opposite charge can attract each other, and sites with the same charge can repel each other. These
forces can be large and have a conspicuous influence on molecular properties, and especially on reactivity, as
we shall see in later chapters. One way of looking at hydrogen bonding is to see it as primarily Coulombic.
The same electrostatic forces also come into play in a less direct way in a number of weaker interactions. For
example the axial lone pairs in the 1,3-dioxan 2.185 can sense the electron deficiency at the para position of
the nitrobenzene ring, and make the conformation with the aryl group axial lower in energy than the
conformation when it is equatorial. The usual pattern is seen in the 1,3-dioxan 2.186 with a benzene ring
in place of the nitrobenzene.215
2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES
123
NO2
H
H
H
Me
H
H
O
H
O
O
H
Me
O
H
Preferred conformation (71:29)
H
Preferred conformation (79:21)
2.185
2.186
Furthermore, polar attractions from one polar molecule to another, or from one strongly hydrogen-bonding
molecule to another, lead such molecules to aggregate, and to exclude nonpolar molecules. This is the basis
for the well-known hydrophobic effect, in which nonpolar molecules stick together to avoid being in water.
2.5.4.2 Dipole-Dipole Attraction. If only one of the molecules is charged or a dipole, it can still respond to
weak polar forces in molecules not traditionally thought of as being polar. Two related examples of weak but
significant dipolar interactions are seen in propanal 2.187216 and propanol 2.188,217 in which the lowerenergy conformations, 2.187a and 2.188a, have the methyl groups close to the oxygen atom. The small
degree of polarisation of the H—C bonds in the methyl groups leaves a weak positive charge on the outside,
and this is attracted to the partial negative charge on the oxygen atoms, making these conformations slightly
lower in energy than the less sterically hindered conformations 2.187b and 2.188b. This phenomenon is
essentially the same as that of hydrogen bonding at the weaker end of its range (Section 2.4.2.2, where the
conformation of propanal was mentioned). We return to this conformational preference in Chapter 5, where
it contributes to our understanding of the Felkin-Anh rule.
H
8 kJ mol–1 Me
H
Me
H
O
OH
H
H
H
2.187a
2.187b
O
Me
H
H
H
4 kJ mol–1
OH
H
H
H
H
H
Me
2.188a
2.188b
There is a somewhat similar phenomenon in which the presence of a dipole within a molecule induces a
temporary dipole, either elsewhere in the molecule or in another molecule. The induced dipole is then
attracted to the inducing charge or dipole, and another small attractive force comes into play that is not
included in the molecular orbital picture at the most simple level of calculation, but is included when larger
basis sets are used. Weak dipolar attractions like these, both the static and the induced, are not strong, and so
nonpolar molecules are not well solvated by polar molecules—the polar solvent molecules would rather
solvate each other and the nonpolar molecules are left to their own devices. As it happens they do not repel
each other as much as one might expect.
2.5.4.3 van der Waals Attraction. In addition to forces directly associated with charge, two molecules
repel each other, because the interaction of the filled orbitals of one with the filled orbitals of the other is
inherently energy-raising. This is the basis for steric hindrance of all kinds. The repulsion is countered by a
small attractive force from the interactions of filled orbitals with unfilled orbitals, which are inherently
energy-lowering. Both forces fall off exponentially with distance, but they are not the only interactions
between nonpolar molecules. If we look at two electrons, one in each of two nonpolar molecules, the electron
in one molecule will repel the electron in the other. At any given moment, if the first electron is on the side of
the molecule facing the other molecule, it will cause its opposite number to spend more of its time on the far
124
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
side of the second molecule. The electrons are said to be correlated. As the two electrons spend, on average,
more of their time far away from each, the two molecules experience a small attractive dipolar electrostatic
attraction. This only comes into play at short distances, with the energy falling off as the inverse sixth power
of the distance apart. The resultant attractive force, countering the simple repulsion, is known as a dispersion
force, or more commonly as the van der Waals attraction. It is responsible, for example, for the weak force
that keeps liquid hydrocarbons in the liquid state, and that helps them to aggregate in polar solvents. In liquid
helium, at very low temperatures, the only attractions holding the atoms together are van der Waals forces.
We saw correlation earlier on p. 5, when we learned that two electrons can be placed into one orbital,
provided, of course, that their spins are opposed. The correlated movement of the electrons within that orbital
keeps them, on average, far apart but there is an energetic penalty from putting a second electron into an
orbital already singly occupied. The electron correlation reduces the severity of the penalty, and is often
needed in calculations to get the right answers. In the same way, van der Waals interactions often have to be
invoked when calculations based on molecular orbitals and dipolar effects do not explain all the attractions or
repulsions found in practice.
2.5.4.4 p-p Interactions and p Stacking.218 Aromatic rings show an aptitude to aggregate that is not
simply explained by van der Waals attractions. The phenomenon shows up in such important areas of
molecular recognition as the stacked interactions between bases within the DNA double helix, in intercalation by drugs and carcinogens into the DNA stack,219 in the aggregation of the chlorin rings in the
chloroplast, in the tertiary structure of proteins, and in many host–guest supramolecules. We have already
seen one way in which they aggregate, edge-to-face 2.181, but a face-to-face stacking arrangement is not
uncommon. However, a stack of nonpolar aromatic rings perfectly lined up directly on top of each other is
straightforwardly repulsive (Fig. 2.27a)—one p system repels the other, whether one sees it as the interactions of filled orbitals with other filled orbitals, or as one negatively charged p cloud repelling another. The
van der Waals attractions are not powerful enough on their own to stabilise this arrangement, but aromatic
rings stacked above one another do find a stable arrangement when one p system is offset relative to the other
(Fig. 2.27b). With the p system of one molecule lying over the edge of the one below, there is an electrostatic
attraction from the positively charged framework with the negatively charged p cloud, especially since the
positive charge is largely on the peripheral and therefore exposed hydrogen atoms.220 This electrostatic
attraction can only come into play in a stack if the rings are offset. The van der Waals forces are proportional
to the area of contact and are weakened by the offset, so a balance is struck by a degree of offset that can be
estimated using an electrostatic model. p Stacking is more common with the larger aromatic systems like
porphyrins, probably because of the greater area for the van der Waals forces to work on, than they are with
simple benzenes, where the arrangement 2.181 and the offset p stack are close in energy.221
negative charge
H
H (C C C C)n H
positive charge
negative charge
H
H
negative charge
repulsion
≡
positive charge
repulsion
H
positive charge
negative charge
H
H
negative charge
(a) Face-to-f ace
attraction
attraction
negative charge
H (C C C C)n H
H
negative charge
stacks
positive charge
H
negative charge
(b) Of f set
stacks
Fig. 2.27 p Stacking
A simple example is found in the crystal packing of [18]annulene 2.189, where the p system of one molecule
lies over the cavity of the molecule below it.222 In the other dimension, not shown, the hydrogen atoms at the
2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES
125
edge of one ring point at the p system of another, as in 2.181. Electron-donating or electron-withdrawing
substituents, or heteroatoms in the aromatic rings, shift the electron distribution, introducing stronger or
opposing electrostatic effects. This can be seen in the crystal packing of tetramethyl-benzoquinone 2.190,223
and in the 1:1 complex 2.191 between 1,2,4,5-tetracyanobenzene and naphthalene.224 In these stacks, areas
of electron deficiency lie above areas of electron excess, achieved in the one case 2.190 by the uneven
distribution of electrons within the one molecule, and in the other case 2.191 by alternating electron-rich and
electron-deficient rings in the stack. In extreme cases like these, the offset is no longer needed for
electrostatic attractions to hold the two planes together, but an offset is still common with many systems,
including those with donor and acceptor substituents like the 1:1 complex between 1,2,4,5-tetracyanobenzene and N,N,N0 ,N0 -tetramethyl-1,4-diaminobenzene.225 No one has looked at the crystal packing in 1,3,5triazene 2.192, but it is a fair guess that it would stack one ring above the other, but with the nitrogen atoms,
carrying an excess of negative charge, directly above the carbon atoms, carrying an excess of positive charge.
O
NC
N
CN
O
O
NC
N
N
CN
O
2.189
2.190
2.191
2.192
Probably the most striking example of a stack of alternating electron-rich and electron-poor benzene rings is
in a 1:1 mixture of benzene and hexafluorobenzene.226 Each of these compounds on its own lines up edge to
face, as in 2.181 and Fig. 2.28a, but the 1:1 mixture stacks face to face with alternating benzene and
hexafluorobenzene rings as in Fig. 2.28b. The simple electrostatic model for the stack explains how the
negatively charged benzene ring is directly above and below the positively charged hexafluorobenzene ring,
and the negatively charged fluorine atoms are above and below the positively charged hydrogen atoms.
Neither compound has a dipole moment, and yet they attract one another electrostatically because of their
high electric quadrupole moments of opposite sign. There is no need to think of them as charge transfer
complexes. The mixture melts 20 °C higher than either of the pure compounds, which is not what usually
happens with a mixture.
(a) Edge-to-f ace stacks
seen in the crystal structures of
benzene and hexaf luorobenzene
Fig. 2.28
(b) Face-to-f ace stacks
seen in the crystal structure of a 1:1 mixture
of benzene and hexaf luorobenzene
Edge-to-face stacking and face-to-face stacking
3
3.1
Chemical Reactions—How Far and
How Fast
Factors Affecting the Position of an Equilibrium
All the attractive and repulsive forces discussed at the end of the preceding chapter, from van der Waals
forces, through hydrogen bonding and other electrostatic effects, to the interactions of the molecular orbitals,
affect not only the shape a molecule adopts within itself but also how favourably it can interact with another
molecule, as indeed we saw in the stacking of aromatic rings in the last few examples. Most of these
interactions, the repulsive forces that help molecules to retain their identity, and the attractive forces, like the
van der Waals forces and hydrogen bonding, that allow them to come close, do not necessarily lead to
reaction. They are important in determining a favourable alignment of two molecules, and hence the
stereochemistry of approach, but for insight into the nature of the events leading to reaction and to
the sources of reactivity, we need to look further, first to find whether two molecules colliding can possibly
create one or more molecules lower in energy than the starting materials—the thermodynamics—and then
whether there is an energetically accessible pathway between the starting materials and the products—the
kinetics. We shall now examine the interactions that lead beyond mere association to chemical reaction, and
begin to find out what factors influence chemical reactivity.
Straightforwardly, a reaction may take place if the total free energy of the starting materials is higher than
the total free energy of the products. There may or may not be a barrier to such a reaction, but that we shall
come to later. As far as feasibility is concerned, we can simply measure experimentally the energy content of
both sides of the reaction, and this will give us the answer. This is useful in all sorts of ways, but what we
want now is some understanding of why the numbers come out the way they do. Thus we can understand
easily enough that the reaction between bromine and ethylene giving dibromoethane is exothermic—it
replaces one p bond (C¼C) with two bonds (C—Br) at the expense of a weak bond (Br—Br). Organic
chemists deduce from this that bromine is a reactive molecule, and allow their knowledge of this and
hundreds of other reactions to inform their sense of which reactions are likely to be feasible and which are
less likely. Factors such as cancellation of charge, improved solvation, the creation of conjugation, in all its
manifestations, and especially aromaticity, and relief of steric repulsions can all be handled in this empirical
way to make sense of the direction reactions are seen to go in.
However, it is not always obvious how strong the bond will be when one molecule combines with another
to form a single new molecule, or what happens to the energy if we exchange parts of one molecule with parts
of another. A useful addition to understanding this sort of problem has been Pearson’s concept of hard and
soft acids and bases (HSAB). It does not replace other perceptions, or conflict with them, but in several
systems it has provided useful extra insight.
Molecular Orbitals and Organic Chemical Reactions: Reference Edition
© 2010 John Wiley & Sons, Ltd. ISBN: 978-0-470-74658-5
Ian Fleming
128
3.2
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
The Principle of Hard and Soft Acids and Bases (HSAB)227
Lewis acids and bases (including Hþ and OH) can be classified as belonging, more or less, to one of two
groups, one called hard and the other called soft. The striking observation is, and this is the basis of the
classification, that hard acids form stronger bonds with hard bases, and soft acids form stronger bonds with soft
bases. For example, a hard acid like the proton is a stronger acid than the silver cation, Agþ, when a hard
base like a hydroxide ion is used as the reference point; but if a softer base like iodide ion had been used, we
would have come to the opposite conclusion. This situation is summarised in the rule: hard-likes-hard and softlikes-soft, introduced, at first into inorganic chemistry,228 but later into organic chemistry as well.229 What it
amounts to is that the equilibrium in Equation 3.1 lies to the right, where H equals hard and S equals soft.
H-Acid : S-Base þ S-Acid : H-Base Ð H-Acid : H-Base þ S-Acid : S-Base
3:1
Pearson’s classification and rank ordering of acids and bases was intended to simplify and illuminate the
problem but it did not, and at that stage was not intended to explain it or give it a quantitative basis. It has proved
to be a durable idea, and furthermore has now been placed, first by Klopman,230,231 and more thoroughly by
Pearson and by Parr,232,233 on a sounder theoretical basis. At its most simple,231 we look at the equilibrium
between a Lewis acid and a Lewis base and the salt they form. The position of the equilibrium is affected both
by charge and by orbital interactions. In outline, it seems that a hard acid bonds strongly to a hard base by
electrostatic interactions. Hard acids and bases have the HOMO of the base and the LUMO of the acid far apart
in energy. This leads, as we saw in Fig. 1.60, to an ionic bond with little overlap, and we can associate the
strength of the bond with the value Ei on that diagram (see p. 53). Also, the smaller the ion or molecule, the
harder it is, because the charges can get closer in the ionic bond, which is Coulombic in nature. A high positive
charge on the acid and a high negative charge on the base will also contribute to the strength of the ionic bond.
However, a soft acid bonds strongly to a soft base because the orbitals involved are close in energy. As we saw
in Figs. 1.3 and 1.20, we get the maximum overlap for covalent bonding when the interaction is between
orbitals of similar energy, and we can associate the strength of the bond with the value E in Fig. 1.3. We can
also see that in practice we shall not often have pure hardness and pure softness in our acids and bases; rather,
there is a continuum, and the C—Cl bond in Fig. 1.58 is a case where the bond strength comes from both types
of interaction. In summary, a hard acid is small, has a high positive charge and a high-energy LUMO, and a
hard base is small, has a high negative charge and a low-energy HOMO. The smaller the ion, the higher the
charge and the higher the energy of the LUMO of an acid, the harder it is as an acid. Similarly, the smaller the
ion, the higher the charge and the lower the energy of the HOMO of a base, the harder it is as a base. Thus a
proton is a hard acid and the silver cation is soft; a fluoride ion is a hard base and an iodide ion is soft.
To go into this idea in more detail, and quantitatively,232 we need definitions of hardness and softness, and
we shall want to rank acids and bases on scales of hardness. This has been done in two ways: one related to
ideas we have already used in molecular orbital theory; and the other based on density functional theory. The
former is perhaps the more accessible, but both provide useful insights.
We define two parameters. One is called the absolute electronegativity, w, and is approximately the same
as electronegativity as Mulliken originally defined it for atoms, namely the average of the ionisation
potential I and the electron affinity A (Equation 3.2). The other is called the absolute hardness, ,234
which is identified with the difference in energy between the ionisation potential I and the electron affinity
A (Equation 3.3). [In earlier versions of Equation 3.3 the term (I – A) was divided by 2 to make the two
equations similar, but it is best left out.]
ðI þ A Þ
2
3:2
¼ ðI AÞ
3:3
¼
3 CHEMICAL REACTIONS—HOW FAR AND HOW FAST
129
Hardness in this definition is therefore identical to the energy change for the reaction in Equation 3.4. The
species R has zero hardness when this disproportionation has no change in energy. This also identifies the
maximum degree of softness, which is therefore defined as the reciprocal of hardness. This definition fits
the earlier qualitative approach to explaining hardness and softness as being associated with polarisability—
those species with a large difference between I and A were the ones that were not easily polarised.
R þ R ! Rþ þ R
3:4
The relationship between the two parameters and w is expressed graphically in Fig. 3.1, using Koopman’s
theorem that the ionisation potential is the negative of the energy of the HOMO and the electron affinity is
the negative of the energy of the LUMO. The figure shows the starting materials and products of two
reactions: the combination of a methyl radical with a fluorine atom on the left and with an iodine atom on the
right. The ionisation potential and electron affinity data, which are taken from Table 3.1, are the negatives of
the energies used in an orbital energy graph like that in Fig. 3.1.
–6.2
6
CH3F
4
2
0
0.08
CH3
0.08
–2
F
0.20
– 3.2
3.40
–4
CH3I
CH3
3.06
– 4.96
I
– 4.9
– 4.96
–6
– 6.76
9.74
–8
–10
9.74
9.82
– 10.41
–12
18.7
9.82
9.50
10.45
CH3
12.5
+
9.30
7.39
I
CH3I
–14
14.02
–16
eV
Fig. 3.1
17.42
CH3
+
F
CH3F
Orbital energies for the reaction of a methyl radical with fluorine and iodine atoms
It is not yet a well established concept in organic chemistry, but it appears that there is a principle of
maximum hardness,235 which says that reactions take place in the direction that increases hardness. We can
use the two reactions in Fig. 3.1 to see how this works. The hardness of a pair of starting materials is
measured by taking the smaller value of I and the more positive value of A, and using Equation 3.3. The
combination of a methyl radical and a fluorine atom has a change from ¼ 9.82 3.40 ¼ 6.42 to ¼ 18.7,
whereas the combination of a methyl radical with an iodine atom has a change from ¼ 9.82 3.06 ¼ 6.76
to ¼ 9.30. Thus the former is the reaction with the greater increase in hardness, with methyl fluoride a very
hard molecule, and is the more exothermic reaction.
The second approach to defining the absolute hardness has a companion parameter taken from density
functional theory, called the electronic chemical potential m. The value of m is essentially the same as the
negative of w, as defined in Equation 3.2, and the value of is essentially the same as in the more
approximate definition in Equation 3.3 but both are defined differently. If the total electronic energy of an
atom or molecule is plotted as a function of the total number of electrons N, the graph takes the form of
Fig. 3.2 in which the only experimental points are at integral values of N but between them it is convenient to
130
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
Table 3.1 Absolute hardness (in eV) for some radicals232
Radical
F
H
OH
NH2
HO2
CN
CHO
Me
Cl
NO
Et
PH2
Br
SH
Ph
I
17.42
13.59
13.17
11.40
11.53
14.02
9.90
9.82
13.01
9.25
8.38
9.83
11.84
10.41
8.95
A
3.40
0.74
1.83
0.74
1.19
3.82
0.17
0.08
3.62
0.02
0.39
1.25
3.36
2.30
0.10
w
10.41
7.17
7.50
6.07
6.36
8.92
5.04
4.96
8.31
4.63
4.00
5.54
7.60
6.40
5.20
14.02
12.85
11.34
10.66
10.34
10.2
9.73
9.74
9.39
9.23
8.77
8.58
8.48
8.11
8.85
Radical
CH2¼CH
CF3
Pri
NO2
MeCO
SeH
I
But
CCl3
PhCH2
SiH3
PhO
PhS
SiCl3
Li
I
8.95
9.25
7.57
>10.10
8.05
9.80
10.45
6.93
8.78
7.63
8.14
8.85
8.63
7.92
5.39
A
0.74
>1.10
0.48
2.30
0.30
2.20
3.06
0.30
1.90
0.88
1.41
2.35
2.47
2.50
0.62
w
4.85
>5.18
3.55
>6.20
4.18
6.00
6.76
3.31
5.35
4.26
4.78
5.60
5.50
5.20
3.00
8.21
<8.15
8.05
>7.80
7.75
7.60
7.39
7.23
6.88
6.75
6.73
6.50
6.16
5.42
4.77
draw a smooth curve. Starting at the neutral point, the addition of an electron can only lower the energy by a
small amount, if anything, and further additions of electrons will probably not be possible, so the curve
flattens out. Taking an electron out of the system will cause a large rise in energy, and it will be harder still to
take more electrons out, so the curve will rise steeply. This picture matches ordinary chemical experience.
The absolute electronegativity is now defined by Equation 3.5, which is the negative of the slope of the
E vs. N curve. This is a continuous function, which allows for nonintegral electron populations, a familiar
concept in organic chemistry. The absolute hardness is then defined as the second integral of the same curve
in Equation 3.6, which is therefore the curvature.
qE
¼
3:5
qN
¼
1
2
q2 E
qN 2
3:6
Table 3.1 gives experimental ionisation potentials and electron affinities for a range of radicals, together with
the absolute hardness and electronegativity calculated from them using Equations 3.2 and 3.3. Table 3.2 does
the same for some molecules.
A useful perception revealed in these tables is that a soft ligand on a hard atom will soften it. (Compare
CF3 with CCl3 in Table 3.1, or BF3 and BCl3 in Table 3.2.) The soft ligand will be effective in transferring
electrons to the central atom, moving it down the curve of Fig. 3.2, and flattening the curvature. This is very
much in line with experience. Lewis acids with electronegative ligands like fluoride and chloride are strong
Lewis acids towards hard bases, because they are themselves harder. It had not been obvious before why
substituents have such a profound effect on the hardness of the reacting atom.
When we come to bases we meet a difficulty—many bases are anions, and are therefore at the foot of the
graph in Fig. 3.2, with a slope and curvature too close to zero to be useful. As a base acts, electrons are
transferred and the curvature becomes larger, so we must choose a point on the graph to reflect this feature.
The choice used to create the data in Table 3.3 is to take the point where one electron has been transferred
from the base, defining the I and A values as those for the base minus one electron. This gives the elemental
3 CHEMICAL REACTIONS—HOW FAR AND HOW FAST
131
Table 3.2 Absolute hardness (in eV) for some molecules232
Molecule
I
A
w
HF
CH4
BF3
H2O
MeF
N2
CO2
H2
NH3
HCN
HCl
Me2O
CO
MeCN
MeCl
MeNH2
HCCH
SiH4
PF3
HCO2Me
Me3N
CH2¼CH2
H2S
AsH3
Me2S
PH3
O2
CH2¼O
16.0
12.7
15.8
12.6
12.5
15.58
13.8
15.4
10.7
13.6
12.7
10.0
14.0
12.2
11.2
9.0
11.4
11.7
12.3
11.0
7.8
10.5
10.5
10.0
8.7
10.0
12.2
10.9
6.0
7.8
3.5
6.4
6.2
2.2
3.8
2.0
5.6
2.3
3.3
6.0
1.8
2.8
3.7
5.3
2.6
2.0
1.0
1.8
4.8
1.8
2.1
2.1
3.3
1.9
0.4
0.9
5.0
2.5
6.2
3.1
3.2
6.70
5.0
6.7
2.6
5.7
4.7
2.0
6.1
4.7
3.8
1.9
4.4
4.8
5.7
4.6
1.5
4.4
4.2
4.0
2.7
4.1
6.3
5.0
22.0
20.5
19.3
19.0
18.7
17.8
17.6
17.4
16.3
15.9
16.0
16.0
15.8
15.0
14.9
14.3
14.0
13.7
13.3
12.8
12.6
12.3
12.6
12.1
12.0
11.9
11.8
11.8
Molecule
Me3P
MeBr
Me2NCHO
MeCHO
Me3As
BCl3
SO2
CCl4
Me2CO
CH2¼CHCN
SO3
O3
MeNO2
HI
benzene
HNO3
pyridine
butadiene
CS2
PCl3
:CH2
MeI
Cl2
PhCH¼CH2
PBr3
Br2
S2
I2
E
I
A
w
8.6
10.6
9.1
10.2
8.7
11.6
12.3
11.5
9.7
10.91
12.7
12.8
11.13
10.5
9.3
11.03
9.3
9.1
10.08
10.2
10.0
9.5
11.6
8.47
9.9
10.56
9.36
9.4
3.1
1.0
2.4
1.2
2.7
0.33
1.1
~0.3
1.5
0.21
1.7
2.1
0.45
0.0
1.2
0.57
0.6
0.6
0.62
0.8
0.6
0.2
2.4
0.25
1.6
2.6
1.66
2.6
2.8
4.8
3.4
4.5
3.0
5.97
6.7
5.9
4.1
5.35
7.2
7.5
5.79
5.3
4.1
5.80
4.4
4.3
5.35
5.5
5.3
4.9
7.0
4.11
5.6
6.6
5.51
6.0
11.7
11.6
11.5
11.4
11.4
11.3
11.2
11.2
11.2
11.1
11.0
10.7
10.7
10.5
10.5
10.5
9.9
9.7
9.5
9.4
9.4
9.3
9.2
8.7
8.3
8.0
7.7
6.8
neutral
N
Fig. 3.2
The electronic energy E as a function of the total number of electrons N
132
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
Table 3.3
Absolute hardness (in eV) for some bases232
Base
I Bþ
ABþ
Base
IBþ
ABþ
B
F
H2O
NH3
H
CO
OH
NH2
CN
H2S
17.42
26.6
24.0
13.59
26.0
13.0
11.3
14.2
21§
3.40
12.6
10.2
0.75
14.0
1.83
0.74
3.6
10.5
14.02
14.0
13.8
12.84
12.0
11.17
10.56
10.6
10.5
PH3
N3
Cl
NO2
ClO
Br
SH
Me
I
20.0
11.6
13.01
12.9
11.1
11.84
10.4
9.82
10.45
10.0
1.8
3.62
3.99
2.2
3.36
2.3
1.8
3.06
10.0
9.8
9.39
8.91
8.9
8.48
8.1
8.02
7.39
Table 3.4 Absolute hardness (in eV) for some acids232
Acid
IA
AA
wA
A
Acid
IA
AA
wA
A
Hþ
Al3þ
Liþ
Mg2þ
Naþ
Ca2þ
Fe3þ
Rbþ
Zn2þ
Tl3þ
Cu2þ
1
120.0
75.6
80.1
47.3
51.2
56.8
27.5
39.7
50.7
36.8
13.59
28.4
5.39
15.03
5.14
11.87
30.6
4.18
17.96
29.8
20.29
1
74.2
40.5
47.6
26.2
31.6
43.7
15.8
28.8
40.3
28.6
1
91.6
70.21
65.07
42.16
39.33
26.2
23.32
21.74
20.9
16.51
Hg2þ
Agþ
CO2
Pd2þ
Cuþ
AlCl3
SO2
Brþ
Cl2
Iþ
I2
34.2
21.5
13.8
32.9
20.3
12.8
12.3
21.6
11.4
19.1
9.3
18.75
7.57
0.0
19.42
7.72
~1
1.1
11.8
2.4
10.5
2.6
26.5
14.6
6.9
26.2
14.0
6.9
6.7
16.7
6.9
14.8
6.0
15.45
13.93
13.8
13.48
12.58
11.8
11.2
9.8
9.0
8.6
6.7
anions like fluoride ion the same values as the fluorine atoms in Table 3.1. The same problem does not arise
for acids in Table 3.4, because they start off further up the curve, and the normal definition works. These
tables give a sense of the large trends, and match the simple version in that the small, charged and
electronegative fluoride ion can be seen to be hard, while the large, uncharged and not strongly electronegative hydrogen sulfide is soft. Similarly, the small, charged proton or the lithium cation can be seen to be
hard, while the large silver cation and the uncharged sulfur dioxide are soft.
A problem interpreting the numbers in Tables 3.3. and 3.4, which are for the gas phase, is that ions in
practice are solvated—heavily so in polar solvents. Thus ions are not carrying their full charge but
substantially sharing it with solvent. The same goes especially for the infinitely hard bare proton, which is
never involved in solution chemistry. In fact, all the data for H, the radical, anion and cation, are unreliable—
hydrogen is a special case.
To overcome the problem with the charges on acids and bases, we can be less ambitious, and make more
restricted comparisons of acidity and basicity.233 To obtain a useful quantitative measure of the hardness of
acids and bases, we apply the concept in Equation 3.1 to the acid:base exchange reaction in Equation 3.7,
which will take place from left to right if A1 and B1 are the harder acids and bases relative to A2 and B2.
A1 : B2 þ A2 : B1 Ð A1 : B1 þ A2 : B2
3:7
3 CHEMICAL REACTIONS—HOW FAR AND HOW FAST
133
We would like to know the bond strengths of A:B with respect to separation into the free acid and the free
base. This only takes us back to the same problem, so we avoid it, since only comparisons will be made, by
using the better documented gas-phase bond dissociations D for separation into the pair of radicals A and B.
For monovalent Lewis acids, we can then take a pair of reference monovalent bases, such as fluoride ion and
iodide ion, one hard and one soft, and for which there are plenty of data. We use the reaction in Equation 3.8
to define the scale of local hardness at the atom in the bond we are using by the difference DFI using
Equation 3.9.
A1 —I þ A2 —F Ð A1 —F þ A2 —I
3:8
DFI ¼DAF – DAI
3:9
The results of these calculations give the scale of local hardness for a range of cations in Table 3.5—the
larger the value of DFI the harder the acid. These numbers allow us to calculate the equilibrium energy for
the competition in Equation 3.8. Thus an extreme case is the equilibrium in Equation 3.10, which is
exothermic by 335 kJ mol1 (80 kcal mol1). The products can be seen as more stable than the starting
materials, not because of any special bonding, but because of the correct matching of hard-with-hard and
soft-with-soft.
335kJmol—1
H3 Si—I þ HO—F Ð H3 Si—F þ HO—I
Table 3.5
Acid
CF3þ
SiH3þ
MeCOþ
CHOþ
Hþ
Phþ
Butþ
CH2¼CHþ
Liþ
Naþ
Priþ
Etþ
DAF
543
619
502
510
568
518
451
497
573
514
447
447
3:10
Empirical hardness (in kJ mol1) for some cationic acids233
DAI
226
301
209
217
297
268
209
263
343
288
222
222
DFI
318
318
293
293
272
251
242
234
230
226
226
226
Acid
CH2¼CHCH2
Meþ
c-C3H5þ
Tlþ
CNþ
NOþ
Csþ
Iþ
Cuþ
Agþ
HOþ
þ
DAF
DAI
DFI
410
456
464
439
468
234
493
280
426
351
217
184
234
247
268
305
84
343
150
314
251
234
226
222
217
171
163
150
150
130
113
100
-17
There appears to be an anomalous order for the alkyl cations, which have decreasing hardness in the order
But > Pri > Et > Me. With the charge expected to be more spread out in the more-substituted cation, one
would have expected the reverse order. The problem is that this applies only to the p energy, delocalised by
hyperconjugation. With the carbon 2s orbital being more electronegative than a hydrogen 1s orbital (Section
1.7.1), the lowest energy molecular orbital for a methyl group has the higher electron population on the
carbon atom, and replacing the hydrogen atoms with alkyl groups actually moves the total electron
population away from the central carbon atom.
The reference acids that Pearson used to estimate the local hardness of bases are the hard proton and the
soft methyl cation. They do not have as large a spread of hardness as the fluoride ion and iodide ion, but the
134
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
Table 3.6
Empirical hardness (in kJ mol1) for some anionic bases233
Base
DHB
DMeB
DHMe
Base
F
OH
AcO
PhO
NH2
NO3
MeO
HO2
NCS
Cl
Br
ONO
SH
O2N
PhNH
PhCH2
I
PrnS
Me
PhS
568
497
443
364
447
426
435
368
401
431
368
326
380
<326
368
368
297
364
439
347
456
385
347
268
355
334
347
288
322
355
293
251
309
255
297
301
234
301
376
288
113
113
96
96
92
92
88
79
79
75
75
75
71
<71
71
67
63
63
63
59
Et
SeH
AsH2
NCCH2
MeCOCH2
CH2¼CHCH2
NC
PH2
Ph
Pri
CH2¼CH
But
HCC
SiH3
MeCO
CF3
GeH3
CN
H
DHB
DMeB
DHMe
410
330
314
389
410
359
460
364
464
397
481
385
543
380
401
443
364
518
435
355
280
263
339
359
309
410
318
418
351
439
343
510
355
380
422
347
510
439
54
50
50
50
50
50
50
46
46
46
42
42
33
25
21
21
17
8
4
data are abundant, allowing Equations 3.11 and 3.12 to create the scale in Table 3.6. A few of the anions are
ambident, a topic that we shall return to in the next chapter. They are the nitrite ion and cyanide ion, for which
two values are given, a harder value for bonding to the more electronegative element and a softer value for
bonding to the less.
Me—B1 þ H—B2 Ð H—B1 þ Me—B2
3:11
DHMe ¼ DHB – DMeB
3:12
The trends in these tables are useful, although the numbers may be less so, because there are situations where
the principle of HSAB does not work well. Some of these are easily recognisable:236
1. When both the acid and the base are intrinsically very strong, the strength can overcome the contribution
of hardness and softness to an equation like Equation 3.7.
2. When some form of bonding is possible in one of the combinations but not the other. Thus, p bonding is
possible from a methyl group (by hyperconjugation) but not from a proton, exaggerating the softness of
those anions, like cyanide, trifluoromethyl, phenyl, vinyl and acetyl, able to indulge in it.
3. There is a significant entropy change.
4. When solvation in one of the combinations is exceptionally better than the other.
5. When there are multiple sites of bonding, as with chelating (bidentate) ligands.
We shall return to the concepts of hardness and softness when we come to discuss kinetics, since it is there
that we shall use them most tellingly.
3 CHEMICAL REACTIONS—HOW FAR AND HOW FAST
3.3
135
Transition Structures
In order to approach the problem of chemical reactivity, let us imagine two molecules which are about to
combine with each other in a simple, one-step, exothermic reaction leading to two possible products A and B
(Fig. 3.3a). We shall assume that we know the energies of the starting materials and the two products.
Chemists have long appreciated that the more exothermic reaction, that leading to the product B, is usually
the faster—it has been called the rate-equilibrium relationship, and is related to the reactivity-selectivity
principle.237 The explanation is easy enough—whatever features lead the product B to be lower in energy
than the product A will have developed in the transition structure to some extent. Thermodynamics does
affect kinetics—a source of endless confusion.
Because it is not always true, nor is it enough, we need to know more about what else affects the energy of
the transition structure. We bear in mind that influences from both sides of the reaction coordinate affect the
transition structure. Perturbation theory238 gives us one way to learn something about the reactant side—we
treat the interaction of the molecular orbitals of the two components as a perturbation on each other.
The perturbation is similar to that which leads to bonding and antibonding orbitals in interaction diagrams
like those in Chapter 1, where two separate orbitals interact to create molecular orbitals. However, as the
perturbation increases, it ceases to be merely a perturbation, and the mathematical basis of the theory fails to
be able to accommodate so large a change. We do not, therefore, have direct access to a good picture of the
transition structure in this way; nevertheless, we do get an estimate of the slope of an early part of the path
along the reaction coordinate leading up to the transition structure (labelled path A and path B in Fig. 3.3a).
Unless something unusual happens nearer the transition structure, the slopes will probably predict which of
the two transition structures is the easier to get to—on the whole, the steeper path is likely to lead to the
higher-energy transition structure.
Transition structure A
Transition structure B
Path A
Path B
Transition structure B
Path A
Path B
Transition structure A
Curve crossing
Starting
materials
Starting
materials
Product A
Product A
Product B
Product B
(a) Thermodynamics and kinetics in concert
(b) Thermodynamics and kinetics in opposition
Fig. 3.3 The energy along two possible reaction coordinates
The situation shown in Fig. 3.3a is the common one: the higher-energy transition structure leads to the
higher-energy product, and the better orbital interaction matches it. However, there are some situations
where this is not so, where there is a crossing of the curves (Fig. 3.3b). Some of the most interesting
mechanistic problems arise when the more exothermic reaction is not the faster—in other words, when
136
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
the thermodynamics and the kinetics do not go together. In these reactions, perturbation theory, which
looks at the reactant side of the reaction coordinate, offers some insight. If the orbital interaction for path
A is stronger than that for path B, as in Fig. 3.3b, it can help to explain the anomalous order of the two
transition structures. Hitherto organic chemists have more often concentrated on the product side, but we
now have a useful, and in some situations unique, tool for examining the reactant side of the reaction
coordinate.
The Hammond postulate says that the transition structure for an exothermic reaction (Fig. 3.4a) is closer in
energy to the energy of the starting materials, and so it has more of the character of the starting materials, or,
looking at the distances along the reaction coordinate, A<B. Equally, the transition structure for an
endothermic reaction (Fig. 3.4b) is product-like, for the same reason, and because B<A.239,240 We can
therefore expect that the nature of the products will be particularly influential in affecting the rates of
endothermic reactions (Fig. 3.4b), but that orbital interactions will be particularly influential in exothermic
reactions (Fig. 3.4a). More often than not, those reactions in which the thermodynamics do not control the
kinetics (Fig. 3.3b) are exothermic reactions—in agreement with the Hammond postulate, they are under the
influence of the reactants. We shall find that orbital interactions are especially powerful in giving some
insight into these anomalous reactions.
Starting
materials
Products
A
B
Products
B
Starting
materials
(a) An exothermic reaction, with a
reactant-like transition structure
Fig. 3.4
3.4
A
(b) An endothermic reaction, with a
product-like transition structure
The Hammond postulate
The Perturbation Theory of Reactivity
Now let us look at the perturbation which the reacting molecules exert upon each other’s orbitals. Let the two
reacting molecules have orbitals, filled and unfilled, as shown in Fig. 3.5. As the two molecules approach
each other, the orbitals interact, assuming that they have the right symmetry. Thus we can take, let us say, the
highest occupied orbital (HOMO) of the molecule on the left and the highest occupied orbital of the molecule
on the right and combine them in a bonding and an antibonding sense, just as we did when making a p bond
from two isolated p orbitals. The new molecular orbitals, in the centre of Fig. 3.5 will then be a first
approximation to two of the orbitals of the transition structure.
The formation of the bonding orbital is, as usual, exothermic (El), but the formation of the antibonding
orbital is endothermic (E2), because there are two electrons which must go into it. As in the attempt to form a
helium molecule from two helium atoms, the energy needed to force the molecules together in an antibonding combination is greater than that released from the bonding combination. This situation will be true for all
combinations of fully occupied orbitals, which all contribute to the normal repulsion experienced by one
molecule when it is brought close to another. This is a major contributor to the activation energy of any
3 CHEMICAL REACTIONS—HOW FAR AND HOW FAST
137
E2
HOMO
HOMO
E1
Fig. 3.5 The interaction of the HOMO of one molecule with the HOMO of another
reaction, and it is the basis for steric hindrance. Combinations of unfilled orbitals with other unfilled orbitals
will have no effect on the energy of the system, because without any electrons in them there is no energy to
gain or lose.
The interactions which do have an important energy-lowering effect are the combinations of filled orbitals
with unfilled ones. Thus, in Fig. 3.6a and Fig. 3.6b, we have such combinations, and in each case we see the
usual drop in energy in the bonding combination, and a rise in energy in the antibonding combination but
without effect on the actual energy of the system, because there are no electrons to go into that orbital. We
can also see in Fig. 3.6a that it is the interaction of the HOMO of the left-hand molecule and the lowest
unoccupied orbital (LUMO) of the right-hand molecule that leads to the largest drop in energy (2EA > 2EB).
The interaction of other occupied orbitals with other unoccupied orbitals, as in Fig. 3.6b, is less effective,
because the closer the interacting orbitals are in energy, the greater is the splitting of the levels (see p. 52).
Now we can see why it is the HOMO/LUMO interaction which we look at, and why these orbitals, the
frontier orbitals, are so important. The other occupied orbital/unoccupied orbital interactions contribute to
the energy of the interaction and hence to lowering the energy of the transition structure, but the effect is
usually less than that of the HOMO/LUMO interactions.
LUMO
HOMO
EA
EB
(a) The interaction of the HOMO with the LUMO
(b) The interaction of a lower f illed
MO with a higher unf illed MO
Fig. 3.6 The interaction of occupied orbitals of one molecule with unoccupied orbitals of another
138
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
The HOMO/HOMO interactions (Fig. 3.5) are large compared with the HOMO/LUMO interactions
(Fig. 3.6a)—both El and E2 in Fig. 3.5 are much larger than EA in Fig. 3.6. This is because HOMO/HOMO
interactions will usually be between orbitals of comparable energy, whereas the HOMO of one molecule and
the LUMO of another are usually well separated in energy. (In the mathematical form of perturbation theory,
the former are first-order interactions, whereas the latter are usually second order.) This will also be true of
many of the interactions of the other occupied orbitals on one compound with the occupied orbitals on the
other. Although the bonding (El) and antibonding (E2) interactions cancel one another out to some extent, the
net antibonding interaction between two molecules will be large—many such orbitals interact in this way, and
their interactions are first order. These interactions give rise to a large part of the activation energy for many
reactions. The second-order interactions, like those of Fig. 3.6, even though they are entirely bonding in
character and reduce the activation energy, are relatively small. The HOMO/LUMO interaction is merely the
largest of a lot of small interactions. We shall discuss this matter further in the next section, where we meet a
formidable looking equation, from which the strength of these interactions can be estimated quantitatively.
We might note that the separation of the interactions into pure filled-with-filled and pure filled-withunfilled, is similar to the way we examined how the orbitals interacted in setting up conjugated systems. We
saw on p. 31 that we could explain the stabilisation from having two p bonds conjugated in butadiene, by first
taking the filled-with-filled interactions, p with p, and p* with p*, and then modifying this large, and overall
energy-raising, effect with the smaller, but energy-lowering, effect from the interactions of filled-withunfilled orbitals, p with p*. There, where we were not talking about reactions, we used the language of
‘mixing in’ the character of one set of orbitals with another in a bonding or antibonding sense. Here we are
talking about reactions, and that language is inappropriate, even though the way we are using the idea is
similar.
3.5
The Salem-Klopman Equation
Using perturbation theory, Klopman230 and Salem241 derived an expression for the energy (DE) gained and
lost when the orbitals of one reactant overlap with those of another. Their equation has the following form:
X
DE ¼ –
ðqa þ qb Þab Sab
ab
|{z}
first term
þ
X
Qk Ql
k<l
"Rkl
|{z}
second term
þ
occ: unocc:
occ: unocc:
X
X X
X
–
r
s
s
2ðSab cra csb ab Þ 2
r
Er – Es
|{z}
3:13
third term
qa and qb are the electron populations (often loosely called electron densities) in the atomic orbitals a and b,
and S
Qk and Ql
"
Rkl
cra
Er
Es
are the resonance and overlap integrals in Equations 1.5 1.7,
are the total charges on atoms k and l,
is the local dielectric constant,
is the distance between the atoms k and l,
is the coefficient of atomic orbital a in molecular orbital r, where r refers to the molecular orbitals on one
molecule and s refers to those on the other
is the energy of molecular orbital r and
is the energy of molecular orbital s.
The derivation of this equation involves, as one might expect, many approximations and assumptions, which
we shall not go into. It is valid only because S will always be small for the overlap of orbitals of p character. The
integral S has the form shown in Figs. 1.13 and 1.23: for a C—C bond being formed by p orbitals overlapping in
a sense, it reaches a maximum value of 0.27 at a distance of 1.74 Å and then rapidly falls off. Thus, any
3 CHEMICAL REACTIONS—HOW FAR AND HOW FAST
139
reasonable estimate of the distance apart of the atoms in the transition structure cannot fail to make S small. The
integral is roughly proportional to S, so the third term of Equation 3.13 above is the second-order term. With S
always small, the higher-order terms are naturally very small indeed, and we neglect them. This is why a
second-order perturbation treatment works. Let us now look at each of the three terms of Equation 3.13.
(i) The first term is the first-order, closed-shell repulsion term, and comes from the interaction of the filled
orbitals of the one molecule with the filled orbitals of the other (as in Fig. 3.5). It is always antibonding in effect.
This term will usually be large relative to the other two terms—it represents a good deal of the enthalpy of
activation for many reactions. Apart from this, its main effect on chemical reactivity can probably be
identified with the well known observation that, on the whole, the smaller the number of bonds to be made or
broken at a time, in a chemical reaction, the better. If a reaction can take place in several, not too difficult
stages, it will probably go in stages, rather than in one concerted process. The concerted process, whatever it
is, must involve the making (or breaking) of more than one bond, and for every bond to be made (or broken),
we must have an energy-raising contribution from the first term of Equation 3.13. Another important reason
for the general preference for stepwise reactions is, of course, the much more favourable entropy term when a
relatively small number of events happen at once.
The interaction of a filled orbital with a filled orbital, as in Fig. 3.5, leads to a small antibonding effect, but
there are many filled orbitals interacting strongly with many filled orbitals, and the total effect is the sum of
many small ones. The overall effect of the first term of Equation 3.13 is, therefore, rather unpredictable, but it
seems that adding up a lot of small items very often averages out the total effect. Thus, if a molecule can be
attacked at two possible sites, we can hope that the first term will be nearly the same for attack at each site.
Similarly, if there are two possible orientations in a cycloaddition, the first term may not be very different in
the two orientations. This appears not to be the case for the other two terms, and it is therefore with them that
we shall mainly be concerned in explaining differential reactivity of this kind. In practice it is not obvious
that we can rely on a benign first term, but we often do, and we seem to be able to get away with it. We shall,
therefore, be largely ignoring the first term from now on, because frontier orbital theory is mainly used to
explain features of differential reactivity. We are on weak ground in doing so, and we should not forget it.
(ii) The second term is simply the Coulombic repulsion or attraction. This term, which contains the products
of the total charges, Q, on each atom, is obviously important when ions or polar molecules are reacting
together. Its contribution to the energy is inversely proportional both to the dielectric constant and to the
distance apart of the two charges.
(iii) The third term represents the interaction of all the filled orbitals with all the unfilled of correct symmetry
(Fig. 3.6). It is the second-order perturbation term, and is only true if Er 6¼ Es. (When Er ¼ Es, the interaction
is better described in charge-transfer terms, and the perturbation is then first order of the form Sab2cracsbab.)
Here we can see again, this time in simple arithmetical terms, that it is the HOMO and the LUMO which are
most important—they are the orbitals with the smallest value of Er Es, and hence they make a disproportionately large contribution to the third term of Equation 3.13.
In summary:
As two molecules collide, three major forces operate.
(i) The occupied orbitals of one repel the occupied orbitals of the other.
(ii) Any positive charge on one attracts any negative charge on the other (and repels any positive).
(iii) The occupied orbitals (especially the HOMOs) of each interact with the unoccupied orbitals
(especially the LUMOs) of the other, causing an attraction between the molecules.
140
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
*
*
3
3
LUMO
2
2
E1
HOMO
LUMO
E2
1
1
HOMO
(+)
(–)
allyl anion
interaction leading to
the transition structure
allyl cation
Fig. 3.7 Orbital interactions in the reaction of the allyl anion with the allyl cation
We are now in a position to apply these ideas to the components of a chemical reaction. Let us begin with a
negatively charged, conjugated system, like the allyl anion 3.1, reacting with a positively charged, conjugated
system, like the allyl cation 3.2. In this imaginary242 reaction, the major contributions to bond-making will be
the very powerful charge-charge interaction (the second term of Equation 3.13) and the very strong interaction
from the HOMO of the anion and the LUMO of the cation (E1 in Fig. 3.7). By contrast, the interaction of the
HOMO of the cation and the LUMO of the anion is much less effective (E2 in Fig. 3.7), because Er Es is
relatively so large. The allyl anion þ allyl cation reaction is most unusual because Er Es for the important
interaction of the HOMO of the anion with the LUMO of the cation. For this reason, the important frontier
orbital interaction is not typical—it is both very strong and first order, not second order like the third term of
Equation 3.13. Nevertheless, it provides a simple illustration of how the ideas behind Equation 3.13 work, and
it also shows how it comes about that in general the important frontier orbitals for a nucleophile reacting with
an electrophile are HOMO(nucleophile)/LUMO(electrophile) and not the other way round.
2
3
1
3
1
2
3.1
3.2
Having identified the causes for the ease of a reaction like this one, we must next use the ideas behind
Equation 3.13 to identify the sites of reactivity in each of the reacting species. To find the contribution of the
Coulombic forces, we need the total electron population on each atom, which we have already seen in
Fig. 1.35. For the allyl anion, the excess charge is concentrated on C-1 and C-3, and it is therefore here that
positively charged electrophiles will attack. For the allyl cation, the overall electron deficiency is
3 CHEMICAL REACTIONS—HOW FAR AND HOW FAST
141
concentrated on C-1 and C-3, where the electron population is lowest, and it is therefore here that a
negatively charged nucleophile will attack. Thus when the reaction takes place, the charge-charge
attraction represented by the second term of Equation 3.13 will lead C-1 (¼ C-3) of the allyl anion to
react with C-1 (¼ C-3) of the allyl cation, and C-2 will have little nucleophilic or electrophilic character.
When we add the contribution from the frontier orbitals, the picture is even more striking. The HOMO of
the anion has coefficients at C-1 and C-3 of – 0.707, and similarly the LUMO of the cation has coefficients
at C-1 and C-3 of þ0.707. In both frontier orbitals the coefficient on C-2 is zero. Thus the frontier orbital
term is overwhelmingly in favour of reaction of C-1 (C-3) of the anion with C-1 (C-3) of the cation. Only
the relatively ineffectual HOMO(cation)/LUMO(anion) interaction shows any profit in bonding at C-2 of
either component.
We have now seen how the attraction of charges and the interaction of frontier orbitals combine to make a
reaction between two such species as the allyl anion and allyl cation both fast and highly regioselective. We
should remind ourselves that this is not the whole story: another reason for both observations is that the
reaction is very exothermic when a bond is made between C-1 and C-1: the energy of a full bond is released
with cancellation of charge, which we could not easily do if reaction were to take place at C-2 on either
component. In other words, we find, as we often shall, that we are in the situation of Fig. 3.3a—the
Coulombic forces and the frontier orbital interaction on one side, and the stability of the product on the
other, combine to lower the energy of the transition structure.
Indeed, you may well feel that there was little point in looking at the frontier orbitals in a reaction like this,
where bonding between C-2 of the anion and C-2 of the cation to give an intermediate 3.3 would be
absurd:243
or
3.1
3.2
3.3
The purpose of doing so was two-fold: in the first place, it did show that we get the same answer by
considering the frontier orbitals as we do from the product development argument; and secondly, it showed
how the allyl anion and allyl cation are nucleophilic and electrophilic, respectively, at both C-1 and C-3
without our having to draw canonical structures.
One of the arguments for retaining valence bond theory has been the ease with which things like the
nucleophilicity of the allyl anion at C-1 and C-3 are explained by drawing the canonical structures. Even as
simple a version of molecular orbital theory as the one presented here does the job just as well. The
drawings chemists use for their structures will inevitably be crude representations—we shall always have
to make some kind of localised drawing, whether it is of a benzene ring, or an enolate ion, or whatever.
At the same time, we shall continue to make, as we already do, considerable mental reservations about how
accurately such drawings represent the truth. If our mental reservations are made within the framework of
the molecular orbital theory, we shall have a better and more reliable picture of organic chemistry at our
disposal.
3.6
Hard and Soft Nucleophiles and Electrophiles
The principle of HSAB has also been applied to kinetic phenomena.244,245 In this connection, organic
chemistry has provided most of the examples, because reactions in organic chemistry are often slow enough
for rates to be easily measured. In organic chemistry, and in ionic organic chemistry in particular, we are
generally interested in the reactions of electrophiles with nucleophiles. These reactions are a particular kind
142
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
of the general acid-with-base type of reaction, and so the principle of HSAB applies equally to the reactions
of electrophiles with nucleophiles.
Hard and soft acid and base theory gives access to an early part of the slope in a reaction profile like that in
Fig. 3.3, just as perturbation molecular orbital theory does. Using the definitions of absolute electronegativity and absolute hardness derived in Equations 3.5 and 3.6, the (fractional) number of electrons DN
transferred is given by Equation 3.14.
DN ¼
El Nu
2ðEl þ Nu Þ
3:14
This says that reaction will take place in the direction in which electrons flow from the species of lower
electronegativity w to the species with higher electronegativity, and the sum of the hardness values in the
denominator holds the reaction back. A large value of N implies a low energy barrier ahead, with the change
in energy given by Equation 3.15.
DE ¼
ðEl Nu Þ 2
4ðEl þ Nu Þ
3:15
This is because the harder a reagent, the less it will give its electrons up to covalent bond formation. A pure
hard-hard interaction, being Coulombic in nature, should offer no barrier to the association of the two
reagents. The barriers that do exist between oppositely charged (or partially charged) hard reagents are more
probably associated with the need to remove solvation, which is inevitably stronger with hard reagents than
with soft.246
The rates with which nucleophiles attack one electrophile are not necessarily a good guide to the rates with
which the same nucleophiles will attack other electrophiles, just as there is no single measure of thermodynamic acidity or basicity. Following the principle of HSAB, we categorise nucleophiles (bases) and
electrophiles (acids) as being hard or soft. Other things being equal, hard nucleophiles react faster with hard
electrophiles, and soft nucleophiles with soft electrophiles.
We can now return to Equation 3.13, which deals with the application of Coulombic effects and
molecular orbital interactions to reaction rates. Essentially, the second term of Equation 3.13 represents
the attraction between the two molecules from a hard-hard interaction, and the third term represents the
contribution to bonding from a soft-soft interaction. We saw from our consideration of the imaginary
reaction of the allyl anion (the base or nucleophile) with the allyl cation (the acid or electrophile) that the
important frontier orbital of a nucleophile is the relatively high-energy HOMO, and the important
frontier orbital of an electrophile is the relatively low-energy LUMO. Since hard reagents are characterised by having a large separation between the HOMO and the LUMO, hard nucleophiles (Tables
3.2, 3.3 and 3.6) are generally those which are negatively charged and have relatively low-energy
HOMOs—typically the anions centred on the electronegative elements. Likewise, hard electrophiles
(Tables 3.2, 3.4 and 3.5) are generally those which are positively charged and have relatively highenergy LUMOs, typically the cations of the more electropositive elements. Thus their reactions with
each other are fast because each makes a large contribution to the second term of Equation 3.13.
However, soft nucleophiles have high-energy HOMOs and soft electrophiles have low-energy
LUMOs, and their reactions with each other are fast because each makes a large contribution to the
third term of Equation 3.13.
To take a simple example, the hydroxide ion 3.4 is a hard nucleophile, at least partly because it has a
charge, and because oxygen is a small, electronegative element. Accordingly, it reacts faster with a hard
electrophile like the solvated proton 3.5 than with a soft electrophile like bromine 3.6. However, an alkene
3.7 is a soft nucleophile, at least partly because it is uncharged and has a high-energy HOMO. Thus it reacts
faster with an electrophile which has a low-energy LUMO, like bromine or the silver cation, than it does with
a proton.
3 CHEMICAL REACTIONS—HOW FAR AND HOW FAST
HO
H
3.4
OH2
3.5
Br
3.7
is f aster than
143
HO
Br
3.4
Br
3.6
H
is f aster than
3.6
Br
3.7
OH2
3.5
The rates of most reactions are affected by contributions from both terms of Equation 3.13, with one often
being more important than the other. It is important to realise, for example, that a hard nucleophile may react
faster with a soft electrophile than a soft nucleophile with the same soft electrophile. Thus the hydroxide ion
almost certainly reacts faster with the silver ion than ethylene does. This is because the hydroxide ion is, for
several reasons, more generally reactive than ethylene. Hardness and softness are most useful when they are
used to differentiate finer grades of reactivity.
In summary:
Hard nucleophiles have a low-energy HOMO and usually have a negative charge.
Soft nucleophiles have a high-energy HOMO but do not necessarily have a negative charge.
Hard electrophiles have a high-energy LUMO and usually have a positive charge.
Soft electrophiles have a low-energy LUMO but do not necessarily have a positive charge.
(i) A hard-hard reaction is fast because of a large Coulombic attraction.
(ii) A soft-soft reaction is fast because of a large interaction between the HOMO of the nucleophile
and the LUMO of the electrophile.
(iii) The larger the coefficient in the appropriate frontier orbital (of the atomic orbital at the reaction
centre), the softer the reagent.
3.7
Other Factors Affecting Chemical Reactivity
Of the many factors controlling chemical reactivity some are obviously involved in the derivation of
Equation 3.13, but some are not. Thus we are including the Coulombic factors which lead ions to react
faster with polar or oppositely charged molecules than with nonpolar or uncharged ones. We are also, at least
in part, including factors such as the strength of the bond being made (it affects ) and the strength of any
bond being broken (it affects Er and/or Es). The Woodward-Hoffmann rules are included in a sense, in that
we have to evaluate whether the overlap integral (S and hence ) is bonding or antibonding; however, it
would be easy to overlook this in a calculation. The loss of conjugation—for example, the loss of aromaticity
in the first step of aromatic electrophilic substitution—is partly taken account of. Thus, the low energy of 1
in benzene leads the value of Er – Es for that orbital to be much larger than if the aromaticity were not present.
The simpler HOMO/LUMO approach, however, makes no such allowance.
A number of other factors are either being ignored in this treatment or at least being underestimated. Strain
in the framework, whether gained or lost, is not included, except insofar as it affects the energies of those
orbitals which are involved. Factors which affect the entropy of activation are not included. Finally, steric
effects are ignored, because we are not using the first term of Equation 3.13. Fortunately, although chemists
in the 1950s had to be persuaded that steric effects were important in organic chemistry,247 that is hardly a
problem today—steric effects are more likely to be overemphasised than ignored.
144
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
We cannot, then, expect this approach to understanding chemical reactivity to explain everything. We
should bear in mind its limitations, particularly when dealing with reactions in which steric effects are likely
to be important, and in which solvent effects are involved. Solvent effects are well known, for example, to be
a large part of the explanation of ambident reactivity and other manifestations of the principal of HSAB.246
Some mention of all these factors will be made again in the course of this book. Arguments based on the
interaction of frontier orbitals are powerful, as we shall see, but they must not be taken so far that we forget
these important limitations.
Even more serious is the problem that most attempts to check the validity of frontier orbital theory by
calculation strongly indicate that the sum of all the interactions of the filled with the unfilled orbitals swamp
that from the frontier orbitals alone. Even though the third term of the Salem-Klopman equation is weighted
in favour of the frontier orbitals, quantitatively they do not account for the many features of chemical
reactions for which they seem to provide an uncannily compelling explanation. This problem has exercised
theoretical chemists mightily, with some success.248,249 Organic chemists, with a theory that they can handle
easily, have fallen on frontier orbital theory with relief, and comfort themselves with the suspicion that
something deep in the patterns of molecular orbitals must be reflected in the frontier orbitals in some
disproportionate way.
As an example of how seductive following the orbitals can be, let us look at a -elimination (Fig. 3.8). To
keep the orbitals simple, we use ethane, and the imaginary removal of a proton from one atom with a hydride
ion as the base and with (unrealistically) a hydride ion as a leaving group from the other to give ethylene.
Since both hydrogen atoms are actually leaving groups, we need words to describe which group leaves with
the electrons and which without—the proton is called the electrofuge, and the hydride the nucleofuge. The
appropriate frontier orbitals will be the HOMO of the nucleophile, the 1sH orbital of the hydride ion, and an
unoccupied molecular orbital of ethane (Fig. 1.22), but not in this case the LUMO, *X, because it has the
wrong symmetry to have anything to do with the formation of a p bond. The next orbitals up in energy are a
degenerate pair, with one of the pair (p*y0 ) having a node through the reaction centres, which means that it
cannot be involved. The other low-lying antibonding orbital (p*z0 ) is the unoccupied orbital that is most
suggestive of a -elimination, since it has antibonding C—H relationships, and a p-bonding relationship
between the two carbon atoms. The attacking hydride ion will move electrons into this orbital, ‘carrying the
system along the E2 reaction coordinate’.132 As the hydride nucleofuge leaves, the p bond of ethylene pz is
filled, reducing all the C—H bonding to zero and fully instating the C¼C p bond. In the face of such an
‘obviously’ important orbital, with the C—H bonds ready to break and the C¼C bond already visible, it is
difficult not to believe that it must play a large part in driving the reaction smoothly on. In practice, of course,
it needs a better nucleofuge than the hydride ion.
LUMO
H
H
H
1sH
Fig. 3.8
H
H
C
C
HOMO
H
H
H
H
*z'
H
C
C
H
H
H H
z
The p*z0 of ethane as a model for the -elimination of hydrogen
4
Ionic Reactions—Reactivity
Ionic reactions are the core of organic chemistry. Trying to understand them in electronic terms challenged
organic chemists from the 1920s onwards, beginning with Lapworth’s and Robinson’s brilliant early
perceptions, and crowned in the 1950s by R. B. Woodward, who, more than anyone else, showed how
mechanistic understanding could shape the thinking leading to a total synthesis of a complex molecule, and
illuminate the reactions used to investigate the structures of natural products. The task is never over—how
many times have you read that something is not yet fully understood? Nothing is ever fully understood.
However, the general outline of understanding has been in place for some time, guided by the principles that
pairs of electrons, illustrated with curly arrows, would flow from the less electronegative elements towards
the more electronegative, that p bonds would be more reactive than bonds, and that conjugation was
energy-lowering, especially if it was aromatic.
More recently, a fundamental re-evaluation is in progress. The problem is that it seems inherently unlikely
that pairs of electrons would act in concert: a pair of electrons in a single orbital spend as much time as far
away from each other as possible—the electrons are described as correlated.—so why would a pair of
electrons act together to move from one bond into another? It seems, somehow, more reasonable for them to
move one at a time. The transfer of one electron from one molecule to another is well known—it is the basis
for one-electron oxidation and one-electron reduction, with many examples in electrochemistry, in sodiumin-ammonia reductions, and in inorganic redox reactions—but is it a common pathway in ionic organic
chemistry, or something that only happens in favourable circumstances?
4.1
Single Electron Transfer (SET) in Ionic Reactions250
Let us look at the key steps in three of the most fundamental reaction types in ionic organic chemistry—the
SN2 reaction 4.1 ! 4.2, nucleophilic attack on an X¼Y double bond 4.3 ! 4.4, where X and Y may be any
combination of C, N, O or S, and electrophilic attack on a C¼C double bond 4.5 ! 4.6. A high proportion of
ionic organic chemistry is covered by these three reactions or their reverse. The standard formulation for the
first has the electron pairs moving in concert from the nucleophile into the Nu—C bond and the simultaneous
movement of the electrons in the C—X bond onto the leaving group. For nucleophilic attack on a p bond, a
lone pair or a p bond provides the electrons for a new bond Nu—X, and a pair of electrons from the p bond
move onto the atom Y which is the more electronegative, or the one better able to stabilise a negative charge.
The subsequent fate of the anion 4.4 will depend upon the rest of the structure. For electrophilic attack by a p
bond 4.5, the pair of electrons moves to make a bond to the electrophile, and leaves behind a carbocation
centre 4.6. The fate of this cation also depends upon the rest of the structure—the two most common fates
being the loss of a proton, when the p bond is part of an aromatic ring, or the capture of a nucleophile, when it
Molecular Orbitals and Organic Chemical Reactions: Reference Edition
© 2010 John Wiley & Sons, Ltd. ISBN: 978-0-470-74658-5
Ian Fleming
146
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
is isolated. For now, we are concerned with the first steps, the attack of the nucleophile or electrophile,
because, more often than not, these are rate-determining.
Nu
X
+
Nu
4.1
X
4.2
Nu
Nu
X
Y
X
4.3
Y
4.4
E
E
4.5
4.6
In the most simple alternative mechanism involving single electron transfer (SET), the two reagents in each
case, which may or may not come together in a loose association called a charge-transfer complex 4.7, 4.10
and 4.12, transfer one electron from the partner with the lower ionisation potential (higher-energy HOMO) to
the one with the higher electron affinity (lower-energy LUMO). In all three types of reaction, this creates a
pair of radicals 4.8, 4.11 and 4.13, which may or may not be charged, depending upon the charge carried by
each of the original reagents. In the SN2 case, the radical anion 4.8 can lose the halide ion X– to give the
radical 4.9. In all three cases, the radical pairs 4.9, 4.11 and 4.13 can be expected to combine together very
fast. Radical-radical couplings are rare, because radicals, usually created in low concentration, do not live
long enough to meet another radical but in this case two radicals are created as a pair within a solvent cage,
effectively in high concentration. With the concentration problem overcome, radical-radical couplings are
inherently fast, because they are so exothermic. It therefore follows that the rate-determining step is likely to
have been the transfer of the electron. At this stage the product 4.2, and the intermediates 4.4 and 4.6, are the
same as those in the conventional mechanism. Occasionally, an even slower step may be involved later on,
but, whatever the overall rate-determining step is, the radical coupling can be expected to be faster than the
electron transfer.
e-transfer
Nu
+
X
Nu
Nu
X
4.7
4.1
X
4.8
radical
X
Nu
Nu
coupling
4.9
4.2
e-transfer
Nu
+ X
Y
Nu
X
radical
Nu
Y
X
Y
Nu
X
Y
coupling
4.3
4.10
4.11
4.4
e-transfer
+ E
4.5
E
coupling
4.12
E
radical
E
4.13
4.6
4 IONIC REACTIONS—REACTIVITY
147
There is good evidence that some nucleophilic substitution reactions do involve a single electron transfer,
but the best established use a slightly different mechanism. These are the SRN1 reactions, with the subscript
RN standing for radical nucleophilic. Examples are the reaction of the nitronate anion 4.14 with pnitrobenzyl chloride 4.15, 251 and the reaction of the pinacolone enolate 4.16 with bromobenzene.252 The
former might have been a straightforward SN2 reaction, but actually takes the SRN1 pathway because the
nitro groups make the electron transfer exceptionally easy. The latter cannot take place by a conventional
SN2 reaction, because aryl (and vinyl) halides are not susceptible to direct displacement, and the SRN1
pathway overcomes this difficulty.
O
N
O
NO2
+
NO2
NO2
Cl
4.14
+
Cl
+
Br
4.15
O
O
+
Br
4.16
In more detail, SRN1 reactions begin with an initiation step in which an electron is transferred to the
electrophile R-X to give a radical anion R-X•–, which breaks apart to give the radical R• and the anion X–.
The radical R• combines with the nucleophile Nu– to give a radical anion R-Nu•–, and this transfers its
electron to the electrophile R-X, giving the product R-Nu and the radical anion R-X•–, making the sequence
cyclic and self sustaining. There is a further subtlety in which the departure of the nucleofugal group X– is
concerted with the electron transfer, in which case the radical anion R-X•– is no longer an intermediate but a
transition structure.
R-X
R-X
R
R-Nu
R-Nu
+
X
Nu
There is equally good evidence that some examples of nucleophilic and of electrophilic attack on a double
bond are preceded by charge-transfer complexation, with bonding resembling that of a Lewis acid-base
interaction, and that either heat or irradiation of the charge transfer complex can provide the energy needed
to transfer the electron from the donor to the acceptor. A charge-transfer species like 4.17 or 4.20 may or
may not be on the direct line for the reaction, but solvation effects, and selectivities in the coupling steps
like 4.18 ! 4.19 and 4.21! 4.22 are powerfully supportive of SET pathways in at least some reactions
like these.253
148
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
Me Me NC
CN
Me Me
e-transfer
Me Sn
Me
Me NC
Me
CN
4.17
NC
CN
NC
CN
Sn
Me
Me
Sn
Me Me
NC
CN
NC
CN
radical
coupling
NC
CN
Me
CN
CN
4.18
4.19
e-transfer
Hg(O2CCF3)2
Hg(O2CCF3)2
4.20
H
HgO2CCF3
radical
HgO2CCF3
coupling
O2CCF3
O2CCF3
4.21
4.22
Given then that SET pathways are almost certainly involved in some nucleophile-electrophile combinations, ought we to consider that they are the most likely pathway in all of them? This is a seductive
proposition, because a unified mechanism for a wide range of reactions has an instant appeal. Most of the
well established SET pathways have been found with reagents conspicuously carrying radical-stabilising
substituents like the nitro group or for substrates like bromobenzene incapable of following the traditional
mechanism. Consequently, the feeling has grown that SET pathways may well be followed in those
substrates well adapted to SET, but that the rest probably retain the more conventional mechanisms. This
may be right, but it is not a good argument. If the radicals inside the cage are well stabilised, they are more
likely to live long enough to escape, and to give us opportunities to detect them, but if the radicals in the
cage are not well stabilised, their coupling is likely to be so fast that they can evade the radical probes with
which we try to detect them. We shall not be able to come to a firm conclusion here. The debate
continues.254,255
Nevertheless, we do need to address the problem of how to use molecular orbital theory, and the principle
of HSAB, to explain all the examples of reactivity and selectivity to be discussed in the rest of this chapter.
The traditional two-electron mechanism and the SET mechanisms will need different wording, and maybe a
different explanation. Fortunately, this is not a great problem. The aspects of molecular orbital theory that we
shall invoke, and of frontier orbital theory in particular, work in much the same way in both families of
mechanism. Thus, a nucleophile will be more nucleophilic if its available pair of electrons is in a high energy
orbital, whether those electrons are used directly to make a bond or one of them is transferred on its own.
Electrophilicity, likewise, will be greater if the reagent has a low-energy LUMO, whether this is encouraging
direct attack by a pair of electrons or the acquisition of a single electron. For this parallel to work, the electron
transfer must be slower than the coupling of the radicals, which it usually is. Regioselectivity in product
formation, however, may need different explanations, since the new bond is formed in the conventional
mechanism in the first step, but in the SET mechanism it is formed in the radical coupling step or, in SRN1
reactions, the step in which a radical attacks the nucleophile.
4 IONIC REACTIONS—REACTIVITY
149
The discussion in the rest of this chapter will be phrased using the conventional two-electron mechanism—that mechanism has yet to be displaced from most discourse about most reactions. If an illuminating
point can be made with the SET mechanism it will be.
4.2
Nucleophilicity
4.2.1 Heteroatom Nucleophiles
In the last chapter we saw that there is no single measure of acidity and basicity. Similarly, there is no single
measure of nucleophilicity and electrophilicity—the rank order of nucleophiles is totally upset when the
reference electrophile is changed. A hard nucleophile like a fluoride ion reacts fast with a silyl ether in an SN2
reaction at the silicon atom, which is relatively hard, but a soft nucleophile like triethylamine does not. In
contrast, triethylamine reacts with methyl iodide in an SN2 reaction at a carbon atom but fluoride ion does
not. These examples, which are all equilibria, are governed by thermodynamics, but there are similar
examples illustrating divergent patterns of nucleophilicity in the rates of reactions.
Hard-hard:
Sof t-hard:
Et3N
F
Me3Si
O
Me3Si
O
F
SiMe3
O
Et3N
Soft-soft:
Et3N
O
+
SiMe3
+
Hard-soft:
Me
I
Et3N Me
+
I
F
Me
I
F
Me
+ I
A scale of nucleophilicity, therefore, requires at least two parameters, and these were first provided
empirically by Edwards with Equation 4.1.256
log
kNu
¼ EN þ H
k0
4:1
where kNu is the rate constant (or equilibrium constant) for a reaction, k0 is the rate constant (or equilibrium
constant) for water as the nucleophile, and EN and H are the two scales of nucleophilicity. The EN scale is
measured by the rate of reaction with methyl bromide, and the H scale is the (pKa þ 1.74), where the 1.74 is a
correction for the pKa of H3Oþ. Thus the two scales reflect both softness (EN) and hardness (H), although
these terms were not in use when Edwards formulated his equation. The extent to which the hard or soft
character of the electrophile contributes will affect the relative sizes of and , which will be different for
each reaction, a high value of / implying a soft electrophile.
Another way of looking at the same problem uses the Salem-Klopman equation that we saw in the last
chapter, and hence follows from the concept of HSAB, instead of preceding it, and is based on theory rather
than experiment. Using only the HOMO of a nucleophile and the LUMO of an electrophile, Klopman
simplified Equation 3.13 to Equation 4.2:
DE ¼
QNu QEl
2ðcNu cEl Þ 2
þ
"R
EHOMOðNuÞ – ELUMOðElÞ
4:2
150
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
As we have seen earlier, using only the frontier orbitals is a risky approximation because the interactions
of the other orbitals will all have an effect, but they all have larger values of Er – Es and thus make a smaller
contribution to the third term of Equation 3.13.
Starting with this simplification, Klopman worked out the contribution of the frontier orbital terms to the
nucleophilicities and electrophilicities of a range of inorganic bases and acids.230 From the known ionisation
potentials and electron affinities, and correcting for the effect of solvation, he calculated values (E‡, Table
4.1, listed with hardness at the top and softness at the bottom) for the effective energy of the HOMO of the
nucleophiles and the LUMO of the electrophiles. The results agree well with Pearson’s original, empirically
derived order of softness, and, if allowance is made for the absence of solvation, with his more theoretically
derived order in Tables 3.3 and 3.4. The higher the value of E‡ for the HOMO of a nucleophile, the softer it is,
and the higher the value of E‡ for the LUMO of an electrophile, the harder it is. Table 4.1 is therefore a useful
practical list.
Table 4.1
bottom)
Nucleophile
F–
H2O
HO–
Cl–
Br–
CN–
HS–
I–
H–
Calculated softness character for inorganic nucleophiles and electrophiles (hard at the top and soft at the
Effective HOMO E‡ (eV)
Electrophile
Effective LUMO E‡ (eV)
–12.18
–10.73
–10.45
–9.94
–9.22
–8.78
–8.59
–8.31
–7.37
Al3þ
La3þ
Ti4þ
Mg2þ
Ca2þ
Fe3þ
Cr3þ
Ba2þ
Cr2þ
Fe2þ
Liþ
Hþ
Ni2þ
Naþ
Cu2þ
Tlþ
Cuþ
Agþ
Tl3þ
Hg2þ
6.01
4.51
4.35
2.42
2.33
2.22
2.06
1.89
0.91
0.69
0.49
0.42
0.29
0
–0.25
–1.88
–2.30
–2.82
–3.37
–4.64
Klopman then used Equation 4.2 to estimate the relative nucleophilicities of a range of anionic
nucleophiles: I–, Br–, Cl–, F–, HS–, CN– and HO– towards a small range of different electrophiles.230
He assumed unit charges and unit values for the coefficients, c. For the EHOMO(Nu) term, he used the
values of E‡ from Table 4.1. Since it is roughly proportional to the overlap integral S, the value of changes, depending on which elements are forming the new bond, but it can readily be calculated.257 This
left only the energy of the LUMO of the electrophile, ELUMO(El), as an unknown on the right-hand side of
the equation. Klopman therefore calculated DE values for a series of imaginary electrophiles with
different values for the energy of the lowest unoccupied orbital ELUMO. His striking results are given
in Table 4.2.
4 IONIC REACTIONS—REACTIVITY
Table 4.2 230
151
Nucleophilicity of inorganic ions towards electrophiles as a function of EHOMO – ELUMO
DE calculated for:
Found:
Nucleophile
EHOMO
ELUMO
–7 eV
ELUMO
–5 eV
ELUMO
þ1 eV
k 104
Equation 4.3
Edwards’ E
Equation 4.4
pKa Equation 4.5
F–
HO–
Cl–
Br–
CN–
HS–
I–
–12.18
–10.45
–9.94
–9.22
–8.78
–8.59
–8.31
1.06
1.49
1.54
1.75
2.30
2.64
2.52
0.82
1.01
0.97
0.98
1.17
1.25
1.07
0.54
0.58
0.52
0.48
0.56
0.55
0.45
0
0
0.001
0.23
10
too fast
6900
1.0
1.65
1.24
1.51
2.79
too fast
2.06
3.2
15.7
–4.3
9.1
7.1
–7.3
(i) Setting ELUMO(El) at –7 eV (a low value) made the EHOMO – ELUMO term small, and hence the frontier
orbital term, the second term of Equation 4.2, made a large contribution to DE. The order of the values
DE was HS– > I– > CN– > Br– > Cl– > HO– > F–, which is the order of nucleophilicities which has
been observed for the attack of these ions on peroxide oxygen (Equation 4.3).258
Nu
HO
OH
Nu
OH
+
4.3
OH
(ii) Setting ELUMO(El) at –5 eV, the order of nucleophilicities is slightly changed, because the frontier
orbital term makes a slightly smaller contribution to DE. The order of DE values is now HS– > CN– > I–
> HO– > Br– > Cl– > F–, which parallels the Edwards E values256 for the nucleophilicities of these ions
towards saturated carbon (Equation 4.4).
Nu
X
+
Nu
X
4.4
(iii) Finally, setting ELUMO(El) very high at þ1 eV, the frontier orbital term is made relatively very
unimportant, and the order of DE values is governed almost entirely by the Coulombic term of
Equation 4.2: HO– > CN– > HS– > F– > Cl– > Br– > I–. This is the order of the pKas of these ions,
in other words, of the extent to which the equilibrium lies to the right in Equation 4.5.
Nu
H
OH2
Nu
H
+
H2O
4.5
Thus, simply by adjusting the relative importance of the two terms of Equation 4.2, we can duplicate the
otherwise puzzling changes of nucleophilic orders as the electrophile is changed. The solvated proton is a
very hard electrophile because it is charged, and especially because it is small. Hence, a nucleophile can get
close to it in the transition structure and R in Equation 4.2 is made small. The oxygen-oxygen bond, however,
has no charge, and, being both weak and between electronegative atoms, it has a conspicuously low-lying *
LUMO for a bond. It is therefore a very soft electrophile. Similarly, with nucleophiles such as F–, Cl–, Br–
and I–, the energy of the HOMO will rise as we go down the periodic table, and with nucleophiles like Cl–,
152
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
HS– and R2P–, the energy of the HOMO will rise as we move to the left in the periodic table. This explains,
therefore, the observations in the reactions above, and in many others, that the ‘softness’ of a nucleophile
increases in these two directions.
Quantitative support for the importance of orbital energies comes from studies259 of the SN2 reaction
between 41 thiocarbonyl compounds 4.23 with methyl iodide and other methylating agents, in which the
Coulombic term was kept small and relatively constant. The rates correlated well with the ionisation
potential of the lone pair on the sulfur atom, measured by photoelectron spectroscopy and a direct measure
of the energy of the HOMO. The lone pair, however, was not always the HOMO. With some donor
substituents R, the bonding p electrons were actually the HOMO but the correlation worked better with
the lone-pair energy. Evidently developing overlap with a nonbonding pair of electrons is more effective,
even when they are lower in energy, than with a bonding pair. The effect would be taken care of by the value
of in Equation 4.2.
R1
Me
I
R1
S
R2
Me
S
I
R2
4.23
4.2.2 Solvent Effects
Solvents have long been implicated in the divergent scales of nucleophilicity and electrophilicity because
small, charged nucleophiles and electrophiles are often highly solvated. Empirically, gas phase SN2 reactions, where there is no solvent, are very different from their solution counterparts.260,261 Nevertheless, gas
phase reactions do show a pattern in which matching the nucleophile to the leaving group can lead to higher
rates, reminiscent of hard-hard and soft-soft pairings, and so it seems that solvent effects are not the whole
story. How important solvent effects are in explaining relative nucleophilicities is still an open question, to
which we shall return from time to time, as we saw that Klopman did by correcting for it.
The orbitals of a solvent interacting with those of the nucleophile and the electrophile are responsible for
some of the energy of solvation, and should be amenable to treatment by perturbation theory. If the orbitals
are close enough in energy for a first-order treatment to be appropriate, reaction would occur; so solvation is
a second-order interaction. The second term of Equation 4.2 will therefore be a good approximation, and the
major interactions will be between the HOMO of the solvent and the LUMO of an electrophile, and between
the LUMO of the solvent and the HOMO of a nucleophile. Using this idea (and hence the second term of
Equation 4.2), and using ionisation potentials and electron affinities as measures of the energies of the
HOMO and the LUMO of a range of solvents, Dougherty262 has been able to explain some otherwise
puzzling changes of solvating power. Thus no single scale of solvating power works for all reactions, just as
there is no single scale of nucleophilicity. We can now see that—amongst other things, no doubt—a balance
between both sets of frontier orbital interactions (HOMOsolvent/LUMOreagent and LUMOsolvent/HOMOreagent)
may help to account for this.
4.2.3 Alkene Nucleophiles
Alkenes 4.24, with a p orbital as the HOMO and no charge, are inherently soft nucleophiles, and their
nucleophilicity ought to have some relationship to the energy of their HOMOs. The relative rates of attack by
different alkenes have been measured for such electrophiles as bromine, peracids, sulfenyl halides, electrophilic 1,3-dipoles (Chapter 6), metal cations (Hg2þ, Agþ) and boranes. These electrophiles fall into two
groups: those like bromine, peracid and sulfenyl halides that show a correlation between the rate and the
ionisation potential of the alkene, and those like 1,3-dipoles, metal cations and boranes, that show significant
discrepancies.263 The first group show little sign of steric effects, since the more substituted alkenes, with the
4 IONIC REACTIONS—REACTIVITY
153
higher energy HOMOs, generally react faster than the less substituted. These reactions have a ratedetermining first step, the electrophiles have a modest steric demand, and they form bridged intermediates
4.25, or, in the case of epoxidation, products. The second group show steric effects, with the more-substituted
alkenes reacting more slowly than expected for their relatively high energy HOMOs. The explanation264,265
for electrophilic 1,3-dipoles is probably steric effects on the first (and only) step, since 1,3-dipoles are
relatively large compared with the first group of electrophiles. The explanation with the metal electrophiles
is that they rapidly and reversibly form an intermediate, but the rate-determining step is the opening of that
intermediate, in a reaction that evidently responds to steric effects.
E
E+
Nu
Nu–
or
E
E
4.24
RDS
correlates with IP of alkene
(Br2, RCO3H, PhSCl)
RDS
affected by steric effects
(Hg2+, Ag+, R2BH)
4.25
Mayr has measured the nucleophilicity of a wide range of alkenes 4.26 being attacked by a family of
diarylmethyl cations 4.27, which, being highly delocalised, are relatively soft for cations.266 These reactions
are like those with metal cations and boranes in having the first step rate-determining, but they are different,
because the formation of the intermediate 4.28 is endothermic.
R2
R1
4.26
Ar
Ar
4.27
R2
RDS
R1
Ar
Ar
4.28
The order of nucleophilicity, graphically illustrated in Fig. 4.1, matches well with expectation—the
better donor substituents are the more effective at increasing the rate of reaction. For alkenes having a
terminal methylene group, an extra methyl group increases the reactivity by four orders of magnitude
(compare propene with isobutylene). A trimethylsilylmethyl group (R1 ¼ Me3SiCH2, R2 ¼ H) and a
tributylstannylmethyl group (R1 ¼ Bu3SnCH2, R2 ¼ H) further increase the nucleophilicity (relative to
R1 ¼ Me, R2 ¼ H) by five and nine orders of magnitude, respectively. An alkoxy group (R1 ¼ EtO,
R2 ¼ H) increases the nucleophilicity by five to six orders of magnitude more than an alkyl group.
Since this is an endothermic reaction, the transition structures are product-like (Fig. 3.4b), estimated in
this case to have something like two-thirds of the charge transferred to the alkene component. As a
consequence, the rates correlate well with the stabilities of the carbocations produced 4.28, but not well
with the ionisation potential (and hence the HOMO energy) of the alkene.267 Donor substituents R1 and
R2, of course, stabilise the cation 4.28 (see pp. 77–78, 87–90 and 92–94), and can be expected to lower
the energy of the transition structure.
The situation changes somewhat for those alkenes 4.29 having substituents on the carbon atom under
attack. Alkyl substituents R2 do not contribute much to the stabilisation of the cation 4.30, but they do
contribute to raising the energy of the HOMO of the alkene 4.29. On the whole, a substituent on the carbon
atom under attack () does increase the rate of attack, with 2-butene about one order of magnitude more
reactive than propene. A large effect from having substituents on the position and a small effect from
having them on the position identifies a transition structure leading to an unbridged intermediate 4.30
154
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
Bu3Sn
1010
109
Bu3Sn
Me3Si
108
EtOH
107
106
k rel
105
Me3Si
EtO
MeO
H2O
EtO
Me3Si
104
103
102
10
1
Fig. 4.1
Relative nucleophilicities of alkenes towards carbocations
(see pp. 90–91).268 In agreement with this, the difference in rates for 2-butene and propene is not as large as
having the extra methyl group on the carbon, as in isobutylene. Most remarkably, the effect of a substituent is more powerful with enol ethers than the effect of an substituent: 1-ethoxypropene is nearly
twice as reactive as 2-methoxypropene. Furthermore, the relative rates for enol ethers correlate well with the
HOMO energy as measured by the ionisation potentials.269 In these reactions, the starting material is reactive
(high in energy), the product cation is stabilised (low in energy) and it is appropriate that the transition
structure should be earlier (Fig. 3.4a) and more responsive to orbital effects in the starting material.
Ar
Ar
2
R
R1
Ar
4.29
4.27
R1
Ar
R2
4.30
It is worth emphasising now that the effects of C-, X-, and Z-substituents on the nucleophilicity of an alkene
often match their effects on the energy of the HOMO. Following the arguments developed in Chapter 2:
C- and X-substituents
raise the energy of the HOMO and increase nucleophilicity.
Z-substituents
lower the energy of the HOMO and decrease nucleophilicity.
4 IONIC REACTIONS—REACTIVITY
155
4.2.4 The a-Effect270
The solvated proton is a hard electrophile, little affected by frontier orbital interactions. For this reason, the
pKa of the conjugate acid of a nucleophile is a good measure of the rate at which that nucleophile will
attack other hard electrophiles. We shall see that carbonyl groups are fairly hard, but somewhat responsive
to frontier orbital effects, more so, anyway, than solvated protons. Thus a thioxide ion, RS–, is more
nucleophilic towards a carbonyl group than one would expect from its pKa: a plot, known as a Brønsted
plot, of the log of the rate constant for nucleophilic attack on a carbonyl group against the pKa of the
nucleophile is a good straight line only when the nucleophilic atom is the same. In other words, there is a
series of straight lines, one for oxygen nucleophiles, one for sulfur nucleophiles, and yet another for
nitrogen nucleophiles.
Some nucleophiles, HO2–, ClO–, HONH2, N2H4 and R2S2, stand out because they do not fit on Brønsted
plots: they are more nucleophilic towards such electrophiles as carbonyl groups than one would expect from
their pKa values.271 These nucleophiles all have a nucleophilic site which is flanked by a heteroatom bearing
a lone pair of electrons (an X-substituent, in other words). The orbital containing the electrons on the
nucleophilic atom overlaps with the orbital of the lone pair of the X-substituent (Fig. 2.12), raising the energy
of the HOMO relative to its position in the unsubstituted nucleophile, as usual with an X-substituent.
Consequently, the denominator of the third term of Equation 3.13 is reduced, and the importance of this
term is increased. The result is an increase in nucleophilicity, called the -effect, which can sometimes be
quite dramatic (Table 4.3). The order of the effect appears to be right: the LUMO of the triple bond of the
nitrile will be lower than that of the double bond of the carbonyl group, which will be lower than that of the bond of the bromide. Hence the frontier orbital term is most enhanced in the case of benzonitrile, and least
enhanced for benzyl bromide and methyl arenesulfonates.272 The -effect is sometimes increased when
reactions are carried out in dipolar aprotic solvents.273 As these solvents do not stabilise anions by solvating
them, orbital effects become more noticeable.
Table 4.3
Electrophile
PhCN
p-O2NC6H4CO2Me
PhCH2Br
Relative nucleophilicity of hydroperoxide ion and hydroxide ion
kHOO–/kHO–
Electrophile
kHOO–/kMeO–
105
103
50
ArSO2OMe
6–11
kHOO–/kHO–
10–4
H3Oþ
However, the energy of the HOMO in a range of -nucleophiles does not actually correlate well enough with
their nucleophilicity274 for this explanation of the effect to be satisfactorily settled. For all that the LUMO
energy is lower for carbonyl groups than for alkyl halides, the latter are conspicuously softer electrophiles,
yet show a much smaller -effect, and do not show it at all in the gas phase.275 Even more puzzling, although
the -effect appears to follow the order digonal>trigonal>tetrahedral, ethynyl methyl ketone, another
digonal electrophile, only has an -effect of about 10. Furthermore, -effect nucleophiles like hydrazine,
unlike ordinary nucleophiles, show a kinetic isotope effect kH/kD of 2.3, indicating that the mechanistic
details are different.276
The problem raised by the small -effect in reactions with alkyl halides, where the LUMO energy is not
conspicuously low, and yet they are soft electrophiles, raises the question of what happens when both charge
and frontier orbital terms are small, and what happens when they are both large? Prediction is not simple in
this situation, but Hudson has suggested the two rules in the box, which are usually but not invariably
observed. In the case of the p-nitrobenzoate and benzyl bromide, we have a 20-fold increase in
156
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
nucleophilicity towards a carbonyl group, accompanied by a 10 000-fold decrease in basicity. It serves to
alert us that carbonyl groups, although mainly responsive, as we shall see, to basicity (charge control), are not
unresponsive to frontier orbital effects.
(i) When both charge and orbital terms are small: nucleophiles and electrophiles will be soft (that is,
orbital control is more important).
(ii) When both charge and orbital terms are large: nucleophiles and electrophiles will be hard (that is,
charge control is more important).
The raised energy of the HOMO also provides an explanation with an SET mechanism, since it allows
an electron to be transferred more easily to the LUMO of the electrophile, and the radical pair then
couple, as usual. A single electron removed from one of the two pairs will leave behind a stabilised
radical, and so the rate constant of a reaction of an -effect nucleophile ought to be more sensitive to
the ionisation potential (LUMO energy) of the electrophile than the rate constant with a normal lonepair nucleophile.277 This proved to be the case in the rates of N-methylation of a series of Nphenylhydroxylamines compared with the rates in some comparable anilines.278 Further support for
an SET mechanism is provided by superoxide anions, RO 2•– , which are exceptionally powerful
nucleophiles benefiting simultaneously from an -effect and from the availability of an unpaired
electron. 279
The -effect is observed not only as a kinetic effect but also as a thermodynamic -effect, as seen in the
equilibrium constants for the removal of acetyl groups from N-acetylimidazole with hydroxylamine derivatives, which parallel their kinetics.280 For an explanation, we may compare an amide 4.31 with a
hydroxamic acid 4.32. The overlap of a lone pair with the p* orbital of a carbonyl group (4.31, arrows,
see also pp. 104–106) is an important part of the reason why amides are stabilised relative to ketones. The
effect of another lone pair is to raise the energy of the first lone pair (Fig. 2.12) and hence to make the overlap
with the p* orbital more energy-lowering.
O
N
4.31
O
N
OH
4.32
The -effect with oximes and hydrazones contributes to making them less electrophilic than other imines.
The overlap of the lone pair on the second heteroatom with the developing lone pair on the nitrogen atom of
the imine is destabilising. This is only part of the explanation, since the same lone pairs will be conjugated to
the C¼N p bond of the starting materials, raising the energy of the HOMO and LUMO, and stabilising the
system.
The energy of the HOMO can, in principle, be raised by through-space interactions 281 as well as by
conjugation in the sense seen with the -effect. A series of amines which might have shown such an
effect were disappointing: the nucleophilicity towards an ester carbonyl group was very similar for the
simple amine 4.33 and the g-methoxyamine 4.34.282 The inductive effect through the bonds reduces
the nucleophilicity of the amine 4.34, and this will be in force in any of the conformations that it
adopts. The through-space effect can only show up in the U-shaped conformation that may rarely be
adopted.
4 IONIC REACTIONS—REACTIVITY
157
HH
HH
N
O
O
MeO
relative rates
1.77:1
N
O
O
Ar
Ar
4.33
4.3
4.34
Ambident Nucleophiles
Nucleophiles which have two sites at which an electrophile may attack are called ambident. The
principle of HSAB often applies in these reactions, with hard electrophiles reacting at the harder
nucleophilic site and soft electrophiles reacting at the softer site. Thus the disulfide 4.35 is cleaved by
hydroxide ion to give the sulfenate ion 4.36, which is an ambident nucleophile. It reacts with the
harder electrophile methyl fluorosulfonate at the oxygen atom, where most of the negative charge
resides, to give the sulfenate ester 4.37. In contrast it reacts with the softer electrophile methyl iodide
at the sulfur atom, the softer of the two nucleophilic sites, made more nucleophilic by an -effect, to
give the sulfoxide 4.38.283
Ar
S
Me
O
OSO2F
Ar
4.36
Ar
S
S
Ar
S
O
Me
4.37
OH
Me
4.35
Ar
S
4.36
O
I
Me
Ar
S
O
4.38
4.3.1 Thiocyanate Ion, Cyanide Ion and Nitrite Ion (and the Nitronium Cation)
Thiocyanate ions, cyanide ions and nitrite ions are well known ambident nucleophiles but the explanation for
their behaviour is not so straightforward. Each can react with an electrophile Rþ, depending upon its nature
and the conditions, to give either of two products: a thiocyanate 4.39 or an isothiocyanate 4.40 from the
thiocyanate ion, an isonitrile 4.41 or a nitrile 4.42 from the cyanide ion, and an alkyl nitrite 4.43 or a
nitroalkane 4.44 from the nitrite ion.
The thiocyanate ion will be softer on the sulfur atom and harder on the nitrogen atom, the cyanide ion will
be softer on the carbon atom and harder on the nitrogen atom, and the nitrite ion will be harder on the oxygen
atom and softer on the nitrogen atom. We might expect that harder electrophiles will give the isothiocyanates
4.40, the isonitriles 4.41 and the nitrites 4.43. However, other factors are at work, and this pattern is
unreliable. Earlier attempts to use these expectations to explain some of the patterns of reactivity in this
area229,284 have been overtaken by more recent work.
The thiocyanate 4.39 is the kinetically preferred product in alkylations by alkyl halides undergoing
SN2 reactions285 and with carbocationic electrophiles in SN1 reactions,286 in spite of the fact that a
carbocation, being charged, is a hard electrophile and the sulfur is the soft end of the nucleophile.
This is partly explained by the relatively small change in bond lengths and in electronic reorganisation required in going from the thiocyanate ion to the thiocyanate product. Thiocyanates 4.39 more or
less rapidly isomerise to isothiocyanates 4.40, which are the thermodynamically preferred products,
the tertiary alkyl thiocyanates rearranging by an SN1 pathway,287 and primary alkyl thiocyanates by
an SN2 pathway.288
158
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
R+
f ast
R
S
C
R+
slow
S
N
R
N
N
4.39
R
N
R+
C
R+
C
R
N
C
N
4.42
R+
O
S
4.40
4.41
R
C
N
O
R+
O
O
N
R
O
N
O
4.43
4.44
Cyanide ions react with the soft (see pp. 151–152) alkyl halides in SN2 reactions and with the hard carbocations
in SN1 reactions to give, almost always, the nitrile 4.42, which is thermodynamically preferred.289 Isonitrile
products are formed along with the nitrile products when the cation is so reactive that the rate has reached the
diffusion-controlled limit, and the reversible reaction that would equilibrate the products is too slow.290 It is
hardly surprising that reactions between a cyanide ion and a carbocation can be fast enough to reach the
diffusion controlled limit, since they are ion-with-ion reactions, which are rather rare in organic chemistry. One
consequence when reactions are as fast as this is that there is a barrierless combination of ions, and selectivity is
not then controlled by the kinetic factors associated with the principle of HSAB.
Other situations in which isonitrile products are formed have special features. Silver cyanide sometimes
leads to isonitrile products291 whereas potassium cyanide gives nitriles. A telling example is the formation of
the isonitrile 4.47 in the reaction with silver cyanide, whereas potassium cyanide gives the nitrile 4.46.292
Since both reactions take place with overall retention of configuration by way of an episulfonium ion 4.45, it
cannot be that the silver ion induces an SN1 reaction. An explanation is that the relatively soft silver is
attached to the carbon of the cyanide ion, leaving the nitrogen end free to be nucleophilic, whereas potassium
is not so attached. Similarly, trimethylsilyl cyanide sometimes gives isonitrile products with carbocations
stabilised only by alkyl groups,293 perhaps because the silyl group is attached to the carbon atom at the time
of reaction, and the isonitriles rearrange too slowly.
Nitrite ions generally give nitroalkanes 4.44 as the major products, which are also thermodynamically
more stable than alkyl nitrites 4.43.294 Again, with carbocationic electrophiles, it is only when the reaction
rate has reached the diffusion-controlled limit that alkyl nitrites can be detected or even be the major
products. Nitrite ions also give mixtures of nitroalkanes and nitrites in SN2 reactions, even though the alkyl
electrophiles are relatively soft.
K+ N
C
H
H
C
Ag
C
SMe
H
4.46
4.45
SMe
H
N
S
Me
H
Br
H
N
H
H
S
Me
4.45
C
H
N
SMe
H
4.47
4 IONIC REACTIONS—REACTIVITY
159
A hint that the principle of HSAB might have some role in explaining ambident reactivity with nitrite
ion comes from the SN2 reactions with methyl iodide (relatively soft), with the trimethyloxonium ion
(harder) and with methyl triflate (hardest) giving mixtures of methyl nitrite and nitromethane in a pattern
like the reactions of the sulfenate ion 4.36. There is an increase in the ratio of methyl nitrite to
nitromethane with the harder electrophiles, rising from 30:70, through 50:50, to 59:41, respectively.294
A similar pattern is seen with the SN2 reaction of primary benzyl bromides with silver nitrite, where the
ratio of nitrite to nitroalkane rises from 16:84 when the benzene ring has a p-nitro substituent, through
30:70 with no substituent to 61:39 with a p-methoxy substituent.295 These are small effects, and little
weight can be placed on any explanation; nevertheless, we can see that the patterns in both series are in line
with the different contributions made to Equation 4.2. The contribution from the first term is greater for the
harder electrophiles because of the greater charge on the carbon atom in methyl triflate than in the less
polarised methyl iodide, and in the greater degree of carbocationic character in the transition structure with
the p-methoxybenzyl bromide.
For the contribution from the second term of Equation 4.2, it is the HOMO of the nitrite ion that we need to
look at. The p orbitals of the NO2 system are shown in Fig. 4.2, with the anion on the right and the cation on
the left. Two of the p orbitals, an orthogonal pair, resemble 2 in the allyl system, with large coefficients on
the oxygens and a node on the nitrogen but the next orbital above them, which is the HOMO in the nitrite
anion, is an orbital resembling 3* in the allyl system, with a large coefficient on the nitrogen. The bent
shape of the HOMO is another example of the HOMO-LUMO interaction (Jahn-Teller distortion) within a
molecule that we saw in Section 2.4.1. The nitrogen will be the nucleophilic site when the second term of
Equation 4.2 is the more important contributor to DE. Furthermore, S and hence for N—C bond formation is
higher than for O—C bond formation (see p. 54); when the frontier orbital term is dominant, this will enhance
the propensity for bond formation to nitrogen, because it is in this term that appears. An alternative or
supplementary explanation is that the solvent gathers around the site of higher charge, the oxygen atoms in
the case of nitrite, and that this hinders the reaction there, and the nitrogen, with so little of the charge, must
be less crowded by solvent molecules.
LUMO
O
N
O
O
N
O
*
LUMO
n
HOMO
O
N
O
O
N
O
HOMO
N
O
n
linear NO2+
Fig. 4.2
O
bent NO2–
Frontier orbitals of the nitronium ion and the nitrite ion
In nitration, where we have an ambident cation, the important frontier orbital will be the LUMO of
NO2þ, and this is a similar orbital to the HOMO of NO2–, except that the cation is linear. The
nitronium ion, NO2þ, always reacts on nitrogen, both with soft nucleophiles like benzene and with
hard ones like water. In the nitration of benzene, the solvent is often nonpolar; thus differential
solvation is unlikely to be responsible for the fact that the nitrogen atom is the electrophilic site. ESR
studies296 of nitrogen dioxide (NO2), which has one electron in the pn* orbital, confirm that the site
of highest odd-electron population is indeed on nitrogen (about 53% of the electron, with the oxygens
sharing the other 47%).
160
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
4.3.2 Enolate lons297
The most important ambident nucleophile is the enolate ion 4.48. Why does an enolate ion react with
some electrophiles at carbon and with others at oxygen? We can now use the explanation based on
the relative importance of the Coulombic and frontier orbital terms to account for this well-known
observation.298 We have seen the p orbitals of an enolate ion calculated in Fig. 2.20, with the general
pattern accounted for in the argument leading to Fig. 2.7. The size of the lobes can be taken as
roughly representing the size of the c-values (or c2-values) of the atomic orbitals which make up the
molecular orbitals. The system is closely related to that of the allyl anion in Fig. 1.33, but the effect
of the oxygen atom is to polarise the electron distribution, with the lowest-energy orbital 1 strongly
polarised towards oxygen, and the next orbital up in energy 2 polarised away from oxygen. The
effective p charge on each atom in the ion is proportional to the sum of the squares of the c-values
for the filled orbitals, namely 1 and 2. Using the values from Fig. 2.20, the total charge on the
oxygen atom is 0.92 þ (–0.41)2 ¼ 0.98 and on the carbon atom it is 0.172 þ 0.72 ¼ 0.52. However, the
c-values in the HOMO are the other way round, –0.41 on oxygen and 0.70 on carbon. With charged
electrophiles, then, the site of attack will be oxygen, as is indeed the case, kinetically, with protons
and carbocations. With electrophiles having little charge and relatively low-lying LUMOs, the
reaction will take place at carbon. In other words, hard electrophiles react at oxygen and soft
electrophiles at carbon. Once again, the fact that values for bonds to carbon are usually higher
than values for bonds to oxygen enhances the tendency for the frontier orbital term to encourage
reaction at carbon. Solvent, of course, also hinders reaction at the sites of highest solvation, which
will generally be the atoms carrying the highest total charge.
O
H
O
MeI
Me
O
H
4.48
We can also explain why the nature of the leaving group on an alkylating agent affects the proportion
of C- to O-alkylation in such enolates as the sodium salt 4.49 derived from ethyl acetoacetate. The
observation is that the harder the leaving group (i.e. the more acidic the conjugate acid of the leaving
group), the lower the proportion of C-alkylation (Table 4.4).299 The softer the leaving group, the
lower will be the energy of the LUMO.300 In addition, the harder the leaving group, the more
polarised is its bond to carbon, and hence the more charge there will be on carbon in the transition
structure. This is the same phenomenon as the effect electronegative ligands have on the hardness of
a Lewis acid (see pp. 77 and 130). As a result, the Coulombic term of Equation 4.2 will grow in
importance with the hardness of the leaving group, making O-alkylation easier, and the frontier
orbital term will grow with its softness, making C-alkylation easier.
Table 4.4
Nucleofugal group, X–
kC/kO
The proportion of C- to O-alkylation as a function of the leaving group
I–
Br–
TsO–
EtSO4–
CF3SO3–
>100
60
6.6
4.8
3.7
4 IONIC REACTIONS—REACTIVITY
161
O
O
O
kC
OEt
O
+
OEt
EtX
EtO
kO
Et
O
4.49
OEt
As before, we must not forget how much solvent effects may be the dominant influence in the regioselectivity. There is ample evidence that both the alkylation and the acylation of enolate ions in the gas phase take
place, more often than not, on oxygen,301 the site that solvents protect. However, frontier orbital effects have
been used to explain those gas phase reactions, and there are several, in which the enolate ion is attacked on
carbon.302
4.3.3 Allyl Anions
The allyl anion itself presents no problems: C-1 and C-3 are overwhelmingly the nucleophilic sites both for
hard and soft electrophiles (Section 3.5). A substituent on C-1 makes the allyl anion 4.50 an ambident
nucleophile, since attack can now take place at C-1, the position, to give the alkene 4.51, or at C-3, the g
position, to give what is usually the thermodynamically favoured product 4.52. The substituent can be C, Z or
X, the geometry can be W-shaped or sickle-shaped, and the regioselectivity for each can be the same for hard
and soft electrophiles, or different for each. There are further complications—allyl anions are not usually
free anions, but can have a metal covalently bonded either to C-1 or C-3, and the nature of the metal and the
position it is attached to, rather than any inherent selectivity in the free anion, may determine the regioselectivity. Steric interactions between a large substituent and a large electrophile can change selectivity
from attack to g attack. Allyl anions, especially those with Z-substituents, are well enough stabilised for the
attack on some electrophiles to be reversible, especially with aldehydes and ketones, the halogens, and
sulfenyl halides. Consequently, some results are thermodynamic and not kinetic, but it is not always easy to
tell which, partly because proving which it is can be difficult. What is clear is that aldehydes and ketones
often show different regioselectivity from other electrophiles, either because of reversibility or, more likely,
because the metal coordinates to the carbonyl group delivering the electrophile in a six-membered ring
transition structure to the allylic position relative to the metal. Finally, solvents, and leaving groups affect the
ratio, and the presence of other substituents at C-1, C-2 and C-3 add even more variables. The outcome, not
surprisingly, is that firm rules about regioselectivity are not yet in place, and the following brief discussion is
far from a complete account.
E
C, Z or X
1 or
4. 50
3 or
C, Z or X
+
E
4. 51
C, Z or X
E
4. 52
4.3.3.1 X-substituted Allyl Anions. The allyl-lithium reagents 4.53–4.56 are relatively simple examples
of X-substituted allyl anions. With oxygen303,304 or nitrogen305,306 substituents, 4.53 and 4.54, g alkylation is
almost always the major pathway, but with sulfur, while g alkylation is known307 4.55, alkylation is much
more common 4.56.308,309
162
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
MeI
MeI
Li
Et3SiO
Li
PhNMe
4.54
Et3SiO
4.53
3:97
S
EtBr
LiS
S
MeI
Li
Li
PhNMe
6:94
EtS
S
4.55
S
4.56
23:77
only
These reactions are kinetically controlled, reasonably regular in their patterns, and explicable. The coefficients in the HOMO can be guessed at by using the simple arguments developed in Section 2.1.2.3, as
illustrated in Fig. 4.3. The HOMO of an X-substituted allyl anion will have some of the character of 2 of the
allyl anion, which is symmetrical but it will also have some of the character of a carbanion conjugated to an
allyl anion, in other words 3* of butadiene, which has a larger coefficient on C-4, corresponding to the g
position, than on C-2. This explains the g selectivity towards soft electrophiles like alkyl halides with the
oxygen and nitrogen substituents. The total p-electron population is also greater at the g position
(0.3712 þ 0.62 þ 0.62 > 0.62 þ 0.3712 þ 0.3712), which would suggest that this ought also to be the site of
attack by hard electrophiles. There are a few examples where protonation is observed at this site with the
oxygen310 and nitrogen substituents, including 4.54 itself,305 supporting this prediction.
The anomalous results with the sulfur-containing anions can also be explained. The stabilisation of an
anion adjacent to sulfur is by overlap with the neighbouring S—C bond (Section 2.2.3.2) and not by overlap
with the lone pairs. If this is operating in the dithian-stabilised anion 4.56, it is no longer an X-substituent, but
a Z-substituent, since the S—C bond is polarised away from the sulfur. Allyl anions with a Z-substituent are
0.600
–0.371
–0.19
X
+
2
–0.707
3*
= HOMO
–0.371
0.707
+
–0.54
0.600
=
0.65
X
Fig. 4.3 Estimating the coefficients of the HOMO of an X-substituted allyl anion
selective for reaction at the position, and so that result is normal. The other sulfur-containing anion 4.55
does not have the possibility of this hyperconjugative overlap, and so it behaves as a normal X-substituted
allyl anion.
From this point on, the regioselectivity of substituted allyl anions is much less regular, and somewhat less
explicable. For a start, X-substituted allyl anions react with carbonyl electrophiles with selectivity. This is
explicable, but it is determined by the site of coordination by the metal, not by the frontier orbitals. We can
contrast the reaction of the oxygen-substituted lithium anion 4.57 with an alkyl halide, which is g selective,
as usual, and the reaction of the zinc anion 4.58 with a ketone, which is selective.304 The oxygen
substituent coordinates to the zinc -bound at the g position, and the aldehyde is then delivered to the position in a six-membered cyclic transition structure 4.59. The same reaction with the lithium reagent 4.57
gives a 50:50 mixture of and g products, and so lithium is not so obviously coordinated in the way that the
zinc is. This type of reaction is often brought under control in the sense 4.59 for synthetic purposes by
4 IONIC REACTIONS—REACTIVITY
163
changing the metal to a better Lewis acid,311 one that can simultaneously coordinate to the substituent and
the carbonyl reagent. It is also possible to change the substituent to make it coordinate better when the metal
is on C-1 (), and thereby make the allyl anion react with carbonyl compounds on C-3 (g).309
I
EtO
Li
EtO
4.57
O
O
EtO
ZnCl
EtO
4.59
4.58
OH
Zn
OEt
Similarly, allyl anions with alkyl substituents almost always react with carbonyl electrophiles at the position, as in the reaction of the prenyl Grignard reagent with aldehydes to give the product 4.61,312
presumably because the metal is attached to the less-substituted end and then delivers the electrophile in a
six-membered transition structure 4.60. In contrast, alkylation of a similar anion with an alkyl halide gives
mainly the product 4.62 of g attack,313 which might be counted as normal for an X-substituted allyl anion
when a cyclic transition structure is not involved. Halogen substituents are anomalous. They are weak p
donors and powerful acceptors, which makes their contributions to regioselectivity difficult to predict. In
practice, the dichloroallyl anion 4.63 reacts with all electrophiles to give products like 4.64 and 4.65 of attack
at the position.314
CHO
H
OH
Mg
O
R = Me, M = MgBr
R
4.60
4.61
M
R
Br
R = Me2C=CH(CH2)2
M = Li
4.62
O
Li
4.63
OH
Cl Cl
4.64
Cl
Cl
20:80
MeI
Cl
Cl
4.65
4.3.3.2 C-Substituted Allyl Anions—Pentadienyl Anions.315 Allyl anions with C-substituents pose a
different problem. Both attack and g attack are known, as illustrated by the reactions of the open-chain
C-substituted anions 4.66,316 and 4.67.317 The problem is not only that the regioselectivity is irregular, but
explaining it is not straightforward either. Simple predictions based on the p orbitals suggest that the
164
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
C-substituted system should be equally reactive at the and g carbons. Mixing any amount of 3 of the
pentadienyl anion into the HOMO of the allyl anion will leave the HOMO coefficients at the and g carbons
equal.
MeBr
Ph
Ph
Na
4.66
92:8
MeI
3
1
Li
4.67
+
C-3:C-5 35:65
5
Me3SiCl
SiMe3 C-3:C-5 1:99
The cyclohexadienyl anion 4.68 has been the focus of most interest because of its importance as the
penultimate intermediate in Birch reduction. It is attacked almost exclusively at the central carbon
atom, C-3, which corresponds to attack on a C-substituted allyl anion. This gives the energetically
less favourable product 4.69 with the two double bonds out of conjugation, and in spite of a 2:1
statistical preference for attack at C-1.318 This selectivity seems to be largely independent of the
nature of the electrophile or of the metal, and the same pattern is found for cycloheptatrienyl systems
too.319 The sums of the squares of the coefficients of the filled orbitals 1, 2 and 3 for the
pentadienylsystem (Fig. 1.42) are equal on C-1 and on C-3 (and, of course, on C-5). The frontier
orbital coefficients for the HOMO 3 are also equal on C-1, C-3 and C-5. However, the simple
Hückel calculation which gives these values, neglects the fact that C-3 is flanked by two trigonal
carbon atoms but that C-1 has only one trigonal carbon adjacent to it and one tetrahedral. Naturally,
this perturbs the system. Total p-electron populations and HOMO coefficients have been calculated320
allowing for the overlap of the C—H bonds at C-6 with the p system (i.e. hyperconjugation), and
these give the values shown in Fig. 4.4a and b, respectively. The presence of a larger coefficient on
C-3 is supported by ESR measurements321 on the radical corresponding to this anion, which clearly
show a larger coupling to the hydrogen on C-3 than to those on C-1 and C-5 (Fig. 4.4c). Thus both
the experiment and the calculation imply that there is a larger coefficient and a higher total charge at
C-3 than at C-1. It is, of course, a highly exothermic reaction—just the kind which should show the
H
H
H
H
1.294
Fig. 4.4
0.350
0.01
0.438
(a) Calculated total electron populations
H
0.318
0.964
1.438
H
(b) Calculated values f or
c f or the HOMO
(–0.102)
0.506
(c) Spin densities obtained f rom ESR and
converted to c values using the
McConnell equation
Electron distribution in the cyclohexadienyl system
4 IONIC REACTIONS—REACTIVITY
165
influence from the interaction of the orbitals of the starting materials, rather than the influence from
the relative energies of the two possible products.
H
1
H
M
5
H
H
E
H
E
3
4.68
4.69
This adjustment to the simple Hückel calculations explains why the cyclic systems differ from the openchain pentadienyl anions, which have no alkyl groups at C-1 and C-5. These systems are evidently delicately
balanced, so much so that quite minor perturbations can lead to high levels of attack at C-3,322 especially
with the harder electrophiles like alkyl triflates.323
4.3.3.3 Z-Substituted Allyl Anions—Dienolate Ions. Electrophilic attack on Z-substituted allyl anions is
almost always selective for attack at the position. The problem is to explain it.
A special group of Z-substituted allyl anions—the boron 4.70324 and 4.71,325 sulfur 4.72,309 and silicon
4.73326 groups have no double bond extending the conjugation but only an electron deficiency conjugated to
the p system of the allyl anion. The boron has an empty p orbital, and the sulfoxide and silyl groups have
negative hyperconjugation with neighbouring bonds polarised from the sulfur and silicon atoms towards
more electronegative atoms (Section 2.2.3.2). The coefficients in the HOMO of an allyl anion conjugated to
an empty p orbital can be modelled by mixing in 2 of butadiene. This serves to increase the coefficient at the
g carbon, where some of the reactions take place. The result with the hindered boron-substituted anion 4.71 is
further explained by the steric repulsions from the mesityl groups. The -selectivity with the sulfoxide 4.72
may represent a contribution from coordination by the sulfoxide group stabilising an lithium, and the same
control can be forced on the silicon series by having a coordinating substituent on the silicon in place of the
methyl groups.
sia2B
R
MeI sia2B
mes2B
Li
Li
4.70
R = n-C5H11
O
Ph
Me2SO4
R mes2B
4.71
mes = 2,4,6-Me3C6H2
O
MeI
S
Li
4.72
Ph
S
PrnI
Me3Si
Prn
Me3Si
Li
: 72:28
4.73
: 34:66
The more usual kind of Z-substituted allyl anions 4.74a have extra conjugation as well as the electron
deficiency, and they are usually drawn as dienolate ions 4.74b. They almost always react faster at the carbon than at the g carbon, both with soft and hard electrophiles,327 just like the more simple Z-substituted
allyl anions 4.70 and 4.72.
166
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
OEt
OEt
OEt
MeI
O
O
4.74a
O
4
2
Me
4.74b
OLi
excess
charge:
LiO
–0.4 –0.2
4.75
Using a model like that in Section 2.1.2.3, the extra conjugation for this kind of Z-substituted allyl anion
will mix 3 of the pentadienyl anion with 2 of butadiene (Fig. 4.5). This also suggests that the terminus,
the g carbon, ought to be the more nucleophilic site. Clearly this is not borne out in practice, but
measurements of the total electron population agree with this result. The excess p charge, calculated
from the 13C-NMR chemical shifts of the lithium dienolate 4.75, show that the charge on C-2, the
carbon, is approximately twice that at C-4.328 The simple version of Hückel theory is inadequate for this
problem.
–0.600
0.371
0.19
Z
+
3
0.576
–0.576
= HOMO
2
–0.371
0.576
=
+
Fig. 4.5
–0.47
0.600
0.59
Z
Crude estimate of the coefficients of the p orbitals of a 1-Z-substituted allyl anion
Changing the conjugated system from a dienolate anion to a dienol ether changes the regioselectivity—the
silyl enol ether 4.76 reacts mainly at the g position.329 The change from the oxyanion to the silyl ether
effectively changes the orbitals from being best thought of as close to a pentadienyl anion to being closer to
those for a 1-X-substituted diene. Using the usual arguments, we can predict that a 1-X-substituted diene will
have some of the character of the pentadienyl anion, but also some of butadiene. Adding the frontier orbitals
together gives the orbitals on the right of Fig. 4.6, where we see that the more butadiene character we add in,
the more the coefficient at C-4 will increase relative to that at C-2.
Me3SiO
Pri2CHO
O
Br
ZnBr2 cat.
Pri2CHO
4.76
A calculation330 on a simple dienol ether 4.77, indicates that the total p-electron population remains higher at
the - than at the g-carbon atom, but another calculation,331 on the same ether, gives HOMO coefficients
4.78, which match those in Fig. 4.6 but with a smaller difference. They support the conclusion that the
g carbon ought to be the more nucleophilic site towards soft electrophiles.
4 IONIC REACTIONS—REACTIVITY
–0.500
167
0.500
0.600
–0.371
*
+
0.500
–0.500
–0.371
0.600
0.576
LUMO
–0.191
0.550
–0.600
2
=
0.600
–0.371
HOMO
–0.473
0.588
0.288
1
3
=
+
X
4
Fig. 4.6
–0.250
–0.300
0.191
+
–0.576
3
=
0.371
0.576
0.550
–0.435
2
Crude estimate of the coefficients of the p orbitals of a 1-X-substituted diene
OMe
1.053
OMe
1.071
0.498
-electron population
4.77
–0.492
HOMO coefficients
4.78
An oxyanion substituent on the diene is more powerfully electron donating than a methoxy substituent. It
seems likely, therefore, that it is the model which is inadequate, not the idea of explaining the high
nucleophilicity of the position along these lines. Thus the reactivity at C-4 shown by silyl enol ethers is
the expected behaviour—it is the reactivity at C-2 in the enolate anions that is hard to explain.
Whatever the cause, the selectivity for the position in a Z-substituted allyl anion is powerful enough to
compete with the more or less reliable g-selectivity for an X-substituted allyl anion when both substituents
are present 4.79.
MeI
NC
Li
NMe2
4.79
NC
NC
+
NMe2
NMe2
50:50
4.3.4 Aromatic Electrophilic Substitution
Aromatic rings, except for highly symmetrical systems like benzene itself, are ambident nucleophiles. In
electrophilic aromatic substitution, the rate-determining step is usually the attack of the electrophile on the
p system, to create the Wheland intermediate332 having a tetrahedral carbon atom and a cyclohexadienyl
cation (or other conjugated cation from nonbenzenoid rings). As with the closely similar reaction between
an alkene and a carbocation (see p. 153), the first step is endothermic, and we can expect that the argument
based on the product side of the reaction coordinate will be strong and satisfying, and so it is. The concept
of ‘localisation energy’ has long been used to account for the rates, and sites, of electrophilic substitution.
It is a calculated value of the endothermicity in a reaction and is therefore part of the argument based
on product development control. The plot of localisation energy against rate constant is a good
straight line.333
168
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
4.3.4.1 Molecular Orbitals of the Intermediates in Electrophilic Attack on Monosubstituted Benzenes. The
standard explanation for the regioselectivity in aromatic electrophilic substitution of monosubstituted benzene rings, appropriately enough for an endothermic rate-determining step, assesses the
relative stability of the possible cyclohexadienyl cations and assumes that the transition structures
leading to them will be in the same order. With anisole 4.80, an X-substituted benzene, substitution
takes place in the ortho and para positions, rather than in the meta position, because the intermediates produced by ortho and para attack 4.81 and 4.82 are lower in energy than the intermediate
4.83 produced by meta attack. The energies of the former intermediates are lower because of the
coherent overlap of the lone pair of electrons on the oxygen atom with the conjugated cyclohexadienyl cation orbitals. This overlap is not possible with the meta intermediate. The overlap is easy
to illustrate with curly arrows, and we can see that arrows cannot be drawn in the same way on the
meta intermediate 4.83.
OMe
OMe
OMe
OMe
H
+
E
E
+
+
H
4.80
E
E H
4.82
4.81
4.83
However, we ought to be clear that this valence bond description is a superficial argument (which fortunately
works). Curly arrows, when used with a molecular orbital description of bonding, work as well as they do
because they illustrate the electron distribution in the frontier orbital, and for reaction kinetics it is the
frontier orbital that is most important. In the present case, we are using a thermodynamic argument, for which
we need to know the energy of all of the filled orbitals, and not just one of them. To assess the energies of the
three possible intermediates 4.81, 4.82 and 4.83, we can, for simplicity, ignore the fact that one of the atoms
is an oxygen atom, and use instead the simple hydrocarbon-conjugated systems 4.85, 4.86 and 4.87 which are
isoelectronic with them. We are using, in other words, the benzyl anion 4.84 as a model for an X-substituted
benzene ring.
H
E+
E
+
+
H
4.84
4.85
E H
4.86
E
4.87
The calculated16 energies and coefficients of the p orbitals of these intermediates are shown in Fig. 4.7. Note
that the larger the value the greater the p-stabilisation and the lower the energy. Although the calculations
do not give good absolute values for the energies, they get the relative energies right, which is all we need be
concerned with.
We can see in Fig. 4.7 that the main reason why the total p stabilisation of 4.85 (3.50) and 4.86 (3.45) is
greater (3.08) than that of 4.87 is that the highest filled orbital, 3 in 4.87, is not lowered in energy (as 3 is
in the intermediates 4.85 and 4.86) because there are no p-bonding interactions between any of the adjacent
atoms—it is a nonbonding molecular orbital. This is, of course, the same point that the curly arrows were
making but we ought to make sure that the two lower-energy orbitals do not compensate for the high energy
of 3 in the intermediate 4.87. In fact, they do to some extent, but not much: we can see that 1 of 4.87 is
4 IONIC REACTIONS—REACTIVITY
169
–0.295
–0.431
0
0
0.730
3
0.521
0
0.436
–0.444
3
0.45
–0.418
0.232
–0.325
0.52
0.521
0.230
3
–0.418
0.444
0.232
0
0.418
0
1.0
2
1.25
1.18
0.500
0.521
0.232
0.316
0.500
2
0.372
–0.195
0.316
2
–0.418
–0.232
–0.512
–0.602
–0.521
0.232
0.316
1.80
0.521
0.325
0.418
1
1.93
0.232
1.90
0.628
0.512
0.602
0.316
1
1
0.500
0.521
0.418
0.230
0.372
0.195
Fig. 4.7 Coefficients and energies of the p molecular orbitals of the intermediates in the electrophilic substitution of the
benzyl anion at the ortho, para, and meta positions
actually lower in energy (larger ) than 1 of 4.85, and 2 of 4.87 is lower than 2 of 4.86. Indeed, the sum of
1 and 2 for 4.87 is greater than ( 1 þ 2) for both 4.85 and 4.86.
We can also see in Fig. 4.7 the reason for both of these results. The circles drawn round the atoms are very
roughly in proportion to the c2-values—in other words, the electron population; the clear and darkened
circles serve to identify changes of sign in the wave function. If we look at 1 of 4.87, we see four atoms with
high coefficients (two of 0.316 and one of 0.512, each flanking one of 0.602) close together and all of the
same sign. This leads to strong p-bonding and a low energy for this orbital. Such qualitative arguments can
also be applied to 2 in each case, and they serve to give us some confidence in the general rightness of the
calculated values of the energies of the orbitals in Fig. 4.7. These small effects on 1 and 2 clearly do not
compensate for the effect of having no p-bonding in 3 in 4.87, but we do now have a more thorough version
of the original explanation for ortho/para substitution in X-substituted benzenes.
H
E+
E
+
+
H
E
4.88
4.89
E
H
4.90
4.91
In a similar way, we can use the benzyl cation 4.88 as a model for a benzene ring having a Z-substituent.
Again we have three possible intermediates 4.89, 4.90 and 4.91. The p systems of these intermediates are the
170
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
same as the ones we have just been looking at, except that this time only 1 and 2 are filled in each case. We
have already observed that the sum of the values for 1 and 2 is greater for the intermediate 4.91 which is
the result of attack in the meta position. This, then, is the product-development argument for meta substitution in Z-substituted benzenes.
Furthermore, we can explain the relatively slow rate of such substitutions and the relatively fast rate of the
ortho and para substitutions in X-substituted benzenes by using only the p energies of the orbitals together
with the argument based on the contribution of product-like character to the transition structure. It is
summarised in Fig. 4.8. The endothermicity of 1.28 on the right is not much greater than that for benzene
(1.27); however, the presence of two positive charges in the intermediate on the right has not been allowed
for, and this will obviously raise the energy of this intermediate above that shown.
H
2.73β
medium rate
E
3.08β
H
4.0β
4.36β
Fig. 4.8
H
slow rate
fast rate
3.50β
E
E
4.36β
Relative rates of aromatic substitutions based on product-like character in the transition structure
This is an adequately satisfying explanation for the well known ortho/para and meta directing effects of
aromatic substituents. For all that the argument from the starting material side of the reaction coordinate is
inherently weak, frontier orbitals are often invoked,334 and so we should look at how well they cope.
Arguments based on the starting material side of the reaction coordinate are worth looking at335 because they
work quite well, as we shall see, in explaining many of the observations in this field.
4.3.4.2 The Frontier Orbitals of Monosubstituted Benzenes. The problem with using frontier orbital
theory with simple aromatic compounds is that there are two or more high-energy molecular orbitals close in
energy, and the HOMO itself is not of such overriding importance. In benzene itself, the HOMO is a
degenerate pair 2 and 3 (Fig. 1.43), which, taken together with equal weight, make the frontier electron
population on each atom equal. When a single substituent is attached, the degeneracy is lifted, with 3
unchanged in energy, because the substituent is in the node, and 2 either raised or lowered in energy
depending upon what kind of substituent it is. For C-substituents, we have already seen the orbitals of styrene
in Fig. 2.2, in which the orbital most resembling 2 is 4, raised in energy above 3. Using the same kind of
arguments that we used earlier, in Section 2.1.2, we can estimate what the orbitals of X-substituted benzenes
look like by mixing into the benzene orbitals a bit of the character of the corresponding orbitals of the benzyl
anion. Similarly, for Z-substituted benzenes we need to mix together some of the character of the benzyl
cation and some of the character of styrene. Thus we need a picture of the orbitals of the benzyl system.
The three lowest-energy orbitals (Fig. 4.9)16 are, like those of styrene, and very similar to those of
benzene. The HOMO of the anion (and the LUMO of the cation) is 4, and this, like the corresponding orbital
in the allyl system, has nodes on the alternate atoms. For this reason, it is a nonbonding orbital, and its p
energy is zero. Two simple rules3 enable us to work out the coefficients in such orbitals: (1) Place a zero on
4 IONIC REACTIONS—REACTIVITY
171
0.756
0
LUMO of the cation
HOMO of the anion
–0.378
4
0.397
0.378
1
0.500
0.116
1.26
–0.500
3
–0.500
2
0.238
–0.354
0.500
–0.562
2.1
0.406
1
0.354
0.337
Fig. 4.9
The lower p orbitals of the benzyl system
the smaller number of alternate atoms, i.e. 4.92 rather than 4.93; this identifies the nodes; (2) the sum of the
coefficients on all the unmarked atoms joined to any one of the marked atoms must be zero. Thus we can start
at the para position in 4.94 and call the coefficient there a. The coefficients on the ortho positions must both
be –a, in order that the second rule may be obeyed when applied to the meta positions marked by the zeros.
Now we look at the ring carbon which has the exocyclic carbon atom joined to it. It has a total of three
unmarked atoms next to it, two of which, we have deduced, have coefficients of –a. The exocyclic atom must
therefore have a coefficient of 2a, in order that the second rule is obeyed. Thus the coefficients in 4 are those
shown in the drawing 4.94. Since the sum of their squares must be one, we can give exact numbers to them,
shown in the drawing 4.95. These are the numbers in Fig. 4.9. They are supported by ESR measurements on
the benzyl radical 4.96 (¼ 1.64).61
0
0
0
0
2a
2/√7
0
0
–a
–a
16.4 gauss
–1/√7
–1/√7
5.1 gauss
and not
0
0
4.92
0
0
0
0
0
a
1/√7
4.93
4.94
4.95
–1.8 gauss
6.1 gauss
4.96
X-Substituents, like C-substituents, raise the energy of the HOMO to create 4, because we mixed in some of 4
of the benzyl anion, but they leave 3 unchanged. In contrast, Z-substituents lower the energy of 2, but also
leave 3 unchanged, making it the HOMO by default. The result of lifting the degeneracy is to create definite
HOMOs and, not far below them, next highest occupied molecular orbitals (NHMOs), as shown in Fig. 4.10.
We can now see that the coefficients of the HOMO of the benzyl anion are high on the ortho and para
positions, and zero on the meta positions. X-substituted benzenes can be expected to reflect this character,
with calculations on phenol, for example, giving HOMO coefficients of 0.34 at the ortho positions, –0.496 at
the para, and –0.22 at the meta.336
However, it is no longer a simple matter to use the HOMO to predict the nucleophilic sites because it is no
longer safely the appropriate frontier orbital separable from all the others. For example, it is clear from the
orbitals in Fig. 4.9 that the ortho and para positions are not strongly differentiated from the meta in
Z-substituted benzenes. The ortho and meta positions are the most electron-rich in the HOMO, but the
NHOMO, not much below the HOMO in energy, adds electron population to the para position. Fukui
172
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
X
C
Z
4
2
4
C
3
X
3
3
Z
3
2
Fig. 4.10 HOMOs and NHOMOs of monosubstituted benzenes
explicitly examined this problem,337 defining the frontier electron population, to combine with the HOMO
any orbitals equal in energy to or just below it. He estimated the effective p-electron population (f) at any
specific site in an aromatic ring using Equation 4.6:
f ¼2
c23 þ c22 eDDl
1 eDDl
4:6
where c3 and c2 are the coefficients at that site in the two highest-energy p orbitals 3 and 2, respectively,
with the one labelled 3 having arbitrarily the higher energy, Dl is the difference in energy between 3 and
2, and D is a constant (3 is used in fact) representing some kind of measure of the contribution of 2 to the
overall effect. As it ought, this expression gives the higher-energy orbital 3 slightly greater weight. We can
use Fukui’s frontier electron population f from Equation 4.6 to correct for the presence of the two highenergy filled orbitals contributing to the third term of Equation 3.13. For benzonitrile 4.98 and nitrobenzene
4.99, typical Z-substituted benzenes, more parameters were needed to cope with the presence of heteroatoms, but the f values for styrene 4.97 and these two compounds do show the right pattern, correcting for the
presence of an awkward pair of frontier orbitals.
0.683
CN
0.259
0.264
0.170
NO2
0.247
0.318
0.098
0.181
0.212
0.335
0.219
0.259
0.246
0.181
4.97
4.98
4.99
Clearly the frontier orbital explanation for reactivity, and for ortho/para and meta selectivity, in the
conventional mechanism for aromatic electrophilic substitution is less than compelling—the orbital effects
are not opposing the standard pattern, but the original argument based on the stability of the intermediates
remains more satisfying, just as it should for an endothermic reaction.
If we turn to the SET mechanism, most of the same features return. The key step is the electron transfer within a
charge-transfer complex, which is often detectable with the more nucleophilic aromatic rings or with highly
conjugated or electron-deficient electrophiles by its long wave UV or visible absorption.338 High reactivity is
encouraged by the formation of well-stabilised radicals, and by a small energy difference between the HOMO of the
aromatic ring and the LUMO of the electrophile. The interesting feature with this mechanism is that the regioselectivityisdeterminedbytheeasewithwhichtheradical couplingtakes placeat each of thesitesinthebenzene ring.
4 IONIC REACTIONS—REACTIVITY
173
This is determined by the coefficients in the singly occupied molecular orbital (SOMO), which will be the orbital
that had been the HOMO of the aromatic ring before the electron was transferred from it. However, we meet again
the presence of another orbital close in energy, and the absence, in effect, of a straightforward SOMO, since a single
electron transfer from the NHOMO to the HOMO (SOMO) does not have a high energy barrier. The explanation for
the regioselectivity therefore uses the same orbitals in both the conventional and the SET mechanism.
4.3.4.3 Halogenobenzenes. It is well known that the halogenobenzenes are unusual in showing a mixture
of the properties of the Z- and X-substituted benzenes. Like Z-substituted benzenes, they undergo electrophilic substitution more slowly than benzene, but, like X-substituted benzenes, they are ortho/para directing.
On the ‘product’ side of the reaction coordinate, we are on weak ground. The intermediates 4.100 and
4.101 could be stabilised relative to the corresponding intermediate in benzene. The halogen is an
X-substituent, with a lone pair of electrons, and there should be some p bonding gained by overlap of the
kind shown by the benzyl anion. As the halogens are so much more electronegative and, below fluorine, so
much larger than carbon, the overlap will be feeble. If the energy of the intermediates is lowered, then we
have a problem in explaining the slower rate of attack by electrophiles. Alternatively, if the cationic centres
are not stabilised, perhaps also because of electron withdrawal in the framework, we have difficulty in
explaining why the ortho and para intermediates 4.100 and 4.101 are selectively formed, rather than the
product of meta attack 4.102. We shall find that there is no paradox in the frontier orbital explanation or in the
SET mechanism—the factors affecting the overall rate are not the same as those affecting regioselectivity.
Cl
Cl
Cl
H
E
H
E
4.100
E
H
4.101
4102
We are however in difficulty, because the nonmathematical description of the orbitals we have been using is
inadequate—even simple Hückel theory is not particularly good when there are strongly electronegative atoms
present.Nevertheless,we havenodifficulty inseeingthat theperturbationtreatment leadingto Equation3.13makes it
possible to have ortho/para substitution at a reduced rate: the o/p orientation is mainly dependent on the coefficients
and overall charges at each of the atoms, and the reduced rate could be largely determined by the energies of the higher
occupied orbitals. The same is true of the SET mechanism which draws on the same features. However, we are in
difficulty in showing that this possibility is indeed true, unless we are prepared to do fairly elaborate calculations.
4.3.4.4 Frontier Orbitals of Polycyclic Aromatic Molecules. In the larger aromatic systems we sometimes have a clear HOMO to use for a frontier orbital treatment, but in many others we have the problem of
more high energy orbitals than just the HOMO contributing to nucleophilicity. The numbers on the structures
in Fig. 4.11 are either (for the first seven compounds) the coefficients of the HOMO of the molecule18,339 or
(for the remaining five) the frontier electron population (f) calculated using an equation like Equation 4.6
modified to deal with the presence of electronegative heteroatoms. The preferred site of electrophilic attack
in the nitration of all the aromatic molecules is indicated by an arrow pointing from it (or them, in some
closely balanced cases).340 There are even more examples in Section 6.5.4.6, where they are introduced in
connection with another problem. Except for the slightly anomalous pyrrocoline, the arrow does indeed
come from the largest (or larger) number. Thus, in all these cases, we have the situation described in
Fig. 3.3a, where the lower-energy product and the lower-energy approach to the transition structure are
connected smoothly by what is evidently the lower-energy pathway. We can feel confident, in a situation like
this, that we have a fairly good qualitative picture of the influences which bear on the transition structure.
174
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
0.315
4%
0.233
0
0.440
0.425
–0.311
–0.042
0.174
–0.340
–0.220
0.263
0.163
0.091
27%
0.415
34%
–0.38
0.543
–0.336
0.368
–0.164
0.371
0.296
0.259
0.600
0
0
N
H
NO2+
–0.38
0.345
0.47
0.595
0.218
0.058
–0.01
0.54
–0.38
0.219
0.217
O
–0.23
0.031
N
H
0.233
0.454
0.191
N
0.141
0.289
0.527
35%
0.214
0.492
all other
electrophiles
0.177
0.454
0.220
0.157
0.364
0.115
0.013
0.394
N
0.534
N
0.362
0.072
0.300
N
0.201
47%
0.322
Fig. 4.11
0.057
Frontier electron populations and the sites (arrowed) of nitration
Fukui341 also suggested another parameter sr, defined in Equation 4.7:
sr ¼
occ : c2
X
j
E
j
j
4:7
in which cj is the coefficient at the atom r in the filled orbital j, and Ej is the energy of that orbital. He called sr
the superdelocalisability, both in unsubstituted and substituted benzene rings. This expression bears an
obvious relation to the third term of Equation 3.13. Using a single electrophile—the nitronium ion—a plot of
the rate constant for nitration at particular sites in a large range of aromatic hydrocarbons against sr gives a
good correlation over several powers of ten in rate constant.270
4.3.4.5 ortho/para Ratios.244,299 The proportion of ortho to para substitution ought to be susceptible to
molecular orbital treatment, but we should not be surprised to find that such treatment has had only a little
success as yet. The changes in ortho/para ratios are relatively small, and steric effects are well known to be
important in reducing the proportion of ortho product in many cases. Furthermore, the molecular orbital
treatment we have been using is far from complete in identifying all the factors which contribute to transition
structure energies.
We can, however, see in the p molecular orbitals that product-like character in the transition structure favours
ortho substitution over para for C-, Z- and X-substituted benzenes. When we look at the sum of the energies for
the filled molecular orbitals of the intermediates 4.85 and 4.86, we see (Fig. 4.7) that the total p stabilisation of
the former (3.50), which is linearly conjugated, is greater than the latter (3.45), which is cross-conjugated.
Similarly with a Z-substituted benzene, the former gives a p stabilisation of 3.05 and the latter 2.93. The
difference is greater in the Z-substituted case, and this is, in fact, the observed trend (Table 4.5): insofar as
4 IONIC REACTIONS—REACTIVITY
175
Table 4.5 o/2p ratios in aromatic nitration of PhR as a function of substituent R342
Type of substituent
R
%o
%m
%p
o/2p
XCZZ-
OMe
Ph
CO2Et
NO2
17
53
28
6
—
—
68
93
83
47
3
0.25
0.10
0.56
4.3
12.8
Z-substituted benzenes give any ortho and para products, the ortho/para ratio is greater than it is for C- and Xsubstituted benzenes, and the more powerfully the Z-substituent is electron withdrawing, the more marked is the
effect.
Turning to the frontier orbitals, we see that a C-substituted benzene ring has a higher coefficient (even
allowing for the presence of two high-energy p orbitals) on the para than the ortho position 4.97. Soft
electrophiles should give more substitution in the para position, which is what is observed with biphenyl
(Table 4.6). Nitration involves a fairly hard electrophile (NO2þ), and so does protonation; the bromonium
ion will be harder than the neutral halogens, and mercuration involves a very soft electrophile (Table 4.1).
The o/2p ratios fall in this order.
Table 4.6
o/2p ratios in aromatic substitution as a function of the electrophile343
Electrophilic substitution
o/2p
for toluene (Ph-X)
o/2p
for biphenyl (Ph-C)
Hydroxylation
Chlorination with Clþ
Bromination with Brþ
Proton exchange
Protodesilylation
Nitration
Chlorination with Cl2
Friedel-Crafts ethylation
Sulfonation
Mercuration
Bromination with Br2
Friedel-Crafts acetylation
2.00
1.63
1.29
1.06–0.3
0.84
0.72
0.97–0.25
0.47
0.25
0.25
0.25–0.11
0.0006
—
—
0.69
1.0–0.19
2.14
1.68
0.32
0.41
—
0.01
0.03
very small
For a Z-substituted benzene ring, the total electron population is usually calculated to be higher on the ortho
than on the para position (and much higher on the meta, of course). The frontier electron population f is also
higher on the ortho than on the para position in nitrobenzene 4.99, so again all three molecular orbital
contributions, the low p energy of the intermediate, the relatively high charge and the frontier orbital
coefficient, combine to explain the observation of high o/2p ratios for this compound in Table 4.5.
For an X-substituted benzene, the total charge in the p system is larger on the ortho position, but the
frontier electron population is larger on the para position (0.34 at the ortho positions, –0.496 at the para for
phenol).336 We again expect the softer electrophiles to give more para substitution. This fits moderately well
(Table 4.6) with some of the experimental observations. Nitration and bromination with Brþ give higher o/2p
ratios with toluene than the softer electrophiles involved in halogenation with molecular halogen and in
mercuration. Furthermore, the halogens, whether as Xþ or X2, are in the right order: chlorine is harder than
176
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
bromine and gives higher o/2p ratios. Friedel-Crafts acylation probably involves an acylium ion, but it seems
likely that this species, although formally charged, will also have a low-energy LUMO and hence accept a
high frontier orbital contribution.
We cannot take this argument far. Steric effects are bound to be present, and there are striking anomalies.
Thus hydroxylation (trifluoroperacetic acid), has a soft electrophile, but gives a high o/2p ratio, and sulfonation
has a relatively hard electrophile (usually solvated SO3), but appears to have a rather low o/2p ratio. This latter
observation is particularly likely to be a steric effect, because sulfonation, not unexpectedly, is unusually
sensitive to steric effects, and it is also unusual in being reversible. There are even a few reactions in which it is
the second step, the proton loss, which is rate-determining and hence product-determining.344
The proportion of ortho attack in any of these reactions is quite dependent upon the reaction conditions
(thus the numbers in Table 4.5 are not the same as those in Table 4.6, the data coming from different sources).
However, none is more sensitive than proton exchange. There is a steady decrease in the proportion of ortho
attack as the acid strength is reduced (Table 4.7). The nearer the electrophile is to being a free proton, the
harder it is, and the more ortho substitution there is. The changes in the o/2p ratio are unlikely to be all steric
in origin, because the same trend is seen with toluene, with biphenyl and with tert-butylbenzene. Thus the
frontier orbital theory is moderately successful in a field notoriously beset with confusing data and multifarious influences on the energies of the transition structures.
Table 4.7
o/2p ratios for proton exchange as a function of acid strength343
Conditions
o/2p
for toluene (Ph-X)
o/2p
for biphenyl (Ph-C)
1.06
1.00
0.98
0.60
0.49
0.50
0.28
—
—
—
0.63
0.60
0.25
0.19
75% H2SO4
71% H2SO4
65% H2SO4
CF3CO2H-H2O
CF3CO2H
Liquid HI
Liquid HBr
4.3.4.6 Pyrrole, Furan and Thiophen. Electrophilic substitution in these three heterocyclic rings takes
place faster at the 2-position than at the 3-position (Fig. 4.11). The p molecular orbitals of pyrrole are
representative of all three—they are shown in Fig. 1.69, where 3 is the HOMO 4.103 (with a node running
through the heteroatom, it is the same as 2 of butadiene). The larger coefficients in the HOMO are at C-2
and C-5, and the frontier orbitals explain the regioselectivity tellingly.345 The pattern is extendible to their
benz analogues (Fig. 4.11). It is also effective in explaining a feature of gas-phase reactions in which most
electrophiles attack C-2, but a few hard electrophiles attack the heteroatom or C-3.346 The total charge
distribution in the p system 4.104 is calculated from the sums of the squares of the coefficients shown in
Fig. 1.69. The heteroatom and C-3 carry more of the charge, and so hard electrophiles can attack there for the
usual electrostatic reasons.
0.37
HOMO (
3)
0.58
charge ( c)
N
H
4.103
0.60
0.54
N
H
0.76
4.104
4 IONIC REACTIONS—REACTIVITY
177
Since this is an endothermic reaction, a better explanation for attack at C-2 ought to reside in the relative
energies of the intermediates 4.105 and 4.106. They both have conjugated systems of four p orbitals, with the
heteroatom at the end in 4.105 and inside in 4.106. It is not obvious why the former should be lower in energy
than the latter, although calculations agree that it is. Without the benefit of a calculation, one is reduced to
saying that the conjugated system 4.105 is linearly conjugated, with the lone pair on the nitrogen atom
overlapping with the p system of an allyl cation 4.105b, whereas the conjugated system 4.106 has the lone
pair on the nitrogen atom overlapping with the p bond and an isolated cation 4.106b. This essentially
valence-bond description hardly amounts to a satisfying explanation, although it does resemble the argument
that a linearly conjugated system (like 4.85) is lower in energy than a cross-conjugated system (like 4.86).
E
H
N
H
E+
3
E
H
+
N
H
4.106a
4.105a
2
E
N
H
H
N
H
E
H
4.105b
+
N
H
4.106b
4.3.4.7 Pyridine N-oxide. A special case of aromatic electrophilic substitution is provided by the
ambident reactivity of pyridine N-oxide 4.107. Klopman230 has used Equation 3.13 to calculate the
relative reactivity (DE values) for electrophilic attack at the 2-, 3- and 4-positions as it is influenced by
the energy of the LUMO of the electrophile. He obtained a graph (Fig. 4.12) which shows that each
position in turn can be the most nucleophilic. At very high values of Er – Es (hard electrophiles), attack
should take place at C-3; at lower values of Er – Es, it should take place at C-4; and, with the softest
2-position
3-position
4
4-position
E
3
N
O
4.107
E LUMO(electrophile)
Fig. 4.12
Electrophilic substitution of pyridine N-oxide
2
178
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
electrophiles, it should take place at C-2. Attack at each of these sites is certainly known: the hardest
electrophile SO3 does attack the 3-position,347 the next hardest (NO2þ) the 4-position,348 and the softest
(HgOAcþ) the 2-position.349 This time, without the complicating steric effect, sulfur trioxide is showing
the expected behaviour.
However, this reaction is really more complicated. The sulfonation, for example, almost certainly takes
place on the O-protonated oxide rather than on the free N-oxide, and this must affect the relative
reactivity of the 2-, 3- and 4-positions. The value of the exercise is not so much in the detail of this
particular example as in the way in which it shows how a single nucleophile, such as pyridine N-oxide,
can, in principle, be attacked at different sites, depending upon the energy of the LUMO of the
electrophile.
4.4
Electrophilicity
Electrophiles in general are characterised by having a low-energy LUMO and electron deficiency, either as a
full positive charge or as a polarised bond with a partial positive charge at one or more sites, but there is no
single scale of electrophilicity, any more than there is for nucleophilicity. Simply from general experience,
halogens, especially assisted by coordination to a Lewis acid, are powerful electrophiles, as is the nitronium
ion. Among other heteroatom electrophiles, nitrosyl chloride, the diazonium ion, and metal halides like
mercury(II) chloride are less electrophilic in approximately that order. Among carbon electrophiles,
carbocations like tert-alkyl, the acylium ion, the trityl cation, protonated carbonyl groups, and iminium
ions are less electrophilic, approximately in that order, following the order of the extent to which the
carbocation is stabilised by conjugation with an X-substituent. Neutral carbon electrophiles like carbonyl
compounds and alkyl halides are less electrophilic still, with the former, breaking a p bond, more electrophilic than the latter, breaking a bond.
4.4.1 Trigonal Electrophiles
Trigonal carbon electrophiles, other than simple carbocations, almost always react with nucleophiles
with the formation of a tetrahedral intermediate or product, and this step, often rate-determining, may be
followed by the expulsion of a nucleofugal group, if there is one. The direct displacement of a nucleofugal
group from trigonal carbon is rare.350 Carbonyl groups, the most important trigonal electrophiles, are
electrophilic in the order: acid chlorides > aldehydes > ketones > esters > amides > carboxylate ions.
This list, where we are comparing like with like, is easily explained. Setting aside the acid chloride for the
moment, the p energy of the conjugated system in the starting materials is lowered by the substituent X,
with the oxyanion (X ¼ O–) most effective, a methyl group the least effective, and a hydrogen atom
making no contribution at all. This allows us to rank the p energy of the starting materials in order on the
left in Fig. 4.13. In the tetrahedral intermediate, this overlap is removed or rather it is reduced to an
anomeric effect (see pp. 96–98) which, being in the system, is less. This means that the energies of the
intermediates, although probably in the same order, are closer together. The activation energy
for disrupting the p stabilisation is therefore least for the aldehyde DEH and greatest for the carboxylate
ion DEO-.
This satisfying approach also works to explain why imines and thioketones are less electrophilic than
ketones, and why ketenes are more electrophilic than isocyanates, which are more electrophilic than carbon
dioxide. It is possible to account for the order of electrophilicity using only the energy of p*CO, which is the
LUMO for each of the carbonyl compounds.351 While gratifying, this explanation is inherently
less satisfactory, since it only looks at one side of the reaction coordinate, but, summarising the effects of
C-, X- and Z-substituents on the energy of the LUMO of a reagent, following the arguments developed in
Chapter 2, leads to the following generalisation:
4 IONIC REACTIONS—REACTIVITY
179
Nu–
X
X=H
Nu
O
X
Nu
O–
X
O–
EH
X = CH3
X = OR
X = NR2
X = O–
Fig. 4.13
EO–
Relative energies of starting materials, transition structures and tetrahedral intermediates for nucleophilic
attack on carbonyl groups
C- Substituents
lower the energy of the LUMO a little and may somewhat increase electrophilicity.
X-Substituents
raise the energy of the LUMO and decrease electrophilicity.
Z-Substituents
lower the energy of the LUMO and increase electrophilicity.
Thus an -diketone is unmistakably more electrophilic than an ordinary ketone—the energy of the starting
material is raised by the conjugation of the two carbonyl groups (see p. 84), and the energy of the LUMO is
lowered, since the extra carbonyl group is a Z-substituent. A simple conjugated ketone, however, has the
LUMO energy lowered by conjugation, but so is the energy of the starting material lowered, and the two
effects work in opposition. In practice ketones like acetophenone are usually less reactive towards nucleophiles than simple ketones like acetone.
Acid chlorides are more electrophilic than aldehydes, even though there is a weak stabilising conjugation
between the lone pair on the chlorine atom and the carbonyl p* orbital. There are three contributions to this
anomaly: (i) the p stabilisation is small, because chlorine is electronegative, and consequently the energy
match is poor; (ii) the p stabilisation is offset by strong inductive electron withdrawal along the C—Cl bond,
raising the electrophilicity of the carbonyl group; and (iii) anomeric stabilisation (see pp. 96–98) in the
tetrahedral intermediate is greater—conjugation of the oxyanion with the C—Cl * orbital pulls down the
energy of the transition structure. Although these effects are also present with esters, they are too small to
override the conjugation of the lone pair on the oxygen stabilising the starting material, but there is a more
delicate balance with acid anhydrides, which are similar in electrophilicity to aldehydes.
In one important case, stabilisation in the intermediate plays a larger role in determining electrophilicity than the differences in the energy of the starting materials. In contrast to the order of
electrophilicity in alkyl halides in SN1, SN2, E1 and E2 reactions (I– > Br– > Cl–>> F–), aromatic
180
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
halides are electrophilic in the opposite order.352 2,4-Dinitrofluorobenzene (4.108, X ¼ F) reacts
600 times faster with methoxide ion than 2,4-dinitrochlorobenzene, and 3100 times faster than
2,4-dinitroiodobenzene. The explanation is that the anomeric effect between the methoxy oxygen
and the C—halogen bond in the intermediate 4.110 combines with stabilisation from negative
hyperconjugation between the C—halogen * orbital and the cyclohexadienyl anion p system. Both
interactions lower the energy more for the C—F bond than for the other halogens, whereas the
overlap of the lone pair on the halogens with the p system of the starting material 4.108 is relatively
small. Thus the energy picture, Fig. 4.14, is like a mirror image of Fig. 4.13. The structure of the
intermediate 4.110 significantly affects the energy of the transition structure 4.109, and the activation
energy for the fluoride DEF is less than that for the iodide DEI. The normal order is restored when the
second step becomes rate-determining, as it does with highly activated systems.
MeO
OMe
O2N
X
NO2
O2N
4.108
4.109
O2N X
4.110
EI
EF
Fig. 4.14
X
O2N
OMe
O2N
X=I
X = Br
X = Cl
X=F
Relative energies of starting materials, transition structures and tetrahedral intermediates for nucleophilic
attack on aryl halides
A striking example of modified electrophilicity is provided by the imine 4.111.353 The conjugation of the
Si—C bonds (Fig. 2.18) with the C¼N p system raises the energy of the LUMO, making it less electrophilic
than an ordinary imine. Furthermore, since the Si—C bonds are X-substituents, they raise the coefficient on
the imine carbon atom in the HOMO and reduce it in the LUMO (Fig. 2.7), further decreasing the
electrophilicity, since that depends upon the coefficient of the atomic orbital as well as on the energy. The
net result is that the imine 4.111 is a stable compound, unlike other methylene imines, which normally
polymerise before they can be isolated.
N
SiMe3
SiMe3
4.111
4.4.2 Tetrahedral Electrophiles
Some of the same features affect the electrophilicity of tetrahedral electrophiles undergoing SN2 reactions.
Thus some donor substituents on the carbon being attacked reduce the electrophilicity of alkyl halides, where
the order of reactivity is methyl > ethyl > isopropyl > tert-butyl. This is usually explained, of course, as a
4 IONIC REACTIONS—REACTIVITY
181
consequence of steric hindrance to attack on the more substituted carbon atoms, but it has also been
explained354 by making allowance for the change of the coefficient on the carbon atom. The same
hyperconjugation which lowers the energy of the LUMO of the C—Br bond in tert-butyl bromide more
than that in methyl bromide also reduces the coefficient on carbon (because the new orbital is now
delocalised over more atoms), and at the same time lowers the overall energy of the starting material.
These effects on the coefficients and the energy may contribute to the lower reactivity (in SN2 reactions) of
tert-butyl bromide relative to methyl bromide.
Z-Substituents and C-substituents conjugated to the site of attack increase the rates of SN2 reactions.355
The Z-substituent, as it does with -dicarbonyl systems, may partly operate by raising the energy of the
starting material, but most probably both the C- and Z-substituents are primarily operating to lower the
energy of the transition structures 4.112 and 4.113, respectively.356 The forming and breaking bonds have
four electrons in total and any delocalisation of these in allylic overlap (see pp. 23–28 and 72) lowers the
energy of the transition structure in a way that has no counterpart in the reactions on trigonal electrophiles.
This explanation is dramatically supported by the difference in the rate of nucleophilic attack on the benzyl
sulfonium salts 4.114 and 4.115, which react at relative rates of 8000:1. Whereas the open-chain system
4.114 can easily allow the forming and breaking bonds to overlap with the p system of the benzene ring, the
cyclic sulfonium salt 4.115 cannot.357
Nu
Nu
Nu
Et
O
X
Bn
X
4.112
Nu
Et
4.113
4.114
Cl
R
S
S
4.115
N3
N3
R
MeCN, H2O
4.116
4.117
X-Substituents can also accelerate SN2 reactions,358 even though the transition structure seems to have an
excess of electrons at the site of substitution. The transition structures can adjust to take energetic advantage
from more or less stretching of the C—X bond, with the extremes being the perfect SN2 and perfect SN1
reactions. For example a series of ring-substituted secondary benzyl chlorides 4.116 react with azide ion to
give the azide 4.117 in an SN2 reaction, as shown by the first-order dependence upon the concentration of
azide ion and inversion of configuration. The Hammett þ value of –2.9 indicates that electron-donating
substituents R are speeding it up.359 Evidently, a feature that energetically helps the stretching of the C—X
bond, such as an X-substituent on the carbon undergoing attack, or conjugated with it in a substrate like the
chloride 4.116, lowers the energy of the transition structure, and speeds up the reaction. Thus we have the
unusual feature that both X- and Z-substituents can accelerate reactions that are formally SN2.360
X-Substituents, of course, easily accelerate SN1 reactions like the solvolysis of the chloride 4.116 in aqueous
acetonitrile, which has a larger Hammett þ value of –5.6, typical for an SN1 reaction with the formation of
the cationic intermediate accelerated by X-substituents (see p. 76), while Z-substituents slow down their
formation.
The better the leaving group, the more electrophilic an alkyl halide or alkyl sulfonate, with alkyl iodides
and trifluoromethanesulfonates exceptionally reactive. Several factors are at work here: the strength of the
182
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
C—X bond (weak for C—I), its degree of polarisation (high for C—OTf), the energy of the (solvated)
nucleofugal group as measured by the pKa of its conjugate acid (low for HOTf, making triflate a good
nucleofugal group), the LUMO energy (low for C—I), and the coefficient on carbon in the LUMO. Not
surprisingly, a many-parameter equation would be needed to measure electrophilicity, and most important
to measure change as the solvent and nucleophile changes, as we shall see.
4.4.3 Hard and Soft Electrophiles
Except for the last paragraph, the discussion above has been about electrophilicity in general, or within a
related group of electrophiles. However, the picture is not straightforward when we make comparisons
from one group of electrophiles to an unrelated group, or when the nucleophile is changed. Electrophiles
can be hard or soft—the hardest electrophiles are small, charged and have a relatively high-energy LUMO,
and soft electrophiles are large, have little charge and have a conspicuously low-energy LUMO. The
proton, because of its size and charge is very hard. Tables of acidity (pKa values) give a rank order of
thermodynamic electrophilicity of protons attached to various ligands, but the only extensive tables
related to electrophilicity for other electrophiles are the lists of hardness in Tables 3.2, 3.4 and 3.5,
where we see that large metal cations like Hg2þ are relatively soft, in spite of their charge. p-Bonded
species like C¼C double bonds conjugated to Z-substituents are inherently soft, with low-energy LUMOs,
as are other uncharged reagents like methyl iodide, sulfenyl halides and iodine. It is not therefore possible
to compare in any absolute sense the electrophilicity of a soft electrophile like iodine and a hard one like an
acid chloride.
There is a special problem in comparing the hardness and softness of alkyl halides and carbonyl
compounds, the two most common carbon electrophiles. In SN2 reactions, the bond being broken is a bond, with a LUMO higher in energy than that of a C¼O p bond, yet alkyl halides are generally softer
than carbonyl compounds. One big difference is that SN2 reactions are exothermic (otherwise they
would not take place) and the transition structure is early, resembling the starting materials more than
the product, whereas addition to a carbonyl group is often endothermic, with a transition structure more
like that of the tetrahedral intermediate. Arguments about the importance or otherwise of orbital
interactions, and of hardness and softness, apply more effectively to SN2 reactions than to carbonyl
additions, and so the anomaly may be illusory. When the halogen is low in the periodic table, like
bromine or iodine, it is not very electronegative. The C—X bond is not strongly polarised, the overlap is
poor, the LUMO energy low for a bond and the charge on the carbon atom is small. With both frontier
orbital and charge effects small (see p. 156), it is a soft electrophile. In attack on a carbonyl group, the
electrophilic carbon has two bonds from carbon to an electronegative atom, and therefore has a greater
electron deficiency on carbon. Since it is a p bond, it also has a relatively low-energy LUMO. With both
charge and frontier orbital effects large (see p. 156), it is a hard electrophile. Carbonyl groups are well
known to be hard relative to alkyl halides in spite of the lower energy of the LUMO—they are notably
more responsive and better correlated to the basicity of the nucleophile. However, for all the endothermicity of their reactions, carbonyl groups are responsive to the frontier orbital terms; thus a sulfur
nucleophile is about 100 times more nucleophilic towards a carbonyl group than is an oxygen nucleophile of the same basicity.361
Nevertheless, it remains seemingly anomalous that an alkyl halide undergoing nucleophilic displacement
should be a soft electrophile, when a carbonyl group undergoing nucleophilic addition is relatively hard. The
anomaly is made more disturbing if we are wedded to the idea of hybridisation (see pp. 15–17). An
examination of the full set of lower-energy molecular orbitals of methyl chloride (Fig. 1.59) may make
the anomaly less disturbing. Were we to use hybridised orbitals (Fig. 1.59b), we should have an antibonding
orbital (sp3*CCl) which is at least as much antibonding as the bonding orbital (sp3CCl) is bonding. However,
this antibonding orbital is no more the LUMO than CCl in Fig. 1.59a is the HOMO. The latter is only one of
the bonding orbitals, and a proper measure of the total C—Cl bond strength would come much lower in
4 IONIC REACTIONS—REACTIVITY
183
energy than CCl, and would correspond to that of the bonding hybrid orbital (sp3CCl in Fig. 1.59b). There
will be a complementary situation among the antibonding orbitals. This imbalance, in which the true LUMO
(*CCl in Fig. 1.59a) is lower in energy than the antibonding hybrid orbital (sp3*CCl in Fig. 1.59b), is not
found in the corresponding p bond of a carbonyl group, because that orbital is not made up of hybridised
orbitals. Thus, in a comparison of alkyl halide chemistry with carbonyl chemistry, the use of hybridisation
appears to exaggerate how high the energy of the LUMO of the carbon-halogen bond is.
The energies of the LUMOs of the four methyl halides are also ranked in an order that might not at first
sight be easy to guess. In setting up the orbitals CX and *CX like those in Fig. 1.59a, we would look at the
interaction of the px orbitals on carbon and the px orbital on each of the halogens, since this is the major
contribution to bonding. Since the halogens are ordered with the most electronegative having the lowest
energy, we might expect that the *CX orbitals would be in the same order. However, the overlap integral between the px orbital on the halogens and the px orbital on carbon is much smaller for iodine than for the
smaller fluorine. The net result, counter intuitively, is that the LUMO energies of the alkyl halides fall in the
order MeF > MeCl > MeBr >MeI. The iodide is the most reactive and the most soft.362
Even within a group of very similar electrophiles, all soft like primary alkyl halides undergoing SN2
displacement, the scale of electrophilicity is not constant. Thus, in the relative rates of the two reactions
4.118 and 4.119, the iodide (X ¼ I) reacts 1674 times faster with the aniline than with ethanol
(kArNH2 =kEtOH ), but the p-bromobenzenesulfonate 4.118 (X ¼ OBs) reacts only 184 times faster. The
other alkyl halides fall in between.363 The amine is the softer nucleophile, since nitrogen is less electronegative than oxygen, and the iodide is the softest and the p-bromobenzenesulfonate the hardest of the
electrophiles. These results could equally have been discussed as examples of the difficulty of setting up a
single scale of nucleophilicity, since they are related to those for O- and C-alkylation of enolates (see p. 160),
and to the whole discussion of ambident reactivity (see pp. 157–167)
X
X
k
/k
ArNH2
4.118
4.5
H2N
Cl
X=I
X = Br
X = Cl
X = OBs
EtOH
1674
694
639
184
4.119
EtOH
Ambident Electrophiles
The attack of a nucleophile on a conjugated system is susceptible to the same kind of analysis that we gave to
the attack of an electrophile on a conjugated system. In most cases, all the molecular orbital factors, both
those affecting the product stability and those in the starting materials, point in the same direction. We use
the LUMO of the conjugated system (and the HOMO of the nucleophile, of course) as the important frontier
orbitals, as in Fig. 4.15, which shows electrophilic reactivity at the site (or sites) where the arrow points for a
range of carbon electrophiles.364 In each case, there is a high coefficient of the LUMO at the site of attack;
each of them also has a high total electron deficiency at this site; and, with the possible exception of pyridine
4.124, the tetrahedral intermediate obtained from such attack is lower in energy than attack at the alternative
sites.
4.5.1 Aromatic Electrophiles365
4.5.1.1 The Pyridinium Cation. The pyridinium cation 4.126 is even more readily attacked by nucleophiles at C-2 and C-4 than pyridine 4.124. Looking at the product side of the reaction coordinate, the linearly
184
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
0.425
0
0.440
0.470
–0.311
0.102
–0.063
0.220
–0.263
–0.091
4.120
–0.290
–0.511
4.121
0.316
4.122
O
0.454
0.749
–0.190
0.521
–0.127
–0.351
–0.383
0.280
–0.232
N
–0.418
0.684
4.123
4.124
4.125
Fig. 4.15 LUMOs of some carbon electrophiles and the sites of nucleophilic attack upon them
conjugated intermediate 4.127, which also benefits from an anomeric effect if the nucleophile is an
electronegative heteroatom,366 is lower in energy than the cross-conjugated intermediate 4.129, and will
therefore be the product of thermodynamic control. Since this step is neither strongly endothermic nor
always reversible, the orbitals and the charge distribution in the starting material may be important when the
reaction is kinetically controlled. The total p electron deficiency 4.126270 at C-2 of þ0.241 and at C-4 of
þ0.165 indicates that charge control (in other words with hard nucleophiles) will lead to reaction at C-2. This
is the case with such relatively hard nucleophiles as the hydroxide ion, amide ion, borohydride ion and
Grignard reagents.367
(0.165+)
Nu–
4
3
2
products
Nu
(0.241+)
N
N
Me
Me
4.126
4.127
H
Nu
H
Nu– = OH–, NH2–, BH4–, R(MgBr)
Nu
–
H
products
N
N
Me
Me
4.128
4.129
H
EtO2C
CO2Et
O
Nu– = CN–, S2O42–,
,
N
Me
4.130
However, if we look at the LUMO (see p. 60), we find that it has the form 4.128, similar to 4* of benzene,
but polarised by the nitrogen atom. The polarisation reduces the coefficient at C-3, and the coefficient at C-4
is larger than that at C-2, as can be seen from the simple Hückel calculation for pyridine itself 4.124,18 which
gives LUMO coefficients of 0.454 and –0.383, respectively, and an energy of 0.56 (compare benzene with
1 for this orbital). Thus, soft nucleophiles should attack at C-4, where the frontier orbital term is largest.
Again this is the case: cyanide ion, bisulfite, enolate ions, and hydride delivered from the carbon atom of the
Hantsch ester 4.130 react faster at C-4 than at C-2.368
4 IONIC REACTIONS—REACTIVITY
185
4.5.1.2 ortho- and para-Halogenonitrobenzenes. It is well-known that ortho- and para-halogenonitrobenzenes are readily attacked by nucleophiles, as we saw in Fig. 4.14. The first step is usually ratedetermining. Product development control should therefore have ortho attack faster than para attack,
because the intermediate 4.131 with the linear conjugated system will be lower in energy, other things
being equal, than the intermediate 4.132 with the cross-conjugated system.
The Coulombic term will also lead to faster reaction at the ortho than at the para position. The frontier
orbital term, however, should favour attack at the para position. Thus the ESR spectrum of the benzyl radical
(see p. 171), which has the odd electron in an orbital which ought to be a model for the LUMO of a Zsubstituted benzene, shows that there is a larger coefficient in the para position than in the ortho.
Nu
Cl
O
Nu
Nu
Cl
O
N
O
O
N
O
4.131
Nu
Cl
Nu
Nu
Cl
N
N
O
O
N
O
O
N
O
O
O
4.132
There is some evidence which supports this analysis (Fig. 4.16).369 (a) With a charged activating group, as in
the diazonium cations 4.133 and 4.134, attack at the ortho position is faster than attack at the para position
HO
HO
F
F
10 times faster than
N
MeO
Cl
4.135
N
N
4.134
4.133
MeO
between 1 and Cl
4 times faster
than
Z
Z
Z = NO2, CN,
4.136
SO2Me and COMe
N
N
N
N
N
Cl
250 times Cl
faster than
NO2
O2N
4.137
Nu
Y
Nu– = PhS– or MeO–
O2N
N
4.138
O
kPhS –
kMeO –
increases F < Cl < Br < I
O
Fig. 4.16
Relative reactivity of halogenonitrobenzenes
186
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
because of the relatively large Coulombic contribution. With the uncharged activating groups in the compounds
4.135 and 4.136, the order is the other way round. (b) In the latter reaction with the nitro compound (Z ¼ NO2),
with the neutral (and hence softer) nucleophile DABCO 4.137, the preference for para attack is enhanced. (c)
The ratio of the rates at which PhS– and MeO– react with 2,4-dinitrohalogenobenzenes 4.138 is highest for the
iodide and lowest for the fluoride. The former will make the Coulombic term less important, and the latter will
make it more important.370 (d) When the rate of the second step is not rate-determining, the aryl fluoride is more
readily attacked than the corresponding aryl chloride, bromide and iodide. As explained on p. 180, this can be
explained by the anomeric stabilisation afforded to the intermediate, but we can add to it a Coulombic
contribution from the electronegative halogen. The data in Table 4.8 show that the degree to which the fluoride
is the more reactive, is greatest for the harder nucleophiles; but the story is complicated, because the second step
of the reaction, the loss of the fluoride ion, does become rate-determining with some weak nucleophiles.
Table 4.8 Effect of the nucleophile on the relative rates of attack on
the fluoro and chlorodinitrobenzenes
Nucleophile
N:
NO2
O
N
0.11
(H2N)2C=S:
Y
O
O2N
3.26
PhS–
H3N:
MeO–
33
460
890
O–
3160
hard soft
Nu
kF/kCl
4.138
NO2
Y = F or Cl
The ease with which fluorine can be displaced from benzene rings is such that it does not always need
activating groups like nitro to stabilise the intermediate anions—oligofluorobenzenes can undergo substitution reactions. An attempt,371 using frontier orbital theory, to explain the selectivity with which one of
several fluorine atoms is displaced has been contested in favour of a more general electrostatic analysis.372
4.5.2 Aliphatic Electrophiles
4.5.2.1 a,b-Unsaturated Carbonyl Compounds. Most nucleophiles attack ,-unsaturated ketones faster
at the carbon atom of the carbonyl group (e.g. 4.140 ! 4.139) than at the position. Attack at the carbon
(e.g. 4.140 ! 4.141) is commonly the result of a slower, but thermodynamically more favourable, reaction.
For this mode of reaction to show up, the first step must be reversible. Conjugate attack is therefore most
straightforward when the nucleophile is a well-stabilised anion, making the first step easily reversible, as it is
when the nucleophile is a cyanide ion.373
HO
CN KCN, K2CO3, ≤15 °C
O
O
KCN, K2CO3, >15 °C
NC
4.139
4.140
4.141
4 IONIC REACTIONS—REACTIVITY
187
Similarly, the simple lithium enolate 4.143 reacts with cyclohexenone at –78 C to give the product 4.142 of
direct attack, but warming the reaction mixture to room temperature allows this step to revert to the starting
materials, and they then form the thermodynamically more stable product 4.144 of conjugate attack.374
-Dicarbonyl enolates, commonly used in Michael reactions, usually do not allow the isolation of the
product of direct attack, since the first step is even more easily reversible in such cases.
O
CO2Me
O
–78 °C
O
OMe
O
MeO2C
+
> –78°C
4.142
4.143
4.144
Taking the most simple ,-unsaturated carbonyl compound, acrolein, even the simple Hückel calculation
used in Fig. 2.3 shows that, while the total p-electron deficiency is greater at the carbon atom of the carbonyl
group, the coefficient of the LUMO is larger at the position. A better calculation than that used in Fig. 2.3
gives the frontier orbital coefficients and energies in Fig. 4.17.375 We can therefore expect that, if any
nucleophile is going to attack directly at the -carbon atom, it will be a soft nucleophile, responsive to the
frontier orbital term.376 This is borne out by the observation that radicals, which are inherently soft (Chapter
7), add at the position, and that the relatively soft Grignard reagents are apt to give more conjugate addition
than the relatively hard organolithium reagents.377
This simple analysis leaves out of consideration the fact that many additions to ,-unsaturated carbonyl
compounds need or take advantage of coordination to the oxygen atom by a metal cation or a proton, or even
just a hydrogen bond. This is especially true for hydride or carbon nucleophiles. The orbitals of the reactive
species are therefore more like those of protonated acrolein, for which the LUMO has the larger coefficient
on the carbonyl carbon, not the position (Fig. 4.17). Thus even soft nucleophiles can be expected to attack
directly at the carbonyl group when Lewis or protic acid catalysis is involved. It may be that the different
degree of regioselectivity shown by Grignard and lithium reagents is largely a consequence of differences in
the effectiveness of the coordination by the metal—with lithium the more powerful Lewis acid—than in
differences in the hardness and softness of the nucleophiles. The effect of the Lewis acid on regioselectivity
is seen with lithium aluminium hydride reacting with cyclohexenone—in ether, the ratio of direct
to conjugate attack is 98:2 but if the lithium ion is sequestered by a cryptand, the selectivity changes
to 23:77.378
0.51
–0.39
LUMO
*
O
2.5 eV
3
0.59
–0.48
0.48
HOMO
–0.58
LUMO
3*
O
–7 eV
0.60
O
–14.5 eV
2
0.58
0.37
–0.09
0.65
–0.30
HOMO
–0.54
O
–23.5 eV
2
O
0.53
O
H
H
–0.70
H
–0.10
H
H
Fig. 4.17
Frontier orbital energies and coefficients for acrolein and protonated acrolein
188
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
Moving to ,-unsaturated esters, hydroxide ion379 and alkoxide ion380 (hard nucleophiles) react with
ethyl acrylate 4.145 by direct attack at the carbonyl group to give ester hydrolysis and ester exchange,
respectively, whereas the -dicarbonyl enolate ion 4.146 (a softer nucleophile) undergoes a Michael
reaction.381 There is no certainty in this latter reaction that the attack of the enolate anion on the carbonyl
group, in a Claisen-like condensation, is not a more rapid (and reversible) process.382
O
RO
O
O
(R = H, alkyl)
O
O
O
+H+
OEt
4.145
OEt
OEt
OR
EtO
4.145
O
EtO
O
4.146
The ease with which sulfur nucleophiles add to ,-unsaturated esters 4.145 ! 4.147 is also ambiguous:
thiolate anions do not react with esters to give thioesters 4.148, because the equilibrium lies in the other
direction; so we cannot tell what are the relative rates of attack at the two sites of an ,-unsaturated ester,
although it is likely that attack is kinetically controlled.
O
PhS
O
PhS–
OEt
OEt
4.147
SPh
PhS–
4.145
O
O
EtO–
4.148
O
NH3
OMe
H2N
4.149
OMe
4.150
4.149
MeO2C
N
H
CO2Me
4.149
MeO2C
N
CO2Me
CO2Me
4.151
4.152
One case, however, is clear—ammonia and amines do react with ordinary esters to give amides, and it is
known383 that the attack at the carbonyl group is rate-determining and effectively irreversible above pH 7.
Ammonia (neutral and therefore a relatively soft nucleophile) reacts in methanol with methyl acrylate 4.149
kinetically at the position to give the primary amine 4.150, and reaction continues in the same sense to give
successively the secondary and tertiary amines 4.151 and 4.152.384
The more a carbonyl group is like that of protonated acrolein (Fig. 4.17), the more likely is it that all
nucleophiles will attack directly at the carbonyl carbon atom. In agreement with this perception, and in
contrast to its behaviour with methyl acrylate, ammonia reacts with acryloyl chloride 4.153, which has a very
electrophilic carbonyl group, at the carbonyl carbon atom to give acrylamide 4.154.385
O
NH3
Cl
4.153
O
NH2
4.154
4 IONIC REACTIONS—REACTIVITY
189
We have just seen that making the carbonyl group more electrophilic increases the probability that
reaction will take place directly at the carbonyl group. A corollary is that reducing the electrophilicity, as
happens when we have an imine in place of the carbonyl group, increases the probability of getting conjugate
attack. An example of the delicate balance possible with ,-unsaturated imines is seen in the two imines
4.155 and 4.156, which show conjugate and direct attack, respectively, simply by adjusting the degree of
electron withdrawal from the substituent attached to the nitrogen atom. This pattern is seen with organolithium nucleophiles, with which direct attack at the imine carbon is most unlikely to be reversible, and the
selectivity correlates with the calculated LUMO coefficients.386
N
C6H11-c
–0.593
0.514
0.531
4.155
Ph
N
–0.426
4.156
The reduction of ,-unsaturated carbonyl compounds by metal hydrides, and the similar addition of organometallic carbon nucleophiles, is a complicated story.387 It is more common than not, in each case, to get direct
attack at the carbonyl group, but delivery of hydride to the conjugate position is well known. The proportion of
conjugate reduction of ,-unsaturated ketones by hydrides increases approximately in the order of increasing
softness: aluminium hydrides less than boron hydrides less than the carbon hydride which is the active species
4.157 involved when lithium aluminium hydride is used in pyridine.388 Hydride delivered from carbon in the
Meerwein-Ponndorf reduction is constrained by the six-membered ring transition structure 4.158 to give direct
reduction.389 Conjugate reduction is avoided, however electronically favourable it might be, because it would
involve an eight-membered ring.
R
Al
N
H
O
R
Al
O
H
H
O
4.157
4.158
These trends agree with the frontier orbital analysis. In particular, the delivery of hydride from carbon breaks
a relatively unpolarised bond, making the hydride notably soft, as we saw earlier in its capacity to attack
pyridinium salts preferentially at the 4-position. The metal hydrogen bond will be more polarised, and metal
hydrides should therefore be harder. Similarly, the delivery of hydride from boron will make it softer than
when it is delivered from the more electropositive metal, aluminium. It also seems that, among ,unsaturated carbonyl compounds, the susceptibility to conjugate reduction increases in the sequence:
ketones < esters < acids < amides; but there are too few examples to be sure.
With two activating substituents, as in the ester 4.159, conjugate reduction (and conjugate addition of carbon
nucleophiles) is fast and almost always observed with any nucleophile.390 The stability of the conjugated
enolate product 4.160, and Coulombic and frontier orbital factors, all readily explain this observation.
Nu
CN
OEt
Nu
CN
O
4.159
OEt
O
4.160
190
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
4.5.2.2 Allyl Halides. The allyl halide system is related to that of , -unsaturated carbonyl compounds, but shows a number of differences. In bimolecular reactions, direct displacement of the halide
ion (SN2) almost always occurs, and conjugate attack (SN20 ) is rare. Indeed, this is a contentious issue, for
there is little evidence for any completely concerted SN20 -type of reaction.391 If an ion pair, such as 4.161,
is the reactive species, we can see that charge control would strongly favour direct displacement, and we
already know that the presence of the double bond stabilises the transition structure 4.112. However,
attack at the ‘p bond’ may be preferred if frontier orbital control becomes more important, although it is
hard to specify what exactly the orbitals are, in an allyl cation made unsymmetrical by ion pairing at one
end of the conjugated system. It is perhaps significant that the few examples of conjugate reaction which
have been observed are with strikingly soft nucleophiles such as phenylthioxide ion,392 cyanide ion, azide
ion, and secondary amines,393 all in nonpolar solvents, and preferably with some steric hindrance at the position.
Cl
Nu–
Nu
SN2'
Cl
(+)
(–)
Nu–
Nu
SN2
4.161
Organocuprates and a few other carbon nucleophiles sometimes react with allylic halides (or acetates) to
give the product of what looks like an SN20 reaction. However, the mechanism is completely different—
preliminary coordination by the copper or other transition metal to the C¼C p bond is the first step, and the
coordination of the copper changes from -2 to -1 or -3 before a reductive elimination step establishes
the C—C bond.394 Each of these steps affects the overall regiochemistry (and the stereochemistry
discussed in the next chapter), which may look like an SN20 or an SN2 reaction, while mechanistically
being neither.
When the allylic system carries X-substituents, and the solvent is polar, the reaction may take a unimolecular path 4.162 ! 4.164, and the reactions are then SN1 and SN10 . The regioselectivity will be wholly
determined by thermodynamic factors if the only available nucleophile is a good nucleofugal group, with the
product 4.164 having the more-substituted double bond usually favoured. This selectivity will be enhanced
by the greater steric hindrance usually present if the nucleophile is bonded to the more substituted site, and a
corollary is that the thermodynamically less stable isomer 4.162 is the more reactive (by a factor of about 3 in
ethanol at 25 C in this case).395
Cl
4.162
Cl
4.163
4.164
However, if the reaction is not under thermodynamic control, the regioselectivity will be determined by
the coefficients and charges at the - and g-carbon atoms of the allyl cation. We can treat an Xsubstituted allyl cation as resembling an ,-unsaturated carbonyl compound. The orbitals of acrolein
show us that a powerful donor substituent like an oxyanion conjugated to an allyl cation (on the left in
Fig. 4.17) leads the -carbon atom (g in the allyl system) to have the higher coefficient. However, the
4 IONIC REACTIONS—REACTIVITY
191
donor substituent in protonated acrolein (on the right in Fig. 4.17) is a hydroxyl group, and it leads to a
higher coefficient on the carbonyl carbon (equivalent to the position in the allyl system). An allyl
cation having a donor less effective than a hydroxyl ought therefore to have a larger coefficient in the
LUMO at the carbon atom adjacent to it than at the other end. As it happens, the simple device we used
(see pp. 70–86) to deduce the pattern of coefficients in substituted alkenes, does not work for substituted
allyl cations. We would mix the orbitals of an allyl cation (equal on C and Cg) with those of 3* of
butadiene (small on C and large on Cg). This covers the situation for a powerful donor, but no amount of
mixing creates a LUMO with a larger coefficient on C than on Cg. In practice, kinetic control with a soft
and not too large nucleophile leads to attack at the carbon, especially as we are usually dealing with
less powerful donor substituents than a hydroxyl. The methyl groups in the prenyl cation 4.163 are not
powerful donors, and yet, when either of the chlorides 4.162 or 4.164 is solvolysed in water, under
conditions that do not equilibrate the products, the major product (85:15) is the tertiary alcohol 4.165,
showing that capture at the more sterically hindered site in the cation 4.163 is indeed faster than attack at
the primary position giving the alcohol 4.166.395
OH
H2O
H2O
85
4.165
HO
15
4.163
4.166
A more extended version of the same idea accounts for the regioselectivity of attack by cyanide ion on the
cation 4.168, derived from furylmethyl chloride 4.167, which leads, counter to the thermodynamics, to the
product 4.169 of an SN100 reaction, and hence to the re-aromatised product 4.170.396
NC–
H2O
Cl
O
4.167
O
4.168
+H+
NC
O
4.169
–H+
NC
O
4.170
4.5.2.3 Unsymmetrical Anhydrides. Unsymmetrically substituted phthalic and maleic anhydrides show
some curious selectivities. The selectivity for attack at one carbonyl group rather than the other is large
enough to be useful to synthetic chemists, and it demands some kind of explanation.
Nucleophilic attack on the carbonyl groups of the maleic anhydrides 4.171 by lithium aluminium hydride
is completely selective for attack at C when R is a methoxy group, and still quite high (88:12) when R is a
methyl group. Both methoxy and methyl are X-substituents conjugated to the carbonyl, and ought to
reduce the coefficient of the atomic orbital at the site. This makes the site the more electrophilic by
default, in spite of the greater steric hindrance there. Calculations support this argument with larger
coefficients at C in the LUMO for methoxy and methyl, and with the difference between them reduced
for the less powerful X-substituent.397
However, when the attacking reagent is larger, as with a phosphorus ylid, the selectivity is in favour of
attack at C when R is a methyl or phenyl group (: 6:94 and 0:100, respectively), although still in favour of
attack at C when R is a methoxy group (: 100:0).398 It appears that the intrinsic (orbital controlled)
reactivity at C is preserved with the better X substituent, but steric effects override it with the others. The
fact that the methoxy group is quite as effective as it is may also be because it can help, by coordination, to
deliver the reagent to the nearer carbonyl group.
192
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
LUMO coefficients
c
c
R=MeO
R=Me
R=Ph
0.39
0.36
0.22
–0.34
–0.35
–0.25
R
O
O
LUMO coefficients
c
c
O
4.171
O
R=MeO –0.26
R=Me
–0.329
R=NO2 –0.21
O
0.30
0.328
0.08
O
R
4.172
This simple hope is not much supported by the results with the anhydride 4.172. The X-substituents,
conjugated to the carbonyl, ought to make the reaction intrinsically selective for attack at C, and the
Z-substituent for attack at C. The coefficients in the LUMO match this expectation, except for R ¼ Me,
when the values are barely different. In spite of the fact that C is still the sterically more hindered
carbonyl group, attack is selectively at C for all three substituents (NaBH4, : 87:13, 57:43 and 83:17,
respectively).399,400
The : ratio is suspiciously dependent upon the solvent, coordination may be playing a part here too,
and there is a further complication in both series. For nucleophilic attack on a carbonyl to take place,
coordination to the oxygen atom by a Lewis or protic acid is often necessary, as we have already seen with
,-unsaturated ketones. This means that there is a pre-equilibrium step between the bare carbonyl
compound, used in the calculations, and the reactive species. There will be a higher concentration of the
intermediate with the metal or other catalyst coordinated to the more basic of the two carbonyl groups,
which will be the carbonyl in 4.171. However, when the coordination is to the less basic carbonyl group,
it will create a more reactive species. The balance of all these effects is hard to predict, and the overall story
is too complicated for simple analysis. This is not an uncommon situation, and care must be taken in any
analysis of subtle steric and electronic effects like those operating here and in much of the discussion about
enones above.
The story is even more remarkable for unsymmetrical succinic anhydrides 4.173, where hydride reduction
takes place with surprising selectivity at the obviously more hindered carbonyl group, giving the lactones
4.174 and 4.175 in a ratio of 95:5.399,401
LUMO coefficients
c
c
0.599
–0.591
LiAlH4 or NaBH4
O
O
4.173
O
+
O
4.174
O
O
95:5
O
4.175
The electronic difference between the two carbonyl groups is that C has a hyperconjugative interaction
with a CMe2 group, and C with a CH2 group. Which has the larger hyperconjugative effect is an
ongoing debate—as mentioned already on p. 86—the hydrogen atom is more electropositive than
carbon, and so the bond is more polarised, and better able to stabilise electron deficiency. On the
other hand, the methyl group has a greater stock of electrons that can participate in delocalisation. The
calculation in this case gave C the larger coefficient in the LUMO, implying that C—H is the better at
hyperconjugation, and agreeing with the experimental result. With Grignard reagents, when steric
effects are more important, attack takes place unexceptionably at the less hindered site, C , and when
the two substituents are chlorine atoms, effectively Z-substituents by negative hyperconjugation, attack
is completely selective for C.
4.5.2.4 Unsymmetrical Epoxides. Epoxides are tetrahedral-carbon electrophiles like alkyl halides, except
that the strain in the three-membered ring adjusts the bond angles further away from perfectly tetrahedral.
4 IONIC REACTIONS—REACTIVITY
193
Nevertheless, the factors that affect the electrophilicity of alkyl halides operate here, and lead to synthetically
useful levels of selectivity. At one extreme, in the presence of Lewis or protic acid, the epoxide opens
towards the side that gives the more stabilised cation, which is usually the more substituted side, leading to
regioselectivity appropriate to an SN1 reaction. At the other extreme, in the absence of Lewis or protic acid,
the reaction is SN2 in character, and takes place on the side best able to support an SN2 transition structure,
which is usually the less substituted side. A simple example is the opening of 1-butene oxide 4.176 with
chloride ion, which gives each of the chlorohydrins as the major product, 4.177 in acidic and 4.178 in neutral
conditions.402
Cl
Cl–
O
OH
OH
Cl
+
pH 4.5-7.0
4.176
4.177
77:23 at pH 4.5
16:84 at pH 7.0
4.178
In more detail in the acid-catalysed reactions, the cation is not always fully formed, but is instead captured by
the nucleophile with overall inversion of configuration, appropriate to an SN2 reaction. Effectively the
protonated oxygen shields the surface from which it departs, but the transition structure has, nevertheless,
substantial cationic character at the carbon atom undergoing attack. If the epoxide has a Z-substituent, as in
the amide 4.179, the Lewis acid catalysed opening avoids the formation of a destabilised cation adjacent to
the carbonyl group (see pp. 77–78). In contrast, in the absence of Lewis acid, the Z-substituent encourages
opening adjacent to itself (see p. 181).403 A particularly intriguing manifestation of the effect of a
Z-substituent is the counter-steric opening of silyl epoxides like 4.180, which cleanly opens adjacent to
the silyl group.404 A silyl group is a Z-substituent by virtue of the negative hyperconjugation of the
Si—methyl bonds (see pp. 79–80) conjugated to the breaking and developing bonds. A C¼C double bond
stabilises both the SN1 and SN2 transition structures, and a C-substituent encourages opening at the allylic or
benzylic position, both with and without acid catalysis, as in the uncatalysed opening of styrene oxide
4.181.405
SPh
PhSH, Ti(OPri)4
O
NMe2
CH2Cl2
O
91:9
NMe2
OH
OH
PhS–, THF
4.179
O
O
NMe2
7:93
SiMe3
LiAlH4
N3
O
SiMe3
H
SPh
NaN3
OH
O
Et2O
4.180
OH
4.181
In between the extremes, relatively weak Lewis acids like the surface of alumina,406 or trimethylsilyl
chloride,407 accelerate the opening of an epoxide, without necessarily having it take place to the more
194
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
substituted side, and several organometallic nucleophiles also show this feature. Thus organoaluminium
reagents are more likely to have the alkyl group attack at the more substituted side of propene epoxide
4.182,408 whereas Grignard reagents and cuprates attack at the less substituted side.409 The aluminium is the
more powerful Lewis acid, and the transition structure adjusts to stretching the bond to the more substituted
side in that case.
Me3Al
OH
EtMgCl
O
OH
4.182
4.5.2.5 Arynes. o-, m- and p-Benzynes are all possible, all three have been implicated in various reactions,
and all three have been studied at a high level of theory.410 The most commonly encountered, however, is obenzyne, which we shall call benzyne from now on. The two p orbitals are bent apart, making their
interaction considerably less than the interaction of two p orbitals in forming the p bond of ethylene. The
HOMO is therefore raised and the LUMO lowered in energy relative to the frontier orbitals of an alkene or a
linear alkyne. The most common reactions of benzynes are cycloadditions, which will be dealt with in
Chapter 6, and nucleophilic addition, made favourable by the low energy of the LUMO. Strikingly, arynes do
not normally attack electrophiles, which ought also to be favourable because of the raised energy of the
HOMO. Although this step is probably exothermic, the most likely explanation can be found on the product
side of the reaction coordinate. The product of nucleophilic attack on a benzyne is a phenyl anion, and the
product of electrophilic attack a phenyl cation. The former is well known—trigonal anions, having a more
exposed nucleus, are stabilised relative to tetrahedral anions, and they are under no particular strain from
being bent. This is one of the reasons why acetylenes in general react more readily than alkenes with
nucleophiles.411 However, trigonal cations like the phenyl cation are high in energy, and the bending in them
raises their energy even more above the already high energy of a digonal cation. The high energy of a digonal
or trigonal cation is probably the main reason why acetylenes in general are less reactive than alkenes
towards electrophiles.
Looking at the starting material side of the reaction coordinate, it has also been suggested, both for
benzyne reactions and for acetylene reactions in general, that bending an acetylene lowers the energy of the
LUMO much more than it raises the energy of the HOMO because of bonding interactions between the p*
and two * orbitals. Mixing these orbitals in lowers the energy of the LUMO, but there is no significant
counterpart affecting the energy of the HOMO.412 The orbital referred to as the HOMO in the discussion
above is not actually the HOMO in benzyne—it is so little raised in energy that one of the benzene p orbitals
is the HOMO.
To be ambident, a benzyne must be unsymmetrical, and the regioselectivity will be determined by the
electronic and steric effects of the substituent. A major factor is the relative stability of the regioisomeric
products, with the benzyne 4.183 giving the lithium intermediate 4.184,413 and the benzyne 4.185 giving the
lithium intermediate 4.186.414 These two substituents are both excellent at stabilising the neighbouring
C—Li bond, the former by coordination, and the latter by conjugation between the C—F bond and the C—Li
bond. Looking at the starting material side of the reaction coordinate, which ought to be important, since it is
an exothermic reaction, the C—F bond is a Z-substituent on the benzyne triple bond. Using the simple device
we used to deduce the pattern of coefficients in substituted alkenes (see pp. 70–76), we can argue that the
C—F bond has some of the character of a cation on carbon 4.187, in which the empty p orbital will be
conjugated to the in-plane bent p bond. The LUMO will resemble that of an allyl cation, and will therefore
have the larger coefficient on C-3 4.188. Finally, C-3 will also be the site with less steric hindrance, but
it is clear from cycloaddition evidence415 that steric hindrance at C-2 is not the reason why nucleophiles
attack at C-3.
4 IONIC REACTIONS—REACTIVITY
Et2N
O
195
Et2N
2
O
F
F
Li
PhSLi
3
3
SPh
4.183
Li
PhLi
2
4.184
Ph
4.185
4.186
F
F
2
has some of the
character of
for which the LUMO is
like that of an allyl cation
3
4.187
4.188
With an alkyl group as the substituent, the product anions are not substantially different, nor are the coefficients on
C-2 and C-3. In practice, the benzyne 4.189 gives attack equally at C-2 and C-3, except when the nucleophile is
larger.416 With an oxyanion substituent, and even more so with an amide anion 4.190, attack at C-2 becomes quite
substantial, perhaps avoiding the formation of a C—Li bond adjacent to the anion.417
NH–
2
Li
KNH2
NH2
NH–
2
+
3
NH2
4.189
Li
KNH2
NH2
4.190
50:50
NH2
+
3
Li
NH–
Li
7:93
When the substituent is out of direct conjugation, the balance becomes more delicate, it no longer has a steric
component, but it is still quite noticeable. The methyl substituent in the benzyne 4.191 slightly encourages attack
by ethanol at C-3, and a chlorine in the benzyne 4.192 substantially encourages attack at C-4.418 The C—Me and
C—Cl bonds are conjugated through the bond between C-2 and C-3 to the p orbital on C-4, lowering and raising,
respectively, the coefficient in the LUMO; the same conjugation destabilises and stabilises, respectively, the
development of anionic charge on C-4.
61%
2
3
Cl
3
4
4
4.191
17%
2
39%
4.192
83%
Pyridynes are inherently unsymmetrical. Nucleophiles readily attack the 2,3-pyridyne 4.193 entirely at C-2.419
A calculation420 shows that the coefficient in the LUMO of 2,3-pyridyne 4.194 is larger at C-2 than at C-3.
Also, the total charge distribution 4.195 is such that C-2 bears a partial positive charge. We can rationalise the
polarisation of the LUMO by comparing the lobes of the p orbitals in the plane of the ring 4.194 with the
p system of the allyl anion. The large coefficient in the LUMO of the allyl anion is on the central atom, just as it
is here. The net result is that nucleophiles attack at C-2, because both Coulombic and frontier orbital
forces favour attack at this site. They also react at the 2-position because the anion formed, a 3-pyridyl
196
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
anion, stabilised by negative hyperconjugation with the C—N bond, is more stable than the alternative 2-pyridyl
anion.
2,3-Pyridyne is difficult to trap with a diene, because nucleophilic attack takes place much faster, even
with relatively poor nucleophiles like acetic acid.421 For the reaction with a diene, Coulombic forces are
small, and large coefficients on both C-2 and C-3 would help. Since, 2,3-pyridyne is quite strongly polarised,
the ionic reaction is made easier than the cycloaddition.
Br
3
KNH2
N
N
NH3
2
N
NH2
4.193
3
–0.25
LUMO
N
+0.23
N
2
total char ge distribution
4.194
4.195
Nucleophiles attack 3,4-pyridyne 4.196 at C-4 only slightly faster than at C-3, and both types of product
4.197 and 4.198 are formed.422 3,4-Pyridyne is much less polarised, because the p orbital on nitrogen is not
directly conjugated with those on C-3 and C-4. It is weakly conjugated to the p orbital on C-4 through the bond between C-2 and C-3, and the p orbital on C-3 is weakly conjugated by an anomeric effect with the
bond between N-1 and C-2.420 The sum of these interactions make the coefficient on C-4 in the LUMO 4.199
slightly larger than the coefficient on C-3, and the total charge distribution 4.200 also makes C-4 the more
electrophilic site. Since the polarisation is quite a bit smaller than that of 2,3-pyridyne, 3,4-pyridyne is less
susceptible to nucleophilic attack and is comparatively easily trapped by a Diels-Alder reaction with
dienes.421
NH2
Br
KNH2
NH2
NH3
N
+
N
N
N
4.196
4.197
4.198
+0.23
4
–0.25
3
LUMO
N
N
total char ge distribution
4.199
4.200
In spite of their high total energy, arynes in general are selective towards different nucleophiles; thus
benzyne 4.201 selectively captures the anion of acetonitrile in the presence of an excess of dimethylamide
ion.423 Nucleophilicity towards benzyne, determined by competition experiments, is in the order organolithium reagent RS– > R2N– RO– and I– > Br– > Cl–, which is an order of softness. The poor overlap of
the p orbitals in the plane of the ring means that the LUMO of an aryne is low in energy, so much so that its
4 IONIC REACTIONS—REACTIVITY
197
interaction with the HOMO of a nucleophile may often be a first-order perturbation. This makes the aryne
both electrophilic and responsive to the energy of the HOMO of the nucleophile. Since it is also uncharged, it
will necessarily be a soft electrophile.
NaNMe2
NMe2
NNa
slow
f ast
CN
4.201
4.5.2.6 Substitution versus Elimination. Alkyl halides react with nucleophiles by undergoing substitution
or elimination, which are in competition with each other. The usual pattern is for the more substituted alkyl
halides to undergo elimination more easily than substitution, and for the less substituted to undergo
substitution more easily than elimination. A major factor in determining this pattern is the greater level of
steric hindrance at the carbon atom of the more substituted alkyl halides, while at the same time the hydrogen
atoms remain inherently unhindered on the periphery (and there are usually more of them). Other factors
favouring elimination are the relief of steric compression as tetrahedral carbons become trigonal, and the
lower energy of the more substituted alkenes.
A more subtle factor affecting the ratio of substitution to elimination is the nature of the leaving group, and
this is amenable to a treatment based on the molecular orbitals involved.424 The LUMO is the important
frontier orbital for both SN2 and E2 reactions. We have already seen that this is largely localised as * for the
C—Cl bond in methyl chloride (Fig. 1.59a), and we have also seen how well set up a low-lying unoccupied
orbital is for elimination in ethane (Fig. 3.8). In a more realistic substrate for elimination like ethyl chloride,
the LUMO is not localised on * for the C—X bond, where X is the electronegative group. We can try to
deduce what the LUMO will look like from the interaction of the orbitals of a methyl group and the orbitals
of a methyl group with an electronegative substituent. The orbitals of the methyl fragment are constructed
from their component 2s and 2p orbitals on carbon and the 1s orbitals of hydrogen, mixed in appropriate
proportions, and they make up the set in Fig. 4.18a, where we see a close similarity to the left-hand half of
some of the orbitals of ethane (Fig. 1.22), except that now the drawing does not try to show the effect of
mixing the 2s and 2px orbitals.
We need to consider the antibonding orbitals, of which *3 and p*z have appropriate symmetry to mix
with the relevant orbitals of an XCH2 group. The *3 orbital is a mix of the 2s and 2px orbitals, and the p*z
orbital is purely a 2pz orbital, both being mixed with the 1s orbitals on hydrogen. When these are to interact
with the orbitals of an XCH2 group, they mix with each other to some extent, because the symmetry has
been broken. The *3 orbital acquires some 2pz character and the p*z orbital acquires some 2s character.
Since they both have a 2pz component, these two orbitals can mix with the p* and * orbitals of the XCH2
group to create two orbitals labelled LUMO and LUMOþ1 in Fig. 4.18b, together with higher-energy
orbitals that we need not consider. In this case, the LUMO is closer in energy to the *3 orbital, and so has
more H—C antibonding character than C—X antibonding character. The two lower gauche hydrogens have
opposite signs in *3 and p*z and nearly cancel, but the hydrogen atom anti-periplanar to the C—X bond
has the same sign and is amplified.425 In addition, p bonding is already present, and elimination is
therefore favoured by attack where the bold arrow approaches. The LUMOþ1 orbital, however, is closer
in energy to the p*CX orbital, and it has much more C—X antibonding character. Because it has also mixed
with the *CX orbital, which has a large 2s component, the upper lobe has been extended, and the lower
reduced, making attack behind the C—X bond, where the bold arrow points, favourable. This argument
suggests that, in the gas phase, and other things being equal, elimination is favoured in this substrate,
because the LUMO is the lower energy of these two orbitals.
Now let us take a different substrate with a leaving group Y, for which the energies of the p*CY and *CY
orbitals are lower. A different picture emerges, in which the LUMO and the LUMOþ1 orbitals more or less
198
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
H
H
H
H
H
H
H
*y
*z
H
H
H
H
H
H
H
LUMO+1
H
H
X
*z
*CX
*CX
H
*3
X
H
H
H
H
H
*3
H
H
X
H
2
H
H
X
(b) The interacting antibonding molecular orbitals of methyl and XCH2 f ragments
H
H
H
LUMO
H
H
H
H
H
H
H
H
H
y
H
*3
H
H
H
*z
LUMO+1
H
H
Y
*CY
z
H
H
H
H
*CY
H
H
1
H
H
(a) The molecular orbitals of
the methyl f ragment
Fig. 4.18
H
H
H
H
H
H
LUMO
Y
H
H
Y
Y
(c) The interacting antibonding molecular orbitals of methyl and YCH2 f ragments with
YCH2 having lower-energy * and * orbitals than XCH2
The LUMO of EtX and EtY where Y is more electronegative than X
change places. In Fig. 4.18c, we see that the LUMO is now closer in energy to the p*CY orbital and has
therefore more C—Y antibonding character, with the large lobe the site of attack for substitution. The
LUMOþ1 orbital is now the one closer in energy to the *3 and p*z orbitals, and it has more of the
character suitable for elimination. Thus with lower energy C—Y antibonding orbitals, substitution should
be favoured, since the orbital pattern in the LUMO favours it. This picture allows us to see how the nature
of the leaving group can affect whether substitution or elimination will be favoured. In practice, the more
electronegative the leaving group the higher the SN2:E2 ratio (ROTs>RCl>RBr>RI>RNþMe3), in
agreement with the analysis in Fig. 4.18, since the more electronegative the atom Y, the lower the energy
of its antibonding orbitals.426
Superimposed on this pattern is the effect of changing the nucleophile, which is called a base if it is
removing a proton in an elimination reaction. Hindered bases will inherently attack the more exposed
hydrogen atoms, encouraging elimination. The hyperconjugation between the anti-periplanar C—H and
C—Cl bonds that is manifest in the LUMO of ethyl chloride also removes charge from the hydrogen atom,
which, because it is so small, will have a relatively concentrated partial positive charge. Hard nucleophiles,
therefore, are more likely to induce an E2 reaction than an SN2 substitution, and soft nucleophiles to attack at
4 IONIC REACTIONS—REACTIVITY
199
carbon. This is the usual observation: the harder the nucleophile/base, the more elimination there is relative
to substitution.427
4.6
Carbenes428
Carbenes are ambiphilic, having simultaneously both nucleophilic and electrophilic properties. We saw the
lower-energy molecular orbitals of the parent singlet carbene CH2 in Fig. 1.16, which are redrawn in
Fig. 4.19 from a better perspective for discussing their reactions. The HOMO is largely a filled p orbital
(labelled n in Fig. 4.19, but z in Fig. 1.16) involved in some of the C—H bonding, but relatively high in
energy, because of its closeness in energy to an isolated p orbital. (Using hybridisation, it would be a
nonbonding filled sp2 hybrid.) The LUMO is an unfilled purely p orbital (pz in Fig. 4.19 and 2py in Fig. 1.16),
which is therefore nonbonding. Thus the HOMO is high in energy, and the LUMO is low in energy, and, not
surprisingly, carbenes are very reactive.
H
H
H
H
HOMO
pz
LUMO
n
H
H
H
H
CH2
CH2
Fig. 4.19 The filled and lowest unfilled molecular orbitals of methylene
Substituents have a profound effect on the reactivity of carbenes. Donor substituents lower the energy more if
they are conjugated to the empty p orbital 4.202, and electron-withdrawing substituents lower the energy more
if they are conjugated to the filled p orbital 4.203. Since these interactions leave the other frontier orbital more
or less unchanged (it is orthogonal), the former still has a high-energy HOMO, and the latter still has a lowenergy LUMO. They become, therefore, relatively nucleophilic and electrophilic, respectively.429
filled
filled
empty
X
X
4.202
empty
empty
Z
filled
Z
4.203
4.6.1 Nucleophilic Carbenes
In practice, donor substituents have the more remarkable effect, since they make it possible actually to
isolate a range of carbenes 4.204.430 With somewhat less stabilisation, the carbene 4.205, although it is
only found as a reactive intermediate, is exceptionally easy to form. It is the key intermediate in all the
metabolic steps catalysed by thiamine coenzymes, and its reactions are characterised by nucleophilicity
towards such substrates as aldehydes. Similarly, dimethoxycarbene 4.206 reacts with electrophiles like
dimethyl maleate and benzoyl chloride to give the intermediates 4.207 and 4.209, and hence the
products 4.208 and 4.210,431 typical of nucleophilic attack, but it does not insert into unactivated
alkenes.
200
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
R
HO
N
OH
P
O
O
OH
P
OH
O
P
O
O
S
O
N
N
N
R
N
4.204
4.205
H2N
CO2Me
OMe
CO2Me
O
CO2Me
MeO
MeO
MeO
OMe
CO2Me
MeO
CO2Me
4.207
4.206
4.208
O
MeO
Cl
Ph
Cl
Me
O
MeO
O
O
Ph
MeO
4.209
O
Ph
4.210
The carbene 4.211 is a revealing case. In spite of having a neighbouring lone pair, it is only mildly
nucleophilic in character, and, unlike strongly nucleophilic carbenes, it inserts into cis- and trans-2-butenes
stereospecifically.432 This carbene has the lone pair and the empty orbital held more or less orthogonal, so
that the orbital overlap which stabilises the carbene 4.202 is no longer possible.
N
N
4.211
The insertion of a carbene into an alkene, to be discussed again in the next chapter, can be viewed as the
simultaneous interaction of the HOMO of the alkene with the LUMO of the carbene, and of the LUMO of the
alkene with the HOMO of the carbene. Which interaction is the more important, and hence leads the bondforming process, depends upon the relative energies of the reacting partners. Nucleophilic carbenes will have
a high-energy HOMO, which will interact strongly with a molecule having a low-energy LUMO (Fig.
4.20a).433 This is why they react well with electrophiles and electrophilic alkenes—in the case of the very
nucleophilic dimethoxycarbene 4.206, bond formation is entirely dominated by the HOMO(carbene)LUMO(alkene) interaction, to the extent that it gives the zwitterionic intermediate 4.207, as shown by the
loss of stereochemistry in going from a cis alkene to a trans cyclopropane, in contrast to the reaction of the
less nucleophilic carbene 4.211, which shows the more usual behaviour for a carbene as a result of the more
even balance of the frontier orbital interactions.
4.6.2 Electrophilic Carbenes
Nucleophilic carbenes like dimethoxycarbene do not undergo cycloaddition reactions with simple alkenes,
nor do they insert into C—H bonds. Electrophilic carbenes, on the other hand, like the bis(methoxycarbonyl)carbene 4.212, with a low-energy LUMO, react with molecules like alkenes that have a high-energy
4 IONIC REACTIONS—REACTIVITY
LUMO
201
X
X
LUMO
LUMO
LUMO
HOMO X
X
HOMO
HOMO
HOMO Z
Z
(a) Frontier orbital interactions f or a
nucleophilic carbene and a good electrophile
Fig. 4.20
Z
Z
(b) Frontier orbital interactions f or an
electrophilic carbene and a good nucleophile
Frontier orbital interactions for carbenes with electrophilic and nucleophilic reagents
HOMO (Fig. 4.20b) stereospecifically to give cyclopropanes 4.213. They also insert into C—H bonds,
especially tertiary C—H bonds, as in the highly selective formation of the malonate 4.214, even though there
are only two tertiary C—H bonds and twelve primary.434 The selectivity for the tertiary C—H bond argues for
a substantial degree of cationic charge on the carbon in the transition structure, characteristic of electrophilic
attack on the H atom. Just as electrophiles in general react with alkenes and (less readily) with alkanes, and
nucleophiles do neither, so the corresponding carbenes behave likewise.
MeO2C
MeO2C
MeO2C
4.213
CO2Me
MeO2C
4.212
MeO2C
MeO2C
+
4.214
MeO2C
93:7
4.215
Dihalocarbenes are characteristically electrophilic in character, inserting easily into the C¼C bonds of
alkenes. As in other effects that halogens have, the inductive withdrawal along the C—halogen bond is
decisive in lowering the electron population on the carbon, even though the chlorine atoms do have lone pairs
that might conjugate in the p system. Calculations bear this out.435
4.6.3 Aromatic Carbenes
Three special carbenes are the cyclopropenylidene 4.216,436 cycloheptatrienylidene 4.217437 and cyclopentadienylidene 4.218. The cyclopropenylidene 4.216 and cycloheptatrienylidene 4.217 have the empty p
orbital conjugated with one and three p bonds, respectively, making them aromatic like the cyclopropenyl
1.13 and tropylium cations 1.12. The filled px orbital is unchanged as a source of nucleophilicity, and these
carbenes are notably nucleophilic, reacting with electrophilic alkenes like fumarate but not with simple
alkenes. Furthermore, cycloheptatrienylidene 4.217 reacts faster with styrenes having electron-withdrawing
202
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
substituents and slower with those having donor substituents, giving a value of þ1.05, in contrast to the value of –0.6 for the relatively electrophilic dichlorocarbene.438
empty
empty
Ph
filled
filled
Ph
4.216
4.217
CO2Me Ph
Ph
CO2Me
+
Ph
CO2Me
CO2Me
+
MeO2C
Ph
4.216 cis or tr ans
MeO2C
CO2Me
trans
4.217
cis and trans 50:50
CO2Me
tr ans
Cyclopentadienylidene 4.218 is not quite so straightforward. It might change the normal configuration for a carbene
4.218a to that shown as 4.218b in order to allow the filled pz orbital to be conjugated with the two p bonds, making
this an aromatic cyclopentadienyl anion 1.11, and the unfilled px orbital would have to take up the orthogonal
role. However this is not without an energetic penalty,439 since it keeps the areas of high electron population
close together on the left-hand side of 4.218b. This carbene is not notably electrophilic, at least in its reactions
with alkenes, where the more-substituted alkenes react with it at much the same rate as the less-substituted,440
but it is somewhat electrophilic, reacting with dimethyl sulfide, for example, to give the ylid 4.219.441
filled
empty
empty
filled
4.218a
4.218b
+
S
S
4.218a
4.219
The superficially similar carbene 4.220, another carbene stable enough to be isolated, has the best of all
worlds. With six electrons for the p system coming from the double bond and the two nitrogen lone pairs, it
has an aromatic sextet without having to fill the pz orbital. Thus the px orbital remains filled, making this a
nucleophilic carbene, which reacts with the electrophile carbon disulfide to give the zwitterion 4.221.442
empty
S
N
N
N
4.220
+
filled
N
N
S
N
S
C
S
4.221
4 IONIC REACTIONS—REACTIVITY
203
4.6.4 Ambiphilic Carbenes
A carbene carrying both a donor and an electron-withdrawing substituent presents a new pattern of
reactivity, often called ambiphilic, since such species can show both nucleophilic and electrophilic properties. Thus chloro(methoxy)carbene 4.222 has a low enough energy LUMO, making it electrophilic towards
simple alkenes, and yet a high enough HOMO to make it able to react with electrophilic alkenes like methyl
acrylate.443 None of the carbenes discussed above is capable of both of these reactions.
Cl
OMe
Cl
a nucleophilic alkene
MeO
CO2Me
Cl
an electrophilic alkene
OMe
CO2Me
4.222
The account given so far leaves no room for anomalies, and yet they abound. Some of the nucleophilic
carbenes do not react with the common electrophilic probes, and some of the electrophilic carbenes do not
react with the common nucleophilic probes. Furthermore, there is quite frequently only a poor correlation
between the calculated frontier orbital energies and the patterns of reactivity. The usual qualifications have
to be invoked—that the frontier orbital theory is not a complete account of all the forces at work. One of the
more obvious of the other forces is steric hindrance, of course, and another is that some carbenes are
unselective, because they are so reactive that they are diffusion controlled.444
Alternatively, the stabilisation given to carbenes by conjugation with either donor or withdrawing groups
can also reduce their overall reactivity. An illustration of this factor is provided by the highly stabilised,
potentially ambiphilic carbene 4.223. This carbene shows little in the way of carbene-like behaviour—it
fragments, probably reversibly, into two molecules of HCN, and it dimerises to give the highly stabilised
diamino dinitrile 4.224, and that is about all.445 These reactions are interesting because they might be
involved in the primordial chemistry from which life evolved.
H2N
H2N
CN
2HCN
NC
4.223
NC
NH2
4.224
Triplet carbenes have a similar set of molecular orbitals to those shown in Fig. 4.19, but with one electron in
each of the orbitals n and pz. The shape of a triplet carbene may be anywhere between tetrahedral, if the
singly occupied orbitals are localised, and linear, if they are well delocalised by substituents. This is
especially noticeable when the carbene has two C-substituents like phenyl groups, which can overlap one
with each of the unpaired electrons.446 The reactions triplet carbenes undergo follow the patterns of radical
chemistry (Chapter 7).
5
Ionic Reactions—Stereochemistry
The control of stereochemistry is often the most challenging and therefore interesting part of a synthesis.
To achieve control, understanding is vital, and understanding requires a feeling for all the factors that
influence the stereochemistry of organic reactions. We begin with two adjectives, stereoselective and
stereospecific, which, with their derived adverbs, are much used and misused. They are used carefully in
this book, and their meaning needs to be established firmly, since the distinction between them is
important.447
A reaction is stereoselective when more of one stereoisomer is produced than of one or more
others. Thus the reduction of camphor 5.1 takes place mainly with attack of the hydride reagent on
the less-hindered face, avoiding the C-8 methyl group on the bridge, to give more isoborneol 5.2 than
borneol 5.3.448 The degree of stereoselectivity is expressed as the diastereoisomer ratio, or dr, the
ratio of isoborneol to borneol 5.2:5.3. It is helpful, in order to make comparisons easy, to normalise
the numbers by presenting them as percentages adding up to 100, 90:10 in this case, without implying
that the yield is 100%.
8
LiAlH4
OH
H3Al
H
O
5.1
+
H
5.2
H
OH
90 : 10
5.3
The less simple term stereospecific is used for those reactions where the configuration of the starting
material and the configuration of the product are related in a mechanistically constrained way. Thus
the diastereoisomeric bromides 5.4 and 5.6 give stereochemically different alkenes 5.5 and 5.7 by
anti elimination. 449 Since each of these reactions produces more of one isomer than the other, they are
also stereoselective, which is the more inclusive term. The characteristic feature of a stereospecific
reaction is that one stereoisomer of the starting material gives one stereoisomer of the product, and a
different stereoisomer of the starting material gives a different stereoisomer of the product.
Molecular Orbitals and Organic Chemical Reactions: Reference Edition
© 2010 John Wiley & Sons, Ltd. ISBN: 978-0-470-74658-5
Ian Fleming
206
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
ButO
H
H
Ph
Ph
Br
KOH, EtOH
anti
Br
Ph
Br
5.4
H
Ph
5.5
ButO
H
H
Ph
Br
Ph
KOH, EtOH
anti
Br
Br
Ph
5.6
H
Ph
5.7
This particular reaction was studied when analytical methods were not available to measure the probably
small degree to which each isomer gave some of the other alkene, either by a different mechanism or by
incomplete stereospecificity in the E2 reaction itself. More recently, the E2 reactions of the tosylates 5.8 and
5.10, giving the trans- and cis-5-decenes 5.9 and 5.11, have been shown not to be 100% anti—each gives a
little, depending upon the solvent, of the product of syn elimination (as well as the isomeric 4-decenes, which
were separated off before the analysis, and the products of removal of the deuterium, which were allowed
for).450 No matter how much stereochemical leakage of this kind there is, as long as the diastereoisomer ratio
is greater than 50:50 (84:16 in both of these cases), the reactions are still stereospecific. It is thus quite
acceptable, although not common, to have reactions that are measurably less than 100% stereospecific, as
this one is.
ButO
H
Bu
D
H
Bu
KOBut, ButOH
OTs
anti
84 parts
5.8
syn
Bu
D
H
Bu
5.9
16 parts
t
Bu O
H
D
Bu
H
Bu
OTs
5.10
KOBut, ButOH
anti
84 parts
D
Bu
H
Bu
5.11
It is not helpful to use the word stereospecific to mean 100% stereoselective, as many people thoughtlessly
do—a useful distinction is lost, and understanding suffers. Furthermore, it is arguable that there are no
reactions that give not even a trace of the stereoisomer, and so all stereospecific reactions, when it is illdefined as those reactions which are completely stereoselective, are at risk of losing their status when a better
analytical method comes along.
Unfortunately, there is a grey area. There are reactions that are, in their fundamental nature, the same as
those we call stereospecific, but for which it is not possible to have two stereoisomers either of the starting
material or of the product. Thus the addition of bromine to an isolated double bond is well known to be
stereospecifically anti, but the corresponding addition to an acetylene cannot be proved to be stereospecifically anti by the usual criterion because there is no possibility of having two stereoisomers of an acetylene.
The same problem arises, of course, for reactions taking place in the opposite direction—in elimination
reactions producing acetylenes, one vinyl bromide may react faster than the other, but they both produce the
same acetylene. It is also possible, in spite of having two stereoisomers of the starting material and of the
5 IONIC REACTIONS—STEREOCHEMISTRY
207
product, to find that, whereas one stereoisomer of the starting material reacts to give one stereoisomer of the
product, the other stereoisomer of the starting material undergoes a quite different reaction.451 Once again it
is not possible to prove that such reactions are stereospecific, even though in their nature that is what they are.
This chapter is divided into two sections, largely separating stereospecific reactions from the merely
stereoselective. The first (Section 5.1) deals largely with stereospecific reactions, and the explanations based
on molecular orbital theory for the sense of that stereospecificity. The second (Section 5.2) deals with
stereoselective reactions, in which a new stereocentre is created selectively under the influence of one or
more existing stereocentres or stereochemical features. The way in which a resident stereocentre controls
which of two surfaces of a p bond is attacked is also sometimes a question of how the orbitals interact. The
stereospecificity that is such a striking feature of pericyclic reactions is covered in the next chapter.
5.1
The Stereochemistry of the Fundamental Organic Reactions
5.1.1 Substitution at a Saturated Carbon
5.1.1.1 The SN2 Reaction.452 It is well known that bimolecular nucleophilic substitution (the SN2
reaction) takes place with inversion of configuration. This is a stereospecific reaction because one enantiomer of the starting material gives largely one enantiomer of the product. A number of factors contribute to
this well nigh invariable result. The solvent is likely to be crowded round the electronegative element,
blocking approach from that side. There will be a repulsion between any negative charge on the incoming
nucleophile and the departing nucleofuge if they were both on the same side. The transition structure for
inversion will be a trigonal bipyramid 5.12, with the electronegative elements in the apical positions. Having
the sites of negative charge apical keeps them as far apart as possible. This is probably the single most
powerful reason ensuring that the SN2 reaction takes place with inversion of configuration.
(–)
Nu
(–)
X
5.12
This same explanation accounts for the stereochemistry of nucleophilic substitution at silicon and phosphorus centres, where the trigonal bipyramid may be an intermediate rather than a transition structure, since
the larger nucleus allows more than four ligands to bond to the second row element with a significant
lifetime. The rules for trigonal bipyramids on phosphorus214 (and presumably on silicon too)453 are: (i) that
nucleophiles enter, and the nucleofugal groups leave, from apical positions, because they have the longer
bonds; and (ii) electronegative substituents in the lowest energy configuration occupy the apical positions,
because that keeps the negative charges as far apart as possible. When either or both the nucleophile and the
nucleofugal group are electronegative, inversion of configuration is the normal observation, typified by
the displacement of chloride by hydroxide ion in Sommer’s definitive work in the silicon series.454 The
intermediate 5.13 has the formal charge on silicon, but the actual negative charge will be distributed largely
to the two electronegative elements, and the silicon will carry a fraction of positive charge. The intermediate
is unlikely to change its configuration, because it will remain in an energy well while the electronegative
elements with their negative charge are apical.
Np-1
HO
Si
Ph Me
5.13
Cl
208
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
However, when the nucleofugal group is not electronegative, as in the silane 5.14 where it is a hydride
ion,455 the initial attack is probably easiest if it takes place from the side opposite to the largest group. This
leads to an intermediate 5.15 in which the hydrogen atom is not apical. Before the hydride can leave, a
pseudorotation 5.15 ! 5.16 has to occur, in order to place it apical. The concept and word pseudorotation
were first applied by Berry in the phosphorus series456 but apply equally here. In a pseudorotation (5.15,
arrows), one basal substituent, the methyl group in this case, remains basal, and is called the pivot; the other
two basal substituents, the phenyl and the hydride become apical, and the two apical substituents become
basal. If the nucleofugal group departs before any further pseudorotations, the product 5.17 is that of
retention of configuration, which is common when either the nucleophile or the nucleofuge is a hydride or
carbon-based group. Another way of identifying this pattern is to note that hard nucleophiles and nucleofugal
groups are apt to give rise to inversion of configuration and soft to retention of configuration.
interchange
HO
Ph Si
Me
Np-1
HO
Si
Ph Me
interchange
5.14
H
H
H
5.15
Np-1
pivot
HO Si Np-1
Me
HO
Me Si Np-1
Ph
Ph
5.16
5.17
The preference for electronegative elements to enter and to retain their apical positions ensures inversion of
configuration when the nucleophile Nu and nucleofugal group X are both electronegative, and the other
substituents are alkyl or aryl groups. When the nucleophile and the nucleofugal group are not both electronegative,
and hence do not stabilise the arrangement in which they are both apical, apical attack may be followed by a
pseudorotation to give a different intermediate, which explains the retention of configuration that is often seen in
silicon chemistry when neither Nu nor X is conspicuously electronegative.454 Retention of configuration by way of
pseudorotation also occurs when structural features, rather than orbital constraints, dictate an alternative to the
simple story above. For example, if the methyl and the phenyl groups in the intermediate 5.15 were joined in a fivemembered ring, this configuration would be high in energy, because a small ring can only bridge from a basal to an
apical position. In that case, even if the hydrogen were replaced by an electronegative element it would have to be in
a basal position when the nucleophile attacks, in order that pseudorotation can give an intermediate like 5.16 with
the small ring bridging a basal and an apical position throughout. The overall result would be retention of
configuration even though both the nucleophilic and the nucleofugal groups are electronegative.453
Although the argument is inherently weaker, we can also explain inversion of configuration in the SN2
reaction by looking at the frontier orbitals, which will be the HOMO of the nucleophile and the LUMO of the
electrophile.457 We saw the orbitals of methyl chloride in Fig. 1.56, from which we can abstract the LUMO
for an alkyl halide in general—it is very largely associated with the C—halogen bond. We can view it,
without hybridisation, as the *CX orbital. The overlap is bonding when the nucleophile approaches the
electrophile from the rear (Fig. 5.1a), but is both bonding and antibonding when the nucleophile approaches
from the front (Fig. 5.1b). The former is clearly preferred.
We can see that there is no orbital impediment to approach from the rear, and we can add that repulsion
between the HOMO of the incoming nucleophile and the higher-energy filled orbitals of the alkyl halide
(Fig. 1.59) is also less from that side, where the carbon atom is left exposed. Nevertheless, the frontier orbital
argument is a much weaker explanation for inversion of configuration in SN2 reactions than the explanation
on p. 207. It is not absolutely impossible that retention of configuration might be found one day,458 and we
can expect that one of the factors that might encourage it would be to have a low electronegativity for the
nucleophile or for the atom being displaced.
Full theoretical treatments have been carried out at many levels of theory, and they agree that the inversion
pathway has the lower energy. The solvent, which is invariably present in everyday chemistry, is not
5 IONIC REACTIONS—STEREOCHEMISTRY
209
bonding
Nu
bonding
H
H
Nu
H
C
*CX
*CX
LUMO
(a) Inversion of conf iguration
Fig. 5.1
X
H
LUMO
HOMO
antibonding
C
X
H
HOMO
H
(b) Retention of conf iguration
Frontier orbitals for the SN2 reaction
automatically included in calculations, and it makes a profound difference. In the absence of solvent, the gasphase SN2 reaction has, both experimentally260,261 and in calculations,459 a double well (Fig. 5.2): the
nucleophile and the alkyl halide combine exothermically with no energy barrier to give an ion-molecule
complex. In a sense the naked nucleophile is solvated by the only ‘solvent’ available, the alkyl halide. The
SN2 reaction then takes place with a barrier and with many of the features of the solution phase SN2 reaction,
such as inversion of stereochemistry, and a dependence on nucleophilicity and nucleofugal power; the
product ion-molecule complex then dissociates endothermically to give the products. Calculations that
include a few molecules of solvent have also been carried out,460 and they reduce the depth of the double
well, approaching the normal pattern of solution-phase SN2 reactions, for which some of the barrier is the
displacement of the solvent but some is the intrinsic component shared with the gas-phase reaction.
H
X
+
H
Y
H
H
H
X
+
X
H
Y
H
Y
H H
H
X
H
Y
H
H
Fig. 5.2
Y
X
HH
Energetics of the gas-phase SN2 reaction
5.1.1.2 The SE2 Reaction. In electrophilic substitution, the substrate is usually an organometallic reagent,
for which we can use methyllithium as the simplest version. We saw the low-energy orbitals of methyllithium with and without hybridisation in Fig. 1.64. The frontier orbitals for the SE2 reaction will be the
HOMO of the nucleophile (the CLi orbital strongly associated with C—M bonding) and the LUMO of the
electrophile, modelled in Fig. 5.3 by an empty p orbital. In this case,457 the frontier orbital interaction
(Fig. 5.3) can be bonding for attack on either side of the carbon atom.
In agreement, electrophilic substitution at a saturated carbon atom sometimes takes place with retention of
configuration 5.18 ! 5.19461 and 5.21 ! 5.22462,463 when it is called SE2ret,464 and sometimes, but more
rarely, with inversion of configuration 5.18 ! 5.20 and 5.21 ! 5.23, when it is called SE2inv.
Retention of configuration is the more usual pattern for electrophilic attack on a C—M bond, especially,
but not invariably, for carbon electrophiles. This may simply be because electrophiles are attracted to the site
of highest electron population, but explanations for changes from retention to inversion in going from one
210
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
bonding
E
bonding
H
E
LUMO
H
H
C
C
Li
H
LUMO
H
Li
H
HOMO
HOMO
(a) Inversion of conf iguration
Fig. 5.3
(b) Retention of conf iguration
Frontier orbitals for the SE2 reaction
Ph
Br
ClCO2Me
CO2Me
retention
H
5.19
Li
H
5.18
ButO
Br2
N
Br
5.20
ButO
O
5.22
Li
Ph
O
5.21
H
inversion
CO2Me
N
retention
Ph
Ar
CO2Me Ar
CHO
Ar
CHO
N
inversion
ButO
O
5.23
electrophile to another, from one metal to another, and from one substrate to another are far from clear. It is
not uncommon to find even one system in which the two pathways are delicately balanced.465 As it happens,
it has only recently become possible for synthetic chemists to use the stereochemistry that this reaction
possesses, as seen with the reagent 5.21 created using butyllithium and (–)-sparteine. The explanation
offered in that case is that reactive electrophiles, those not requiring Lewis acid catalysis, are apt to react
with inversion of configuration, while those that need to coordinate to the metal to experience some Lewis
acid catalysis, are apt to react with retention of configuration, because the electrophile is necessarily being
held on the same side as the metal. One of the complicating factors in trying to explain the stereochemistry is
that organolithium reagents are not monomeric in solution, or usually at the time of reaction.
5.1.2 Elimination Reactions
5.1.2.1 The E2 Reaction. -Elimination, which is usually but not always stereospecifically anti,466 is the
frequent accompaniment to substitution, as we saw in Section 4.5.2.6. We have also already seen in Section
2.2.3.4 some discussion about why anti arrangements are preferred in the anomeric effect, where we saw that
it is not solely because it allows all the groups to be staggered and not eclipsed. The same is true for
elimination reactions. While both conformations for -elimination, 5.24 and 5.25 in Fig. 5.4, obey the
primary rule of having the orbitals developing into a p bond coplanar, the syn elimination 5.24 has all the
substituents eclipsed, while the anti elimination in 5.25 has them staggered. The energy DE associated with
the eclipsing in 5.24 is still substantially present in the transition structure, whereas it has not developed to
the same extent in the transition structure corresponding to 5.25. Since both reactions are giving the same
product, the difference in energy DE between the starting conformations is still present to some extent DE‡ in
the transition structures, and the anti elimination is therefore faster.
As with the anomeric effect, this is not the whole story, because there are systems where this factor is not
present, and yet there is still a preference for anti elimination. Thus the anti elimination of the vinyl chloride
5.26 giving the acetylene 5.27 is over 200 times faster at 97 C than the syn elimination of the vinyl chloride
5 IONIC REACTIONS—STEREOCHEMISTRY
B
H
211
X
E‡
syn E2 elimination
5.24
5.24
E
B
5.25
H
alkene product
X
anti E2 elimination
5.25
Fig. 5.4
The difference in energy of two starting materials affecting the energy of the transition structures
5.28,467 and this in spite of the almost certainly higher energy of the latter, which has the two large
substituents, the phenyl groups, cis.
H
NaOH
Ph
Ph
Ph
Ph
k rel 208
Cl
H
NaOH
Cl
Ph
k rel 1
Ph
5.27
5.26
5.28
In one sense, the stereochemistry at the carbon carrying the nucleofugal group X in the anti-periplanar
process 5.29 can be seen as an inversion of configuration, since the electrons supplied by the C—M bond
flow into the p bond of the product 5.30 from the side opposite to the C—X bond, just as they do in an SN2
reaction. This is the simplest perception available to the organic chemist to account for why E2 reactions
take place with an anti-periplanar geometry.468 This crude idea can be reformulated somewhat more
explicitly using the tau bond model (see p. 61). The pair of electrons originally in the C—M bond in the
starting material 5.29 moves into the upper tau bond, marked in bold in the product 5.31, effectively
creating the new bond from behind the C—X bond with inversion of configuration. Since the electrons
coming from the C—M bond move into the tau bond on the top side of the molecule, this corresponds to
retention of configuration at the carbon atom carrying the electrofugal group M. In a syn elimination, the
events would have to be seen as either retention at both sites or inversion at both sites—retention in an SN2
reaction is essentially unknown, and inversion in an SE2 reaction is less common than retention.469 Thus
the stereochemistry for the anti-periplanar process bears some resemblance to the only acceptable event
for the SN2 reaction and to the more common event in an SE2 reaction, but this is hardly a satisfying
account for why E2 reactions are so often faster if the stereochemistry can be anti-periplanar rather than
syn-coplanar.
M
H
H
H
H
M+
H
H
H
H
X
5.29
retention
M+
H
H
X–
X–
5.30
inversion
H
H
5.31
212
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
1.111Å
HH
H
F
F
1.405Å
+
HH
HF
H
F
2.234Å
H
H
2.268Å
F
H
1.394Å
H
H
H
H
F
F
F
H
HH
HH
H
H
H
H
F
H
H
1.503Å
Fig. 5.5
F
Energetics of the gas-phase anti E2 reaction
As with substitution reactions, calculations have been performed, and the anti stereochemistry is the
pathway found to be lower in energy.424 In the gas phase, the energy profile is not like that shown in
Fig. 5.4—there is again a well with a reactant complex before the transition structure for elimination
(Fig. 5.5). In the reactant complex for ethyl fluoride, the base, modelled by a fluoride ion, is bonded
to the hydrogen atom that is about to leave, stretching that H—C bond, and allowing the C—F bond to
stretch too. From here it is easy to see how the molecular orbitals flow into those of the product, an
exercise we saw earlier (see p. 144) without the benefit of a good nucleofugal group. The transition
structure, in the absence of solvation, has the hydrogen atom coordinated to both carbons, but both
bonds are long and the C—F bond even longer. The corresponding transition structure for syn
elimination is higher in energy, it has an even longer H—C bond but a shorter C—F bond, and the
transition structure resembles that for carbanion formation ahead of elimination, in other words an
E1cb mechanism.
5.1.2.2 The E20 Reaction. The stereochemistry of the E20 process is even less well understood. It is
exemplified by some decarboxylative eliminations 5.32 ! 5.33 and 5.34 ! 5.35 set off by treatment
with dimethylformamide dineopentylacetal. They are stereospecific and largely, although not exclusively, syn. The same reaction with -hydroxy acids is highly anti selective, in the usual way for eliminations. There are a number of other examples of largely syn elimination mostly in cyclic
systems.470
CO2H
HO
H
H
(ButCH2O)2CHNMe2
syn
5.33
(syn:anti 90:10)
5.32
HO
H
H
5.34
CO2H
(ButCH2O)2CHNMe2
syn
5.35
(syn:anti 83:17)
5 IONIC REACTIONS—STEREOCHEMISTRY
213
The tau bond model appears to provide a quick and easy explanation. An anti interaction between
each of the breaking bonds and the lower tau bond leads to a syn selective reaction for each
diastereoisomer.
HO
H
CO2H
H
H
HO
H
5.33
CO2H
HH
H
5.35
H
5.32
5.34
The change from anti for an E2 reaction to syn for an E20 is a satisfying pattern, for it matches the
change from retention for SE2 to inversion for SN2—in both cases adding two electrons to the
transition structure changes the stereochemistry. The same pattern is found for aromaticity, where
each added pair of electrons changes the system from aromatic to antiaromatic, and back again. There
is a natural supposition that each added pair of electrons ought to cause stereochemistry to alternate.
We shall see that alternation of stereochemistry as the number of electrons changes works well for
pericyclic reactions (Chapter 6), but it is not reliable here. In the first place, we already know that the
SE2 reaction does not always take place with retention of configuration, and in the second place,
adding one more double bond for the E200 reaction does not cause it to change back to being
selectively anti. The tau bond model would support this expectation—successive anti overlap through
the tau bonds down the chain 5.36 and 5.39 suggests that decarboxylative elimination should be anti.
In practice, the base-induced elimination of the ethers 5.37 and 5.40 is largely syn, with the major
products in each case being the dienes 5.38 and 5.41, respectively. (The decarboxylative elimination
of the corresponding hydroxyacids, similar to the reactions of the acids 5.32 and 5.34, was without
significant stereoselection from either isomer.)
Obser ved:
Pr edicted:
MOMO
H
H
HH
H
CO2H
MOMO
H
H
CO2H
6MeLi
syn
5.37
5.36
5.38
(syn:anti 86:14)
overall anti
MOMO
H
H
MOMO
HH
HH
CO2H
5.39
overall anti
H
CO2H
6MeLi
syn
5.40
5.41
(syn:anti 90:10)
Furthermore, several constrained systems, designed to make anti-periplanar overlap with the tau
bonds impossible, do not show the pattern of stereoselectivity implied by the tau bond model. The
nucleofugal group in both hydroxyacids 5.43 and 5.46 is held rigidly so that the overlap with the tau
bond must be syn 5.42 and 5.45, and this ought to force anti eliminations. In practice, the hydroxy
acids 5.43 and 5.46 undergo elimination with syn selectivity, just like their less constrained counterparts 5.32 and 5.34, giving largely the dienes 5.44 and 5.47, respectively. The predicted anti
elimination in the latter would have led to the lower-energy diene 5.44, and yet this is the minor
product.
214
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
Pr edicted:
Obser ved:
CO2H
OH
H
H
OH
H
H
H
(ButCH2O)2CHNMe2
H
H
CO2H
H
syn
5.42
5.44 (syn:anti 99:1)
5.43
CO2H
OH
H
H
OH
H
HH
H
syn
CO2H
H
H
(ButCH2O)2CHNMe2
5.45
5.47 (syn:anti 60:40)
5.46
Clearly some other electronic factors are at work. One possibility is that the electrofugal group (derived from
the carboxylic acid) has substantially broken off, making the stability of the intermediate allyl anion a factor
in determining the stereochemistry, and weakening or removing the element of concertedness. That sickleshaped anions are favoured over the W-shaped and U-shaped (see p. 108) has been invoked to explain the
stereochemistry of some desilylative E20 reactions, where there was a notable selectivity for the formation of
a Z double bond at the carbon atom losing the silyl group, but no stereospecificity of the kind seen in the
decarboxylative eliminations above.471
The tau bond model is an intriguing, but evidently defective approach to understanding the stereochemistry of
elimination reactions. The problem therefore remains—there is no simple and satisfying way to explain the
stereochemistry beyond the simple -elimination. We shall return to the problem later, when we come to
discuss how bonds adjacent to a p bond influence the stereochemistry of attack on the p bond, but first we
must discuss the angle of attack on a p bond, and the stereochemistry of their addition and substitution reactions.
5.1.3 Nucleophilic and Electrophilic Attack on a p Bond
5.1.3.1 Nucleophilic Attack on a p Bond—The Bürgi-Dunitz Angle.472 Nucleophilic attack on the p
bond of a carbonyl group is widely recognised to take place from above (or below) the plane of the double
bond, but not directly down the axis of the pz orbital 5.48. Bürgi and Dunitz deduced, from an examination of
a large number of X-ray crystal structures, that the angle in the transition structure 5.49 was obtuse,
typically close to 107 and not 90. The angle is called the Bürgi-Dunitz angle. It is a common
misunderstanding to think that the Bürgi-Dunitz angle implies that the two angles f are acute. They can
be sometimes, but they are not usually—the angles f are also obtuse in the transition structure, but to a
somewhat smaller extent.
Nu–
Nu(–)
O
5.48
O(–)
5.49
That both and f will be obtuse is hardly surprising—as the reaction proceeds, the carbon atom of the
carbonyl group is changing from trigonal to tetrahedral, and the transition structure is almost certain to have a
geometry at this atom somewhere in between. Only at long distances, with little bonding developed, is there
any chance that f will be acute. This is borne out by the X-ray structures, which show that f is less than 90
5 IONIC REACTIONS—STEREOCHEMISTRY
215
1st t er m:
2nd term:
3r d t er m:
HOMO
HOMO
Nu
–
Nu–
antibonding
repulsion
repulsion
HOMO
Nu–
O
5.50
Fig. 5.6
(+) (–)
O
LUMO
O
5.51
5.52
The Salem-Klopman equation applied to the Bürgi-Dunitz angle
only when the nucleophile is more than 2.5 Å from the carbon atom. The essence of Bürgi and Dunitz’s
perception is that is a slightly larger angle than f.
There are several reasons why should be larger than f. On the product side of the reaction coordinate, the
tetrahedral intermediate will have a large repulsion between the charge developing on the oxygen atom and
any charge on the nucleophile, especially when it is based on an electronegative atom. On the starting
material side (Fig. 5.6), the repulsive interaction of the filled orbitals with the filled orbitals 5.50, the first
term of the Salem-Klopman equation 3.13, will push the nucleophile away from the oxygen atom, because
the HOMO of the carbonyl group has the larger coefficient there. The Coulombic forces alone, the second
term of the equation, will lead the nucleophile to approach along the line of the C—O bond 5.51. For the third
term, the attraction is between the HOMO of the nucleophile and the LUMO of the carbonyl group, which
has the large coefficient on the carbon atom, but there will also be a repulsion from the oxygen atom, because
of the orbital of opposite sign on it 5.52. All three factors make an obtuse angle, but only the first, with
repulsions from the filled orbitals of the substituents, makes f an obtuse angle. Calculations suggest that the
repulsion between the filled orbitals 5.50 is quantitatively the most important of the three factors.473
Superimposed on the Bürgi-Dunitz angle is an angle defined by in the view of an unsymmetrical carbonyl
group seen from above 5.53. This angle is called the Flippin-Lodge angle, and it is expected to be positive when
the group R1 is larger than the group R2. A calculation, for example, makes it 7 for hydride attack on
pivalaldehyde (R1 ¼ But, R2 ¼ H).474 It becomes more significant when one of the substituents R is an
electronegative group. At the extreme of a carboxylate ion, when one of the R groups is an oxyanion, the angle
would be 60 5.54, with full eclipsing with the remaining R group. Carboxylate ions are not susceptible to
nucleophilic attack, but esters and amides are. We can predict, from considerations like those embedded in the
drawings 5.50–5.52 in Fig. 5.6, that the angle will be positive for esters and amides 5.55 if the steric repulsion
from the R group is not too forbidding. Calculations suggest that the angles are close to 40 for an ester and 50
for an amide.473 Considerations about the angles of approach, sometimes called ‘trajectory analysis’,475 become
important in the discussion of how stereogenic centres adjacent to the carbonyl group affect the stereoselectivity.
O
R1
Nu–
O
R2
O
(–)
O
(–)O
R
R
O
R2N or RO
R
60°
5.53
5.54
5.55
The same angles, the Bürgi-Dunitz and the Flippin-Lodge, will have their counterparts for nucleophilic
attack on a C¼C bond, but the former at least ought to be muted, because all three factors 5.50–5.52 will be
reduced when the oxygen atom of the carbonyl group is replaced by a carbon atom.
216
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
5.1.3.2 Electrophilic Attack on a C=C Double Bond by Nonbridging Electrophiles—Nonstereospecific
Addition Reactions.476 Electrophilic attack by a proton or a cationic carbon on a C¼C double bond is not
quite so straightforward, because it may give an open cation 5.57 or a bridged cation 5.59. We have met the
problem of hyperconjugating and bridged cations before (see p. 90), and the same problem arises here, for we
cannot be sure that protons and carbon electrophiles will always create open cations.
E
E
E
5.56
E
5.57
5.58
5.59
If we assume that the cations are not usually bridged, then we can expect protons and carbon electrophiles to
attack from outside the double bond 5.56. As with nucleophilic attack, the carbon atom is moving from
trigonal to tetrahedral, and the angle analogous to the Bürgi-Dunitz angle will be obtuse in the transition
structure. On the starting material side of the reaction coordinate (Fig. 5.7), the first term of the SalemKlopman equation would push the electrophile away from the centre of the double bond 5.60 and discourage
attack there, or anywhere else, but the other two terms would encourage attack from inside 5.58, 5.61 (where
the concentration of charge in the p cloud is represented as a minus sign) and 5.62.477 It seems likely that,
while the early approach may be from inside 5.58, the electrophile may have moved outside to give an obtuse
angle by the time the transition structure has been reached. Thus the angle of approach in an electrophilic
attack, acute or obtuse, will depend upon how early the transition structure is.
HOMO
E
repulsion
E
E
repulsion
bonding
LUMO
bonding
HOMO
HOMO
5.60
5.61
5.62
Fig. 5.7 The Salem-Klopman equation applied to electrophilic attack on a C¼C bond
The stereochemistry of the second step of an addition initiated by a nonbridging electrophile like a proton
will be controlled by which surface of the intermediate cation 5.57 is more easily attacked by the nucleophile.
The addition of hydrogen chloride to an alkene is not stereospecifically anti, because the chloride does not
necessarily attack the cation either specifically anti or syn to the proton,478 in contrast to addition initiated by
bridging electrophiles like bromine, or metallic electrophiles like the mercuric ion, described below. The
stereochemistry will depend instead on ion pairing or on the substituents in the cation 5.57, and how they
influence the conformation at the time the nucleophile attacks.
5.1.3.3 Nucleophilic and Electrophilic Attack by One p Bond on Another. A combination of nucleophilic and electrophilic attack on double bonds is the core of the aldol reaction, where both the nucleophile
and the electrophile are p bonds.479 The ideas we have seen in the previous two sections can be combined to
understand the transition structure 5.63 calculated for this reaction in the gas phase.480 This transition
5 IONIC REACTIONS—STEREOCHEMISTRY
217
structure has obtuse approach angles both for the electrophilic and for the nucleophilic double bonds, the two
reagents have all their substituents staggered, when viewed down the developing bond 5.63b, and the two
oxygen atoms are as far apart as possible, presumably repelling each other because of the partial negative
charges they both carry. However, there are alternative conformations such as 5.64, which maintain the
obtuse angles and the staggered groups 5.64b, and are not much higher in energy. The transition structure
5.63 is described as anti-periplanar and the transition structure 5.64 is described as synclinal.
(–)
H
H
O
H
≡
H
O (–)
H
H
5.63a
H
O (–)
H (–)
O
H
H
H
H
(–) O
H
H
5.63b
≡
H
O (–)
5.64a
(–)
H
O
H
O (–)
H
H
H
5.64b
Those aldol reactions in which a lithium or boron atom is coordinated to both oxygens are certainly synclinal,
since the metal coordinates to both oxygens and the transition structure is cyclic,480 and usually chairshaped—as first proposed by Zimmerman and Traxler. There are, however, many related reactions, when a
C¼C and C¼O group or two C¼C groups combine, in which this problem is less settled, either by theory or
experiment. Examples are the reactions between enamines and Michael acceptors, and the Lewis acidcatalysed reactions between allylsilanes or allylstannanes and aldehydes 5.65, and between the same
reagents and Michael acceptors 5.66, in none of which is there a cyclic component holding the reagents in
a synclinal geometry. There is experimental evidence for synclinal481,482 and anti-periplanar483 preferences
for various examples of these reactions, and we must conclude that there is only a small energy difference
between them. In most of the open-chain reactions thought to be synclinal, one or other of the oxygen atoms
in the aldol reaction (or both of them) is replaced by a carbon atom, reducing both the Coulombic repulsion
and the repulsion between the filled orbitals that favour the anti-periplanar transition structure. There will
also be a frontier orbital attraction,484,485 favouring the synclinal transition structure, which can be modelled
by the interaction 5.67 between an allyl anion and an alkene, but it hardly seems likely that this can be of
overriding importance.
O MXn
O MXn
LUMO
HOMO
MR3
5.65
MR3
M = Si or Sn
5.66
5.67
5.1.3.4 Electrophilic Attack on a C=C Double Bond by Bridging Electrophiles—Stereospecific Addition
Reactions. Heteroatom electrophiles, like peracids, sulfenyl halides and the halogens, all of which are
based on electronegative heteroatoms, nearly always give bridged products in the first step. The difference
between these electrophiles and the proton or carbon electrophiles discussed above is that the electrophilic
atoms carry a lone pair, so that the bridging bonds 5.69 have a total of four electrons. (The bridging in the
structure 5.59 only had two electrons to share between the two bonds.) The factors from the SalemKlopman equation illustrated as Fig. 5.7 now lead the electrophile straight onto the p bond 5.68, since they
match the product-like character, instead of opposing it. In detail, the two bonds may be unequal, if the
double bond is unsymmetrical, with the electrophile tilted to the side carrying the higher electron
218
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
population or charge. Depending upon what E is, the intermediate 5.69 may be stable, or it may open to
give the product of anti addition 5.70, as a consequence of the preference for inversion of configuration in
the SN2-like ring-opening step.
E
E
inv.
E
Nu
5.68
Nu
5.69
5.70
The more available the lone pair, the more firmly is bridging followed. Epoxidation gives directly a bridged
product, with no intermediate, and often stops there; the addition of sulfenyl halides is well established as the
electrophilic addition most strictly following the anti rule;486 and halogenation, with relatively tightly bound
lone pairs, shows significant loss of stereospecificity, corresponding to some degree of attack avoiding the
bridged intermediate, especially when the alkene has a good cation-stabilising substituent like a phenyl
group and the solvent is polar.487
Hydroboration, oxymercuration, oxypalladation and other additions to alkenes in which the electrophilic
heteroatom is electropositive, are less straightforward. They probably involve coordination by the metal to
the alkene as a first step, but whether that coordination is best represented as a bridged structure 5.58 or 5.59
is not so clear, since these metals do not necessarily have accessible lone pairs to create two full bonds 5.69.
Whether it is represented as bridged or involved in hyperconjugation 5.57, the transition structure for the
next step has the nucleophile attacking with high levels of stereocontrol—syn in hydrometallation,
carbometallation and metallo-metallation reactions, but anti in oxymetallation reactions. The hydro-,
carbo- and metallo-metallations are stereospecifically syn because the nucleophile is delivered from the
metal 5.71.488 (These reactions look superficially like pericyclic cycloadditions, and we shall return to them
in Chapter 6.) The oxymetallations are stereospecifically anti, either because the nucleophile attacks a
bridged intermediate, or because it attacks anti-periplanar to the donor substituent in the lowest-energy
conformation 5.72, in which the empty p orbital is stabilised by hyperconjugation with the M—C bond (see
p. 92). This kind of addition is the reverse of a -elimination, and responds to the same stereochemical
constraints in favour of the anti-periplanar pathway. Just because a reaction is stereospecifically anti does not
prove that it takes place by way of a bridged intermediate.
M
H
sy n
M
M
H
ant i
–
5.71
Nu
M
Nu
5.72
5.1.3.5 Baldwin’s Rules. The direction of attack on and p bonds affects the ease with which rings
can form. Baldwin pointed out that when a nucleophile is tethered to an electrophile, it matters
whether the bond being attacked, whether single, double or triple, is part of the ring or outside it.489
He noted that essentially all the reactions in which the bond was outside the ring were straightforward, and usually favourable processes. In contrast, when the bond was within the ring, there were
some cases where ring formation appeared to be difficult, even when the ring being formed was not
strained. Thus conjugate additions of the type 5.73 are easy and high yielding, but the superficially
similar conjugate addition 5.74 does not take place; instead, the oxyanion attacks directly at the
carbonyl group 5.75.490
5 IONIC REACTIONS—STEREOCHEMISTRY
219
O
O
O
OEt
O
EtO
O
OMe
5.73
5.74
O
5.75
Baldwin identified the problem as occurring most dramatically when a five-membered (or smaller) ring
was being formed by attack on a double bond within the ring being formed, as in 5.74. He labelled this
reaction a 5-endo-trig process, with the 5 referring to the size of the ring being formed, the endo referring
to the double bond being within the ring, and the trig referring to the trigonal carbon under attack. Thus the
easy reactions, 5.73 and 5.75, are both 5-exo-trig, with which there is evidently no difficulty.
The explanation for this difference comes when we look at the ease with which the nucleophilic atom in
each case can reach the appropriate position in space for attack on the double bond. In both cases, the
nucleophile must approach from above and behind the p bond with approach angles resembling those in the
transition structure 5.49. We can flesh this out for the 5-exo-trig reactions 5.73 and 5.75 in the drawing 5.76.
The carbon under attack, C-1, will be on its way to becoming tetrahedral, and the chain of atoms attached to
it, culminating in the oxyanion, can easily fold to put the oxyanion in a nearly ideal position 5.76. For the
corresponding 5-endo-trig process 5.77, the chain of atoms C-1, C-2 and C-3 must all be in the same plane.
The oxyanion is then only two atoms away from C-3 and it cannot reach to the position it needs to in order to
attack at C-1. The chain is simply too short when it is trying to form a five-membered ring. Baldwin
suggested that the problem is much less serious with a chain of six atoms, which is evidently just long enough
to reach, but a chain of four atoms is even more problematic.
O
O
1
1
X
2
3
O
EtO
5.76
5.77
Similar arguments apply to reactions in which the double bond is the nucleophile. Thus 5-exo-trig enolate
reactions of the type 5.78 are easy and high yielding, but the superficially similar 5-endo-trig enolate
alkylation 5.79 does not take place, and O-alkylation 5.80 takes place instead.491
5-exo-tr ig
O
Br
Br
O
5-endo-trig
O
5.78
O
Br
5.79
5.80
With electrophilic attack on a C¼C double bond, the angle of approach depends upon the type of
electrophile—bridging or nonbridging. In ring-forming reactions it is not often going to be a bridging
electrophile, and an obtuse approach angle leading to a tetrahedral intermediate 5.56 is likely. The
geometric constraints for electrophilic attack will make the 5-exo-trig process 5.81 easy and the 5-endotrig process 5.82 difficult, just as they did for nucleophilic attack. The O-alkylation 5.80 does not meet the
220
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
problem because there are lone pairs on the oxygen atom which can easily line themselves up with the back
side of the C—Br bond.
X
X
1
2
1
O
3
O
5.81
5.82
Baldwin considered all the possibilities, of ring size and of tetrahedral, trigonal or digonal atoms under
attack, and produced a set of rules for which reactions are favoured and which disfavoured. Briefly, and
augmented by later work, the disfavoured reactions are the n-endo-tet processes with n<9, the n-endo-trig
processes with n<6 discussed above, and the n-exo-dig processes with n<5. Exceptions to some of the rules
are known, but many of these are only apparent exceptions, because the compounds involved find different
mechanisms, avoiding the disadvantageous features of a more obvious mechanism.492 Others simply have no
alternative paths, and the constraints are not so forbidding as to make the disfavoured path absolutely
impossible. Pericyclic reactions (Chapter 6) abound with exceptions—Baldwin’s rules appear to have little
validity there, where there are many electrocyclic reactions that are 5-endo-trig, 4-endo-trig and even
3-endo-trig at both ends. Nevertheless the rules are a most helpful guide in planning a synthesis—if you
choose one of the disfavoured reactions for a key step, it is just as well to have a good reason for expecting it
to work in your case before you embark on the earlier steps.
That the 6-endo-tet process is disfavoured had been established by Eschenmoser, who showed that the
alkylation 5.83 only took place in an intermolecular sense.493 This is understandable from our knowledge
that the SN2 process takes place with inversion of configuration (see p. 207). There is evidently, a strong
preference, not only for inversion, but also for a nearly linear transition structure, which becomes reasonable
only with a ring size of 9 in the reaction 5.84.494,495 There must be a considerable energetic penalty for
bending, as Ingold observed when drawing attention to why even primary neopentyl substrates are so
extraordinarily resistant to SN2 displacements496—the transition structure 5.85 would have to be bent.
O
O
S
O
O
O
S
O
O
S
CH3
CH3
SO2Tol
SO2Tol
H
H
H
N
5.83
5.84
X
O
O
H
H
Nu
5.85
The epoxide opening 5.86, giving a product with a four-membered ring, is unusual because five-membered
rings are usually formed more rapidly than four-membered rings, and there appears at first sight to be a
perfectly reasonable pathway 5.87 giving a five-membered ring. The explanation lies with Baldwin’s rules.
The opening 5.86 is uncomplicatedly 4-exo-trig at the nucleophilic carbon, which is an anion derived from a
nitrile. At the electrophilic end, the observed reaction 5.86 is 4-exo-tet, whereas the alternative reaction 5.87 is
6-endo-tet, which is not favoured by Baldwin’s rules.497 Note that there is a source of confusion in the naming
of this process for Baldwin’s rules—the reaction 5.87 is simultaneously 5-exo-tet and 6-endo-tet. This reaction,
if it were to occur, would set up a five-membered ring, and the opening of the 5-6 bond is exocyclic to that
ring—hence the designation 5-exo-tet. Alternatively, and more pertinently in this case, following the chain of
5 IONIC REACTIONS—STEREOCHEMISTRY
221
atoms sequentially from 1 to 6 shows that breaking the 5—6 bond is endo to that chain, and it is this 6-endo-tet
aspect that makes the reaction giving a five-membered ring less favourable than that giving the four-membered
ring. As with the earlier endo-tet reaction 5.84, the problem lies in aligning the nucleophile more or less directly
behind the C—O bond being broken, namely the 5—6 bond in the epoxide 5.87.
N
3
4-exo-trig
NC
4
1
and not
O
4-exo-tet
2
5
O
6
OH
N
5-exo-tet and 6-endo-tet
5.86
5.87
4
5-exo-tet
5
3
O
OH
and not
7
O
6
2
1
5-exo-trig
CN
6-exo-tet and 7-endo-tet
N
N
5.88
5.89
The similar reaction 5.88 of another epoxide is unexceptionally 5-exo-trig at the nucleophilic carbon and 5exo-tet at the epoxide carbon. The alternative reaction 5.89 would be simultaneously 6-exo-tet and 7-endotet, the latter because the 6—7 bond is endo within a seven-membered ring. In this case, the normal kinetic
preference for the formation of a five-membered ring is amplified by the difficulty in a 7-endo-tet reaction.
Although these reactions show Baldwin’s rule being obeyed, other intramolecular openings of
epoxides and related species provide special cases of endo-tet reactions that appear to break the
rule. Changing the level of substitution so that the terminus is less substituted than the other carbon,
or is made allylic, allows the 7-endo-tet processes 5.90 and 5.91 to take place even in competition
with the 5-exo-tet.497,498 The structural changes encourage the SN2-like reaction at the less-substituted
or allylic carbons, overcoming their endo-tet nature. Evidently it is not difficult to overcome the
barrier to six-membered ring formation. The most probable explanation for these reactions with endotet character taking place at all is that the strain inherent in epoxides changes the angles of productive
attack, so that the rule of strict linearity in the SN2 reaction is lifted. This idea can be seen more
precisely in the orbitals of cyclopropane (1.38 or Fig. 1.53), which are not on the direct line between
the atoms in the ring. Attack by a nucleophile on orbitals like these will similarly not be diametrically
opposite the line of the bonds that we draw on paper. Calculations also support the delicate balance
between the five- and six-membered ring-forming reaction, and the acceptability of a less than
perfectly colinear transition structure when epoxides are involved.499
OH
OH
O
O
H
N
7-endo-tet
and 6-exo-tet
5.90
O
CN
O
7-endo-tet
and 6-exo-tet
5.91
222
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
Surprisingly 5-endo-dig cyclisations appear to be favoured. One example of many is the formation of the
carbocyclic ring 5.93.500 The nucleophilic carbon and the electrophilic carbon in the starting material 5.92
appear to be nowhere near within reach of each other, yet somehow they have become bonded. At first it was
suspected that the approach angle for nucleophilic attack on alkynes might be acute, but this seems to be
neither reasonable nor supported by good evidence—an obtuse angle of approach is surely preferred.501 The
best suggestion for why the far end of the triple bond can be reached is that C—C bending in alkynes, as
measured by the bending frequencies in IR spectra, is much easier than in alkenes, allowing the carbon under
attack to bend reasonably often towards the nucleophilic centre, and thus allow an approach angle 5.94 closer
to the optimal.411
Ph
Ph
Li
Ph
Li
Li
5.92
5.93
5.94
5.1.4 The Stereochemistry of Substitution at Trigonal Carbon
Both nucleophilic and electrophilic attack on trigonal carbon can take place by two pathways (Fig. 5.8)—
direct attack on one of the bonds attached to the double bond (path a), or by attack on the p bond (path b),
with the formation of an ionic intermediate, followed by the loss, respectively, of a nucleofugal group X or an
electrofugal group M. There are also formally unimolecular pathways, SN1 and SE1, with ionisation followed
by capture by the nucleophile or electrophile, but the former is neither favourable nor common,502 and the
latter unknown.
The stereochemistry of the direct attack can be expected to resemble the corresponding reactions at a
saturated carbon (Sections 5.1.1.1 and 5.1.1.2)—inversion for nucleophilic substitution, and retention, or
perhaps occasionally inversion, for electrophilic substitution. In practice, SN2 reactions at trigonal carbon are
rare,503 and their stereochemistry, where inversion is known,504 barely established. Electrophilic attack, like
the reactions of vinyllithium reagents with protons, aldehydes and carbon dioxide, takes place invariably
a
Nu
X
a
Nu
E
M
M
a
a
E
b
b
Nu
X
E
M
b
b
Nucleophilic substitution
Fig. 5.8
X
Electrophilic substitution
Direct and stepwise substitution reactions at a double bond
with retention of configuration. This pattern ties in with the greater difficulty of configurational inversion at
trigonal atoms than at tetrahedral atoms that we saw in Section 2.4.1. The necessity for inversion in SN2
reactions makes them very difficult at trigonal carbon, and the delicate balance between retention and
inversion in SE2 reactions at tetrahedral carbons becomes overwhelmingly in favour of retention at trigonal
5 IONIC REACTIONS—STEREOCHEMISTRY
223
carbon. The more remarkable stereochemical features are found in those reactions that take the indirect path
(path b), with addition followed by elimination.
5.1.4.1 Nucleophilic Substitution by Addition-Elimination.505 Nucleophilic attack takes place on the p
bond in the activated alkene 5.95, creating an intermediate, typically an enolate 5.96. Rotation about the bond can take place either clockwise by 60 to give the intermediate 5.97, or anticlockwise by 120 to give
the intermediate 5.99. Since the C—X bond is lined up with the p system of the enolate in each of these
intermediates, the loss of the nucleofuge can take place to give, respectively, the products 5.98 of retention of
configuration, or 5.100 of inversion of configuration. There is a similar sequence of events for attack from
below the p bond, which would give the enantiomers of all the intermediates, and is therefore equally
probable, and there is a similar sequence for the reaction taking place on the s-trans conformation of the
starting material 5.95.
60°
H
Nu
Z
O
clockwise
O
H
Z
X
O
5.95
H
O
H
X
Z
X
Nu
Z
X
5.98
5.97
Nu
Nu
fast
slow
5.96
O
anticlockwise
X
X
120°
Nu
O
Nu
Z
H
5.99
H
Z
5.100
In practice, retention of configuration is commonly observed, as in the stereospecific reactions of the
geometric isomers 5.101 ! 5.102,506 showing that the 60 rotation, to give the intermediate 5.97, is
understandably more frequent than the 120 rotation.
Cl
Cl
CN
E-5.101
EtS
EtS
E-5.102
CN
SEt
CN
Z-5.101
EtS
CN
Z-5.102
Furthermore, the loss of the nucleofugal group is evidently faster than rotation about the single bond 5.97
!5.99. The 60 clockwise rotation causes the stabilising negative hyperconjugation (Section 2.2.3.2)
between the X—C bond and the p system of the enolate steadily to increase as the dihedral angle between
the two systems drops from 60 to 0. This rotation probably occurs in concert with the formation of the X—C
bond and the intermediate 5.96 may never be formed as such. Only when the intermediate 5.97 has a long
lifetime, either because X is a poor nucleofugal group like alkoxide or fluoride, or because the anionstabilising substituents Z are especially good like nitro, is the stereospecificity lost. However, the possibility
of a very short lifetime for the intermediate, like less than one bond vibration, is equivalent to a mechanism
that merges with the SN2 mechanism, and a continuum of mechanistic possibilities has been proposed.
5.1.4.2 Electrophilic Substitution by Addition-Elimination. Electrophilic attack has an exactly parallel
series of events, which is best known from the electrophilic substitution of vinylsilanes. The electrophile
attacks from above (or below) the p bond in the vinylsilane 5.103, moving towards the creation of an
intermediate carbocation 5.104. Rotation about the bond can take place either clockwise by 60 to give the
224
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
intermediate 5.105, or anticlockwise by 120 to give the intermediate 5.107. Since the C—Si bond is lined up
with the empty p orbital in each of these intermediates, it is thermodynamically stabilising, but it is
simultaneously kinetically unstable because it is aligned for removal by a silicophilic nucleophile X to
give, respectively, the products of retention of configuration 5.106, or inversion of configuration 5.108.
60°
H
A
clockwise
E
H
B
SiMe3
A
H
5.103
H
SiMe3
E
A
fast
E
B
X
5.105
B
SiMe3
A
E
XSiMe3
B
5.106
slow
X
5.104
XSiMe3
A
B
E
H
SiMe3
120°
B
H
A
E
anticlockwise
5.107
5.108
In practice507 retention of configuration is the normal pattern in protodesilylation, aliphatic Friedel-Crafts
reactions, and similar reactions with other cationic carbon electrophiles. Examples are the ring closures
5.109 ! 5.110 and 5.111 ! 5.112, stereospecifically setting up the exocyclic double bond geometry with
retention of configuration by the intramolecular attack of an oxocarbenium ion on the vinylsilane.508 The
intermediate 5.105 is stabilised by hyperconjugation (Section 2.2.2) to such an extent that rotation 5.105 !
5.107 is slow relative to the ease with which the silyl group is removed. Again, the 60 rotation is easier than
the 120 rotation, and the attack and the 60 rotation are probably concerted without formation of the
intermediate 5.104 as such.
Bu
Bu
SnCl4
O
SiMe3
Bu
O
O
SnCl4
SiMe3
Bu
O
MEMO
MEMO
5.109
5.110
5.111
5.112
The exception to this pattern is bromodesilylation, and a few similar reactions, in which the electrophilic
attack 5.113 is followed by nucleophilic opening of the bridged intermediate 5.114.507 Rotation 5.115,
followed by anti elimination of the silyl group and bromide ion 5.116, give the product of inversion of
configuration 5.117.
Br
Br
H
A
X
inv.
Br
B
SiMe3
H
Me3Si
Br
A
B
Br
5.113
5.114
AB
H
Me3Si
Br
5.115
Me3Si
AB
XSiMe3
Br
Br
H
A
H
Br
5.116
B
Br
5.117
Except for this type of reaction, retention of configuration is observed in electrophilic substitution, whether it
is direct with a vinyllithium (path a in Fig. 5.8) or indirect with a vinylsilane (path b in Fig. 5.8). It is
conceivable that even reactions with vinyllithium reagents take the indirect path, for a concerted attack on
5 IONIC REACTIONS—STEREOCHEMISTRY
225
the p system and a 60 rotation would lead to an even better stabilised cation with an Li—C bond than with an
Si—C bond, and the stabilisation would lead to faster reaction.
5.2
Diastereoselectivity509
We have been concerned so far only with double bonds in which the top and bottom surfaces are either the
same or enantiotopic and it has made no difference to the argument which we chose to use to illustrate the
principle. We must now turn to those cases where the attack on one surface gives one diastereoisomer, and
attack on the other surface gives a different diastereoisomer, when the surfaces are said to be diastereotopic.
Early success in controlling stereochemistry came by tying a molecule into a tight ring system, so that only
one stereochemistry was possible, or only one surface of a double bond was exposed. This approach,
breathtaking in its day and still much used, achieves a high level of stereocontrol, sometimes complete, at
the expense of having to build in to the synthetic scheme many extra steps to set up the ring systems, and yet
more to unravel them. Control in open-chain reactions has, more often than not, been achieved by arranging
for the reactions to have cyclic transition structures for which one conformation was much preferred over
another—a chair-like six-membered ring, for example, with the larger substituents in equatorial positions.
Some high levels of stereocontrol have been achieved in this way, but rarely complete, since inherently the
energy differences between conformations is not all that great.
Understanding how to control genuinely open-chain reactions, those without even a cyclic transition
structure, has become possible from a combination of empirical observation and an appreciation of the
electronic forces at work. This approach rarely achieves the high levels of selectivity that the constraints in a
ring system can impart, whether from the starting material, the product, or the transition structure. The
differences between one stereochemistry and another are rarely more than a few kJ mol1, often less than 20.
Fortunately for synthetic chemistry, even differences as small as 10–20 kJ mol1 are enough to get very
workable levels of selectivity. Understanding in terms of the charge and molecular orbital interactions is
hampered by having only a crude and approximate tool with which to explain small differences in energy.
Nevertheless, whenever a measurable, and especially a useful level of control is achieved, it is beholden upon
the discoverer to make some attempt to explain it. Some explanations are inevitably feeble, because there is
nothing obviously better, but it is always worth trying. Steric effects,510 in which a large substituent hinders
the approach of a reagent from one direction, is nearly always a component of such explanations. This is, in
one sense, an orbital interaction, since steric effects are the results of the interaction of filled orbitals with
filled orbitals, for which there is nearly always an energetic penalty.
There have been several attempts to explain, with more or less rigour, the transmission of electronic effects
into a double bond and along a conjugated chain, but none has yet settled in as the accepted way to picture what
is happening in orbital terms. In the most colourful approach, the electrostatic attraction of a point positive
charge to the surface of each of the conformations of a starting material is calculated, and then mapped onto the
surface with a colour code—red for maximum attraction and blue for minimum attraction.181,511 The results are
beautiful pictures showing red hot spots on the molecular surface, and they give an immediate and vivid sense
of where electrophilic reagents are likely to attack. There are methods based on the molecular orbitals, critically
compared by Dannenberg,512 introduced by Klein513 (and modified by Ashby514), by Fukui,515 by Burgess and
Liotta (called the Principle of Orbital Distortion),516 by Gleiter and Paquette,517 by Morokuma,518 by
Dannenberg (given the abbreviation PPFMO),519 by Tomoda (given the abbreviation EFOE),520 and by
Ohwada,521 as well as electrostatic models presented by Chandrasekhar and Mehta,522 and by Wipf.523
The problem is that a p orbital on its own must be symmetrical on the top and bottom surfaces. For the top
and bottom surfaces to have differently sized lobes, whether it leads simply to pyramidalisation (if the p
orbital is filled), or to differential electrophilicity (if it is empty), some fraction of an s orbital must be mixed
in to create a hybrid (Fig. 5.9). An s orbital of one phase will push the lobe up, and an s orbital of the opposite
phase will push it down. The problem comes in finding out what sign the s orbital will have in the frontier
226
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
+
+
Fig. 5.9
Mixing in s orbital character to desymmetrise a p orbital
orbital, or any other orbital for that matter, in any given situation. The sign can be extracted from
calculations,181 but the sense is far from intuitive when it is induced by a neighbouring stereogenic centre.
None of the methods listed above is simple enough to work at the level aimed at in this book. They cannot
easily be taken and used with confidence in everyday situations, and the best that can be said is that this
problem is still a challenge to theoreticians and physical organic chemists alike.
The following sections attempt to indicate what factors might be involved, especially those associated
with the molecular orbitals. They should be viewed with some suspicion, for comprehension in this area of
chemistry is neither complete nor agreed. Steric effects and other electronic effects are difficult to disentangle, and the discussion here might be accused of exposing the wound more than healing it.
5.2.1 Nucleophilic Attack on a Double Bond with Diastereotopic Faces
The earliest reaction to be studied showing open-chain diastereoselectivity was nucleophilic attack on a
carbonyl group, either a carbonyl group with a stereogenic centre adjacent to it, first systematised by Cram in
the formulation of his rule, or a carbonyl group like that in 4-tert-butylcyclohexanone, where the diastereotopic surfaces are distinguished by being axial or equatorial. We must now try to explain the stereoselectivity
found in reactions like these. We shall find that this is still a hotly debated area.
5.2.1.1 The Felkin-Anh Rule.524 The attack of a nucleophile on a carbonyl group adjacent to a stereogenic
centre is covered by Cram’s rule. When the three substituents differ only in size, and not in electronic nature,
there is little difficulty. The explanation suggested by Felkin and Anh is now so widely accepted that it is often
referred to as the Felkin-Anh rule. The code used has the groups ranked simply as large L, medium-sized M,
and small S. Felkin suggested that the incoming nucleophile would attack the p bond anti to the large
substituent,525 and Anh added that we must take the Bürgi-Dunitz angle into account too.526 There are
therefore two possibilities 5.118, with the medium-sized group ‘inside’ (i.e. eclipsing or partly eclipsing the
C¼O double bond) and 5.119 with the small group ‘inside’. The latter is higher in energy, because the
incoming nucleophile is pushed back, close to the medium-sized group, by the forces controlling the BürgiDunitz angle, whereas in the former it is close to the small group. They also reasoned that the steric repulsion
from any eclipsing between the medium-sized group and the carbonyl group would be small, since there are no
substituents on the oxygen atom. As it happens there is no need for special pleading to account for why the
medium-sized group sits ‘inside’, since propanal adopts the conformation 2.187a (see p. 123) with the methyl
group inside, with the two hydrogen atoms on C-2, one above and one below the plane of the p bond. The
sense of attack is therefore firmly covered by 5.118. Ketones (R ¼ alkyl or aryl) and aldehydes (R ¼ H)
reliably react predominantly in this sense, with aldehydes a little less selective than ketones, perhaps because
they react some of the time in the sense 5.119 with the medium-sized group avoiding the inside position.
S
Nu
L
Nu–
M
R
O
L
lower in energy than
S
M
R
Nu
5.118
–
5.119
M
O
S
O
R
L
5.120
5 IONIC REACTIONS—STEREOCHEMISTRY
227
Just as the attack angle is not exactly 90, so none of the angles in the transition structure has to correspond
to those drawn schematically in 5.118, and in particular the large group does not have to be exactly at right
angles to the p bond. Angles close to those shown in 5.120 would seem to be near the minimum, although
obviously affected in detail by the relative steric requirements of the R, Nu, S, M and L groups.476,527
We need to graft onto this picture consideration of the Flippin-Lodge angle (see p. 215). In aldehydes, with
only a hydrogen atom on one side of the carbonyl group, the nucleophile will be tilted away from the
stereogenic centre, and hence away from its influence, offering a second and perhaps better explanation for
why aldehydes show lower selectivity than ketones. In those reactions in which a Lewis acid is coordinated
to the oxygen atom, it will be cis to the hydrogen atom, increasing the steric bulk on that side, and making the
Flippin-Lodge angle smaller. In agreement, the degree of stereoselectivity increases for these reactions, and
for Lewis acid catalysed attack on acetals.528
The Felkin-Anh rule is reasonably, but not invariably,529 followed when the argument is based only on
steric effects, but the picture becomes more complicated when one of the groups on the stereogenic centre is
either more electropositive than carbon or more electronegative, when we need to take into account the
electronic effect of having polarised bonds next to the reaction site. The lowest-energy conformations of the
starting materials are fairly understandable for both cases. A bond to an electropositive element like a silicon
atom will be conjugated to the carbonyl p bond 5.121, because hyperconjugation with an electron deficient
group like a carbonyl is stabilising (see p. 94). However, Cornforth argued that a bond to an electronegative
element, like a halogen, oxygen or nitrogen, will avoid the conjugation with the carbonyl group, since it is
energy raising, and an -haloketone will have the lowest energy when the dipoles are opposed 5.122.530
A σ-donor (electropositive) substituent
A σ-withdrawing (electronegative) substituent
H
H
R
X
O
H
Me3Si
H
O
R
5.122
5.121
In both cases, calculations support the idea that conformations close to these are the lowest in energy,
although the dihedral angles vary slightly from calculation to calculation, and they are, of course, affected by
whatever groups R and X are present on the stereogenic centre.531,532 In both cases, the stereochemistry of
attack corresponds to attack from the less hindered side of these conformations, as in the examples 5.123 !
5.124533 and 5.125 ! 5.126.534,535
Li
H
Me
C5H11
O
Prn
SiMe3
5.123
ClMg
HO
C5H11
Prn
SiMe3
5.124
91:9
Me
Cl
H
HO
H
H
O
Me
Cl
5.125
5.126
88:12
The problem with these explanations is that the lowest energy conformations are in neither case necessarily
the most reactive. We have to take the Curtin-Hammett principle into account. The conjugation of the Si—C
bond with the carbonyl group in the -silyl aldehyde 5.121 should raise the energy of the LUMO. Both the
overall stabilisation and the higher-energy LUMO ought to make this a less reactive conformation than one
in which the silyl group is orthogonal to the p bond. Nevertheless, the silyl group is the large group, and a
transition structure 5.127 with the silyl group anti to the incoming nucleophile might be expected to be
preferred, simply using the Felkin-Anh arguments based on steric effects. Furthermore, Cieplak has argued
that the incompletely formed bond to an incoming nucleophile is inherently electron deficient in the
228
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
transition structure.536,537 This orientation also matches the preferred anti-periplanar arrangement for elimination, which is essentially the reverse of nucleophilic attack. It follows that the transition structure will
be lowered in energy if a donor substituent is placed anti-periplanar to the incoming nucleophile, and this
picture, in which we ignore the thermodynamic stabilisation and LUMO-lowering, is more or less accepted.
However, there is some evidence that the argument needs to be a little more subtle. Calculations on the
transition structure for lithium hydride attack on an -silyl aldehyde, with an SiH3 group in place of the
SiMe3 group, show that the hydride approaches the carbonyl group syn to the silyl group 5.128, presumably
because there is an electrostatic attraction between the negatively charged hydride and the positively charged
silicon.538 This is the opposite to the experimental observations, but a similar calculation, using an SiMe3
group, confirms that attack anti to the silyl group 5.127 is lower in energy.539 Evidently the steric effect is the
dominant reason for the attack in the usual Felkin-Anh sense, with the three methyl groups shielding the
positively charged silicon nucleus.
Nu–
H
R
H
O
R
SiMe3
5.127
Me
O
R
H Li
SiH3
5.128
When one of the three groups on the stereogenic centre is an electronegative element like chlorine, the
problem is more vexing. This time, the substituent could be activating—in the higher-energy conformation
5.129 the overlap of the C—Cl bond with the p bond lowers the energy of the LUMO, and therefore activates
the carbonyl group for nucleophilic attack. The sense of the attack in this transition structure is the same as in
the transition structure 5.125. The outcome, whatever the explanation, corresponds to the Felkin-Anh rule if
the electronegative element is treated as the large substituent, whatever its actual size relative to the other
substituents, and this is how the rule is usually presented. If this is the correct picture, rather than 5.125, then
the effect of the chlorine atom can most easily be understood as two-fold—in the first place it activates the
carbonyl group to attack, and in the second the fraction of negative charge it carries will repel the incoming
nucleophile. However, if Cieplak is right, an electron-withdrawing group like this ought to raise the energy
of the transition structure, since it is anti-periplanar to the electron-deficient bond that is forming to the
nucleophile. This uncomfortable perception is often disguised when the incoming nucleophile is seen as
providing electrons, and that therefore the electron-withdrawing group stabilises the transition structure. At
the present time, it is not clear what the right answer is. Calculations for transition structures for nucleophilic
attack by hydride and cyanide on aldehydes and ketones with electronegative substituents like fluorine,
chlorine, methoxy, and dimethylamino give a transition structure similar to 5.129,526,540 –542 but a good case
has been made for reviving the Cornforth explanation.543
Nu–
H
R
R
O
Cl
5.129
Thus, for both electropositive and electronegative substituents, the stabilisation or destabilisation of the
transition structure and the activation or deactivation of the starting material are in opposition, yet experimentally they appear to react in the same sense. What makes the present situation so uncomfortable is that we
are accepting the steric effect as paramount for electropositive substituents like the trimethylsilyl group, but
accepting the activating effect on the starting material as paramount for electronegative substituents like
5 IONIC REACTIONS—STEREOCHEMISTRY
229
chlorine. It is worth remembering that the differences in electronegativity between Si and C is actually
greater (0.62) than the difference between Cl and C (0.33), but this is misleading as a guide to the relative
degree of polarisation in the Si—C and Cl—C bonds. The polarisation of an Si—C bond caused by the
difference in electronegativity between the two elements is shared among four bonds, whereas the whole of
the difference in the Cl—C bond is located there. Nevertheless, true consistency to the Anh formulation that
the most electronegative substituent be treated as the large group, would require that we placed the carbon
group R in the -silyl ketone 5.121 anti to the incoming nucleophile, since it is the most electronegative
substituent, but this would give the wrong diastereoisomer. Alternatively, consistency to the Felkin model
5.127 would require that we placed the halogen in the -halo ketone 5.122 ‘inside’ and the R group anti to the
incoming nucleophile, which also gives the wrong diastereoisomer. Organic chemists are notorious for
accepting explanations that work, without being too concerned about consistency; this is one of those cases.
There is one further complication, but this time easily resolved, well understood, and supported by high
level calculations.541 When the electronegative element coordinates to a metal that can simultaneously
coordinate to, and activate, the carbonyl group, the conformation will be that of a ring. The electronegative
element and the carbonyl oxygen are held synclinal, or at most gauche, to each other, both in the lowest
energy conformation and in the transition structure. The attack from the less hindered side, opposite to the
group R, is then relatively easily predicted 5.130, and is the opposite of that predicted from the Felkin-Anh
rule. It has long been known as Cram-chelation control.
R
Me
R
O
M
O
H
Nu–
5.130
5.2.1.2 Nucleophilic Attack on Cyclohexanones. At first sight, attack on a cyclohexanone with a locked
conformation 5.131 would appear to resemble the problem covered by the Felkin-Anh arguments. The
equatorial hydrogen atoms on C-2 and C-6 are forced to be the inside groups, more or less eclipsing the
carbonyl group. The top surface of the carbonyl group, as drawn, is conjugated to the bonds between C-2 and
C-3 and between C-5 and C-6, and the bottom surface is conjugated to the axial hydrogen atoms on C-2
and C-6. The steric difference between the two surfaces is therefore clear—the lower surface is less hindered,
and we predict that equatorial attack should be favoured, giving more of the axial alcohol 5.132 than of the
equatorial alcohol 5.133. This is what happens with large nucleophiles, and with hydride delivered from
hindered reagents like selectride.544 The problem comes with small nucleophiles like hydride delivered from
lithium aluminium hydride or sodium borohydride, or with cyanide or acetylide ion, when axial attack is
favoured, giving more of the equatorial alcohol 5.133.514 There is evidently some electronic effect making
axial attack inherently favourable.
H
5
O
6
3
OH
Nu
Nu
H
H
H
5.131
2
Nu
–
+
OH
+
(+ H )
LiBH(Bus)3
LiAlH4
5.132
5.133
93:7
10:90
All sorts of explanation have been invoked for this curious result, which is not a consequence of differential
solvation, since it is observed in the gas phase too.545 The most simple is Cieplak’s.472,546 He argues that
230
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
C—H bonds are better donors by hyperconjugation than C—C bonds (H is more electropositive than C, see
pp. 50 and 89), and that the better donors should stabilise the transition structure for nucleophilic attack when
they are anti-periplanar to the incoming nucleophile. This idea does not command universal agreement, the
more obvious problem, already alluded to above, is that it is not universally accepted that the better donor
should be anti to the incoming nucleophile, and the less obvious problem is that it is not possible to be
dogmatic about which group actually is the better at hyperconjugation. The subject of C—H versus C—C
hyperconjugation has a long and not particularly dignified history,547 but there is structural and spectroscopic evidence in favour of the relatively heterodox idea that C—H bonds are intrinsically better donors, of
which the following are representative: (a) propionaldehyde in its lowest-energy conformation in the gas
phase has both C—H bonds conjugated to the p bond 5.134 (¼ 2.185a), and the methyl group is in the
sterically most crowded position;216,548 (b) triethylborane 5.135, with the empty p orbital on boron making it
isoelectronic with a tertiary carbocation, has the C—H bonds conjugated to the empty orbital;549 (c) enolate
formation from the ,-unsaturated ester 5.136 favours the formation of the cis double bond 5.137,
indicating that the starting material has the C—H bonds conjugated through the double bond to the carbonyl
group;550 (d) UV spectra in the gas phase show longer wavelength 0-0 maxima for toluene than for tertbutylbenzene, and for trans-2-butene than for trans-1,2-di-tert-butylethylene; (e) the chemical shifts in the
NMR spectra of alkenes551 and p-alkylbenzyl cations552 indicate greater electron release successively from
methyl groups than from ethyl, i-propyl and tert-butyl groups, which is known as the Baker-Nathan order;
and (f) the Perlin effect (see pp. 64 and 85) indicates the a C—H bond is more effective in hyperconjugation
than a C—C bond.
H
H
Me
H
O
Me
H
H
H
H
H
5.134
B
Me
Me
H
5.135
H
H
MeO
Me
LiNPri2
O
H
H
H
MeO
Me
OLi
H
H
5.136
5.137
There are other explanations for each of these pieces of evidence, and there is also plenty of contrary
evidence suggesting that the larger alkyl groups are better donors,553 especially when the electron demand is
high. Presumably the larger number of electrons available in the larger alkyl groups can be drawn upon,
inverting the Baker-Nathan order. Since the attack of a nucleophile on a carbonyl group is not making a large
demand, the idea that it is controlled by superior C—H hyperconjugation cannot easily be dismissed.
Because of the unsettled reception for Cieplak’s idea, other theories are still current. The most thoroughly
accepted draws attention to the fact that the C¼O bond is not perfectly eclipsing the equatorial C—H bonds
on C-2 and C-6—it is pointing 4–5 lower, as can be seen in the Newman projection 5.138 along the C-1 to
C-6 bond of 5.131. Equatorial attack, therefore, would have to squeeze in closer to the axial C—H bonds on
C-2 and C-6, and push the oxygen past the two equatorial hydrogen atoms. Axial attack, however, creates an
approach to the transition structure 5.138, in which the oxygen can move down into an equatorial position
without developing any eclipsing.
H
5
3
Nu
O
6
5
H
O
H
2
H
H
5.131
4-5°
2
H
5.138
The energetic cost of the eclipsing which has to occur when the attack is equatorial is described as
torsional strain. It is evidently greater than the energetic cost suffered by small nucleophiles from the
5 IONIC REACTIONS—STEREOCHEMISTRY
231
1,3-diaxial interactions with the hydrogen atoms on C-3 and C-5 during axial attack.527,540,554
Somewhat similar considerations apply to tertiary methylcyclohexyl cations, which are slightly
pyramidalised, like the carbonyl carbon, with the methyl group moved towards an equatorial orientation, exposing the axial direction to attack.555 Further complications arise when there is a substituent
to the carbonyl group.556 An chlorine with an axial configuration encourages axial nucleophilic
attack, and hence anti to the halogen, in conformity with a picture combining 5.129 and 5.138.
However if the axial halogen is fluorine, or the halogen is in an equatorial configuration,
nucleophilic attack is predominantly equatorial.
In contrast to cyclohexanones, the dioxan-5-one 5.139 (R¼tBu) is attacked by nucleophiles in the gas
phase from the equatorial direction,557 because of electrostatic repulsion from the fraction of negative charge
carried by the two oxygen atoms in the ring, as Houk had predicted.558 The selectivity is not particularly high
(67:33), because the usual torsional strain is still present, enhanced in this case by the shorter C—O bond
lengths making the ring less puckered, and increasing the dihedral angle by which the carbonyl oxygen atom
is pushed below the neighbouring C—H bonds. In solution, however, the ketone 5.139 (R¼Ph) is attacked
from the axial direction,559 just like cyclohexanones. Evidently the solvent insulates the charge on the
OH
O
n-BuSiH4–
t
Bu
gas
phase
O
H
O
67:33
S
O
R
O
5.139
OH
O
R
H
LiAlH4
Et2O
O
Ph
O
OH
S
S
R
S
H
R = tBu, n-BuSiH4–, gas phase: 84:16
5.140
R = Ph, LiAlH4, Et 2O: 85:15
97:3
incoming nucleophile from the electrostatic repulsion, the torsional strain remains high and there are no axial
substituents hindering axial attack.
The sulfur atoms in the dithia analogues 5.140 are less electronegative than the oxygen atoms in the acetals
5.139, but the axial lone pairs bulge further up, and are not heavily solvated. However, the carbonyl group is
displaced even further down by the changes in bond length and bond angles from having two C—S bonds in
the ring. The one effect makes axial attack less favourable, and the other makes equatorial attack less
favourable. In the event both solution and gas phase reactions take place with a strong preference for
equatorial attack.
5.2.1.3 Nucleophilic Attack on Cyclic Oxonium and Iminium Ions. Whatever the final reception for
Cieplak’s idea, there is little doubt that nucleophiles attack cyclic oxonium ions and iminium ions from the
direction that builds an anti-periplanar lone pair. This is another version of the anomeric effect (Section
2.2.3.3), but applied now to reactivity instead of simply to structure. We have already seen that axial
anomeric bonds are longer than their equatorial counterparts, that they are weaker, and that they ionise
more easily. The corollary, because the transition structure is low in energy for both the forward and back
reactions, is that nucleophiles attack more rapidly from the anomeric direction. There is an abundance of
evidence that the more lone pairs that can be anti to the leaving group or incoming nucleophile, the easier
the reaction is in either direction.560 Thus the orthoester 5.141 reacts with Grignard reagents to give the
product 5.142 of axial attack, whereas the equatorial isomer is unreactive.561 Both the departure of the
methoxy group and the attack by the nucleophile are axial, which can be explained by the contribution of
the anti-periplanar lone pairs to weakening the axial bond, and yet stabilising the forming bond in the
second step.
232
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
MeBrMg
BrMg Me
OMe
MeMgBr
O
O
O
O
O
O
5.141
5.142
The same pattern is seen, with only one lone pair, in tetrahydropyrans, when nucleophiles like allylsilanes
and allylstannanes attack axially in Lewis acid catalysed reactions in pyranyl sugars.562 The same pattern is
also found in imminium ions563 as Stevens demonstrated in several syntheses. He showed that nucleophiles
attack from the direction that most easily sets up an anti and axial lone pair, especially if it can create a chair
conformation, as in the reduction of the imminium ion 5.143 to give monomorine-I 5.144.564
Nu
H
NaCNBH3
N
N
Bu
Bu
5.144
5.143
5.2.1.4 Vinylogous Felkin-Anh Rules. There are two reactions that can be called vinylogous versions of
attack on a carbonyl group adjacent to a stereogenic centre, in the first of which an intervening double bond
makes the attack vinylogous with respect to the carbonyl group 5.145.565 The most common reactions of this
type are organocuprate conjugate additions,566 although others with heteroatom nucleophiles are known.
Bu
Ph
–
Bu2CuLi, BF3
CO2Et
Ph
CO2Et
O
Nu
Me
L
Me
S
M
Bu2CuLi, BF3
Ph
5.145
Me
70:30
Bu
E-5.146
CO2Et
Ph
CO2Et
Me
70:30
Z-5.146
The factors affecting which side of the double bond is attacked ought to be the same as in the Felkin-Anh
rule, but with the conformation of the starting material affected by the fact that it is a C¼C double bond and
not a C¼O.567 The presence of a substituent on the double bond cis to the stereogenic centre, even when it is
only a hydrogen atom, increases the A1,3 allylic interaction with the medium-sized group 5.147.
H
Ph
Nu–
Me
H
CO2Et
H
Felkin product
Me
H
H
CO2Et
H
anti-Felkin product
Ph
5.147
Nu–
5.148
When the medium-sized group is a methyl group, and when the substituent cis to it is a hydrogen atom, as in
the trans alkene E-5.146, it appears that the Felkin-Anh conformation for the transition structure 5.147, with
the medium-sized group inside, is still the lowest in energy in spite of the A1,3 allylic interaction, and attack
5 IONIC REACTIONS—STEREOCHEMISTRY
233
on the double bond takes place in the Felkin-Anh sense from above, as drawn. The conformation with the
methyl group inside is almost certainly higher in energy, but in the transition structure 5.147 it allows the
nucleophile to approach close to the hydrogen atom, lowering the energy of this transition structure. This is
called the ‘inside-methyl’ effect. However, when the substituent cis to the stereogenic centre is larger, as in
the corresponding cis alkene Z-5.146 (or the alkene with two ester groups), this conformation gives way to
the alternative 5.148 in which the small group is rotated into the inside position, and the nucleophile is
therefore directed to the bottom surface, in order for it to be anti to the large group. This picture works
reasonably well, provided that the group cis to the stereogenic centre is a hydrogen atom and the mediumsized group is relatively small like a methyl group, accounting for the major products in the examples above.
The rule is sometimes referred to as a modified Felkin-Anh rule—as well as being modified, it is more
complicated, because of the ‘inside-methyl’ effect. It is also more sensitive to variation in the nucleophile,
possibly because the nucleophile changes the mechanism.568
When one of the substituents is an electronegative element, the story becomes even more complicated.569
The conjugate additions to the silyl ethers E-5.149 and Z-5.149570 have the opposite stereochemistry to that
which might have been expected from the reactions of the esters E-5.146 and Z-5.146. They follow the
modified Felkin-Anh rules only if the silyloxy group is treated as the medium-sized substituent, or if it is
delivering the reagent after coordination in conformations like 5.147 and 5.148 with the silyloxy group
occupying the same position as the phenyl group. A silyloxy group is not thought to be a strong Lewis base,
and coordination is not usually a problem with it; no other coherent picture emerges.
Me
ButMe2SiO
CO2Et
Me2CuLi, BF3
ButMe2SiO
Me
E-5.149
Me
73:27
Me
Me2CuLi, BF3
ButMe2SiO
Me
CO2Et
ButMe2SiO
CO2Et
CO2Et
Me
87:13
Z-5.149
These explanations applied to cuprate reactions assume that the stereochemistry-determining step is the initial
coordination of the copper to the C¼C double bond, with the subsequent -bonding of the copper to the carbon and the reductive elimination step which establishes the C—C bond taking place from this intermediate.
This may not always be the case, and it is possible that the relative ease with which either the -bonding or the
reductive elimination takes place determines the stereochemistry. Thus lithium dimethylcuprate and the cyclic
enone 5.150 give mainly the conjugate addition product 5.153 with the incoming nucleophile syn to the oxygen
atom. In the presence of trimethylsilyl chloride, however, the major product is 5.151 with the methyl group anti
to the oxygen atom.571 Corey’s explanation is that the intermediate 5.152, although the minor isomer formed in
the coordination step, is the more rapidly broken down in the absence of the silyl chloride.
CuMe2
major
O
O
slow
O
O
O
O
O
5.150
minor
O
CuMe2
5.152
5.151
O
fast
O
5.153
234
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
Changing the nucleophile from a cuprate to an amide anion causes the conjugate addition 5.154 ! 5.155
to change sense—it straightforwardly obeys the modified Felkin-Anh rule with the silyloxy group taken as
the large substituent and the methyl inside with the trans alkene. The degree of selectivity is low, but
becomes quite high when the silyloxy group is made even larger.572 Many other examples of stereoselective
conjugate addition with an electronegative substituent on the stereogenic centre exist, but with no comprehensively satisfying explanation, and sometimes with no explanation at all.
ButMe2SiO
CO2But
LiNBnSiMe3
SiMe3
N
Ph
ButMe2SiO
Me
CO2But
Me
5.154
5.155
54:46
The other kind of vinylogous reaction related to the Felkin-Anh rule is direct attack on the carbonyl group
5.156 instead of the conjugate attack 5.145. The stereochemical information must now be transmitted either
through the double bond or through space. Except when coordination delivers the reagent from one of the
three substituents,573 or when the double bond is cis and the stereogenic centre is close enough to exert its
effect predominantly through space as a steric effect,471,574 these reactions usually,575 but not always, show
little diastereoselection. One remarkable exception is the open chain ketone 5.157, which is reduced to give
largely the alcohol 5.158.576 Another exception is in the relatively rigid cyclohexadienone system 5.159,
which is more or less free from ambiguity about the conformation at the time of reaction. The ring is flat, and
the two surfaces of the p system are different by virtue of one being cis to the C—O bond and the other cis to a
C—C bond. Grignard reagents add selectively to the surface syn to the alkyl group and anti to the oxygen to
give the alcohol 5.160.523
SPh
SPh
LiEt3BH
O
O
L
OH
5.157
S
5.158
97:3
M Nu–
5.156
O
O
MeMgBr
O
OH
O
O
5.159
5.160
97:3
To try to explain these results, we need a theory that allows us to identify the differential effect of the two bonds, C—C and C—S or C—O, on the upper and lower surfaces of the p system. To some extent we did this in
considering how electropositive and electronegative groups influenced the attack on a carbonyl group, but
the way the argument was developed there only applies to attack at the neighbouring carbon—it cannot be
extended along a conjugated system.
5.2.1.5 Pyramidalisation. The simplest possibility is to extend the idea used to explain axial attack on
cyclohexanones by unhindered nucleophiles (see p. 230). The carbon atom and the oxygen atom of the
carbonyl group and the two substituents C-2 and C-6 do not lie perfectly in the same plane—C-1 is a little
above the plane defined by C-2, C-6 and the oxygen atom in the drawing 5.138. The carbon is said to be
pyramidalised.577 Attack from the axial direction merely increases the degree of pyramidalisation, avoiding
5 IONIC REACTIONS—STEREOCHEMISTRY
235
the torsional strain induced by equatorial attack, which would have forced the equatorial hydrogens to pass
through a conformation in which they eclipse the C—O bond. There is therefore the possibility that all we
need to know is the sense of pyramidalisation to predict the stereochemistry of attack on a trigonal carbon,578
and to a large extent the stereochemistry of many reactions is well correlated to the sense of quite small
degrees of pyramidalisation as measured by X-ray crystal structure determinations.579
The direction of pyramidalisation in open-chain systems is also fairly easy to predict from first principles—it takes place away from the substituent held most nearly at right angles to the plane of the carbonyl
group, because it leads to a greater degree of staggering 5.161 in that direction. It is independent of whether
the substituent is an electron donor or an acceptor, as calculations for 2-silylacetaldehyde 5.162 and
2-fluoroacetaldehyde 5.163 show.580 The former, with an Si—C—C—O dihedral angle of 92.4 is the global
minimum (compare 5.121), but the latter has to be constrained to the same angle before optimisation of bond
and dihedral angles, otherwise a structure with the fluorine in the plane of the carbonyl group is obtained
(compare 5.122). The fluorine atom leads to a slightly greater degree of pyramidalisation, perhaps because it
has some of the character of an anomeric effect. The sense of pyramidalisation in these two cases matches the
sense of nucleophilic attack discussed in Section 5.2.1.1.
H3Si
R
R
R
O
R
1.6° H
O
H
H
5.161
92.4°
5.162
F frozen
O
H
H
3.2° H
5.163
Another suggestion, based on high level calculations on cyclohexanone,581 is that p*CO is unsymmetrically
disposed, bulging axially, above the plane of the p bond when the ring is drawn as in 5.131 and 5.138. Since
this is the LUMO, overlap with the HOMO of the nucleophile is better from the axial direction.
If pyramidalisation is induced by increasing the degree of staggering, the trigonal carbon atoms in a
conjugated chain ought to be pyramidalised along the chain in alternating directions. Thus a C¼C double
bond 5.164 pyramidalised downwards at C-2 by the anti-periplanar R group on C-1 ought, other factors being
equal, to be pyramidalised upwards at C-3, and so on, alternating down a longer chain. Thus we can try to
predict what the pyramidalisation will be in the ketones 5.157 and 5.159. If we assume that they react with
nucleophiles when the electronegative substituent is conjugated to the carbonyl group, lowering the energy
of the LUMO, as in the usual Felkin-Anh picture 5.129, then the reactive conformations will be pyramidalised as shown exaggerated in 5.165 and 5.166, both of which imply preferred attack from below, which is
O
SPh
R
2
3
1
5.164
O
H
O
O
5.165
5.166
what is observed. A simple application of predictions like these, however, is not reliable, because the benzyl
ether, corresponding to the phenythioether 5.157, gives largely the opposite diastereoisomer on reduction.
The difficulty of using pyramidalisation is further compounded by some known cases where the X-ray
structure shows pyramidalisation in one direction, when reactions are known to take place from the opposite,
but these are from electrophilic attack on a C¼C double bond, which we shall deal with later in Section 5.2.2.
5.2.1.6 The SN20 Reaction. The SN20 reaction, in which an allyl system equipped with a nucleofugal group
undergoes attack at C-3, is the vinylogous version of the SN2 reaction. As discussed earlier (see p. 181), an
236
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
allyl halide usually undergoes a straightforward SN2 reaction, with direct attack at C-1 and inversion of
configuration at that centre. On the special occasions when the SN20 reaction does take place, it can, in
principle, do so with syn 5.167 ! 5.168 or anti stereochemistry 5.167 ! 5.169, and the story is complicated
further by there being two syn reactions and two anti reactions. The characteristic feature of a stereospecific
SN20 reaction would be that it gave a mixture of only two of the four possible products, say both of the syn
products 5.168a and 5.168b, not necessarily in equal amounts since that only depends upon which
conformation 5.167a or 5.167b is the more reactive, but neither of the anti products 5.169a and 5.169b.
The two syn products 5.168 differ from each other in two respects—double bond geometry and configuration
at the stereogenic centre, whereas they each differ from one of the anti products in only one stereochemical
feature. Equally a stereospecific reaction might give both of the anti products but neither of the syn.
BA
Nu
C
D
Nu
Nu
syn
X
Nu
H
A
B
Nu
anti
5.167a
anti
B
H CD
A
B
Nu
A
syn
anti
5.168a
A
Nu
syn
syn
B
X
C
D
5.168b
D
5.167b
BA
anti
C
D
C
Nu
5.169a
C
D
5.169b
Both syn and anti reactions have been observed, and it is not yet clear what all the factors are that favour the
one over the other. The heart of the problem is to know how the stereogenic centre carrying the nucleofugal
group X differentially affects the charge and the orbitals on the top and bottom surfaces of the double bond.
We can begin again by treating this as a problem of predicting the direction of pyramidalisation, with the
advantage that this time we can be confident that the nucleofugal group in a concerted reaction will be
conjugated to the double bond at the time of reaction as it is in each of the conformations 5.167, and will
therefore be the prime influence inducing the pyramidalisation. The picture we obtain, using the 5.167b
conformation is 5.170, implying that the preferred reaction ought to be on the upper surface of C-3 in this
case, syn to the leaving group X. We come to the same conclusion with tau bonds—the attack on the upper
surface of C-3 is anti to the lower tau bond 5.171, showing inversion of configuration at that atom, and that in
turn is anti to the leaving group X, which is also effectively displaced with inversion. A similar sequence
using either pyramidalisation or the tau bonds can be drawn for the 5.167a conformation which would
suggest that the preferred side of attack was from below. The expectation is for the SN20 reaction to be
stereospecifically syn.
X
2
A
B
3
H
syn
Nu
syn
1
C D
A
B
C
D
Nu
H
A
B
inv.
inv.
5.170
5.168b
X
C
D
5.171
However primitive these treatments are,582 the conclusion has a certain appeal for it implies that having two
more electrons in the transition structure changes the stereochemistry, from inversion in the SN2 reaction to
syn in the SN20 reaction. We saw the same change in substitution reactions, retention for SE2 to inversion for
SN2, and for elimination reactions, anti for E2 to syn for E20 (Section 5.1.2.2), but in both those cases, and in
the SN20 reaction, it is not reliable.
5 IONIC REACTIONS—STEREOCHEMISTRY
237
Experimentally, the first problem to overcome is that allylic electrophiles nearly always react by the SN2
pathway, rather than by the SN20 pathway (Section 4.5.2.2). This can be overcome by building up steric
hindrance near the nucleofugal group, and there is then a trend in favour of the syn reaction. In the first
examples to which stereochemistry was assigned, Stork found that the trans allylic mesitoate trans-5.172
gave largely the trans amine trans-5.173, and the cis mesitoate cis-5.172 gave largely the cis amine
cis-5.173, showing that these reactions were stereospecifically syn.583 However, Stork found that changing
to a sulfur nucleophile reduced the degree of stereospecificity from almost completely syn to variably syn or
anti, depending upon the solvent, showing that the syn stereospecificity is not fixed immutably.584
O2CAr
O2CAr
sy n
sy n
N
HN
N
HN
trans-5.172
cis-5.172
tr ans-5.173
cis-5.173
In this pair of stereoisomeric starting materials, the problem had been simplified by using a cyclic alkene so
that there are no longer two conformations a and b to complicate the analysis, but this device brings with it its
own complication. Studying stereochemistry using compounds with rings and resident stereochemical labels
like the isopropyl group in these compounds means that the ring system and the resident centres create a
conformation in the starting materials that can override whatever inherent stereochemistry the reaction itself
might have. In an open-chain system 5.174, designed to minimise this problem by having only the one
stereocentre, only the difference between hydrogen and deuterium at C-3 and relying on the preference for
forming a trans double bond, the reaction 5.174 ! 5.175 was highly syn stereospecific (>96:4),585 but a
closely similar reaction with a carboxylate leaving group was syn to a much less marked degree (<64:36).586
Other examples of SN20 reactions showing syn stereochemistry, without having any obvious bias in the
system, are some cyclobutenyl halides with oxygen nucleophiles,587 and an intramolecular cyclopropaneforming reaction in which the nucleophile was an enolate carbon atom.588
Et2NH
H
H
D
Cl
H
syn
Et2N
H
Me
D
5.174
H
Me
5.175
There are also a few reactions showing more or less preference for an anti SN20 reaction, including a
cyclopentane-forming reaction with an enolate nucleophile,589 and a sulfur nucleophile.590 In addition, the
reactions of alkyl cuprates with allylic acetates are always stereospecifically anti 5.176 ! 5.177, although
the formation of racemic product shows that regiocontrol has been lost.
Me2CuLi
+
OAc
5.176
anti SN2'
5.177
inversion SN2
238
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
The cuprate reactions are not mechanistically SN20 reactions, since they involve in the first step coordination of the copper on the lower surface of a p-allyl system, followed by the delivery of the methyl to the same
surface, and equally to both ends of the allylic system, in a reductive elimination step.591 It seems likely that
the decisive step determining the stereoselectivity is the coordination of the copper. It might well coordinate
reversibly and equally easily to both surfaces, in an alkene like 5.176, but the chloride will only depart when
the copper is anti to it. The same explanation might be offered for a similar result in the reduction of
propargyl derivatives with lithium aluminium hydride, in which coordination by the aluminium is
probable.592
If we move on to the SN200 reaction, with one more double bond, there are reactions in which
nucleophilic attack has changed sides again, and is anti 5.178 ! 5.179.593 In this example, the ring
system has a bias that is likely to lead nucleophiles to attack from the side opposite the oxygen atom,
whether this reaction takes place in one step or two, whatever inherent preference there might be for the
SN200 reaction.
OMe
OMe
t
Bu O2C
t
NaOMe
OH
Bu O2C
O
anti
5.178
5.179
5.2.2 Nucleophilic and Electrophilic Attack on Cycloalkenes
We have seen cycloalkenes in the previous section, but in those cases it was the fundamental stereochemistry
of the reaction that was under consideration. We now turn to the stereochemistry governed by the ring system
itself, and we shall look at both nucleophilic and electrophilic attack, since they usually have similar
stereochemical preferences rather than contrasting preferences. There is a problem with electrophilic attack
that we do not meet with nucleophilic attack—the attacking reagent does not always reveal the stereochemistry. If the electrophile is a proton, for example, it usually attaches itself to the less-substituted carbon,
where there may already be a hydrogen atom, and the stereochemistry observed is that of the subsequent
nucleophilic attack. Similarly, the initial electrophilic attack may take place rapidly and reversibly on either
surface, but it is the ease with which the second step, a loss of a proton, for example, or the gain of a
nucleophile, which may determine which of the intermediates leads on to the major product.594 We shall not
be concerned with reactions like these here. However, in addition to several reactions that are straightforwardly electrophilic attack, we shall be concerned with several which can be described as electrophilic in
nature, like the reactions of alkenes with osmium tetroxide, with peracids, with some 1,3-dipoles, and with
boranes, and of dienes with dienophiles in Diels-Alder reactions. Some of these reactions are pericyclic, the
pericyclic nature of which we shall meet in Chapter 6. For now, it is only their diastereoselectivity that will
concern us.
5.2.2.1 Monocyclic alkenes. Cycloalkenes have a preferred conformation, which may or may not
influence the stereochemistry of attack upon the double bond. The attack is always more or less along
the line of the p orbitals, as discussed in Section 5.1.3, but there may be steric or electronic effects
operating to affect which of the two surfaces of the double bond is best presented to an incoming
reagent. At its most simple, a single substituent on a four- or five-membered ring usually causes
electrophiles (and nucleophiles) to attack anti to it as in the allylation of the enolate 5.180.595 The
uncomplicated explanation is that the large group hinders approach from the side it occupies, and
supporting this argument the enolate 5.180 is highly selective only when the side chain carries a
noticeably large protecting group.
5 IONIC REACTIONS—STEREOCHEMISTRY
239
H
O
Ph3CO
H
Br
O
O
Ph3CO
5.180
MCPBA
But
But
+
O
O
H
O
But
60:40
5.181
The relatively small degree of kinking away from a flat conformation in these small rings can usually be
ignored, but it cannot be ignored with six-membered and larger rings. In a six-membered ring a large group
will be equatorial in the most abundant conformation, but the two surfaces of a cyclohexene like 5.181 are
sterically not very different. This alkene is attacked by peracid with little selectivity, and what little there is
happens to be in favour of attack syn to the resident group.596
In the epoxidation reaction, electrophilic attack is taking place concertedly at both carbons of the double bond.
If pyramidalisation is important, it gives us no help, because one of the carbon atoms of the double bond can be
expected to be pyramidalised upwards and one down. In contrast, when the attack is only at one of the two
carbons, the degree of stereocontrol in a six-membered ring becomes high. One simple way to appreciate this is
to see the pyramidalisation as taking place to move the cyclohexene conformation from a half chair closer to a
full chair. The enolate methylations 5.182 and 5.184 are selective for axial attack, leading to chair conformations
5.183 and 5.185 in the product.597 In the former, the attack is anti to the tert-butyl group and in the latter it is syn,
in contrast to what happens in five-membered rings. The reason can be seen on both sides of the reaction
coordinate—in the presumed pyramidalisation of the starting material, and in the greater ease of forming a chair
conformation rather than a boat in the product. There are similar explanations for the stereochemistry of
nucleophilic attack in six-membered rings such as 5-substituted cyclohexenones,598 which again allow stereochemistry to be transmitted effectively from one stereogenic centre to another three atoms away.
CD3I
But
But
CD3
O
O
5.182
CD3I
But
But
O
O
5.183 70:30
5.184
CD3
5.185 83:17
Medium-sized rings have a different feature allowing high levels of diastereoselectivity.599 In these rings, a
double bond does not lie flat in the average plane of the ring. Instead it presents one face towards reagents,
while the other is obscured by the ring wrapped around behind it. If the conformation can be controlled, high
levels of stereocontrol can be achieved, whether attack is by an electrophile 5.186 or a nucleophile 5.187.
The problem with medium-sized rings is to predict their conformation. Only with simple cases is it easy to
see why conformations like 5.186 and 5.187 are the most populated, with the rings kinked in the direction
that makes the methyl group equatorial, and why attack from the front surface as drawn is most favourable.
O
O
MeI
O
O
Me
I
5.186
O
O
BF3:OEt2
O
86:14
Me2CuLi
O
CuMe2
5.187
99:1
240
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
5.2.2.2 Bicyclic alkenes. Bicyclic systems like the alkenes 5.188 and 5.189 are well known to be attacked
from the exo direction,600,601 on the less hindered convex face of the bicyclic system. Similarly high levels of
stereocontrol are found for nucleophilic attack on bicyclic systems, as in the reduction of the ketone 5.190, in
which the preference for exo attack overwhelms the steric hindrance offered by the adjacent methyl group.602
Bicyclic systems, especially like these with a zero bridge, are often used in synthesis to give reliably high
levels of stereocontrol, with the penalty that there may be many steps needed to open them up to reveal a
target structure.
N
CH2N2
H
1. B2H6
OH
N
2. NaOH, H2O2
5.188
5.189
OMe
OMe
O
O
NaBH4
H
MeO2C
MeO2C
O
5.190
OH
However, there are anomalies, where a steric effect is clearly not enough to explain the observed stereoselectivity. The steric argument, although commonly invoked, is weak for norbornene 5.191 and for the
bicycloocta[2.2.2]diene 5.192, but the selectivity for exo attack in the former and endo in the latter is
strong.603,604
exo
O
OsO4
OH
OH
O
O
O
O
endo O
5.192
5.191
More convincingly, the steric argument is nearly nonexistent for the diene 5.193, but it shows high levels of
diastereoselectivity in Diels-Alder reactions, with attack in the endo direction, which is, if anything, the more
hindered.605
CO2Me
CO2Me
endo
5.193
One possible explanation for these results is based on the sense of pyramidalisation at the reacting trigonal
carbons. In norbornene they are measurably pyramidalised with the p orbitals bulging in the exo direction
5.194, anti to the two-carbon bridge, since the bonds leading to them, marked in bold, are better aligned for
overlap with the orbitals of the p bond 5.195 than the bonds of the one-carbon bridge.606 Even though the
degree of pyramidalisation is small, electrophilic attack from the exo direction will induce less torsional
strain,607 just as axial attack by nucleophiles does on cyclohexanones. The double bond undergoing attack in
5 IONIC REACTIONS—STEREOCHEMISTRY
241
the bicyclooctadiene 5.192 pyramidalises with the p orbitals bulging downwards 5.196, because the bonds
from the tetrahedral carbons, marked in bold, are more effective donor substituents than the bonds from the
trigonal carbons. The latter have more bonding involving the 2s orbitals than the former, making the
tetrahedral carbons effectively more electropositive than the trigonal carbons (Fig. 1.57). This can be
justified most succinctly using hybridisation—they are sp3 and sp2, respectively—but, even without using
hybrid orbitals, it can be seen that using one p orbital exclusively in the p bond, inherently means that more of
the 2s orbital contributes to bonding in the bonds to the trigonal carbons. In the diene 5.193, the alternation
of pyramidalisation along a chain of double bonds (see p. 235) implies that the termini of the double bonds
would be pyramidalised downwards, exaggerated and shown for the HOMO in 5.197, and that is the
direction from which the electrophilic dienophile attacks.
≡
H
H
H
H
H
H
5.195
5.194
5.196
5.197
However, pyramidalisation is not the whole story, for there are alkenes known to be pyramidalised in one
direction, which nevertheless react in another,608 and we shall come to further anomalies in using only
pyramidalisation when we come to discuss SE20 reactions in Section 5.2.3.4.
5.2.3 Electrophilic Attack on Open-chain Double Bonds with Diastereotopic Faces
5.2.3.1 The Houk Rule for Steric Effects in Electrophilic Attack on Open-Chain Alkenes. As in
nucleophilic attack on a C¼C double bond (Section 5.2.1.4), the conformation of an open-chain alkene
with a neighbouring stereogenic centre is likely to have the small group inside 5.198, more or less eclipsing
the double bond.609 Electrophilic attack on such a double bond, by a bridging or nonbridging electrophile, is
then, in the absence of stereoelectronic effects, likely to be anti to the large group. This explanation for the
stereochemistry of electrophilic attack on most alkenes has been advanced a number of times, first by
Zimmerman,610,611 then by Barton,612 by Kishi,613 and most thoroughly, and with computational support by
Houk.488 An exception to this pattern is when the medium-sized group M is small, as with a methyl group,
and when, at the same time, the substituent A on the double bond, cis to the stereogenic centre, is a hydrogen
atom. In this case, the conformation 5.199, with the medium-sized group inside, although not usually the
lowest in energy, is populated, and attack from the less hindered side in this conformation becomes plausible,
especially as it is now taking place syn to the small group instead of syn to a medium-sized group. This is the
‘inside-methyl’ effect, which we have already met on p. 233 in connection with nucleophilic attack on a
double bond. Furthermore, the size of the group R will affect the outcome—if it is large, the conformation
5.199 can actually be lower in energy than conformation 5.198. As with nucleophilic attack on a carbonyl
group, the dihedral angles will not have the large group precisely at right angles, and the transition structure
may well be more like that shown in 5.200, which applies to a nonbridging electrophile attacking with an
E+
L
M
L
S
R
M
S
A
B
R
A
B
L
E+
5.198
R
M
S
+
5.199
E
5.200
242
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
obtuse angle outside the double bond. Electrophilic attack is often exothermic, and the structure of the
starting material is therefore likely to be a good guide to the transition structure.
A straightforward example illustrating this sense of attack is the methylation of the lithium enolate 5.201.
The substituent A (as in 5.198) is larger than a hydrogen atom, since it is either a methyl group or an oxyanion
(the enolate is actually a mixture of stereoisomers), and the substituent R is a hydrogen atom. Thus the
alternative conformation, corresponding to 5.199, is probably not significantly populated, and methylation
takes place with a moderate degree of selectivity in the sense 5.201 to give mainly the ketone 5.203.614 When
the group R is not too large, there is evidently no change to this pattern—when it is a methyl group and the
electrophile is a proton, the reaction 5.202 still takes place in the sense 5.198, this time to give mainly the
diastereoisomeric ketone 5.204. Other examples fitting this pattern are the epoxidation and hydroboration of
alkenes having substituents A larger than a hydrogen atom.615
O
H
+
H
or
O
H
O
O
Me
Me
H
I
OH2
5.201
5.202
75:25 from 5.201
20:80 from 5.202
5.203
5.204
An example of a reaction in the alternative sense 5.199, with an inside methyl group, is the cycloaddition of a
nitrile oxide to a terminal alkene, which gives mainly the diastereoisomer 5.207 by way of the transition
structure 5.205.616 Nitrile oxide cycloadditions are among those dipolar cycloadditions (Chapter 6) which
are electrophilic in nature. The substituent A (in 5.199) is a hydrogen atom, and the medium-sized group is
only a methyl group, so it fits the criteria for an ‘inside-methyl’ effect. It is still a little surprising that reaction
takes place in this sense, because a conformation like 5.199 in the starting material ought to be higher in
energy than 5.198. Houk suggested that, with the electrophilic attack making obtuse angles at both carbon
atoms, the transition structure 5.205 would leave room for the methyl group to sit inside with little energetic
penalty. In the alternative conformation 5.206, the need for the methyl group to avoid eclipsing the incoming
oxygen atom would force the isopropyl group closer towards eclipsing the double bond, raising the energy.
Thus the relative energies of the transition structures are the other way round from the starting materials.
N
O
Ar
H
or
H
H
H
O
O
N
major
5.205
Ar +
H
minor
5.206
N
H
O
Ar
N
Ar
5.207
65:35
5.208
The ‘inside-methyl’ effect explains a puzzling result, in which the stereochemistry of the double bond of the
enol ethers Z-5.209 and E-5.209 appears to control the diastereoselectivity of the protonation. The enol ether
Z-5.209, with the alkoxy group cis to the stereogenic centre at C-17 is the normal one, reacting in the sense
5.198, with the hydrogen atom inside, and the proton attacking C-20 on the upper surface 5.211 anti to the
tertiary alkyl centre at C-13 to give largely the aldehyde 20S-5.210. The enol ether E-5.209 has a hydrogen
atom cis to the stereogenic centre and a relatively small group, the C-16 methylene group, which can sit
comfortably inside, especially as it is effectively no larger than a methyl group with the rest of its bulk turned
5 IONIC REACTIONS—STEREOCHEMISTRY
243
away as part of the D-ring. Protonation now takes place anti to the tertiary centre but on the bottom surface
5.212 to give largely the diastereoisomeric aldehyde 20R-5.210.614,617
OR
H
20
13
17
H
CHO
20
OR
HF, MeCN
H
H
16
CHO
20
H
H
HF, MeCN
H
H
20S-5.210 80:20
Z-5.209
17
16
13
H
H
20
20R-5.210 80:20
E-5.209
H
13
OR
H
16
H
13
5.211
OR
H
H
5.212
Bridging electrophiles, as in epoxidation, are fairly well behaved in the sense 5.198, possibly because the
acute approach angle does not leave room for the medium-sized group to sit inside.614 Bromination,
however, is reversible in the first step, and the stereochemistry actually observed, although often in the
sense 5.198, is partly governed by the relative ease with which each of the diastereoisomeric epibromonium
ions is opened. As a consequence, the ratio of diastereoisomers is not reliably a measure of the relative rates
of attack on the diastereotopic faces of the alkene.618
5.2.3.2 The Influence of Electropositive Substituents. The story remains the same in the presence of the
stereoelectronic effect of a donor substituent. A silyl group on the stereogenic centre is the best studied
among these, where it is notable for imparting a strikingly high level of open-chain stereocontrol in the sense
5.198 in a wide variety of reactions: enolate alkylations 5.213,619 dihydroxylation, epoxidation620 and
hydroboration 5.214621 of allylsilanes, and Diels-Alder reactions of pentadienylsilanes.622 In all of them,
the silyl group is not only the donor substituent but also the large group, and it is not clear whether there is any
electronic component to the diastereoselectivity.623
What is clear is that an electronic component will encourage attack anti to the silyl group, since it is
generally agreed that the bond to an incoming electrophile is electron deficient, and that the transition
structure will be especially well stabilised by an antiperiplanar donor substituent like silyl. Equally, a
calculation580 of the pyramidalisation of the carbon atom adjacent to the stereogenic centre shows that it
bulges 1.3 away from the donor substituent in the lowest energy structure 5.215, in which the Si—C bond is
SiMe2Ph
Ph
H
H
MeI
SiMe2Ph
MeI
OMe
Li+
O
Ph
SiMe2Ph
CO2Me
Ph
H
Me
dr 97:3
H3Si
1.3°
2. –OOH
H BR2
5.214
5.213
107.2°
H
H
H
5.215
H
H
SiMe2Ph
1. 9-BBN
Ph
OH
dr >99:1
244
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
conjugated to the double bond, raising the energy of the HOMO. The problem which arose in attack on a
carbonyl group, about whether a donor or an electron-withdrawing group ought to be anti-periplanar to
an incoming nucleophile (see p. 228), does not arise here. The high level of diastereoselectivity in
electrophilic reactions may be a consequence of the match between the steric and electronic effects, but
there is no conclusive evidence on this point, since the silyl groups are unmistakably the large
substituent.
The only exceptions to attack taking place in the sense 5.198 are, as usual, when the medium-sized
group is a methyl (or similarly small) group and the substituent A is a hydrogen atom, when reaction
quite often, but not always, takes place in the conformation 5.199. Dihydroxylation by osmium tetroxide
on a trans double bond 5.216 ! 5.217624 shows this pattern more strongly than the corresponding
epoxidation, just as it did in the cases controlled only by steric effects, but when the group A is larger
than a hydrogen atom, as with the corresponding cis double bonds, this reaction switches to the normal
pattern 5.198. All these reactions, whether taking place from the conformation 5.198 or 5.199, still follow
the pattern of attack anti-periplanar to the donor substituent, as also do the SE20 reactions discussed in the
next section.
OsO4
Me
H
H
PhMe2Si
OH
H
Me
PhMe2Si
OH
+
SiMe2Ph
OH
5.216
OH
5.217
66:34
5.218
5.2.3.3 SE20 and SE200 Reactions. The SE20 reaction is a special case of electrophilic attack on a C¼C
double bond with a donor substituent on the stereogenic centre—the difference from the reactions described
in Section 5.2.3.2 is that the attack is at C-3, and it is followed by the loss of an electrofugal group from the
stereogenic centre. The most studied of these are the electrophilic substitution reactions of stereodefined
allylsilanes, which take place in the anti sense 5.219 ! 5.220 with a wide range of electrophiles, especially
when the group R is large, as with R ¼ Ph.625,626
X–
E+
Me3Si
R
1
3
2
5.219
E
R
E = DO2CCF3 and
t
BuCl, RCHO and
RCOCl + Lewis acid
5.220
In more detail, in the specific case of the enantiomerically pure allylsilane 5.219 (R ¼ Me) reacting with the
adamantyl cation, the attack takes place in each of the conformations 5.221 and 5.226, since the mediumsized group is a methyl group and the substituent cis to the stereogenic centre is only a hydrogen atom. The
intermediate cations 5.222 and 5.227 are stabilised by overlap of the empty p orbital with the Si—C bond
(see p. 94), and are not substantially free to rotate to give their rotamers 5.224 and 5.229 before the silyl
group is removed to give the major products 5.223 and 5.228. The attack appears to be very largely anti to
the Si—C bond, as shown by the high level of enantiomeric enrichment in the Z-alkene products 5.228:5.225
(>99:1),627 but the E-alkene 5.223 was not enantiomerically pure, being contaminated with 10% of its
enantiomer 5.230. This small loss of stereospecificity can be explained in two ways: either there was a small
amount of leakage by rotation 5.227 ! 5.229, or there was a small amount of attack in the syn sense on the
conformer 5.221. It seems likely that a small amount of rotation is the better explanation, and that the
electrophilic attack is in fact very highly anti, because the same reaction in the corresponding allenylsilane
5 IONIC REACTIONS—STEREOCHEMISTRY
245
5.231 ! 5.233 is, within experimental error (–1%), completely stereospecific in the anti sense. In this case,
there is no ambiguity about conformation and no opportunity for rotation in the intermediate cation 5.232.628
Ad+
+
36%
Ad
H
H
3
2
H
Me3Si
H
Me3Si
5.221
Ad
36%
5.222
36%
5.223
<1%
+
Me3Si
3
Ad
Ad
H
2
H
H
5.224
5.225
<1%
+
Me3Si
64%
Me3Si
3
H
H
2
H
H
5.226
Ad
60%
Ad
Ad+
5.227
60%
5.228
4%
+
3
+
H
H
2
Ad =
Ad
H
Ad
Me3Si
5.229
5.230
4%
Ad+
Ad
Ad
H
H
H
Me3Si
Cl–
5.231 (er 99:1)
Me3Si
5.232
5.233 (er 99:1)
There are a number of syn SE20 reactions, which are significantly different in nature. The electrophile is
typically an aldehyde, which is coordinated at the time of reaction to the electropositive group on the
stereogenic centre, characteristically a metal like boron, tin, zinc or a silyl group carrying one or more
electronegative elements. These reactions are cyclic in nature, usually use chair-like transition structures, are
sometimes called metalla-ene reactions, and are inherently syn in their overall stereochemistry.629,630
In Section 5.2.3.2, we saw that attack on the atom adjacent to a stereogenic centre was regularly anti to an
electropositive substituent. Now we find that the attack on the next atom, C-3, is also anti, whereas previously we
have argued that there is some evidence for alternation in the side of attack as one moves atom by atom down a
conjugated chain of double bonds. This is especially what we expect if we use only the argument based on
pyramidalisation, where we saw on p. 235 that, if one end of a double bond is pyramidalised down, the next atom
can be expected to be pyramidalised up. If we go back to the calculation on the allylsilane 5.215, but look at the
other end of the double bond 5.234, we see that C-3 is indeed pyramidalised upwards, although only to a very small
extent (0.2). Clearly this does not match the sense of electrophilic attack on this atom. There is another
complication in using alternating pyramidalisation as a guide, in that a bridging electrophile would have to form
246
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
one of its two bonds to an atom pyramidalised the wrong way. The tau bond model 5.235, however, does not have
problems with a bridging electrophile, and does correctly predict the sense of electrophilic attack, with the tau bond
anti to the donor substituent M as the site of attack, whether the electrophile is attacking C-2 or C-3 or both together.
M
H3Si
1.3°
3
H
H
H
H
H
2
H
3
0.2°
ret.
ret.
E
5.234
5.235
Predicting the stereochemistry of an SE200 reaction is even less convincing. Both alternating pyramidalisation, greatly exaggerated in 5.236, and the tau bond model 5.237 predict that electrophilic attack at C-5
should be from above, syn to the donor substituent.
E
M
4
2
3
5.236
5
M
2
3
4
5
5.237
In spite of this agreement, the small number of known examples of SE200 reactions prove to be anti, with a low
degree of stereoselection, typically 60:40.627 Clearly the most simple theories do not explain the sense of
selectivity, and there is nothing more convincing to fall back on than a general sense that a donor on the top
surface of a conjugated system evidently encourages attack on the bottom surface. When the electrophile is
large enough, and the silyl group is held close enough, by having the double bond between C-2 and C-3 cis,
the level of stereoselection can rise to 90:10 in the anti sense but this is explained simply by steric repulsion
between the silyl group and the incoming electrophile.631 Conceivably all these result with silyl substituents
are essentially controlled by steric effects alone, with the silyl group able to hinder the surface it is on, even
over quite large distances, and this is probably as good an explanation as we have at present.
5.2.3.4 The Influence of Electronegative Substituents. The real problem explaining the diastereoselectivity of electrophilic attack comes when one of the bonds on the stereogenic centre is to an electronegative
atom, making it an electron-withdrawing group. We shall leave out of consideration those cases where an
oxygen atom delivers the reagent by hydrogen bonding or Lewis acid-base coordination—reactions like
epoxidation632 and the Simmons-Smith reaction on allylic alcohols.633 These reactions have cyclic transition
structures, and the diastereoselectivity is determined by the conformation of the ring—any molecular orbital
considerations are secondary.
A C—X bond conjugated with a p bond will lower the energy of the HOMO, and make the alkene less
reactive towards electrophiles. Consequently, when it is not delivering the reagent, an electronegative
substituent often adopts a conformation in which the C—X bond is not in conjugation with the p bond. For
example, in a cyclic alkene, dipolar cycloaddition takes place syn to the chlorine atoms in the dichlorocyclobutene 5.238,634 and the Diels-Alder reaction on acetoxycyclopentadiene 5.239635,636 takes place syn to the
acetoxy substituent. These results are in striking contrast to the reactions on small rings, which usually take
place anti to the resident substituents whatever they are. These compounds will be more reactive when the
electron-withdrawing substituents are as little conjugated to the double bonds as possible. Relatively mild
distortions of the conformation at the time of reaction can allow the C—H bonds to be lined up to overlap with
the p bond, as drawn in 5.240 and 5.241, with the C—Cl and C—O bonds mostly lifted out of conjugation.
5 IONIC REACTIONS—STEREOCHEMISTRY
247
N
CH2N2
Cl
Cl
5.238
N
+
Cl
Cl
N
N
Cl
Cl
96:4
AcO
AcO
OAc
+
"100:0"
5.239
H
H
OAc
Cl
Cl
H
5.240
5.241
The incoming reagent will approach anti to the H, even though the approach is formally syn to the
electronegative elements. In both cases pyramidalisation with the p orbital bulging away from the C—H
bonds will be on the same side as the electronegative atoms. This simple explanation ties in with the
theory advanced by Cieplak, mentioned earlier (see p. 230), in which he pointed out that the bond in the
transition structure forming towards the incoming reagent was inherently electron-deficient, and so
ought to line up anti to the better donor. This idea did not work to explain the Felkin-Anh rule when
applied to nucleophilic attack on a carbonyl compound having an electronegative substituent, but it
does when applied to electrophilic attack instead of nucleophilic attack. We can feel comfortable with
the idea that the electrons coming from the double bond towards the electrophile will leave antiperiplanar to a donor substituent, and will be helped if the electron-withdrawing groups are not in
conjugation with the p bond.
In open chain alkenes there is more flexibility for the bond to the electronegative substituent to avoid
conjugation with the double bond. It can be in an outside position with respect to the C¼C double bond or
inside.637 In either case, the preferred conformation at the time of reaction will have the bond to the
substituent avoiding conjugation with the p bond, and hence avoiding being anti-periplanar in the transition
structure. When the substituent A (in 5.198) is larger than a hydrogen atom, we might expect most reactions
to take place with a transition structure like 5.198, with the electronegative atom as the medium-sized group
oriented to be as little in conjugation with the double bond as possible. In practice this is rarely the case, and
reaction in this sense appears to be most likely when the group A is significantly larger than a methylene
group and the group R larger than a hydrogen atom. An example is the dihydroxylation of the Z-alkene
Z-5.242 with osmium tetroxide, in which the A1,3 interaction between the inside hydroxyl group and the
ethoxycarbonyl group is too severe for the conformation Z-5.242a to be significantly populated. The ethyl
group counts as the large group, and the hydroxyl as the medium-sized group, and dihydroxylation takes
place in the conformation Z-5.242b to give only the lactone 5.243.638
O
H
OH
CO2Et
H
Z-5.242a
OH
HO
H
CO2Et
H
OsO4
Z-5.242b
CO2Et
O
3
OH
HO
HO
5.243
OH
248
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
When the substituent A is a hydrogen atom, it appears that the lowest energy conformation in the
transition structure is often that with the electronegative substituent inside. Reactions therefore take
place in the sense 5.199 with the electronegative element treated as the medium-sized group, which
it often is, in contrast to its role in the Felkin-Anh rule, where it is treated as the large group
whatever its actual size. An example is the dihydroxylation of the E-alkene E-5.242. Whereas
the corresponding Z-alkene Z-5.242 reacts in a conformation avoiding an A1,3 interaction, the
E-alkene can adopt a conformation E-5.242 with the hydroxyl group inside, and the product is
the lactone 5.244 with the opposite stereochemistry at C-3 from that of the product 5.243 derived
from the Z-isomer.638640 This propensity for an electronegative substituent to be inside is known
as the ‘inside oxygen’ or ‘inside alkoxy’ effect,641 when the electronegative atom is an oxygen
substituent. Only when the substituent A is larger, as it is with the ethoxycarbonyl group in the
alkene Z-5.242, is the hydroxy or alkoxy group pushed into an outside position. Other reactions
cleanly showing this stereochemistry are nitrile oxide cycloadditions616,642 and Diels-Alder reactions with acetylenic dienophiles.643,644
OsO4
H
OH
OH
O
OH
H
CO2Et
O
CO2Et
3
OH
OH
OH
5.244
E-5.242
In contrast to the cases described in Sections 5.2.3.1 and 5.2.3.2 above, with purely steric effects and with
donor substituents, reactions often take place with the oxygen substituent inside, even when the substituent A
is larger than a hydrogen atom. Both the E- and the Z-alkenes 5.245 react in the sense 5.199 with oxygen
inside, even though it has an A1,3 interaction with an alkyl group in the latter. The result is that the new
stereogenic centre at C-3 in the major products syn-5.246 and anti-5.246 is created in the same sense from
both alkenes, but the stereochemistries at C-4 are opposite to each other because of the stereospecificity of
the syn addition.639
OsO4
Ph
H
OBn
O
H
H
3
BnO
3
4
OH
4
OH
BnO
E-5.245
OBn
OH
+ BnO
81:19
syn-5.246
OH
syn-5.247
OsO4
Ph
H
OBn
O
H
3
4
H
BnO
3
OH
4
OH
BnO
Z-5.245
anti-5.246
OBn
OH
+ BnO
90:10
OH
anti-5.247
One puzzling feature in this pair of reactions is the higher degree of stereoselectivity in the Z-alkene Z-5.245
(90:10) relative to that in the E-alkene E-5.245 (81:19). This is the opposite of what might have been
predicted by the theory advanced above, and it has led to the suggestion that electrophilic attack takes place
5 IONIC REACTIONS—STEREOCHEMISTRY
249
anti to the alkoxy group in a conformation 5.248 with the hydrogen atom inside. We dismissed this
possibility earlier on the grounds that conjugation of the O—C bond with the double bond would reduce
its nucleophilicity and destabilise the transition structure, but one suggestion is that in this conformation the
oxygen lone pairs overlap through space with the p orbitals on the lower surface, and that this pushes the
electron population out onto the upper surface 5.249.639
OsO4
OsO4
H
BnO
Ph
BnO
H
H
H
H
O
Ph
O
5.248
5.249
Whatever the merits of this idea,645 it, like all the other approaches to explaining diastereoselectivity, cannot
be applied to all the systems in which it might operate. For example, this idea applied to acetoxycyclopentadiene 5.239 suggests that it ought to react with dienophiles anti to the substituent, in contrast to the
experimental result. In a related system to which it might also apply, the epoxide 5.250 does show complete
attack anti to the oxygen atom,646 but it has been pointed out that the oxygen lone pairs, both in the
cyclopentadiene 5.239 and in the epoxide 5.250, lie in a node of the HOMO of the diene, and cannot interact
with what ought to be the most important orbital in a Diels-Alder reaction. Lifting this restriction with the
diol diene 5.251 restores the syn selectivity (94:6),647 implying that the idea of through-space overlap is far
from generally applicable.
O
O
O
N
Ph
O
O
PhN
5.250
OH
5.251
O
OH
O
N
Ph
O
O
OH
OH
PhN
O
In contrast to the dihydroxylations, the epoxidation of allylic halides648 is poorly selective in the sense 5.199,
even when the substituent A is only a hydrogen atom, and there are several reactions which actually take
place in the opposite sense 5.198. These include the hydroboration of both the E-allylic alcohol E-5.252 and,
less surprisingly, the Z-allylic alcohol Z-5.252,649 and Diels-Alder reactions on the related dienes with
dienophiles like maleimides.643 Evidently the ‘inside alkoxy’ effect, prominent in nitrile oxide cycloadditions and especially in osmium tetroxide dihydroxylations, does not apply to all reactions. The pattern that
osmium tetroxide reactions are always the ones most showing attack in the sense 5.199, regardless of
whether the medium-sized group is based on an oxygen atom or not, would again seem to argue against the
explanation implied in 5.248. It is probably significant that the ‘inside alkoxy’ effect is most noticeable with
reagents which are relatively electrophilic in nature, and much less so with boranes, which are only mildly
electrophilic.
250
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
Bu
OH
H
HO
H
H
Bu
BBN
Bu
OH
Bu
Bu
BBN
OH
Bu
H
E-5.252
90:10
Bu
OH
H
HO
H
Bu
H
Bu
Bu
OH
Bu
BBN
BBN
OH
Bu
H
Z-5.252
>94:6
5.2.4 Diastereoselective Nucleophilic and Electrophilic Attack on Double Bonds Free of Steric
Effects.521,650
On account of the delicate balance between steric and electronic effects, and the difficulty of teasing them
apart, a number of reactions have been carried out on substrates designed as far as possible to remove the
steric component, and to leave an electronic one. Substrates which have been used in this kind of experiment
include the adamantanones 5.253 (Y ¼ O), the norbornanones 5.254 (Y ¼ O), and the cyclopentanone 5.255,
for nucleophilic attack, and the corresponding alkenes 5.253 (Y ¼ CH2), 5.254 (Y ¼ CH2) and 5.256 for
electrophilic attack by such electrophiles as peracid, dichlorocarbene and dichloroketene. These ketones and
alkenes are designed to have the possibility of purely electronic effects transmitted rationally through the framework, and they do all show diastereoselectivity, occasionally to a high degree.
R
Y
R
Y
O
R
R
R
5.253
5.254
5.255
5.256
As an example of the kind of experiment that is carried out in this area, borohydride attack on the ketone 5.257
(R ¼ F) gave the alcohol 5.258 (R ¼ F) as the major product, with attack syn to the electron-withdrawing
substituent, whereas the ketone 5.257 (R ¼ SnMe3) gave the alcohol 5.259 (R ¼ SnMe3) as the major product, with
attack anti to the electron-donating substituent. The degree of stereoselectivity is unimpressive, but the electronwithdrawing fluorine and the electron-donating trimethylstannyl group exert their effects in opposite senses.
O
HO
H
H
OH
5.258:5.259
NaBH4
+
R
5.257
R=F
R = SnMe3
R
5.258
R
5.259
62:38
48:52
5 IONIC REACTIONS—STEREOCHEMISTRY
251
In trying to explain these results, we no longer have to worry about which bond is conjugated to the
carbonyl group at the time of reaction—the bonds are fixed in their orientation, and attack is always axial in
one ring and equatorial in the other. Furthermore, the effect of the substituent on stereochemistry is no longer
influenced by its effect on the overall rate, as it was with the ‘inside alkoxy’ effect. One explanation is that
the C—F bond in the ketone 5.257 (R ¼ F) is conjugated to the C—C bonds, emphasised in 5.260. This
conjugation makes these C—C bonds less electron-donating than the C—C bonds on the other side of the
carbonyl group, emphasised in 5.261. Following the Cieplak argument, the nucleophile duly attacks the side
opposite the better donor. With the electron-donating trimethylstannyl group, it is the bonds on the side of the
stannyl group, emphasised in 5.262, that are made the better donors, and the nucleophile attacks anti to them.
O
O
O
F
F
5.260
SnMe3
5.261
5.262
The azaadamantanone 5.263 is reduced selectively by sodium borohydride syn to the amine function. Here the
argument is not so clear, because the lone pair on the nitrogen atom is conjugated to the bonds in the sense of
the bold lines in 5.264, making them better donors, and this ought to have encouraged anti attack. However, the
nitrogen atom itself is an electronegative element, and one might argue that attack should take place syn to it just as
it does for the fluoride 5.257 (R ¼ F). Support for the latter idea comes from the corresponding N-oxide 5.265,
which is reduced with even greater selectivity in the syn sense now that the effect of the lone pairs has been
removed.651
O
O
38
O
62
5
N
95
N
N
O
5.263
5.264
5.265
Similarly, since Cieplak’s argument suggests that electrophiles will also attack anti to the better donor, the
corresponding electrophilic attack on the alkenes 5.266 by borane is also syn selective for the fluoroadamantane system (R ¼ F), and anti selective for the trimethylsilyladamantane system (R ¼ SiMe3). Curiously, this
selectivity is reversed in sense when the hydroboration is catalysed by rhodium complexes, and the explanation
may be that coordination by the rhodium is best when it is anti to the electron-withdrawing group.652
OH
OH
H
H
5.267:5.268
1. BH3.THF
R
5.266
R=F
R = SiMe3
+
2. NaOH, H2O2
R
5.267
R
5.268
63:37
47:53
252
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
Although these experiments, and several others similar to them, largely support Cieplak’s contention,
there are enough exceptions and unexplained features to make this account of the selectivity neither
complete nor accepted.653 For example, the substituents do affect the shape of the molecule,654 and hence
the degree of pyramidalisation at the carbonyl carbon atom, and there are electrostatic effects operating
through space, rather than being relayed through the bonds.655
6
Thermal Pericyclic Reactions
Pericyclic reactions656,657 are the second distinct class of the three, more or less exclusive categories of organic
reactions—ionic (Chapters 4 and 5), pericyclic (this Chapter) and radical (Chapter 7). Their distinctive features
are that they have cyclic transition structures with all the bond-making and bond-breaking taking place in
concert, without the formation of an intermediate. The Diels-Alder reaction and the Alder ‘ene’ reaction are
venerable examples.
O
O
O
O
O
O
O
O
A Diels-Alder reaction
O
H
H
O
O
O
An Alder ene reaction
The curly arrows can be drawn in either direction. Here they are drawn so as to imply a clockwise movement
of electrons, but the arrows could equally well have been drawn anti-clockwise. There is no absolute sense to
the direction in which the electrons flow. Similarly, there is no absolute sense in which the hydrogen atom
that moves from one carbon atom to the other in the ene reaction is a hydride shift, as seems to be implied by
the curly arrows, or a proton shift, as it would seem to be if the arrows were to have been drawn in the
opposite direction. In other words, neither component can easily be associated with the supply of electrons to
any of the new bonds. The curly arrows therefore have a somewhat different meaning from those used in
ionic reactions. In this they resemble somewhat the curly arrows used to show resonance in benzene, where
the arrows show where to draw the new bonds and which ones not to draw in the canonical structure, but in
the drawing of arrows interconnecting resonance structures there is neither a sense of direction nor even an
actual movement. The analogy between the resonance of benzene and the electron shift in the Diels-Alder
reaction is not farfetched, but it is as well to be clear that one, the Diels-Alder reaction, is a reaction, with
starting materials and a product, and the other, resonance in benzene, is not.
All pericyclic reactions share the feature of having a cyclic transition structure, with a concerted movement
of electrons simultaneously breaking bonds and making bonds. Within that overall category, it is convenient to
divide pericyclic reactions into four classes. These are cycloadditions, electrocyclic reactions, and sigmatropic rearrangements (Fig. 6.1), and the relatively less common group transfer reactions, each of which
possesses features not shared by the others, and some of which employ a terminology that cannot be used
without confusion if applied to a reaction belonging to one of the other classes. It is a good idea to be clear
Molecular Orbitals and Organic Chemical Reactions: Reference Edition
© 2010 John Wiley & Sons, Ltd. ISBN: 978-0-470-74658-5
Ian Fleming
254
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
(a) Cycloadditions
(b) Electrocyclic reactions
Fig. 6.1
(c) Sigmatropic rearrangements
The three major classes of pericyclic reactions
about which class of reactions you are dealing with, in order to avoid using inappropriate terminology. We
shall begin by illustrating the identifying features of each of the classes, simply to establish what they are.
6.1
The Four Classes of Pericyclic Reactions
Cycloadditions are characterised by two components coming together to form two new bonds, one at each
end of both components, joining them together to form a ring, with a reduction in the length of the conjugated
system of orbitals in each component (Fig. 6.1a). Cycloadditions like the Diels-Alder reaction are by far the
most abundant, varied, featureful and useful of all pericyclic reactions. They are inherently reversible, and
the reverse reaction is called a retro-cycloaddition or a cycloreversion.
Cheletropic reactions are a special group of cycloadditions or cycloreversions in which the two bonds
are made or broken to the same atom. Thus sulfur dioxide adds to butadiene 6.1 to give an adduct 6.2, for
which the sulfur has provided a lone pair to one of the bonds and has received electrons in the formation of
the other. As far as the sulfur dioxide is concerned, it is an oxidative addition, changing the sulfur from SIV to
SVI. The reaction is readily reversible on heating, and so sulfur dioxide can be used to protect dienes,
allowing the adduct 6.2 to be heated in the presence of dienophiles as a convenient (liquid) source of
butadiene.
SO2
SO2
6.1
both bonds
made to the same
atom
6.2
Electrocyclic reactions are invariably unimolecular, in contrast to cycloadditions, which are characterised by
having two components, usually two different molecules, coming together to form two new bonds. They
are characterised by the creation of a ring from an open-chain conjugated system, with a bond forming
across the ends of the conjugated system, and with the conjugated system becoming shorter by one p orbital
at each end (Fig. 6.1b). The reactions are inherently reversible, with the direction they take being determined
by thermodynamics. Most electrocyclic reactions are ring-closings, since a bond is created at the expense
of a p bond, but a few are ring-openings, because of ring strain. Representative electrocyclic reactions are the
ring-opening of cyclobutene 6.3 on heating to give butadiene 6.1, and the ring-closing of hexatriene 6.4 to
give cyclohexadiene 6.5. In the case illustrated, butadiene 6.1 is lower in energy than cyclobutene 6.9 by
about 50 kJ mol1.
150°
6.3
132°
6.1
6.4
6.5
6 THERMAL PERICYCLIC REACTIONS
255
Sigmatropic rearrangements are often the most difficult to identify. They are unimolecular isomerisations,
and formally involve overall the movement of a bond from one position to another, with a concomitant
movement of the conjugated systems in order to accommodate the new bond (Fig. 6.1c). The oldest known
example is the first step in the Claisen rearrangement,658 when a phenyl allyl ether is heated. The first step is the
sigmatropic rearrangement in which the single bond, drawn in bold, in the starting material 6.6 moves to its new
position in the intermediate 6.7. It has effectively moved three atoms along the carbon chain (from C-1 to C-3),
and three atoms along the chain of the oxygen atom and two carbon atoms (O-10 to C-30 ). This type of
rearrangement is called a [3,3]-shift, with the numbers identifying the number of atoms along the chain that
each end of the bond has moved. The second step forming the phenol 6.8 is an ordinary ionic reaction—the
enolisation of a ketone. It is perhaps a timely reminder that ionic reactions often precede or follow a pericyclic
reaction, sometimes disguising the pericyclic event.
1
1'
2
O
O
3
2'
OH
200°
3'
H
85%
6.6
6.7
6.8
A quite different looking sigmatropic rearrangement is the hydrogen atom shift 6.9 ! 6.10, also long known
from the chemistry of vitamin D.659 In this case, the end of the H—C bond attached to the hydrogen atom
(H-10 ) necessarily remains attached to the hydrogen, but the other end has moved seven atoms (C-1 to C-7)
along the conjugated carbon chain. This reaction is therefore called a [1,7]-shift.
7
HO
1'
H
6
5
1
2
4
H
60°, 24 h
HO
R
R
3
6.9
6.10
Another quite different looking sigmatropic reaction is the Mislow rearrangement 6.11 ! 6.12, which is invisible
because it is thermodynamically unfavourable, but the ease with which it takes place explains why allyl sulfoxides,
with a stereogenic centre at sulfur, racemise so much more easily than other sulfoxides.660 Here, one end of the
C—S bond moves from the sulfur (S-10 ) to the oxygen atom (O-20 ) and the other end moves from C-1 to C-3. This is
therefore called a [2,3]-shift, the bond marked in bold moving two atoms at one end and three at the other.
Tol
1'
2'
S
O
1
51°
S
3
2
6.11
Tol
O
t 1 2.5 h
2
6.12
Group transfer reactions make up the fourth category; they have few representatives, with ene reactions by
far the most common. Stripped to their essence, ene reactions have the form 6.13 ! 6.14, but in practice
the enophile usually needs to have electron-withdrawing groups attached to it. They usually take place
256
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
from left to right, since overall a p bond is replaced by a bond, but they are, of course, reversible. They
resemble [1,5]-sigmatropic rearrangements, since a bond moves, and they also resemble cycloadditions
like Diels-Alder reactions, since one of the p bonds of the diene has been replaced by a bond in the ene.
Nevertheless, since the reaction is bimolecular and no ring is formed, they are neither sigmatropic rearrangements nor cycloadditions.
H
H
6.13
6.14
Ene reactions 6.13 have a hydrogen atom moving from the ene to the enophile, but other atoms can in
principle move. In practice, the only elements other than hydrogen that are commonly found in this kind of
reaction are metals like lithium, magnesium or palladium, when the reaction 6.15 is called a metalla-ene
reaction.630 The carbon chain may also have one or more oxygen or nitrogen atoms in place of the carbons.
Thus if the atom carrying the hydrogen is an oxygen atom and the atom to which it is moving is also an
oxygen atom, it becomes an aldol reaction. Aldol reactions are usually carried out with acid or base catalysis,
and most are not significantly pericyclic in nature. Other well known types of group transfer reaction are
represented by the concerted syn delivery of two hydrogen atoms from the reactive intermediate diimide 6.16
to an alkene or alkyne,661 and the syn elimination of selenoxides 6.17, and related reactions.
M
M
N
N
6.15
6.2
H
H
6.16
N
N
H
+
Ph
Ph
O
Se
H
O
Se
H
H
6.17
Evidence for the Concertedness of Bond Making and Breaking
The characteristic feature of all pericyclic reactions is the concertedness of all the bond making and bond
breaking, and hence the absence of any intermediates. Naturally, organic chemists have worked hard, and
devised many ingenious experiments, to prove that this is true, concentrating especially on Diels-Alder
reactions and Cope rearrangements. The following is an oversimplified description of some of the most
telling experiments.
The Arrhenius parameters for Diels-Alder reactions show that there is an exceptionally high negative
entropy of activation, typically in the range 150 to 200 J K1 mol1, with a low enthalpy of activation
reflecting the exothermic nature of the reaction.662 Bimolecular reactions inherently have high negative
entropies of activation, but the extra organisation for the two components to approach favourably aligned,
so that both bonds can form at the same time, accounts for the exceptionally high value in cycloadditions. The
compact transition structure is also in agreement with the negative volumes of activation measured by carrying
out the reaction under pressure.663 The rates of Diels-Alder reactions are little affected by the polarity of the
solvent.664 If a zwitterionic intermediate were involved, the intermediate would be more polar than either of
the starting materials, and polar solvents would solvate it more thoroughly. An example of a solvent effect on a
stepwise reaction, and not on a Diels-Alder reaction, is illustrated on p. 280. Typically, a large change of
dipole moment in the solvent, from 2.3 to 39, causes an increase in rate by a factor of only 10. In contrast,
stepwise ionic cycloadditions take place with increases in rate of several orders of magnitude in polar solvents.
This single piece of evidence rules out stepwise ionic pathways for most Diels-Alder reactions, and the only
stepwise mechanism left is that involving a diradical.
6 THERMAL PERICYCLIC REACTIONS
257
Deuterium substitution on the four carbon atoms changing from trigonal to tetrahedral as the reaction
proceeds, gives rise to inverse secondary kinetic isotope effects, small, but measurable both for the diene
6.18 and the dienophile 6.19.665,666 If both bonds are forming at the same time, the isotope effect when both
ends are deuterated would be geometrically related to the isotope effects at each end. If the bonds are being
formed one at a time, the isotope effects are arithmetically related.667 It is a close call, but the experimental
results, both for cycloadditions and for cycloreversions, suggest that they are concerted. Similar isotope
effects in Cope and Claisen rearrangements,668 and in the ‘ene’ reaction,669 come even more firmly to the
conclusion that these are concerted reactions.670
H(D)
H(D) (D)H
+
H(D) (D)H
H(D)
6.18
6.19
(D)H H(D)
H(D)
NC
CN NC
+
H(D)
(D)H H(D)
NC
6.20
CN
R*O2C
vs.
6.21
CO2R*
CN
6.22
6.23
Another way of testing how one end of the dienophile affects the other end is to load up the dienophile with
up to four electron-withdrawing groups, and see how each additional group affects the rate. A stepwise
reaction between butadiene 6.20 and tetracyanoethylene 6.22 ought not to take place much more than
statistically faster than a similar reaction with 1,1-dicyanoethylene 6.21, but a concerted reaction ought to,
and does, take place much faster.671 Furthermore the relative rates can be compared with the rate of
nucleophilic attack on the dienophile as a model for a stepwise reaction, and they prove to be very different.
A somewhat similar device has been used with dienophiles like fumarate esters 6.23 having chiral auxiliaries
R* on one or both ester groups. A stepwise reaction would be expected to show some chiral induction if the
bond is formed next to the ester having the chiral auxiliary, but no extra chiral induction from having a chiral
auxiliary at the other end at the same time. A concerted reaction, however, ought to have more than additive
effects from having both chiral auxiliaries present. The results from both of these experiments support a
concerted mechanism.672
High level molecular orbital calculations have been carried out, with ever increasing levels of sophistication, on the reaction between ethylene and butadiene. Most, but not quite all, agree that the concerted
pericyclic pathway gives the lowest energy transition structure.673 Calculations even more strongly support
the evidence for concertedness from the isotope effect studies.674 A diradical intermediate would have an
allylic radical at one end of the diene and the configuration would not have changed from trigonal to
tetrahedral. The two isotope effects in a stepwise diradical mechanism, that at the end undergoing bonding
and that at the end carrying the odd electron, should therefore be very different. Since they are not, but more
than arithmetically reinforce each other, the reaction is most probably concerted. There is one cycloadditionlike reaction, actually cycloreversion-like, that is unmistakably concerted. The gas phase pyrolysis of
cyclohexa-1,4-diene 6.24 gives benzene and, syn stereospecifically, hydrogen.675 There is no sensible
stepwise mechanism available, since free hydrogen atoms are much too high in energy to be plausible
intermediates. In addition, the relationship between the primary isotope effect for replacing one hydrogen by
deuterium kD/kH ¼ 0.5, and that for replacing them both kD2/kH ¼ 0.25 is geometric, i.e. related by the
expression (kD/kH)2 ¼ (kD2/kH), and not arithmetic, i.e. related by the expression (kD2/kH) ¼ 2(kD/kH) – 1,
providing compelling evidence for the only plausible mechanism, a concerted cycloreversion (6.24,
arrows).676 The only complication here is that it is not strictly a cycloreversion since no ring is broken,
but neither is it a member of any of the other classes. Its relationship to a cycloreversion and to a group
transfer reaction is obvious, but this type of reaction is unique in pericyclic chemistry.
258
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
(D)H
H(D)
180°
+
H(D)
H(D)
6.24
Finally, the single most impressive piece of evidence comes from the very fact that pericyclic reactions obey the
rules that we are about to expand upon. These rules only apply if the reactions are concerted. To have a few
reactions accidentally obeying the rules would be reasonable, but to have a very large number of reactions
seemingly fall over themselves to obey strict stereochemical rules, sometimes in what look like the most
improbable circumstances, is overwhelmingly strong evidence about the general picture. Of course, no single
reaction can be proved to be pericyclic, just because it obeys the rules—obedience to the rules is merely a
necessary condition for a reaction to be considered as pericyclic. In the case of cycloadditions, the suprafacial
nature of the reaction on both components in a very high proportion of reactions at least says that the second bond,
if it is not formed at the same time as the first, is formed very quickly after the first, before any rotations about single
bonds can take place. It seems more than likely that most reactions thought to be pericyclic actually are.
6.3
Symmetry-allowed and Symmetry-forbidden Reactions
Between 1965 and 1969 Woodward and Hoffmann presented rules for each of the different classes of
pericyclic reaction.677 They showed that the allowedness or otherwise of reactions depended critically upon
the number of electrons involved and on the stereochemistry of the reaction. We shall go through the rules
twice: first the rules class by class, and then again using the single generalised rule that they presented in
1969 that applies to all classes of pericyclic reactions.
6.3.1 The Woodward-Hoffmann Rules—Class by Class
6.3.1.1 Cycloadditions. A cyclic movement of electrons can be drawn for any number of cycloadditions, but
not all of them take place. Thus butadiene undergoes a Diels-Alder reaction with maleic anhydride (see p. 253), but
ethylene and maleic anhydride do not give the cyclobutane 6.25 when they are heated together.
O
O
heat
O
O
O
6.25
O
It is not that this cycloaddition is energetically unprofitable—in spite of the ring strain, the cyclobutane is lower in
energythanthetwoalkenes—sotheremustbeahighkineticbarriertothecycloadditionofonealkenetoanother.This
is a deeply important point, and it is just as well that it is true—if alkenes and other double-bonded compounds could
readily dimerise to form four-membered rings, there would be few stable alkenes, and life would be impossible.
Diels-Alder reactions are classified as [4 þ 2] cycloadditions, and the reaction giving the cyclobutane
would be a [2 þ 2] cycloaddition. This classification is based on the number of electrons involved. DielsAlder reactions are not the only [4 þ 2] cycloadditions, although they are by far the most numerous and the
most important. Conjugated ions like allyl cations, allyl anions and pentadienyl cations are all capable of
cycloadditions. Thus, an allyl cation can be a 2-electron component in a [4 þ 2] cycloaddition, as in
the reaction of the methallyl cation 6.27, derived from its iodide 6.26, with cyclopentadiene giving a
6 THERMAL PERICYCLIC REACTIONS
259
seven-membered ring cation 6.28.678 The diene is the 4-electron component. The product eventually isolated
is the alkene 6.29, as the result of the loss of the neighbouring proton, the usual fate of a tertiary cation. This
cycloaddition is also called a [4 þ 3] cycloaddition if you were to count the atoms, but this is a structural
feature not an electronic feature. In this chapter it is the number of electrons that counts.
I
AgO2CCF3
H
6.27
SO2
40%
6.26
6.28
6.29
An allyl anion such as the 2-phenylallyl anion 6.31, prepared in an unfavourable equilibrium by treating
-methylstyrene with base, undergoes a cycloaddition to an alkene such as stilbene 6.30, present in situ, to give
the cyclopentyl anion 6.32, and hence the cyclopentane 6.33 after protonation.679 The complication here is that
anions are often ill-defined intermediates, usually being organometallic species with a carbon-metal bond with
substantial covalent character, as we have seen before (see pp. 56, 78, 86, 96 and 117). It is not always legitimate to
think of conjugated anions, let alone to draw them, simply as symmetrical conjugated systems of p orbitals.
Nevertheless, the pericyclic pathway has the energetic benefit of forming both new bonds in the same step, and
so this type of reaction is quite plausibly pericyclic. The anionic product 6.32, having lost the allyl conjugated
system, needs the anion-stabilising phenyl group to make the reaction favourable. Allyl anionþalkene cycloadditions are rare, and calculations suggest that the few that are known are actually stepwise.680 It is evidently a penalty
of the fact that allyl anions are not usually simple conjugated systems of p orbitals, making it difficult for the
overlap to develop at both ends simultaneously. Structurally this is a 3 þ 2 cycloaddition, but electronically it is a
[4 þ 2] cycloaddition, just like the Diels-Alder and the allyl cationþdiene reactions.
Ph
6.30
LiNPri2
Ph
Ph
Ph
Ph
+H+
Ph
41%
Ph
THF
45°, 150 h
Ph
Ph
Ph
6.31
6.32
6.33
Yet another [4 þ 2] cycloaddition, rather rare, is that between a pentadienyl cation and an alkene. The best
known example is the perezone-pipitzol transformation 6.34 ! 6.36, where it is heavily disguised, but all the
more remarkable for that.681 It can be understood as beginning with an intramolecular proton transfer to give
the intermediate 6.35, which can then undergo an intramolecular [4 þ 2] cycloaddition with the pentadienyl
cation, emphasised in bold, acting as the 4-electron component and the pendant alkene, also bold, as the
2-electron component.
H
O
O
H
HO
O
O
O
O
O
6.34
6.35
O
6.36
260
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
1,3-Dipolar cycloadditions 6.37 þ 6.38 ! 6.39, however, are a large group of [4 þ 2] cycloadditions
isoelectronic with the allyl anion þ alkene reaction. There is much evidence that these reactions are
usually, although perhaps not always,682 concerted cycloadditions.683 They also have a conjugated system
of three p orbitals with four electrons in the conjugated system, but the three atoms, X, Y, and Z in the
dipole 6.37 and the two atoms A and B in the dipolarophile 6.38, are not restricted to carbon atoms. The
range of possible structures is large, with X, Y, Z, A and B able to be almost any combination of C, N, O
and S, and with a double 6.37 or, in those combinations that can support it, a triple bond 6.40 between two
of them.684
6.37
Y
A
6.40 X
Y
Z
X
X
A
B
6.38
Y
Z
Z
Y
X
B
A
6.39
B
Z
A
6.38
B
6.41
All the reactions described so far have mobilised six electrons, but other numbers are possible, notably a
few [8 þ 2] and [6 þ 4] cycloadditions involving 10 electrons in the cyclic transition structure. It is no
accident, as we shall see in Section 6.4.1, that all these reactions have the same number of p electrons
(4n þ 2) as those possessed by aromatic rings. A conjugated system of eight electrons would normally have
the two ends of the conjugated system far apart, but there are several molecules in which the two ends are
held more or less rigidly and close enough to participate in cycloadditions to a double or triple bond. Thus,
the tetraene 6.42 has the two ends of the conjugated system pulled together by the methylene bridge,
allowing it to react with dimethyl azodicarboxylate 6.43 to give the [8 þ 2] adduct 6.44.685 Tropone 6.45
adds as a 6-electron component to cyclopentadiene, which is a 4-electron component, giving the adduct
6.46.686
NCO2Me
20°
NCO2Me
40%
6.43
NCO2Me
NCO2Me
6.44
6.42
O
r.t, 3 d
O
6.45
6.46
Very crudely, but adequately for most purposes, we may state a rule for which cycloadditions can take place
and which not.
A thermal pericyclic cycloaddition is allowed if the total number of electrons involved can be expressed
in the form (4nþ2), where n is an integer. If the total number of electrons can be expressed in the form
4n it is forbidden.
6 THERMAL PERICYCLIC REACTIONS
261
This rule needs to be qualified, because it applies to those reactions taking place in the sense shown in
Fig 6.2a, in which the orbital overlap that is developing to form the new bonds takes place on the same
surface of each of the conjugated systems, represented here by a curved line, but implying a continuous set of
overlapping p orbitals from one end to the other. The dashed lines represent the two developing bonds.
Most cycloadditions have this stereochemistry, but an alternative possibility is that one of the two components might develop overlap with one bond forming on the top surface and the other on the bottom surface in
the sense shown in the component on the left in Fig. 6.2b. Obviously considerable twisting in the conjugated
systems has to take place before this kind of overlap can develop, and reactions showing this feature are
exceedingly rare. Yet another possibility, even more farfetched, is that both components have this feature in
the sense shown in Fig. 6.2c.
suprafacial
component
antarafacial
component
antarafacial
component
suprafacial
component
antarafacial
component
suprafacial
component
(a) Supraf acial overlap
developing in both components
Fig. 6.2
(b) Supraf acial overlap developing
in one component and antaraf acial
overlap developing in the other
(c) Antaraf acial overlap
developing in both components
Suprafacial and antarafacial defined for cycloaddition reactions
When both new bonds are formed on the same surface of the conjugated system, that component is described
as undergoing suprafacial attack. When one bond forms to one surface and the other bond forms to the other
surface, that component is described as undergoing antarafacial attack. The rule above applies to the
common, indeed almost invariable, case where both components are attacking suprafacially on each other.
In principle it also applies to the case where both components are antarafacial, but reactions with this
awkward geometry are essentially unknown. The generalisation does not apply to the case where one
component is suprafacial and the other antarafacial—these are allowed when the total number of electrons
is a (4n) number. One example of this type of reaction may be the [14 þ 2] cycloaddition 6.47 of
heptafulvalene to tetracyanoethylene, where the heptafulvalene is attacked in an antarafacial manner 6.48,
one of the dashed lines, on the left, showing overlap developing to the bottom surface of the conjugated
system, and the other to the top surface, presumably helped by some twisting in the conjugated system. This
reaction may not be pericyclic, and the suprafacial attack on the tetracyanoethylene is not proved, but it is
striking that the two hydrogens at the point of attachment in the product 6.49 are trans to each other,
revealing that the heptafulvalene behaved as an antarafacial component, whatever the detailed
mechanism.687
NC
CN
NC
CN
6.47
H
NC
NC
6.48
6.49
H
CN
CN
262
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
A more complete set of rules for cycloadditions can now be expressed, but we should remember that the
all-suprafacial rule in the box above covers a very high proportion of the known cycloadditions.
If the total number of electrons involved can be expressed in the form (4nþ2), where n is an integer, a
thermal pericyclic cycloaddition is symmetry allowed when both components react in a suprafacial
manner (or both components react in an antarafacial manner). If the total number of electrons can be
expressed in the form (4n), it is allowed if one of the components reacts in a suprafacial manner and the
other antarafacial.
6.3.1.2 Electrocyclic Reactions. The parent members of the most simple electrocyclic reactions, both
those of neutral polyenes and of conjugated ions are shown below. They are the equilibria between butadiene
6.50 and cyclobutene 6.51, between hexatriene 6.52 and cyclohexadiene 6.53, between octatetraene 6.54 and
cyclooctatriene 6.55, between the allyl cation 6.56 and the cyclopropyl cation 6.57, between the pentadienyl
cation 6.58 and the cyclopentenyl cation 6.59, between the heptatrienyl cation 6.60 and the cycloheptadienyl
cation 6.61, and between the corresponding anionic systems 6.62–6.67. There are of course heteroatomcontaining analogues, with nitrogen or oxygen in the chain of atoms, and the systems can be decked out with
substituents and other rings. The strained ring of the cyclobutene 6.51 makes this reaction take place in the
ring-opening sense, while the hexatriene 6.52 and octatetraene 6.54 reactions are ring closures. There are
heteroatom-containing analogues of the anionic systems, with nitrogen and oxygen lone pairs rather than a
carbanion centre. These reactions are rarely seen in their unadorned state, and the direction in which they go
is determined by such factors as ring strain, the gain or loss of aromaticity, and the substituents or
heteroatoms stabilising the ionic charge on one side of the equilibrium or the other.
6.50
6.51
6.56
6.57
6.62
6.63
6.52
6.53
6.58
6.59
6.64
6.65
6.54
6.55
6.60
6.61
6.66
6.67
In contrast to cycloadditions, which almost invariably take place with a total of (4nþ2) electrons, there are
many examples of electrocyclic reactions taking place when the total number of electrons is a (4n) number.
However, those electrocyclic reactions with (4n) electrons, like the butadiene-cyclobutene equilibrium, 6.50
6.51, differ strikingly in their stereochemistry from those reactions mobilising (4nþ2) electrons, like the
hexatriene-cyclohexadiene equilibrium, 6.52 ! 6.53. This is only revealed when the parent systems are
6 THERMAL PERICYCLIC REACTIONS
263
decked out with substituents. The stereochemistry is not dependent upon the direction in which the reaction
takes place, but it does depend upon whether there are (4n) or (4nþ2) electrons.
There are two possible stereochemistries for the ring-closing and ring-opening reactions. They are called
disrotatory and conrotatory, and are illustrated for the general cases in Fig. 6.3. Looking at the ring-closing
disrotatory reaction 6.68 ! 6.69, the two outer substituents R move upwards, so that the top lobes of the p
orbitals turn towards each other to form the new bond. The word disrotatory reflects the fact that the
rotation about the terminal double bonds is taking place clockwise at one end but anticlockwise at the other.
In the corresponding ring-opening, 6.69 ! 6.68, there is similarly a clockwise and anticlockwise rotation as
the bond breaks, and the two upper substituents R that start off cis to each other move apart to become the
outer substituents in the open-chain conjugated system. There is an equally probable disrotatory ring closure,
not illustrated, in which both R groups fall, with the lower lobes of the p orbitals forming the new bond, and
there is a possible alternative disrotatory ring opening, in which both R groups move towards each other,
although whether this happens depends, among other things, upon the size of the R groups, and the extent to
which they meet steric hindrance by moving inwards.
developing overlap
R
the movement of the cis substituents
away from each other
disrotatory ring closing
R
clockwise
rotation
anticlockwise
rotation
R
R
disrotatory ring opening
6.68
6.69
R
R
conrotatory ring closing
R
R
conrotatory ring opening
6.70
clockwise
rotation
clockwise
rotation
6.71
Fig. 6.3
Disrotatory and conrotatory defined
In contrast, in conrotatory ring-closing, 6.70 ! 6.71, one of the outer substituents and one of the inner
substituents, both labelled R, rise to become cis, so that the bottom lobe of the p orbital at one end forms a bond by overlap with the top lobe of the p orbital at the other end. The rotations are now in the same sense,
either both clockwise or both anticlockwise. It follows that the two R groups become cis to each other on
cyclisation but the two outer substituents, in contrast to the disrotatory path, become trans to each other on
cyclisation. In the ring-opening, 6.71 ! 6.70, the two substituents that are cis to each other move in the same
direction, one to an outer position and the other to an inner position by clockwise rotations, as drawn here, or,
of course, they could both move by anticlockwise rotations. The rules for which stereochemistry is followed
by which system are summarised in Table 6.1.
These were the first of the rules, introduced by Woodward and Hoffmann in 1965. They look difficult to
absorb all at once, but a simplification makes them easy to learn.
Thermal electrocyclic reactions involving a total number of electrons that can be expressed in the form
(4nþ2) are disrotatory, and thermal electrocyclic reactions in which the total number of electrons can
be expressed in the form (4n) are conrotatory.
264
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
Table 6.1 The Woodward-Hoffmann rules for electrocyclic reactions
Parent equilibrium
Butadiene ¼ cyclobutene
Hexatriene ¼ cyclohexadiene
Octatetraene ¼ cyclooctatriene
Decapentaene ¼ cyclodecatetraene
Cyclopropyl cation ¼ allyl cation
Cyclopropyl anion ¼ allyl anion
Pentadienyl cation ¼ cyclopentenyl cation
Pentadienyl anion ¼ cyclopentenyl anion
Heptatrienyl cation ¼ cycloheptadienyl cation
Heptatrienyl anion ¼
cycloheptadienyl anion
Nonatetraenyl cation ¼ cyclononatrienyl cation
Nonatetraenyl anion ¼ cyclononatrienyl anion
Electrons
Stereochemistry
4
6
8
10
2
4
4
6
6
8
conrotatory
disrotatory
conrotatory
disrotatory
disrotatory
conrotatory
conrotatory
disrotatory
disrotatory
conrotatory
8
10
conrotatory
disrotatory
Examples showing stereochemistry in agreement with these rules are the cyclobutene openings 6.72 ! 6.73
and 6.74 ! 6.75,688 and the hexatriene closings 6.76 ! 6.77 and 6.78 ! 6.79.689 The conrotatory opening
6.72 ! 6.73 and the disrotatory closing 6.76 ! 6.77 are stereochemically contrathermodynamic, with the
products in both cases the less stable stereoisomer. It was this striking feature that led Woodward to an
appreciation of the special nature of pericyclic reactions, because it was clear that some powerful factor was
overriding the normal thermodynamic preferences.
CO2Me
CO2Me
130°, 20 min
con
CO2Me
130°, 20 min
con
CO2Me
CO2Me
CO2Me
CO2Me
6.72
CO2Me
6.73
6.74
6.76
6.75
140°, 5.5 h
140°, 5.5 h
dis
dis
6.77
6.78
6.79
Among ions, the cyclisation of an allyl cation to a cyclopropyl cation is exemplified by the fate of the
intermediate 6.82 when the diazoalkane 6.81 reacts with the ketene 6.80. The intermediate enolate ion will
have the E-configuration, because the attack on the ketene will take place anti to the tert-butyl group. The
diazonium ion then loses nitrogen to give the W-cation 6.83, which undergoes a disrotatory electrocyclisation to give the cyclopropanone 6.84. The cyclopropyl cation product in this case is a ketone—it is not
uncommon to think of a carbonyl group as a highly stabilised carbocation, and in this case it drives the
reaction in the direction of ring closure. The tert-butyl groups are forced by the rules to be cis, in spite of the
steric forces against such an arrangement. In detail, it is likely that the cation itself is not an intermediate, but
that the cyclisation takes place concertedly with the departure of the nitrogen molecule. Nevertheless the
rules still apply in the transition structure, in which electron deficiency has started to develop at the carbon to
which the nitrogen is attached.690
6 THERMAL PERICYCLIC REACTIONS
265
N
O
+
O
N
O
O
dis
6.80
6.81
H
H
N2
6.82
6.83
6.84
The same power of the rules to override a powerful steric effect is seen in the ring closure of an allyl anion
created by the loss of a nitrogen molecule from the dihydrothiadiazole 6.85. The loss of the nitrogen is a
6-electron all-suprafacial 1,3-dipolar cycloreversion, and will have taken place, with the nitrogen molecule
leaving from the lower surface as drawn, to create the sickle-shaped zwitterion 6.86. The p system in this
intermediate is isoelectronic with an allyl anion, and its ring closure is therefore conrotatory, forcing the two
tert-butyl groups into the hindered cis arrangement in the episulfide 6.87.691
But
N
S
N
N
But
S
–N2
But
con
S
S
6.85
H
H
But
N
6.86
6.87
This reaction does not prove the stereospecificity, because it has only the one stereoisomer, although that is a
telling one since it leads to the more hindered product. The full stereospecificity of the cyclopropyl anion to
allyl anion interconversion is exemplified by the conrotatory opening of the trans and cis aziridines 6.88,
which are isoelectronic with the cyclopropyl anion. They open to give the W and sickle-shaped ylids 6.89,
respectively, which are isoelectronic with the corresponding allyl anions. This step is an unfavourable
equilibrium, which can be detected by the 1,3-dipolar cycloaddition of the ylids to dimethyl acetylenedicarboxylate, which takes place suprafacially on both components to give the cis and trans dihydropyrroles
6.90, respectively.692
Ar
MeO2C
N
MeO2C
CO2Me
N
CO2Me
N
MeO2C
CO2Me
W-6.89
MeO2C
tr ans-6.88
Ar
Ar
con
CO2Me
MeO2C
CO2Me
cis-6.90
Ar
MeO2C
N
MeO2C
CO2Me
cis-6.88
Ar
Ar
con
N
N
MeO2C
CO2Me
sickle-6.89
MeO2C
CO2Me
CO2Me
MeO2C
CO2Me
trans-6.90
The conrotatory closing of a pentadienyl cation can be followed in the NMR spectra of the ions 6.91,693 and
the disrotatory closing of a pentadienyl anion can be seen in what is probably the oldest known pericyclic
reaction, the formation of amarine 6.93 from the anion 6.92.694
266
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
–83°
–83°
con
con
E,E-6.91
Z,E-6.91
Ph
N
Ph
Ph
Ph
H
PhLi
N
Ph
–130°
N
dis
N
Ph
N
NH
+H+
Ph
Ph
Ph
6.92
6.93
6.3.1.3 Sigmatropic Rearrangements. Sigmatropic rearrangements in which a hydrogen atom moves
are all [1,n] sigmatropic rearrangements. Those involving a total of (4nþ2) electrons take place with the
hydrogen atom moving from one surface of the conjugated system to the same surface at the other end in the
general sense of Fig. 6.4a. This is called a suprafacial shift. Those involving a total of (4n) electrons show the
alternative stereochemistry in which the hydrogen atom leaves one surface of the conjugated system and
arrives at the other end on the opposite surface in the general sense of Fig. 6.4b, which shows the hydrogen
atom leaving the upper surface, above C-1, but arriving on the lower surface, below C-n. This is called an
antarafacial shift. Note that, although there is an obvious relationship between the words suprafacial and
antarafacial used here and the same words used in the section above on cycloadditions, they refer to
somewhat different features. In the section on cycloadditions, they refer to the stereochemical sense of the
developing overlap, whilst here they refer to the structural change.
1
H
1
[1,n]
H
n
1
[1,n]
H
H
n
1
(a) Supraf acial shif t of H
Fig. 6.4
(b) Antaraf acial shif t of H
Suprafacial and antarafacial defined for a [1, n] migration of hydrogen
Sigmatropic rearrangements of hydrogen are suprafacial if the total number of electrons is a (4nþ2)
number and antarafacial if the total number of electrons is a (4n) number.
The [1,5]-suprafacial shift is found in open-chain systems695 and in rings, where it is striking that the shift
in the cyclopentadiene 6.94 equilibrates the three isomers 6.94–6.96 at room temperature,696 whereas the
cycloheptatriene 6.97 does not undergo the analogous but forbidden suprafacial [1,7]-shift. Instead it
undergoes the geometrically more contorted, but allowed, suprafacial [1,5]-shift, 6.97 (arrows) at a much
higher temperature.697 Both reactions 6.94 and 6.97 are described as [1,5]-shifts, because they are made
possible by the overlap along the set of atoms from C-1 to C-5. The former is structurally a [1,2]-shift, since
the hydrogen atom moves to the adjacent carbon, but it is not mechanistically a [1,2]-shift. The bond between
C-1 and C-5 plays no electronic part in the mechanism—it merely serves to hold the two atoms close to
each other, speeding up the reaction. The same reaction can take place when that bond is not present, but is
6 THERMAL PERICYCLIC REACTIONS
267
then much slower. Similarly the reaction 6.97 ! 6.98 might have been called a [1,4]-shift, but again that
would only refer to one way of looking at the structural change, whereas electronically it is a [1,5]-shift.
H1
5
4
H
H
H
H
r.t.
3
1
2
6.94
6.95
H
6.96
1
1
5
>146°
H
etc.
4
3
H
2
6.98
6.97
[1,7]-Antarafacial shifts in heptatrienes can only occur in open-chain systems, as in the reaction 6.9 !
6.10, because it is sterically impossible in a ring like that in a cycloheptatriene 6.97 for a hydrogen atom
leaving one surface of the ring to develop overlap onto the other side of the ring. The antarafacial
stereochemistry of the reaction 6.9 ! 6.10 was deduced from its appearance only in open-chain systems,
but it has been supported by the proof of antarafacial shifts in the model system 6.99, which gives only the
10S-6.100 by antarafacial deuterium shift from C-15 (arrows), and only 10R-6.100 by antarafacial
hydrogen shift from C-15 on the top surface of the triene 6.99 to the bottom surface at C-10 (using steroid
numbering).698
C8H17
C8H17
H
C8H17
15
100°
D
D
OH
6.99
10
10S-6.100
H
OH
+
D
10
H OH
10R-6.100
When the migrating group in a [1,n]-shift is a carbon atom, two more possibilities arise, not available to
hydrogen atoms. In addition to moving either suprafacially or antarafacially, the migrating group can
migrate with retention of configuration or with inversion of configuration.
When the total number of electrons is a (4nþ2) number, [1, n] sigmatropic rearrangements of elements
other than hydrogen are either suprafacial with retention of configuration in the migrating group or are
antarafacial with inversion of configuration in the migrating group.
When the total number of electrons is a (4n) number, [1, n] sigmatropic rearrangements of elements
other than hydrogen are either antarafacial with retention of configuration in the migrating group or are
suprafacial with inversion of configuration in the migrating group.
Thus the [1,2]-shift of an alkyl group towards an electron deficient atom always takes place with retention
of configuration, whether it be towards carbon in a Wagner-Meerwein rearrangement 6.101, towards
nitrogen in a Beckmann or Curtius rearrangement, or towards oxygen in a Baeyer-Villiger rearrangement.
268
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
These reactions use two electrons, and the allowed suprafacial migration is geometrically reasonable. In the
corresponding anion, there would be four electrons, and neither of the allowed pathways 6.102 and 6.103 is
reasonable. Accordingly anions do not normally rearrange, and when they do they use a stepwise pathway
(see p. 281).699
retention
inversion
suprafacial
suprafacial
retention
antarafacial
6.102
6.101
6.103
Examples for which inversion of configuration in the migrating group has been proved are the suprafacial
[1,3]-shift of the bridge in the bicyclo[3.2.1]heptene 6.104700 and the [1,4]-shift in the bicyclo[3.1.0]hexenyl
cation 6.105.701 The stereochemistry in the latter case is overwhelmingly proved simply by the NMR
spectrum: as the rearrangement takes place all the methyl groups attached to the five-membered ring become
equivalent on the NMR timescale, but the signals of the two methyl groups labelled i (for inside) and o (for
outside) remain distinct. It is sometimes a source of confusion that the inside methyl group remaining inside
corresponds to an inversion of configuration, but the bond between C-1 and C-10 is on the front face of C-10 in
6.105, and the bond that is forming from C-4 to C-10 is on the back side, which marks the event as an
inversion of configuration at C-10 , which is the migrating group.
1'
i
i
o
o
inversion
AcO
D
6.104
AcO
D
inversion
4
3
2
1
6.105
The rules for [m,n]-sigmatropic rearrangements, where m 6¼ 1 and n 6¼ 1, are more complex still. The bond
can migrate suprafacially or antarafacially on either component, with the great majority of known reactions
being suprafacial on both components, as in Fig. 6.5a, where the heavy bond labelled 1,1 is migrating to the
dashed bond labelled m,n. The carbon atoms labelled 1 and 1 are tetrahedral in the starting material, and the
atoms labelled m and n are trigonal. In the product, the atoms that were labelled 1 and 1 have become trigonal
and the atoms that were labelled m and n have become tetrahedral. This is the most common event, simply
because it is relatively easy for molecules to adopt this arrangement.
In principle, however, both migrations could be antarafacial, as in Fig. 6.5b. Alternatively, one could be
antarafacial and the other suprafacial as in Fig. 6.5c. In almost all cases, if the rules demand an antarafacial
component, it is difficult to maintain continuous overlap in such systems—they have to be long and
flexible—and [m,n]-sigmatropic rearrangements with antarafacial components are correspondingly rare.
The rules for [m,n]-sigmatropic rearrangement are:
When the total number of electrons is a (4nþ2) number, [m,n]-sigmatropic rearrangements are allowed
if both migrations are suprafacial or both antarafacial.
When the total number of electrons is a (4n) number, [m,n]-sigmatropic rearrangements are allowed
if one migration is suprafacial and the other antarafacial.
6 THERMAL PERICYCLIC REACTIONS
269
m
1
m
1
n
[m,n]
[m,n]
n
1
1
(a) Supraf acial shif t in both components
(b) Antaraf acial shif t in both components
m
1
n
[m,n]
1
(c) Supraf acial shif t in one component (n), antaraf acial shif t in the other (m)
Fig. 6.5
Suprafacial and antarafacial defined for [m(n]-shifts in general
The great majority of [m,n]-sigmatropic rearrangements involve the all-suprafacial participation of (4nþ2)
electrons. Much the most common are the various [3,3]-sigmatropic rearrangements, such as the Claisen
rearrangement 6.6 ! 6.7, the Ireland-Claisen rearrangement 6.106 ! 6.107, which is demonstrably
stereospecific, with a chair-like transition structure,702 and the all-carbon version, which is called a Cope
rearrangement, as in the reaction of cis-1,2-divinylcyclobutane giving cis,cis-1,4-cyclooctadiene 6.109,
which must have a boat-like transition structure 6.108.703 Whether a boat or a chair is intrinsically favoured
is discussed in Section 6.5.5.1.
O
OSiMe3
LDA, –78°
O
25°, 1 h
O
Me3SiCl
anti:syn
O
87:13
Me3SiO
E-6.106
anti-6.107
O
OSiMe3
LDA, –78°
O
HMPA
Me3SiCl
25°, 1 h
O
O
Me3SiO
Z-6.106
syn-6.107
H
120°, 10 min
H
6.108
6.109
19:81
270
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
Other common all-suprafacial [2,3]-sigmatropic rearrangements are the Mislow reaction 6.11 ! 6.12, and
the anionic 2,3-Wittig rearrangement 6.110 ! 6.111 of the anions made from diallyl ethers by treatment with
strong base.704
BuLi
Pri
Pri
Pri
6.110
Pri
[2,3]
O
O
O
OH
6.111
There are a few sigmatropic rearrangements with more than six electrons, such as the 10-electron doubly
vinylogous Stevens rearrangement 6.112 ! 6.113,705 and the 10-electron benzidine rearrangement
6.114 ! 6.115.706
Ph
NMe2 NaOMe
Ph
NMe2
Ph
NMe2
[4,5]
r.t., 12 h
6.112
H2N
NH2
NH2
6.113
NH2
[5,5]
H2N
H
6.114
H
NH2
benzidine
6.115
6.3.1.4 Group Transfer Reactions. There are so few of these reactions that a fully general rule for
them can wait until the next section, where we see the final form of the Woodward-Hoffmann rules.
For now, we can content ourselves with a simplified rule which covers almost all known group
transfer reactions.
When the total number of electrons is a (4nþ2) number, group transfer reactions are allowed with
all-suprafacial stereochemistry.
The stereochemistry of the ene reaction 6.116 þ 6.117 ! 6.119 is such that the hydrogen atom delivered
to the enophile 6.117 leaves from the same surface of the ene 6.116 as the surface to which the C—C bond is
forming, and the hydrogen atom is delivered to the same surface of the enophile as the forming C—C bond
6.118, so that both components are reacting suprafacially.707 The full stereochemistry is not proved in this
example, because neither the methyl group, C-1, nor the carbon has any stereochemical label, but the
all-suprafacial pathway provides a plausible explanation for the relative stereochemistry set up between the
carbon and C-3.
6 THERMAL PERICYCLIC REACTIONS
1
MeO2C
H
Cl
271
EtAlCl2
AlEtCl2
MeO
+
R
O
Cl
MeO2C
*
H
3
R
6.117
R
6.118
6.116
H
Cl
*
3
6.119
In a double hydrogen atom transfer between cis-9,10-dihydronaphthalene 6.120 and 1,2-dimethylcyclohexene 6.121, analogous to the diimide reduction 6.16, the two hydrogens leave from the same surface of the
dihydronaphthalene, and arrive on the same surface of the cyclohexene to give the cis-dimethylcyclohexane
6.122 in another all-suprafacial reaction.708 However, the 10-electron reaction in which 1,4-cyclohexadiene
6.123 reduces anthracene 6.124, is also allowed in the all-suprafacial mode, but deuterium labels on the
cyclohexadiene show that it is not stereospecifically a syn delivery of hydrogen; it is almost certainly
stepwise, with two successive hydrogen atom transfers, and neither pericyclic nor governed by the rules of
pericyclic chemistry.709 This is a timely reminder that not all reactions that appear to obey the rules can be
assumed to be pericyclic. However, reactions that do not obey the rules are almost certainly not pericyclic.
H
150°, 48 h
+
H
H
6.120
H
6.121
6.122
200°
+
6.123
+
6.124
6.3.2 The Generalised Woodward-Hoffmann Rule
We have now seen a large number of rules, presented in the boxes above, expressed differently for each kind
of pericyclic reaction. Learning them would seem to impose a considerable burden, but Woodward and
Hoffmann saved us from this effort by rewriting them in 1969656 in one all-encompassing rule that applies to
all thermal pericyclic reactions:
A ground-state pericyclic change is symmetry allowed when the total number of (4qþ2)s and (4r)a
components is odd.
This admirably concise statement is compelling, but we must now see what it means, and learn how to apply
it to each of the classes of pericyclic reaction.
6.3.2.1 Cycloadditions. Let us begin with the bare bones of the Diels-Alder reaction in Fig. 6.6. The
components of a cycloaddition are obvious enough—we have been using the word already to refer to the core
electronic systems undergoing change. For a Diels-Alder reaction the components are the p orbitals of the
272
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
4s
(4q+2)s: 1
(4r)a: 0
Total: 1
√
2s
Fig. 6.6
The Diels-Alder reaction as a [p4sþp2s] reaction
diene, containing four electrons, and the p bond of the dienophile, containing two electrons. We ignore all
substituents not directly involved, treating them only, for the purposes of following the rule, as stereochemical labels. What we have to do is to ask ourselves two questions: (1) which of these components is
acting in a suprafacial manner and which in an antarafacial manner; and (2) in which of these components
can the number of electrons be expressed in the form (4qþ2) and in which in the form (4r), where q and r are
integers? For the Diels-Alder reaction both components are undergoing bond formation in a suprafacial
sense, as shown by the dashed lines in Fig.6.6, and so the answer to the first question is: both components.
The diene has four electrons, a number that can be expressed in the form (4r), with r ¼ 1. Since the new
bonds are forming on the diene in a suprafacial manner, both lines coming to the lower surface, the diene is a
(4r)s component, where the subscript s denotes a suprafacial pathway. The dienophile has two electrons, a
number that can be expressed in the form (4qþ2), with q ¼ 0. Since the new bonds are forming on the
dienophile in a suprafacial manner, both lines coming to the upper surface, the dienophile is a (4qþ2)s
component. Thus, the Diels-Alder reaction has one (4qþ2)s component and no (4r)a components. We ignore
(4qþ2)a and (4r)s components, when there are any. The total number of (4qþ2)s and (4r)a components is
therefore 1, and, since this is an odd number, the reaction is identifiably symmetry-allowed by the rule. The
Diels-Alder reaction is, as we have been calling it all along, a [4 þ 2] cycloaddition. Since it takes place
suprafacially on both components, it is more informatively described as a [4sþ2s] cycloaddition, and finally,
because both components are p systems, it is fully described as a [p4sþp2s] cycloaddition.
The description [p4sþp2s] for a Diels-Alder reaction does not supplant the older name—it is not the only
reaction that is [p4sþp2s]. 1,3-Dipolar cycloadditions 6.37 þ 6.38 are equally easily drawn as [p4sþp2s], and
so are the combinations: allyl cation 6.27 and diene, allyl anion 6.31 and alkene, and pentadienyl cation 6.35
and alkene. Furthermore, [p4sþp2s] is not the only way of describing a Diels-Alder reaction. It would be easy
to overlook the fact that the diene can be treated as one component, and to see it instead as two independent p
bonds. Although it makes extra work to see it this way, it does not cause the rule to break down. For example,
the drawing on the left of Fig. 6.7 might have been used instead of the one in Fig. 6.6. The dashed line
representing the developing overlap for the formation of the p bond is from the lower lobe on C-2 to the lower
lobe on C-3. This makes all three components suprafacial—the p bond between C-1 and C-2 has both dashed
lines to the lower lobes, and the p bond between C-3 and C-4 also has both dashed lines to the lower lobes. In
other words both are suffering suprafacial development of overlap. The same is true for the p bond of the
2s
2a
2
3
1
4
2s
2s
Fig. 6.7
2
(4q+2)s: 3
(4r)a: 0
Total: 3
√
1
3
2a
4
(4q+2)s: 1
(4r)a: 0
Total: 1
√
2s
The Diels-Alder reaction as a [p2sþp2sþp2s] and as a [p2sþp2aþp2a] reaction
6 THERMAL PERICYCLIC REACTIONS
273
dienophile. Overall the sum is changed to having three (4qþ2)s components, which is still an odd number,
and so the reaction remains allowed. It is now described as a [p2sþp2sþp2s] cycloaddition, but it is of course,
no matter which of these descriptions we use, the same reaction.
Another drawing, on the right of Fig. 6.7, still representing the same reaction, places the dashed line
between the upper lobes on C-2 and C-3. This changes each of the p bonds of the diene to suffering notional
antarafacial development of overlap. It is just as valid a representation as either of the earlier versions, and
the sum still comes out with an odd number of (4qþ2)s components and no (4r)a components. The two p2a
components do not have to be counted, because they are (4qþ2)a and not (4r)a. The reaction is now a
[p2sþp2aþp2a] cycloaddition. Clearly, the three designations [p4sþp2s], [p2sþp2sþp2s] and [p2sþp2aþp2a]
are all the same reaction, and none of them defines a Diels-Alder reaction. The three designations, in fact,
define where the dashed lines have been drawn in the three drawings in Figs. 6.6 and 6.7, and no reaction
should be described in this way in the absence of a drawing like these.
It is easy enough to see how to extend the labelling of cycloaddition reactions to those involving larger
conjugated systems. As just one example, the cycloaddition of heptafulvalene to tetracyanoethylene is
shown in Fig. 6.8. The developing overlap is taking place on opposite sides of the 14-electron component,
which is therefore a (4qþ2)a component, and does not count towards the sum. The overlap on the 2-electron
component, although not proved, is probably suprafacial, and the (4qþ2)s component does count.
14a
(4q+2)s: 1
(4r)a: 0
Total: 1
√
2s
Fig. 6.8
The cycloaddition of heptafulvalene to tetracyanoethylene as a [p14aþp2s] reaction
6.3.2.2 Electrocyclic Reactions. In order to move on to electrocyclic reactions, we need to see
how the words suprafacial and antarafacial are defined for bonds. In order to have a single orbital
associated with the bond, it is a great convenience to use orbitals made from overlapping spn hybrids. Just
as a suprafacial event on a p bond has overlap developing to the two overlapping lobes that contribute to
bonding, so with bonds (Fig. 6.9a), overlap that develops to the two large lobes of the spn hybrids is
suprafacial. Less obviously, overlap that develops to the two small lobes is also suprafacial, because it is the
counterpart to overlap developing to the other two lobes in a p bond. Antarafacial overlap is when one bond
is forming to an inside lobe and one to an outside lobe, either way round (Fig. 6.9b).
The electrocyclic interconversion of the cyclobutene 6.72 and the cis,trans-butadiene dicarboxylic ester
6.73 is shown in Fig. 6.10a. The components for the ring opening are the bond made from two sp3 hybrids
drawn in front and the p bond drawn at the back, and the conrotatory ring opening is shown as a [2aþp2s]
process. In the ring-closing direction there is only one component, the p system of the diene, and the
conrotatory ring closing is shown as a [p4a] process. The small sums show that they are allowed by the
(a) Supraf acial bond f ormation
Fig. 6.9
(b) Antaraf acial bond f ormation
Suprafacial and antarafacial defined for bonds
274
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
4a
2s
(4q+2)s: 1
(4r)a: 0 MeO2C
Total: 1
CO2Me
√
CO2Me
CO2Me
(4q+2)s: 0
(4r)a: 1
Total: 1
√
2a
(a) The allowed conrotatory interconversion of a cyclobutene and a butadiene
6s
4s
(4q+2)s: 1
(4r)a: 0
Total: 1
√
Me
Me
Me
(4q+2)s: 1
(4r)a: 0
Total: 1
√
Me
2s
(b) The allowed disrotatory interconversion of a hexatriene and a cyclohexadiene
Fig. 6.10
The allowed electrocyclic reactions
Woodward-Hoffmann rule. Notice how the dashed lines and the curved arrows correspond to the clockwise
direction in which the substituents move in the ring opening and anticlockwise in the ring closing, and that
the geometry shown in the products matches these movements in both directions. We could have drawn the
equally probable reaction with anticlockwise conrotatory movements, but we would have had to change both
dashed lines so that the ends coming into the p bond came into the lower lobes of the p orbitals instead of the
upper. A drawing of the ring opening could also have been made by replacing the left hand dashed line with a
dashed line coming out of the inside lobe of the bond and dropping to overlap with the lower lobe of the
left-hand p orbital. The ring opening would have been the same as that shown in Fig. 6.10a, clockwise
conrotatory, but the description would then have been [2sþp2a].
The symmetry-allowed disrotatory ring closing of the trans,cis,trans-dimethylhexatriene 6.76 and the
disrotatory ring opening of the cis-dimethylcyclohexadiene 6.77 are shown in Fig. 6.10b as [p6s] and
[2sþp4s] processes. Again there are other dashed lines that could be drawn to describe these movements,
and there is a similar reaction in both directions interconverting the cis,cis,cis-triene and the cis-dimethylcyclohexadiene, in which the methyl substituents move inwards in the ring opening, instead of outwards,
following an energetically less favourable pathway, but one that is equally allowed by symmetry.
In order to describe the ring opening of the aziridine 6.80, we need to define what suprafacial and
antarafacial mean when applied to a p orbital. This is shown in Fig. 6.11, and applied there to the conrotatory
aziridine opening. When both lines are drawn into the same lobe it is suprafacial, and when there is one line
dawn into the top lobe and one into the bottom, it is antarafacial. Since this is neither a p nor a orbital, it is
given the Greek letter o. The same designations apply whether the orbital is filled (on the left) or unfilled (on
the right), and whether it is a p orbital or any of the spn hybrids.
In the aziridine opening shown in Fig. 6.11, the aryl group behind the nitrogen atom is left out. The dashed
lines are drawn from the large lobes of the bond, making this a [2s] component. Both substituents move
anticlockwise in the conrotatory mode, so the dashed line on the left of the bond goes up to overlap with the
upper lobe of the p orbital on the nitrogen atom, and the dashed line on the right goes down to overlap with
the lower lobe. With one overlap drawn as developing to the top and one to the bottom, the p orbital is an
[o2a] component, making the overall reaction drawn in this way a [2sþo2a] process. In the opposite
direction, the clockwise conrotatory ring closing of the azomethine ylid 6.81 is simply a [p4a] process.
The conrotatory process taking place in the clockwise direction would place both methoxycarbonyl
groups inside in a U-shaped ylid; this would be thermodynamically less favourable but just as allowed by
6 THERMAL PERICYCLIC REACTIONS
275
2s
0s
2a
2a
(4q+2)s: 1
(4r)a: 0
4a
con
MeO2C
N
Total: 1
2s
N
MeO2C
√
Fig. 6.11
0a
CO2Me
(4q+2)s: 0
(4r)a: 1
Total: 1
√
CO2Me
Suprafacial and antarafacial defined for a p orbital, and the allowed conrotatory interconversion of an
aziridine with an azomethine ylid
symmetry. In the corresponding cis-disubstituted aziridine, the stereochemistry is still conrotatory, but now
the geometry of the ylid is sickle-shaped, with one of the methoxycarbonyl groups outside and the other
inside.
6.3.2.3 Sigmatropic Rearrangements. The overlap developing in a suprafacial [1,5]-hydrogen shift in a
diene is drawn at the top in Fig. 6.12 both as a [2sþp4s] process and as a [2aþp4a] process. In both cases, the
[1,5]-shift is suprafacial in the structural sense, but the overlap developing is selected in different ways in the
two drawings—all-suprafacial on the left and all-antarafacial on the right. Thus the word suprafacial does not
have the same meaning in the two contexts in which it is used here, although there is an obvious relationship.
Both drawings, of course, are equally valid, and both would show that the reaction is symmetry-allowed if we
were to complete the little sum that has accompanied all the drawings up to this point, but which we shall
leave out from now on.
The antarafacial [1,7]-hydrogen shift is similarly drawn in two ways at the bottom of Fig. 6.12. One
component is suprafacial and one antarafacial in each, but in both the hydrogen atom shifts in a structurally
antarafacial sense, and the reaction is the same.
4a
4s
H
H
A suprafacial [1,5]-shift in a diene:
2a
2s
6a
6s
An antarafacial [1,7]-shift in a triene:
H
H
2s
2a
Fig. 6.12 The [1,5]-suprafacial shift of an H atom drawn as [2sþp4s] and [2aþp4a] processes and the
[1,7]-antarafacial shift of an H atom drawn as [2sþp6a] and [2aþp6s] processes
276
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
The [1,2]-shift of an alkyl group with retention of configuration in the migrating group, shown for the
carbocation 6.101 on p. 268 has a dashed line identifying it as a suprafacial migration. A second dashed line
connecting the lower end of the bond to the same lobe of the empty p orbital would make it [2sþo0s], but
the same reaction could equally be described with a different line coming from the lower lobe of the empty p
orbital to the lower side of the carbon atom of the bond, making it [2aþo0a]. Similarly, the [1,3]-shift of an
alkyl group with inversion of configuration in the migrating group, shown for the bicyclo[3.2.0]heptene
6.104, already has the dashed lines identifying it as a [2aþp2s] process, and the [1,4]-shift of an alkyl group
with inversion of configuration, shown for the bicyclo[3.1.0]hexyl cation 6.105, has the dashed lines for a
[2aþp2s] process, both of which are allowed by the unified rule.
The [3,3]-sigmatropic rearrangement, found in the Claisen and Cope rearrangements, is drawn for the
chair and boat transition structures 6.125, each of which is known and each of which is allowed. In both cases
they are drawn as all-suprafacial processes in the middle of Fig. 6.13, and as one suprafacial and two
antarafacial processes on the right. In both cases, the bold bond marked 1,10 is leaving the lower surface of
the conjugated system from C-1 and arriving on the lower surface at C-3; the same bond is leaving the upper
surface at C-10 and arriving on the upper surface at C-30 . Thus the reaction, whether chair-like or boat-like
and however it is described for the purposes of the Woodward-Hoffmann rule, involves a structurally
suprafacial migration of the bond across each of the surfaces as defined for the general case in Fig. 6.5a.
[2,3]-Sigmatropic rearrangements, like the 2,3-Wittig rearrangement 6.110, which has sulfur and aza
analogues, are drawn for the general case in Fig. 6.14, where X¼O, S, SRþ, or NR2þ. An envelope-shaped
transition structure is almost always involved, because this allows the smooth development of head-on
overlap in the formation of the bond between C-20 and C-3 at the same time that the bond between C-10
2
3
1'
2a
2s
2'
3'
2s
chair-6.125
1
2a
2s
1'
3'
2a
2s
2
3
2s
2s
1
2s
2a
2s
2'
boat-6.125
Fig. 6.13
A [3,3]-sigmatropic rearrangement drawn as [2sþp2sþp2s] and [2sþp2aþp2a] processes
2s
2'
X
1'
X
X
3
1
Fig. 6.14
2s
2s
2
A [2,3]-sigmatropic rearrangement drawn as a [2sþo2sþp2s] process
6 THERMAL PERICYCLIC REACTIONS
277
and C-1 is conjugated with the p bond. These reactions all have an o component in the form of a lone pair or
the p or hybrid orbital of a carbanion, and can be described in the all-suprafacial mode drawn in Fig. 6.14 as
[2sþo2sþp2s].
6.3.2.4 Group Transfer Reactions. The ene reaction 6.118 is drawn again on the left of Fig. 6.15, showing
that it can be described as a [2sþp2sþp2s] process, and a dihydrogen transfer similar to that in diimide
reduction or the reaction of 9,10-dihydronaphthalene 6.120 is redrawn on the right of Fig. 6.15, showing that
it can be described as a [2sþ2sþp2s] process.
MeO2C
Cl
2s
2s
2s H
R
Fig. 6.15
H
2s
2s
H
2s
An ene reaction drawn as a [2sþp2sþp2s] process and a dihydrogen transfer drawn as a [2sþ2sþp2s]
process
6.3.2.5 Some Hints about Drawing Diagrams for the Woodward-Hoffmann Rule. The first requisite
for a good understanding of a pericyclic reaction is to have a good drawing of the transition structure. Begin
with the flat, curly arrow-based representation, because this helps to identify the components—they are the
lone pairs and the bonds that the curly arrows apply to—the bonds that are broken and the bonds that are
made, and the lone pairs that are mobilised or localised. Then try to draw a three-dimensional view, in order
to assess how reasonable the reaction is. Boat-like, chair-like and envelope transition structures are common,
easily drawn, and are likely to be a good starting point. A good drawing will show the component orbitals
lined up to develop overlap with the right geometry—head-on if it is creating a bond or sideways-on if it is
creating a p bond—as drawn for the ene reaction in Fig. 6.15. Sometimes this is not possible, especially with
electrocyclic ring-closing reactions. Any attempt to bring the orbitals at the ends of the diene in Fig. 6.10a
and the triene in Fig. 6.10b into a position to show the developing overlap will so distort the conjugated
systems that the drawing will be hard to read. The reactions take this path, but it is probably wise to avoid
drawings close to the transition structures in cases like these.
Then there is the problem of assessing whether the reaction is symmetry-allowed or not using the
Woodward-Hoffmann rule. If there is an odd number of curly arrows, then the overall reaction uses
(4nþ2) electrons. All such reactions are allowed in the all-suprafacial mode, and so it is helpful to draw
the dashed or solid lines (or better still use a line with a distinctive colour) to show the developing overlap
with only suprafacial components, as in Fig. 6.6, for example. The (4qþ2)s components will then add up to
an odd number, and the task is done. If the dashed, bold or coloured lines are not those for an all-suprafacial
reaction, as in the right-hand side of Fig. 6.7, for example, all is not lost—simply do the sum to find out
whether the drawing corresponds to an allowed reaction or not. The all-suprafacial drawing is no better than
the other representations, but it is a quick way to arrive at a drawing showing that a (4nþ2) reaction is
reasonable and allowed. This simplification works for a very high proportion of pericyclic reactions.
Reactions involving a total of (4n) electrons, in which the number of curly arrows is even, are relatively
rare. They will be allowed if there is one antarafacial component and all the others are suprafacial. In this
case, if the dashed, bold or coloured lines include only one antarafacial component, the number of (4qþ2)s
and (4r)a components will add up to an odd number, and the drawing will show the geometry of a
symmetry-allowed reaction.
278
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
When working out whether or not a reaction is obeying the rule, it is inappropriate to shade the orbitals—
what we have been doing in the whole of Section 6.3 is not a frontier orbital treatment, which we shall come
to later. No particular orbital is being considered when analyses like those in Figs. 6.6–6.15 are carried out.
There is no real need to draw the lobes at all, as long as the perspective used to make the drawings and the
placing of the dashed, bold or coloured lines clearly identify the surfaces of the conjugated systems onto
which the new bonds are developing and from which the old bonds are breaking. The dashed lines on the
drawings 6.104 and 6.105 on p. 268 clearly illustrate [p2sþ2a] processes without drawing the lobes.
6.3.2.6 Some Symmetry-Allowed but Geometrically Unreasonable Reactions. Some reactions are
symmetry-allowed, but they do not take place because they cannot attain a geometry that allows the
continuous development of overlap. The [2 þ 2] reaction shown in Fig. 6.16a is a [p2sþp2a] reaction, fully
allowed by the Woodward-Hoffmann rule, but it does not take place because the molecule is not flexible
enough for the overlap developing on the left-hand side to take place at the same time as the overlap
developing on the right-hand side. A longer conjugated system might have the necessary flexibility, and this
could be the case in the reaction between heptafulvalene and tetracyanoethylene in Fig. 6.8. As we shall see
in the next section, the development of the overlap on the left-hand side alone is not forbidden, but the
reaction is not then pericyclic.
2a
2a
2s
2a
1
2s
2
1
2
3
3
2s
(a) A symmetry-allowed but
unreasonable [ 2s+ 2a] cycloaddition
Fig. 6.16
(b) A symmetry-allowed but
unreasonable [ 2a+ 2s] [1,3]sigmatropic rearrangement
(c) A symmetry-allowed but
unreasonable [ 2s+ 2a] [1,3]sigmatropic rearrangement
Symmetry-allowed but geometrically inaccessible reactions
Another examples of an allowed but essentially impossible pathway is the [1,2]-shift in an anion, whether it
is suprafacial with inversion of configuration in the migrating group 6.102 or antarafacial with retention of
configuration in the migrating group 6.103. Slightly less unlikely are [1,3]-sigmatropic shifts, which are also
allowed to be either suprafacial with inversion ([2aþp2s] in Fig. 6.16b) or antarafacial with retention
([2sþp2a] in Fig. 6.16c). Neither looks geometrically reasonable, but the former may just possibly explain
the stereochemistry of the reaction of the bicyclo[3.2.0]heptene 6.104,710 and it appears to make a contribution, if not an overriding one, to the stereochemistry of the [1,3]-shift seen in vinylcyclopropanes giving
cyclopentenes.711 Perhaps most convincingly it is seen in the [1,3]-shift of a silyl group, which takes place
with inversion of configuration at the silicon atom.712 This reaction is made easier than it is in the carbon
series by the bonds to the migrating silicon atom being longer than those to a migrating carbon atom, giving
greater flexibility, and to the possbility that the bond making to the silicon atom and breaking from it need not
be so precisely oriented as they would be in the corresponding carbon shift. There is no good example of an
antarafacial [1,3]-shift with retention of configuration, a symmetry-allowed but geometrically even less
probable reaction.
6.3.2.7 Some Geometrically Reasonable but Symmetry-Forbidden Reactions. Equally, there are
symmetry-forbidden reactions, for which the small sum adds up to an even number. As a result, most of
them do not take place, and none of them takes place in a concerted manner. Let us take [2 þ 2] and [4 þ 4]
6 THERMAL PERICYCLIC REACTIONS
279
cycloadditions, for which the only reasonable transition structures are for suprafacial attack on both
components. The dashed lines are shown in Fig. 6.17, where we see in both cases that, however geometrically reasonable the reactions may look, there are either two p2s components or two p4s components, and
the sums add up to even numbers.
2s
4s
(4q+2)s: 2
(4r)a: 0
Total: 2
x
2s
Fig. 6.17
(4q+2)s: 0
(4r)a: 0
Total: 0
x
4s
Symmetry-forbidden [2 þ 2] and [4 þ 4] cycloadditions
[2 þ 2] Cycloadditions and [4 þ 4] cycloadditions are only forbidden if they are concerted—there is nothing
forbidden about the formation of one bond, provided that the other is not forming at the same time. The
dashed line on the left in Fig. 6.17 can lead to a bond, as long as overlap is not developing at the same time in
the sense of the dashed line on the right. If only one bond forms, it will create either a zwitterionic or a
diradical intermediate. The ionic pathway becomes reasonable if either or both of the ionic centres in the
zwitterionic intermediate is equipped with stabilising groups: C or Z for anions and C or X for cations. Thus
the enamine 6.126 reacts with the ,-unsaturated ester 6.127 to give the cyclobutane 6.129.713 This reaction
is stepwise with the intermediate zwitterion 6.128 having a cationic centre stabilised as an iminium ion by the
lone pair of the amino group, and an anionic centre stabilised as an enolate ion by the adjacent carbonyl
group. The reaction is still a cycloaddition, but it is not pericyclic.
O
Me2N
6.126
O
OMe
Me2N
85°, 2 h Me2N
6.128
6.127
CO2Me
OMe
6.129
Equally, not all [4 þ 2] cycloadditions are concerted.714 If a zwitterionic or diradical intermediate is well
enough stabilised, one bond can form ahead of the other, as in the reaction between the same enamine 6.126
and the ,-unsaturated ketone 6.130 giving the dihydropyran 6.132.715 This is formally a hetero DielsAlder reaction, but it is almost certainly stepwise, taking place by way of the zwitterion 6.131. The advantage
for a stepwise reaction is that forming only one bond does not suffer from the same high negative entropy of
activation that forming both together does. The advantage for a concerted Diels-Alder reaction, although it
suffers from a high negative entropy of activation, is that it does not demand the high degree of stabilisation
found in intermediates like 6.128 and 6.131.
Me2N
6.126
O
6.130
r.t., 20 min
Me2N
O
6.131
Me2N
O
6.132
280
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
A beautiful illustration of a delicate balance between a stepwise and a concerted reaction has been found in
the reactions of 1,1-dimethylbutadiene 6.133.716 This diene rarely adopts the s-cis conformation necessary
for the Diels-Alder reaction with tetracyanoethylene giving the cyclohexene 6.136. However, it can react in
the more abundant s-trans conformation in a stepwise manner, leading to a moderately well stabilised
zwitterion 6.134. The intermediate allyl cation is configurationally stable, and a ring cannot form to C-1,
because that would give a trans double bond between C-2 and C-3 in the cyclohexene 6.137. Instead a
cyclobutane 6.135 is formed. All this is revealed by the solvent effect. In the polar solvent acetonitrile the
stepwise ionic pathway is favoured, and the major product (9:1) is the cyclobutane 6.135. In the nonpolar
solvent hexane, the major product (4:1) is the cyclohexene 6.136 with the Diels-Alder reaction favoured.
NC
NC
NC
NC
CN
CN
NC
NC
CN
CN
CN
CN
H
H
3
2
1
6.134
s-trans-6.133
6.135
s-cis-6.133
NC
NC
NC
CN CN
CN
H
CN
CN
NC
CN CN
H
CN
6.136
6.137
Stepwise reactions by way of diradical intermediates are also possible; such reactions often require rather
high temperatures, but radicals are probably involved in the formation of cyclobutanes like that from the
halogenated alkene 6.138 and butadiene giving the cyclobutane 6.140.717 As we saw in Chapter 2 (Section
2.1.5), any group, C, Z or X, can stabilise a radical. Both radical centres in the intermediate 6.139 are
stabilised, the one on the left by the -chlorines and the -fluorines, and the one on the right because it is
allylic. There are a number of reactions like this—all that is required is enough radical-stabilising
substituents.
F
Cl
F
Cl
6.138
F
82°
13 h
F
F
F
Cl
Cl
6.139
Cl
Cl
6.140
Again, the diene does not need to be in the s-cis conformation—as long as the substituents stabilise the
radicals well enough, as they do here, the first bond can form while the diene is still in its more abundant strans conformation. The allyl radical 6.139 produced from the s-trans diene is configurationally stable, just
as the allyl cation 6.134 was, and it will not be able to cyclise to give a trans-cyclohexene. Rotation about the
bond between C-2 and C-3 is evidently too slow to compete with the radical combination giving the
cyclobutane 6.140.
Some other stepwise reactions, puzzling at one time, because they seemed to disobey the rules, are
the [1,2]-shifts of ylids, like the Stevens rearrangement 6.141 ! 6.143.718 The symmetry-allowed
geometry, like that in the [1,3]-shifts in Fig. 6.16b and 6.16c, is either suprafacial-with-inversion or
6 THERMAL PERICYCLIC REACTIONS
281
antarafacial-with-retention. These pathways are unreasonable—there is no flexibility for migration
across only two atoms, and yet reactions like this take place easily. It is now clear that most such
reactions take place stepwise by homolytic cleavage 6.141 ! 6.142, followed by a rapid recombination
of the radicals 6.142 ! 6.143.719 It is probably significant that the radical 6.142 is captodative. No matter
how reliable that idea is (see p. 82), the radical is highly stabilised, making the reaction even easier than it
might at first seem.
Ph
Ph
Ph
53°, 4 h
N
Me2N
Me2N
Ph
Ph
O
6.141
Ph
O
O
6.142
6.143
6.3.2.8 Reactions of Ketenes, Allenes and Carbenes which Appear to be Forbidden. Some [2 þ 2]
cycloadditions only appear to be forbidden. One of these is the cycloaddition of ketenes to alkenes.
These reactions have some of the characteristics of pericyclic cycloadditions, such as being stereospecifically syn with respect to the double bond geometry, and hence suprafacial at least on the one
component, as in the reactions of the stereoisomeric cyclooctenes 6.144 giving the diastereoisomeric
cyclobutanones 6.145.720 However, stereospecificity is not always complete, and many ketene
cycloadditions take place only when there is a strong donor substituent on the alkene. An ionic
stepwise pathway by way of an intermediate zwitterion is therefore entirely reasonable in accounting
for many ketene cycloadditions.
O
r.t.
H
O
H
Cl
Cl
+
Cl
Cl
cis-6.144
cis-6.145
O
r.t.
H
O
H
Cl
Cl
+
Cl
trans-6.144
Cl
trans-6.145
Somewhat similarly, dimethylallene 6.146 undergoes a cycloaddition to dimethyl fumarate and dimethyl
maleate giving mainly the cyclobutanes trans- and cis-6.147, respectively, together with a little of the
regioisomers trans- and cis-6.148, but with a high level of stereospecificity, implying either that the reaction
is concerted and suprafacial on the unsaturated ester, or, less probably, that any intermediate diradical or
zwitterion has not had time to lose configurational information.721 Allenes also undergo cyclodimerisation,
with enantiomerically enriched allenes leading to enantiomerically enriched products, with the details in
agreement with the possibility that the reactions are concerted cycloadditions.722
282
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
CO2Me
MeO2C
+
MeO2C
CO2Me
trans-6.147
MeO2C
92:8
CO2Me
tr ans-6.148
6.146
+
CO2Me
MeO2C
MeO2C
CO2Me
cis-6.147
MeO2C
~85:15
CO2Me
cis-6.148
It seems likely that some of these ketene and allene cycloadditions are pericyclic and some not, with the
possibility of there being a rather blurred borderline between the two mechanisms, with one bond forming so
far ahead of the other that any symmetry control from the orbitals is essentially lost.723 However, if it is
pericyclic, how does it overcome the symmetry-imposed barrier? One suggestion is that the two molecules
approach each other at right angles, with overlap developing in an antarafacial sense on the ketene or allene
like that in Fig. 6.16a, making the reaction the allowed [p2sþp2a] cycloaddition that we have dismissed as
being unreasonable. This is the simplest explanation, but it is unsatisfactory.
Calculations uniformly fail to support it; alkynes, which can easily achieve a transition structure with the
same or less steric hindrance in the approach of the two p bonds as this, do not undergo cycloadditions to
alkenes at all easily. The probability of some [2 þ 2] cycloadditions of ketenes and allenes being concerted is
more likely to be a consequence of the fact that ketenes and allenes have two sets of p orbitals at right angles to
each other.724 Overlap can develop to orthogonal orbitals 6.149 (solid lines), and in addition there might be
some transmission of information from one orbital to its orthogonal neighbour (dashed line). In the case of the
allene 6.150 there is an implied direction of rotation of the terminal groups on the double bond not involved in
forming the cyclobutane ring, a detail which becomes important later when we consider regio- and
stereochemistry.725
2s
2a
2a
O
2s
6.149
(4q+2)s: 1
(4r)a: 0
Total: 1
√
2s
2s
(4q+2)s: 3
(4r)a: 0
Total: 3
√
6.150
This is a legitimate but somewhat contrived way of making the electronic connection cyclic and hence
pericyclic. This version identifies the reactions as allowed [p2sþ(p2aþp2a)] or [p2sþ(p2sþp2s)] cycloadditions. The [p2sþ(p2aþp2a)] version is shown for the ketene and the [p2sþ(p2sþp2s)] for the allene, but the
dashed lines and these descriptions could have been interchanged. In essence the ketene or allene is able to
take up the role of antarafacial component by using an orbital that has turned through 90° towards the alkene
component. Several calculations support this picture, giving a transition structure with substantial C—C
bonding to the carbonyl carbon (1.71–1.78 Å) and much less (2.43–2.47 Å) at the other C—C bond, and with
a severely twisted four-membered ring.726,727 There is also experimental evidence, from the microwave
6 THERMAL PERICYCLIC REACTIONS
283
spectrum of a ketene-ethylene van der Waals complex, that the two molecules stick together in an orientation
similar to that calculated for the transition structure, but with much longer C—C bond distances.728
A variant of the approach, perhaps the simplest way of thinking about these reactions, is to omit the
overlap drawn with dashed lines in 6.149 and 6.150, and to concentrate on the key, -bond-forming events.
This removes the symmetry-imposed barrier, because the reaction is no longer being thought of as strictly
pericyclic. The two bonds are still being formed more or less in concert, but independently, without having to
worry about symmetry information being transmitted from one orbital to the other.
Related to ketene cycloadditions are the group of cycloadditions with vinyl cation intermediates. The
reaction between 2-butyne 6.151 and chlorine giving the dichlorocyclobutene 6.153 is the Smirnov–
Zamkow reaction,729 and there is a similar reaction between allene 6.154 and hydrogen chloride giving
the dichlorocyclobutane 6.156.730 The Smirnov-Zamkow reaction takes place by cycloaddition of the
vinyl cation 6.152 to another molecule of the acetylene, and the allene reaction takes place by attack of
the vinyl cation 6.155 on another molecule of allene. Vinyl cations, like ketenes, have two p orbitals at
right angles to each other, and overlap can develop to each simultaneously, just as it did with ketenes. In a
sense, a ketene is merely a special case of a vinyl cation, with the carbonyl group a highly stabilised
carbocation.
Cl
Cl
Cl2, BF3
–20°
6.151
Cl
Cl
Cl
6.152 6.151
6.153
+
H
Cl
+ H+
Cl
HCl
+ Cl–
6.154
6.155 6.154
Cl
6.156
There are several reactions in organometallic chemistry which also, at first sight, appear to contravene the
rule, but which can be explained in a somewhat similar way. Hydrometallation 5.71 on p. 218, carbometallation, metallo-metallation, and olefin metathesis reactions all have the feature of being stereospecifically suprafacial additions to an alkene or alkyne. Hydroboration, for example, might be classed as a
[2 þ 2] addition of a bond to a p bond, for which the all-suprafacial pathway is forbidden. Although
hydroboration begins with electrophilic attack by the boron atom, it is known not to be fully stepwise,
because electron-donating substituents on the alkene do not speed up the reaction anything like as much as
they do when alkenes are attacked by electrophiles. Nevertheless, the reaction is stereospecifically syn—
there must be some component of hydride addition more or less concerted with the electrophilic attack.731
The empty p orbital on the boron is the electrophilic site and the s orbital of the hydrogen atom in the B—H
bond is the nucleophilic site. These orbitals are orthogonal, and so the addition 6.157 is not properly
pericyclic.732
B
H
6.157
284
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
Another anomalous cycloaddition is the cheletropic insertion of a carbene into an alkene. Six-electron
cheletropic reactions are straightforwardly allowed pericyclic reactions, which we can now classify with the
drawing 6.158 for the suprafacial addition of sulfur dioxide to a diene.733 Similarly, we can draw 6.159 for
the 8-electron antarafacial addition of sulfur dioxide to a triene.734 The problem comes with the insertion of a
carbene into a double bond, which is well known to be stereospecifically suprafacial on the alkene with
singlet electrophilic carbenes (see p. 201) like dichlorocarbene.735 This is clearly a forbidden pericyclic
reaction if it takes place in the sense 6.160.
O
2s
S
Cl
6a
O
2s
2s (4q+2)s: 1
(4r)a: 0
S O
Total: 1
O
√
(4q+2)s: 1
(4r)a: 0
Total: 1
√
4s
Cl
6.158
2s
(4q+2)s: 2
(4r)a: 0
Total: 2
x
6.160
6.159
This is known as the linear approach, in which the carbene, with its two substituents already lined up where
they will be in the product, comes straight down into the middle of the double bond. The two sulfur dioxide
reactions above, 6.158 and 6.159, are also linear approaches, but these are both allowed, the former because
the total number of electrons (6) is a (4nþ2) number, and the latter because the triene is flexible enough to
take up the role of antarafacial component. The alternative for a carbene is a nonlinear approach 6.161,736 in
which the carbene approaches the double bond on its side, and then has the two substituents tilt upwards as
the reaction proceeds, in order to arrive in their proper orientation in the product 6.162.
2s
0a
Cl
Cl
Cl Cl
Cl
Cl
2s
6.161
6.162
(4q+2)s: 2
(4r)a: 1
Total: 3
√
6.163
There is experimental evidence for the nonlinear approach based on isotope effects,737 and calculations also
support it, although they suggest that the reaction takes place in two steps by way of a short-lived
diradical.738 Whatever the detailed mechanism, the carbene is effectively able to take up the role of the
antarafacial component; as with ketenes, it is possible to connect up the orthogonal orbitals, as in 6.163
(dashed line), to make the nonlinear approach classifiably pericyclic and allowed. This avoids any problem
there might be with reactions like 6.158 and 6.159 being pericyclic and the clearly related reaction 6.161 !
6.162 seeming not to be.
Somewhat similar considerations apply to the insertion of carbenes into bonds, except that in this case
the reaction can only involve four electrons, and there is no 6-electron alternative.739 We shall return to the
carbene insertion reactions later when we discuss periselectivity: why carbenes choose to react with a double
bond by the nonlinear approach even with dienes, which would make a 6-electron linear approach analogous
to the sulfur dioxide reaction 6.158 allowed.
6.3.2.9
Reactions of Singlet Oxygen, Nitroso Compounds and Triazolinediones which are
Symmetry-Allowed but may be Stepwise.740 The three reactive compounds, singlet oxygen
6.164, nitroso compounds 6.166 and triazolinediones 6.168 are anomalous in treading a delicate balance
between a pericyclic pathway in some of their reactions, and taking a stepwise pathway, even when an
allowed pericyclic pathway is available. All three show a capacity to undergo Diels-Alder reactions with
6 THERMAL PERICYCLIC REACTIONS
285
dienes but all three show a propensity to form one strong bond in the transition structure to one of the two
electronegative heteroatoms, and a relatively weak or essentially nonexistent bond to the other. When the
second bond is relatively weak the pathway is that of an asynchronous pericyclic reaction, but when it is
nearly nonexistent, the pathway is diradical in nature.
1
+
O
O 1.886Å
O
O
O
O
2.962Å
6.164
+
6.165
O
O 2.049Å
O
N
N
N
R
R
6.166
N
N
R
6.167
O
+
2.690Å
O
2.000Å
N
NR
NR
O
N
N
N
NR
2.668Å
O
O
6.168
O
6.169
These three reagents share the singular feature of having a high-energy HOMO in the form of the p*
combination of two adjacent lone pairs, like that in the -effect (see pp. 155–156), and a low-energy LUMO,
which is a p* orbital low in energy, low because it is made up from the p orbitals of two electronegative
elements. In the case of singlet oxygen, the unperturbed HOMO and the LUMO are identical except for the
one being occupied and the other empty. The presence of a high-energy HOMO and a low-energy LUMO
leads to exceptional reactivity, and accounts for why these reagents can take a stepwise pathway and
dispense with the high level of organisation needed for a pericyclic reaction. The LUMO of the dienophile
can interact with the HOMO of the diene at the same time as the HOMO of the dienophile can interact with
the LUMO of the diene. The combined energy-lowering effect of these interactions is strong enough to allow
a bond to develop at one atom on each component.
In detail, calculations for the Diels-Alder reactions suggest that nitroso compounds and triazoline diones
adopt a highly asynchronous but concerted pathway with transition structures 6.167 and 6.169, respectively
(bond lengths calculated for R ¼ H).741,742 Singlet oxygen, the most reactive of the three, however, adopts a
stepwise pathway by way of a diradical intermediate 6.165.743 Aromatic compounds behaving as dienes,
being inevitably less reactive, induce singlet oxygen to revert to an asynchronous concerted pathway.
The same three reagent types also undergo ene reactions with alkenes having an allylic hydrogen atom.
Calculations744 suggest that all three reagents take a highly asynchronous course, probably best described
as being by way of a diradical 6.170, with a substantial bonding interaction marked with a dashed curve,
together with a weak hydrogen bond from the Y atom to the hydrogen on C-3, restricting the rotation about
the C1—C2 bond. This explains why these reactions are stereospecific, as they are known to be, without
necessarily following a pericyclic pathway. The zwitterionic structures 6.171 have been suggested as
intermediates—they may even be formed, but they are not on the direct pathway, because they open back
to the same diradical structure before giving the ene product by way of the hydrogen abstraction step. The
three reagents have subtly different features, but all three appear more or less to follow this type of
pathway.
286
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
X
Y
R
H
X
Y
R
1
Y
R
H
H
2
X
3
6.170
R
X
Y
H
6.171
With these three reagents, and their singular properties, we are straying into an unusual borderline region
between pericyclic and stepwise reactions. Elsewhere, this is less of a problem, and the existence of a large
class of reactions safely called pericyclic is well established. We must now turn to the ideas, based on
molecular orbital theory, which have been advanced to explain why the Woodward-Hoffmann rules work so
well.
6.4
Explanations for the Woodward-Hoffmann Rules
Broadly speaking three levels of explanation have been advanced to account for the patterns of reactivity
encompassed by the Woodward-Hoffmann rules. The first draws attention to the relationship between
aromaticity, with its (4nþ2) electrons in a cyclic conjugated system, and the (4nþ2) electrons found in
most cycloadditions, which could be seen as having an aromatic transition structure.745 The second makes
the point that the interaction of the appropriate frontier orbitals in the bimolecular reactions matches the
observed stereochemistry, and that even unimolecular reactions could be covered if, rather artificially, the
molecule is separated into two fragments, with one assigned the role of the HOMO and the other the role of
the LUMO.4 The third is to use orbital and state correlation diagrams in a compellingly satisfying treatment
for those cases with identifiable elements of symmetry.746 Molecular orbital theory is the basis for all these
related747 explanations, and all organic chemists must now have some familiarity with molecular orbital
theory in order to understand pericyclic reactions.
6.4.1 The Aromatic Transition Structure
We saw earlier that the all-suprafacial [4 þ 2], [8 þ 2], and [6 þ 4] thermal cycloadditions are common, and
that [2 þ 2], [4 þ 4], and [6 þ 6] cycloadditions are rare, mostly stepwise or, as we shall see in Chapter 8,
photochemically induced. The total of electrons in the former are (4nþ2) numbers, analogous to the number
of electrons in aromatic rings. This wonderfully simple idea was the first explanation for the patterns of
allowed and forbidden pericyclic reactions. At first sight, it is a bit more difficult to explain those pericyclic
reactions that take place smoothly in spite of their having a total of 4n electrons. They all show stereochemistry involving an antarafacial component, but it is possible to include this very feature in the aromatic
transition structure model. If the p orbitals that make up a cyclic conjugated system have a single twist, like a
Möbius strip, then the appropriate number of electrons for an aromatic system becomes 4n rather than
(4nþ2).748 The antarafacial component in a conrotatory electrocyclic closure, for example, with overlap
developing from the top lobe at one end to the bottom lobe at the other (6.70 in Fig. 6.3), is equivalent to
the twist in a Möbius conjugated system. The concept of Möbius aromaticity can be applied to many
topologically complex reactions.749
6 THERMAL PERICYCLIC REACTIONS
287
6.4.2 Frontier Orbitals
The second explanation is based on the frontier orbitals—the highest occupied molecular orbital (HOMO) of one
component and the lowest unoccupied orbital (LUMO) of the other. Thus if we compare a [2 þ 2] cycloaddition
6.172 with a [4 þ 2] cycloaddition 6.173 and 6.174, we see that the former has frontier orbitals that do not match
in sign at both ends, whereas the latter do, whichever way round, 6.173 or 6.174, we take the frontier orbitals.
LUMO
2
HOMO
repulsion
1
1
4
1
2'
2'
1'
LUMO
4
1'
HOMO
2'
1'
LUMO
6.173
6.172
HOMO
6.174
In the [2 þ 2] reaction 6.172, the lobes on C-2 and C-20 are opposite in sign and represent a repulsion—an
antibonding interaction. There is no barrier to formation of the bond between C-1 and C-10 , making stepwise
reactions possible; the barrier is only there if both bonds are trying to form at the same time. The [4 þ 4] and
[6 þ 6] cycloadditions have the same problem, but the [4 þ 2], [8 þ 2] and [6 þ 4] do not. Frontier orbitals
also explain why the rules change so completely for photochemical reactions, as we shall see in Chapter 8.
Applying frontier orbital theory to unimolecular reactions like electrocyclic reactions and sigmatropic
rearrangements is inherently contrived,750 since we are looking at only one orbital. To set up an interaction
between frontier orbitals, we have artificially to treat a single molecule as having separate components. To take
one of the less dubious examples, since the component orbitals are at least orthogonal, the electrocyclic
conrotatory opening of a cyclobutene can be treated as the cycloaddition of the HOMO of the single bond with the LUMO of the double bond p* 6.175, where the dashed lines connect the lobes of the atomic orbitals of
the same sign. For the ring-closing direction, which is more dubious, since the component orbitals are
conjugated, we can treat the double bonds as separate components 6.176, one bond providing the HOMO, p
on the left, and the other the LUMO, p* on the right. Alternatively, we can look only at the HOMO of the diene,
2 in 6.177, where the development of bonding from C-1 to C-4 corresponding to conrotatory ring-closing does
not have a sign change. It is hardly compelling to take just one orbital out of the set, even if it does work.
LUMO
HOMO
LUMO
HOMO
or
HOMO
6.175
6.176
6.177
The frontier orbital treatment for vinyl cation cycloadditions, such as those of ketenes, has some merits. It
satisfyingly shows that the bond forming between C-1 and C-10 develops mainly from the interaction of the
LUMO of the ketene (p* of the C¼O group) and the HOMO of the alkene 6.178, and that the bond between
C-2 and C-20 develops mainly from the interaction of the HOMO of the ketene ( 2 of the 3-atom linear set of
orbitals analogous to the allyl anion) and the LUMO of the alkene 6.179.
LUMO
1
2
O
HOMO
1
O
2
2'
1'
2'
1'
HOMO
6.178
LUMO
6.179
288
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
Hydroboration is another case where the frontier orbital pictures 6.180 and 6.181 reinforce the perception that the
two bonds are formed independently. The former illustrates the electrophilic attack by the borane, and the latter
the nucleophilic attack by the borane, simultaneously explaining the regioselectivity for an X-substituted alkene.
LUMO
HOMO
LUMO
B
H
HOMO
6.180
B
6.181
Carbene cycloadditions following the nonlinear pathway 6.163 are also illuminated by the frontier orbitals
6.182 and 6.183, where the HOMO of the carbene is the lone pair and the LUMO is the empty p orbital. Each
of these orbitals, when presented to the double bond with the carbene on its side, matches the signs of the
appropriate atomic orbitals on the double bond (dashed lines). Once again, by separating the formation of the
two bonds into overlap developing independently to orthogonal orbitals on the carbene, we no longer need
to see the reaction as strictly pericyclic. Carbenoids, in which a C—M bond and a C—halogen bond are
typically present in place of the filled and empty orbitals of a genuine carbene, give rise to equivalent
pictures, and equally favour the nonlinear pathway.751
LUMO
HOMO
Cl
Cl
LUMO
6.182
Cl
Cl
HOMO
6.183
Nevertheless, frontier orbital theory, for all that it works, does not explain why the barrier to forbidden
reactions is so high. Perturbation theory uses the sum of all filled-with-filled and filled-with-unfilled
interactions (Chapter 3), with the frontier orbitals making only one contribution to this sum. Frontier orbital
interactions cannot explain why, whenever it has been measured, the transition structure for the forbidden
pathway is as much as 40 kJ mol1 or more above that for the allowed pathway. Frontier orbital theory is
much better at dealing with small differences in reactivity. We shall return later in this chapter to frontier
orbital theory to explain the much weaker elements of selectivity, like the effect of substituents on the rates
and regioselectivity, and the endo rule, but we must look for something better to explain why pericyclic
reactions conform to the Woodward-Hoffmann rules with such dedication.
6.4.3 Correlation Diagrams
Correlation diagrams provide a compelling explanation, at least for those reactions that have well defined
elements of symmetry preserved throughout the reaction. The idea is to identify the symmetry elements
maintained throughout the reaction, classify the orbitals undergoing change with respect to those
symmetry elements, and then see how the orbitals of the starting materials connect with those of the
product. The assumption is that an orbital in the starting material must feed into an orbital of the same
symmetry in the product, preserving the symmetry throughout the reaction. Substituents, whether they
technically break the symmetry or not, are treated as insignificant perturbations on the orbitals actually
undergoing change.
6 THERMAL PERICYCLIC REACTIONS
6.4.3.1 Orbital Correlation Diagrams.
289
We shall begin with an allowed reaction, the ubiquitous Diels-Alder.
Step 1. Draw the bare bones of the reaction 6.184, and draw the curly arrows for the forward and backward
reactions. Ignore any substituents that may be present, in order to focus on the key bonds being made and broken.
6.184
Step 2. Identify the molecular orbitals undergoing change. The curly arrows help you to focus on the
components of the reaction—what we want now is the molecular orbitals of those components. For the
starting materials, they are the p orbitals ( 1- 4*) of the diene unit and the p orbitals (p and p*) of the
C¼C double bond of the dienophile. For the product, they are the p bond (p and p*) and the two newly
formed bonds ( and * for each).
Step 3. Identify any symmetry elements maintained throughout the course of the reaction. There may be
more than one. For a Diels-Alder reaction, which we know to be suprafacial on both components, there is
only the one, a plane of symmetry bisecting the bond between C-2 and C-3 of the diene and the p bond of
the dienophile 6.185. Any substituents, even if they make the diene or dienophile unsymmetrical, do not
fundamentally disturb the symmetry of the orbitals directly involved.
3
2
a plane of
symmetry
intersects the
page here
3
2
6.185
Step 4. Rank the orbitals by their energy, and draw them as energy levels, one above the other, with the
starting material on the left and the product on the right (Fig. 6.18).
Step 5. Beside each energy level, draw the orbitals, showing the signs of the coefficients of the atomic
orbitals. All the p bonds are straightforward, but we meet a problem with the two bonds in the product,
which appear at first sight to be independent entities. In the next step we have to identify the symmetry
these orbitals have with respect to the plane of symmetry maintained through the reaction, and it is not
obvious how to do this for a pair of independent-seeming orbitals. The answer is to combine them; they
are, after all, held one bond apart, and they must interact in a p sense. The interaction of the two bonding orbitals (Fig. 6.19a) and the two antibonding * orbitals (Fig. 6.19b) leads to a new set of four molecular
orbitals 1, 2, 3* and 4*, one pair (1 and 3*) lowered in energy because of the extra p-bonding, and
the other pair (2 and 4*) raised in energy because of the extra p-antibonding.
Step 6. Classify each of the orbitals with respect to the symmetry element. Starting at the bottom left of Fig.
6.18, the lowest energy orbital is 1 of the diene, with all-positive coefficients in the atomic orbitals, in
other words with unshaded orbitals across the top surface of the conjugated system. The atomic orbitals on
C-1 and C-2 are reflected in the mirror plane, intersecting the page at the dashed line, by the atomic
orbitals on C-3 and C-4, and 1 is therefore classified as symmetric (S). Moving up the left-hand column,
the next orbital is the p bond of the dienophile, which is also symmetric with respect to reflection in the
plane. The next orbital is 2 of the diene, in which the atomic orbitals on C-1 and C-2 have positive
coefficients, and those on C-3 and C-4 have negative coefficients, because of the node half way between
C-2 and C-3. The atomic orbitals on C-1 and C-2 are not reflected in the mirror plane by the orbitals on C-3
and C-4, and this orbital is antisymmetric (A). It is unnecessary to be any more sophisticated in the
290
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
4*
A
A
*
3*
A
4*
S
3*
A
*
S
A
2
S
S
S
1
a plane of
symmetry
intersects the
page here
Fig. 6.18
A
2
S
1
Orbital correlation diagram for the Diels-Alder reaction
description of symmetry than this. The remaining orbitals can all be classified similarly as symmetric or
antisymmetric. Likewise with the orbitals of the product on the right, 1 is symmetric, 2 antisymmetric,
and so on.
Step 7. Fill in the orbital correlation (Fig. 6.18). Following the assumption that an orbital in the starting
material must feed into an orbital of the same symmetry in the product, draw lines connecting the orbitals of
the starting materials to those of the products nearest in energy and of the same symmetry. Thus, 1 (S)
connects to 1 (S), p (S) connects to p (S), and 2 (A) connects to 2 (A), and similarly, with the unoccupied
orbitals, 3* (S) connects to 3* (S), p* (A) connects to p* (A), and 4* (A) connects to 4* (A).
Let us go through the same steps for a symmetry-forbidden reaction, the [p2sþp2s] cycloaddition 6.186.
We first draw the reaction and put in the curly arrows—the orbitals are evidently the p and p* of each of the
p bonds. There are two symmetry elements maintained this time—a plane like that in the Diels-Alder
reaction, bisecting the p bonds, but also another between the two reagents, which reflect each other
through that plane.
a plane of symmetry
intersects the page here
a plane of
symmetry
intersects the
page here
6.186
6.187
6.188
6 THERMAL PERICYCLIC REACTIONS
291
4*
2
*
*
3*
1
(a) The combination of the
Fig. 6.19
orbitals
(b) The combination of the * orbitals
Molecular orbitals from a pair of interacting orbitals
In order to classify the symmetry of the orbitals with respect to that plane, we have to take the approaching
p bonds and pair them up in a lower energy symmetric 6.187 and a higher energy antisymmetric
combination 6.188. These are the molecular orbitals developing as the two molecules approach each
other. Pairing the orbitals like this is essentially the same device as pairing the bonds in setting up 1-4*
in Fig. 6.19. We shall also have to repeat that exercise in this case, to deal with the two bonds in the
cyclobutane product.
We are ready to construct the orbital correlation diagram Fig. 6.20, but we must classify the symmetry of
the orbitals twice over, once for the plane bisecting the p bonds, represented by the vertical dashed line in
Fig. 6.20, and then for the plane between the two reagents, the horizontal dashed lines. Thus the lowest
energy orbital in the starting materials is the bonding combination p1 of the two bonding p orbitals. This
orbital is reflected through both planes and is classified as symmetric with respect to both (SS). The next
AA
4*
AA
4*
SA
3*
AS
2
SA
1
SS
AS
SS
Fig. 6.20
3*
2
1
Orbital correlation diagram for a [p2sþp2s] cycloaddition
292
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
orbital up is the antibonding combination p2 of the two bonding p orbitals. This orbital is reflected through
the first plane, but not in the second, so it is classified as symmetric with respect to one and antisymmetric
with respect to the other (SA). Working up through the two antibonding p orbitals reveals that p3* and p4*
are AS and AA, respectively. The product side is similar—except for the addition of the second symmetry
classification, it reproduces the pattern for the bonds that we saw in Fig. 6.18.
We can now complete Fig. 6.20 by correlating the energy levels, feeding the orbitals in the starting
materials into orbitals of the same symmetry in the product, SS to SS, SA to SA, AS to AS, and AA to AA.
This time, the filled, bonding orbitals of the starting materials, p1 and p2, do not lead to the ground-state
orbitals of the product—one of them, p1, leads to the lower bonding orbital 1, but the other, p2, leads to one
of the antibonding orbitals 3*.
It is normal to stop at the orbital correlation diagrams, because we can already see in Fig. 6.18 for the
allowed reaction that the electrons in the bonding orbitals of the starting materials move smoothly into the
bonding orbitals of the product, whereas, in Fig. 6.20 for the forbidden reaction, the electrons in the bonding
orbitals in the starting materials move into both bonding and antibonding orbitals in the product. However,
an important feature is revealed if we construct state correlation diagrams.
6.4.3.2 State Correlation Diagrams. Going back to the Diels-Alder reaction in Fig. 6.18, the ground
state of the starting materials is designated ( 12p 2 22). Because all the terms are squared (each of the
orbitals is doubly occupied), it is also described as overall symmetric (S). Similarly the ground state of
the product is (1222p2), and it too, with all its terms squared, is symmetric. The lines connect the
orbitals of the ground state on the left with the orbitals of product on the right, and the state correlation
diagram is correspondingly easy, at least as far as we need to take it. Because the individual orbitals of
the ground state in the starting material correlate with the individual orbitals of the ground state of the
product, the important part of the state correlation diagram (Fig. 6.21) consists simply of a line joining
the ground state with the ground state, and for present purposes we do not need to know what any of the
other states correlates with.
2 2 2
1
2
GS
S
S
GS
2 2 2
1 2
Fig. 6.21 State correlation diagram for the Diels-Alder reaction
In contrast, the state correlation diagram for the forbidden cycloaddition (Fig. 6.22) is not so simple. The
ground state of the starting materials on the left, p12p22, is overall symmetric, because both terms are
squared. Following the lines across Fig. 6.20, we see that this state feeds into a doubly excited state, 123*2,
in the product, which is also symmetric because both terms are squared. If we now start at the ground state of
the product, 1222, and follow the lines (SS and AS) in Fig. 6.20 back to the orbitals of the starting material
from which they are derived, we find another doubly excited state p12p3*2. Both of these states, with both
terms squared, are again symmetric. Any hypothetical attempt by the molecules to follow these paths in
either direction, supposing they had the very large amounts of energy necessary to do so, would be thwarted
because states of the same symmetry cannot cross. The hypothetical reaction would in fact lead from ground
state to ground state, but it would have to traverse a very substantial barrier, represented in Fig. 6.22 by the
line E, which leads up to the avoided crossing. This barrier provides, at last, a convincing explanation of why
the forbidden [2 þ 2] cycloaddition is so difficult—the energy needed to surmount it is far above that
available in most thermal reactions.
6 THERMAL PERICYCLIC REACTIONS
293
2
2
1 3*
S
2
2
1 3*
S
A
2
1 2 3*
1st ES
A
1st ES
2
1 2 3*
E
2 2
1 2
GS
S
S
Fig. 6.22
GS
2 2
1 2
State correlation diagram for a [p2sþp2s] cycloaddition
We should look now at the first excited state in the starting materials, p12p2p3*, which is produced by
promoting one electron from p2 to p3*. Following the lines in Fig. 6.20 from the occupied and the two halfoccupied orbitals on the left (SS, SA and AS), we are led to the orbitals of the first excited state of the product
on the right, 1223*. In the state correlation diagram, Fig. 6.22, both of these states are antisymmetric,
and there is a line joining them, passing close to the avoided crossing in the ground-state correlation. The
value of E is approaching the energy of electronic excitation. It also explains why the photochemical
[2 þ 2] reaction is allowed—the electrons in the orbitals of the first excited state move smoothly over into
the orbitals of the first excited state of the product. This does not mean that the reaction ends there, for the
electron in 3* must somehow drop into 2 to give the ground state, disposing of a large amount of
energy—by no means a simple event. All we need to understand in the present context is that
the photochemical reaction does not meet a symmetry-imposed barrier like that for the ground-state
reaction.
Correlation diagrams have given us a convincing sense of where the barriers come from for those reactions
that we have been calling forbidden. In principle, of course, no reaction is forbidden—what these reactions
have is a formidable symmetry-imposed barrier, and something very unusual is needed if barriers of this
magnitude are to be crossed.
Correlation diagrams take quite a bit of thought, and there are some pitfalls in their construction—
however satisfying they may be, they are not for everyday use, and it was for this reason that Woodward
introduced the simple rule that we covered in Section 6.3.2.
6.4.3.3 Following Orbitals along the Reaction Coordinate. It is possible by calculation to follow the
substantial electronic reorganisation taking place in a Diels-Alder reaction, and to estimate the degree of
- and p-bonding that has developed, and the degree of p-bonding lost, as the reaction proceeds.752,753 In
the orbital correlation diagram in Fig. 6.18 the electrons from 1 of the diene move into the 1 orbital of
the product, those in 2 move into 2, and the electrons in the p orbital of the dienophile move into the p
orbital of the product. In that diagram the connections were straight lines, because we were concerned
only with matching symmetry. Now we can look at them again, and reconsider what happens to the
energy of these orbitals and the electron distribution as the reaction proceeds from left to right in the
diagram. Greatly simplified it looks like Fig. 6.23, with the abscissa showing the distance apart of the two
carbon atoms becoming bonded, C-1 and C-10 (and C-4 and C-20 ), and the ordinate showing the orbital
energy.
Fig. 6.23 allows us to see a connection between the correlation diagrams and the explanations based on
frontier orbital interactions. The two solid curves follow the interaction of the symmetric orbitals, 1 and
294
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
2
1
2
E
TS
3.5
3.0
2.5
d(C1—C1')
Fig. 6.23
1
2.0
1.5
Å
Orbital following along the reaction coordinate of a Diels-Alder reaction
p, which begin to interact when C-1 and C-10 are about 3.5 Å apart. As they are both filled, have the same
symmetry, and are not far apart in energy, they repel each other strongly.754 The lower curve, in which they
interact in phase, drops steadily in energy as -bonding develops, and the upper, in which they interact out
of phase, rises. To begin with, the rise in p is steeper than the drop in 1, making the overall effect
repulsive, as usual when two filled orbitals interact. At the transition structure at about 2.2 Å the drop in
energy is estimated to be about 95 kJ mol1 and the rise about 206 kJ mol1. Shortly after passing the
transition structure, as the energy of p rises to become closer to that of 3*, a HOMO(dienophile)/
LUMO(diene) interaction takes over, lowering the energy, and moving the electrons into the p orbital of
the product.
The dashed curve follows this other frontier orbital interaction, and is notably different. The energy begins
to rise a little at first, as the p system distorts, reaching 55 kJ mol1 at the transition structure. Only at about
2.4 Å, do these frontier orbitals, 1 and p*, start to interact to lower the energy, turning the curve over just
before the transition structure is reached. After this point the curve falls rapidly as -bonding develops in the
orbital 2. It thus appears that both pairs of frontier orbitals have significant but different parts to play, with
the HOMO(diene)/LUMO(dienophile) countering the mildly repulsive interaction in the dashed curve, and the
HOMO(dienophile)/LUMO(diene) countering the strongly repulsive interaction in the upper full curve. Thus we
have a better, but less immediately applicable version resembling frontier orbital theory.
The bond-order changes indicate that the p bond between C-2 and C-3 is well advanced (66%) in the
transition structure 6.189, whereas the p bonds in the dienophile and the diene are not much weakened
(32% and 22%, respectively). Likewise, the bonds are little formed (22%). The larger changes in the
p-bonding in the diene suggest a late transition structure, and the small changes in the -bonding and in
the p-bonding of the dienophile suggest an early transition structure. This asynchronicity reflects the
sum of the HOMO(diene)/HOMO(dienophile) interactions and substantial contributions from both frontier
orbital interactions when the effect of the change in their energies as the reaction proceeds is taken into
account.
6 THERMAL PERICYCLIC REACTIONS
295
1.37Å
1.33Å
2.20Å
1.51Å
1
1.47Å
1.34Å
2
1'
3
2'
1.39Å
1.40Å
1.35Å
1.53Å
4
6.189
6.5
Secondary Effects
The Woodward-Hoffmann rules arise fundamentally from the conservation of orbital symmetry seen in
the correlation diagrams. These powerful constraints govern which pericyclic reactions can take place
and with what stereochemistry. As we have seen, frontier orbital interactions are consistent with these
features, but they are not the best way of explaining them. In contrast, there are many secondary effects
for which the frontier orbitals do provide the most immediately telling explanation. These are the
substituent effects on rates and regioselectivity; secondary stereochemical effects like the endo rule for
Diels-Alder reactions; periselectivity; and torquoselectivity. We are still on weak ground, for all the
usual reasons undermining frontier orbital theory when it is applied too ruthlessly (see p. 143), but for
the organic chemist seeking some kind of explanation for all these phenomena, it is nearly
indispensable.
6.5.1 The Energies and Coefficients of the Frontier Orbitals of Alkenes and Dienes
In order to apply frontier orbital arguments to these phenomena, we need to know the effect of C-, Z- and
X-substituents on the frontier orbitals of alkenes. In Section 2.1.2 we deduced, without carrying out any
calculations, that all three kinds of substituents, C, Z and X, lowered the overall energy. Using the same
arguments, we also deduced the relative energies of the frontier orbitals of C-, Z- and X-substituted alkenes.
The effect of a C-substituent (vinyl and phenyl) poses no problem, because it is seen in the orbitals of a
simple alkene and a diene—the HOMO is raised in energy in going from ethylene to butadiene (or to
styrene), and the LUMO is lowered in energy (Figs. 1.39 and 2.2). For a Z-substituted alkene like acrolein,
we saw in Fig. 2.4 that the HOMO energy is close to that of a simple alkene at 1 below the level. It lies
somewhere between the HOMO of an allyl cation ( 1), lower in energy, and the HOMO of a diene ( 2),
higher in energy, having the character of both. However, the LUMO energy of a Z-substituted alkene is well
below that of a simple alkene, because it lies somewhere between the LUMO of an allyl cation ( 2 at 0) and
the LUMO of butadiene ( 3* at 0.62), both of which are lower in energy than p* of a simple alkene at 1
above the level. The argument for an X-substituted alkene was even easier: we saw in Fig. 2.6 that it simply
mixes in a bit of allyl anion-like character to the unsubstituted alkene, raising the energy of the HOMO
relative to the energy of the HOMO of the simple alkene on the left, and, to a smaller extent, raising the
energy of the LUMO relative to the energy of the LUMO of the simple alkene.
The same arguments can be used for dienes with a substituent on C-1. A C-substituent raises the energy
of the HOMO and lowers the energy of the LUMO, in going from butadiene to hexatriene (Fig. 1.42). For a
Z-substituent, the comparison would be between a pentadienyl cation on the one hand and hexatriene on
the other, and for an X-substituent, the comparison would be between a pentadienyl anion and the
unsubstituted diene. The orbitals for these systems can be found in Fig. 1.42, and estimating an average
between the extremes will show that the HOMO of a Z-substituted diene is either unaffected or lowered
slightly in energy relative to the HOMO of butadiene, and that the LUMO is distinctly lowered in energy
relative to the LUMO of butadiene. Similarly, the HOMO of a 1-X-substituted diene is distinctly raised in
energy relative to the HOMO of butadiene, and the LUMO is slightly raised in energy.
296
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
For dienes with substituents at C-2, similar arguments are used and similar results obtained, as seen in
Fig. 6.24. For the Z-substituent, some allyl cation character is mixed into the orbitals of 2-vinylbutadiene,
and, for an X-substituent, some allyl anion character is mixed into the orbitals of butadiene.
0.44
–0.23
0.518
–0.33
LUMO
–0.23
0
Z
0.63
0.44
0.44
0.23
0.518
–0.71
0.71
–0.33
HOMO
0.23
1.414
–0.63
0.44
Z
–0.50–0.71–0.50
(a) 2-Z-Substituted diene
–0.71
0.50
–0.37
0.50
1.414
0.60
0.618
C-
LUMO
0.71
–0.37
–0.71
X
0
0.60
0.60
0.37
HOMO
0.618
X
–0.37
–0.60
Fig. 6.24
(b) 2-X-Substituted diene
Estimating the frontier orbitals of a 2-substituted diene
In summary, the conclusions with respect to the energies of the frontier orbitals, are:
C- (extra conjugation)
raises the energy of the HOMO and lowers the energy of the LUMO
Z- (an electron-withdrawing group)
slightly lowers the energy of the HOMO and substantially lowers the energy of the LUMO
X- (an electron-donating group)
substantially raises the energy of the HOMO and slightly raises the energy of the LUMO
6 THERMAL PERICYCLIC REACTIONS
297
X
3.0
3
2
1.5
C
1.0
1
Z
0
0
–1
–8
C
–9.1
X
–9.0
–9
–10
–10.5
Z
–10.9
–11
(a) Dienophiles
X
3
2
1.0
1
Z
0.5
–0.5
0
–1
–8
2.5
C
C
X
Z
–8.2
–9.1
–8.5
–9.5
–9
–10
–11
(b) 1-Substituted dienes
2.3
3
2
1.0
1
0.7
X
–0.3
0
C
–1
–8
–9
Z
–9.1
–8.5
–9.3
C
–10
–8.7
X
Z
–11
(c) 2-Substituted dienes
Fig. 6.25 Frontier orbital energies (in eV) and coefficients of alkenes and dienes. The energies are representative values
for each class of alkene and diene (1 eV ¼ 23 kcal ¼ 96.5 kJ)
298
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
Another way of looking at the effect of a 2-substituent is to say that the C-, Z- and X-substituents are
attached to the carbon atom of butadiene which has the smaller coefficient in the HOMO and the LUMO, the
effect of a substituent being roughly proportional to the square of the coefficient at the point of attachment.
The result is that the energies are shifted in the same direction, but to a lesser extent than they are when the
substituent is attached to C-1. The HOMO and LUMO are brought closer in energy by extra conjugation, the
HOMO and LUMO are lowered by a Z-substituent, and the HOMO and LUMO are raised by an Xsubstituent; but none of these effects is quite as large as it is in a 1-substituted diene.
The rates of cycloadditions are principally accounted for by looking at the energies of the frontier orbitals.
They must also be affected by the size of the coefficients in the frontier orbitals, but this factor is rarely
needed.755 The relative sizes of the coefficients are principally used to account for regioselectivity. We now
need to return to the similar arguments that were used in Section 2.1.2 to estimate the relative magnitude of
the coefficients of the atomic orbitals in the frontier orbitals.
We saw in Figs. 1.37 and 2.2 that a C-substituted alkene has higher coefficients at the unsubstituted
terminus than at the atom carrying the substituent, both in the HOMO and the LUMO. We saw in Fig. 2.5 that
a Z-substituent has only a small effect on the HOMO, with the coefficient at the unsubstituted terminus
probably the larger. We also saw that the LUMO was strongly polarised, with the coefficient at the terminal
carbon substantially the larger. Finally, we saw in Fig. 2.7 that an X-substituent increases the coefficient in
the HOMO at the terminal carbon and reduces it in the LUMO. Similar arguments can be carried over
to 1- and 2-substituted dienes.
Putting all these arguments onto a firmer base, Houk estimated energies for the HOMOs and
LUMOs of alkenes and 1- and 2-substituted dienes with representative C-, Z- and X-substituents,
using experimental measurements of photoelectron spectra for the occupied orbitals, and a combination of electron affinity measurements, charge transfer spectra and polarographic reduction potentials
for the unoccupied orbitals.63 They are summarised in Fig. 6.25, to which we shall constantly refer in
discussing the rates and regioselectivity of Diels-Alder reactions and 1,3-dipolar cycloadditions. The
circles represent a cross-section of the lobes of the p orbitals looked at from above the plane of the
paper, and the shaded and unshaded circles are of opposite sign in the usual way. They are not
s orbitals.
6.5.2 Diels-Alder Reactions662
In discussing the frontier orbtial explanation for the Woodward-Hoffmann rules, we were indifferent as to
which of the two components of a cycloaddition would provide the HOMO and which the LUMO. The two
pairs of frontier orbitals bear a complementary relationship to each other, and they invariably give the
same answer with respect to the rules, as in the drawings 6.173 and 6.174 for the Diels-Alder reaction. To
explain the effects of substituents on rates, we need to know the effect they have on frontier orbital
energies,756,757
6.5.2.1 The Rates of Diels-Alder Reactions. Most Diels-Alder reactions require that the dienophile
carries a Z-substituent before they take place at a reasonable rate. Butadiene will react with ethylene, but
it needs a temperature of 165 °C, high pressure and gives a low yield.758 It reacts with itself a little easier, at
150 °C, but the reaction with acrolein 6.190 is easier taking less time at the same temperature.759 A second
Z-substituent increases the rate even more, with methylenemalonate 6.191760 and maleic anhydride761
reacting at room temperature. An X-substituent on the diene, on C-1 or C-2, increases the rate further,
with trans-piperylene 6.192 and isoprene 6.193 reacting with acrolein at 130 °C,762 and 1-methoxybutadiene
6.194763 and 2-methoxybutadiene 6.195764 at slightly lower temperatures. Times and temperatures are not a
reliable way of measuring relative rates, but all these reactions were taken to the point where the yields of
isolated product are close to 80%.
6 THERMAL PERICYCLIC REACTIONS
299
165°, 17 h
+
150°, 10 d
+
900 atmospheres
CHO
+
MeO2C
+
CHO
150°, 0.5 h
6.190
1
CHO 130°, 6 h
CHO
CHO
+
2
6.193
6.190
OMe
1
CHO
130°, 6 h
6.190
OMe
CHO
+
100°, 2 h
CHO 120°, 6 h
CHO
+
2
6.195
6.190
CHO
MeO
MeO
6.194
CO2Me
CO2Me
25°, 24 h
6.191
+
6.192
CO2Me
6.190
Since the substituents are not stabilising charge in a zwitterionic intermediate, it is not at first obvious how
they can affect the rates so dramatically. The simplest explanation comes from the frontier orbitals. In the
reaction of butadiene with acrolein, the Z-substituent lowers the energy of the LUMO. Fig. 6.26a shows the
energy separations between the frontier orbitals of butadiene and an unsubstituted dienophile, and Fig. 6.26b
shows that the energy separation between the HOMO of butadiene and the LUMO of a Z-substituted
dienophile is less than that between the HOMO of butadiene and the LUMO of ethylene. The smaller the
energy gap in any particular case, the faster the reaction ought to be because a strong and a weak interaction
LUMO
LUMO
LUMO
LUMO
LUMO
LUMO
HOMO
HOMO
HOMO
HOMO
HOMO
HOMO
X
Z
(a) Frontier orbital interactions
for butadiene with an
unactivated dienophile
Fig. 6.26
(b) Frontier orbital interactions
for butadiene with a
Z-substituted dienophile
Z
(c) Frontier orbital interactions
for an X-substituted butadiene
with a Z-substituted dienophile
Frontier orbital interactions for Diels-Alder reactions
300
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
(as in Fig. 6.26b) is more effective at lowering the energy of the transition structure than two medium-sized
interactions (as in Fig. 6.26a). (This may not be immediately obvious, but it follows from the fact that the
energy separation, ErEs, is in the denominator of the Salem-Klopman equation, Equation 3.13.) Taking
numbers from Fig. 6.25, a normal Diels-Alder reaction is dominated by the interaction of the HOMO of the
diene (at 9.1 eV) and the LUMO of the dienophile (at 0 eV). The difference in energy is 9.1 eV, emphasised
with a bold, double-headed arrow in Fig. 6.26b, whereas the difference in energy of the LUMO of the diene
(at 1.0 eV) and the HOMO of the dienophile (at 10.9 eV) is 11.9 eV. To be a good dienophile in a normal
Diels-Alder reaction, the most important factor is a low-lying LUMO. Thus, the more electron-withdrawing
groups we have on the double bond, the lower the energy of the LUMO, the smaller the separation of the
HOMO(diene) and the LUMO(dienophile), and the faster the reaction. Tetracyanoethylene is a very good
dienophile. Similarly, with an X-substituent on the diene raising the energy of the HOMO, the energy
separation between the HOMO of the diene and the LUMO of the Z-substituted dienophile, 8.5 eV in Fig. 6.25,
is even smaller (Fig. 6.26c). The interaction is correspondingly stronger, and the reaction faster still.
Another way of producing a low-lying LUMO is to have an oxygen or nitrogen atom in the p bond.
Because p orbitals on these atoms lie so much lower in energy than those on carbon, the p molecular orbitals
that they make will inevitably have a lower-energy HOMO and LUMO. This is what happens with O¼O and
—N¼N— double bonds, which is one reason why singlet oxygen, and azadienophiles like dimethyl
azodicarboxylate, are such good dienophiles.765
In principle, it ought to be possible to increase the rate of a Diels-Alder reaction by adding electrondonating (X-) groups to the dienophile; these raise the energy of the HOMO, and we might expect to
approach the situation in Fig. 6.27b, which has one pair of frontier orbitals LUMO(diene)/HOMO(dienophile)
separated in energy to a similar extent to the HOMO(diene)/LUMO(dienophile) in Fig. 6.26b. In practice, dienes
with electron-donating substituents do not react with simple dienes. However, by attaching a Z-substituent to
the diene as well, the energy separation between the HOMO of an X-substituted dienophile and the LUMO of
the diene (9 eV from Fig. 6.25) becomes small enough for reaction to occur (Fig. 6.27c). Dienes with
LUMO
LUMO
LUMO
LUMO
LUMO
LUMO
HOMO
HOMO
HOMO
HOMO
HOMO
HOMO
Z
X
(a) Frontier orbital interactions
for butadiene with an
unactivated dienophile
Fig. 6.27
(b) Frontier orbital interactions
for butadiene with an
X-substituted dienophile
X
(c) Frontier orbital interactions
for a Z-substituted butadiene
with an X-substituted dienophile
Frontier orbitals for Diels-Alder reactions with inverse electron demand
6 THERMAL PERICYCLIC REACTIONS
301
electron-withdrawing substituents reacting with dienophiles with electron-donating substituents are
described as Diels-Alder reactions with inverse electron demand.766
For example, the ‘diene’ 6.196, which must have a low-energy LUMO, since it is an iminium ion, reacts
faster with the enol ether 6.197a, a dienophile with electron-donating substituents, than with acrylonitrile
6.197c, a dienophile with an electron-withdrawing substituent.767 Allyl alcohol 6.197b, which probably has
HOMO and LUMO energies very close to those of ethylene itself, reacts at an intermediate rate.
R1
1
R2
2
R
R
+
N
N
*
*
6.196
6.197
a R1=R2=OEt
b R1=CH2OH, R2=H
c R1=CN, R2=H
75% reaction in 4 min at 25 °C
75% reaction in 275 min at 100 °C
75% reaction in 1080 min at 100 °C
It has long been known that it is much more effective to carry out Diels-Alder reactions with X-substituted dienes
and/or Z-substituted dienophiles, than to use inverse electron demand. Diels-Alder reactions with inverse electron
demand are much less common and require more powerful donor and acceptor groups before they work. A striking
example is seen when a diene with a donor substituent 6.198 and a diene with an electron-withdrawing substituent
6.199 are allowed to react with each other—the diene with the electron-withdrawing substituent always takes up the
role of dienophile, and the diene with the electron-donating substituent is the diene.768 Since the separation in
energy of the frontier orbitals is identical, whichever diene takes up the role of dienophile, it is not obvious why it
should always be the one with the Z-substituent. Even more general, the two HOMO/LUMO separations for
butadiene and ethylene are the same but it is much better to raise the energy of the HOMO on the diene and lower the
energy of the LUMO on the ethylene than to try to influence the orbital energies the other way round.
Me3SiO
MeO2C
Me3SiO
+
OMe
6.199
CO2Me
OMe
6.198
The different ways in which the two frontier orbitals influence the orbital changes, and the asynchronicity in
their operation, discussed on p. 294 using Fig. 6.23, may explain this long-standing puzzle. Other suggestions have been made,769 but a particularly simple way of appreciating the same set of interactions has been
suggested by Fukui.770 He points out that as the reaction proceeds electrons are moving from the p bonds into
the space between the reacting components to make the bonds. If the major supply of electrons is from the
diene, the node in the HOMO 2 ensures that the electrons flowing from the diene are not concentrated in the
centre of the reacting system, but are concentrated at the sides where the bonds are forming (Fig. 6.28a). In
Fig. 6.23 this was seen in the way the electrons in 2 move into 2. In contrast, if the major supply of
electrons is from the dienophile, the HOMO of this component has no node and the electrons are moving into
the space in the middle (Fig. 6.28b), interacting strongly with the filled orbitals of the diene, and repelling it.
In Fig. 6.23 this was seen both in the way the electrons in p in the dienophile move into p in the product, and
in the repulsion between p and 1. There is a useful contrast here with the reaction of a bridging electrophile
like bromine with an alkene, where the same movement of electrons into the middle is exactly what is
required to produce the two bonds of the bridged epibromonium ion intermediate.
302
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
HOMO
HOMO
(a) Normal Diels-Alder reaction
HOMO(diene)/LUMO(dienophile)
Fig. 6.28
(b) Inverse electron demand
LUMO(diene)/HOMO(dienophile)
Differences in the dominant electron shift in normal Diels-Alder reactions and Diels-Alder reactions with
inverse electron demand
In addition to normal and inverse electron demand, we can set up other situations by adjusting
the energies of the HOMO and LUMO of both the diene and the dienophile. For example,
Konovalov771 found that tetracyclone 6.200 reacts with the unsubstituted styrene 6.201 (R ¼ H)
slower than with the substituted styrenes, whether the substituent is electron-donating or electronwithdrawing. The energies of the HOMO and LUMO of this diene are evidently so placed, with
respect to those of the styrenes, that when R is H neither HOMO/LUMO interaction is much stronger
than the other. When R is an electron-withdrawing substituent, the LUMO of the dienophile is
lowered, bringing it closer in energy to the HOMO of the diene, and when R is an electron-donating
substituent, the HOMO of the dienophile is raised, bringing it closer in energy to the LUMO of the
diene.
O
Ph
Ph
Ph
O
Ph
+
Ph
R
Ph
Ph Ph
R
6.200
6.201
R:
k 2 ( 106 mol–1s–1):
p-NMe2
338
p-OMe H p-Cl m-NO2
102
73 78
79
p-NO2
88
Sustmann collected data for a wide range of Diels-Alder reactions of normal electron demand.772 Using
the electron affinities of the dienophiles and the ionisation potential of the dienes, he estimated the
separations in energy between the LUMOs of the dienophiles and the HOMOs of the dienes, and showed
that they correlated quite well with the log of the rate constant—with the higher rates for the reactions
having the smaller energy gap. The points fitting least well on the graph were for cyclopentadiene, which
was too fast, and cycloheptatriene, which was too slow. In cyclopentadiene, the termini of the diene unit
are held closer together than in open-chain dienes, and in cycloheptatriene they are held further apart. It
seems likely that this explains why cyclopentadiene is regularly a good dienophile and cycloheptatriene a
poor one, and there are now several other dienes showing reactivity dependent upon the distance apart of
the ends of the diene.773 There have been many other studies since Sustmann’s pioneering work
establishing correlations between Diels-Alder rates and frontier orbital properties as measured by
ionisation potentials and electron affinities, and as calculated from molecular orbital theory.774
6 THERMAL PERICYCLIC REACTIONS
303
6.5.2.2 The Regioselectivity of Diels-Alder Reactions. Regioselectivity refers to the orientation of a
cycloaddition: for example, methoxybutadiene 6.194 reacts with acrolein 6.190 to give more of the
‘ortho’ adduct 6.202 than of the ‘meta’ adduct 6.203.775 To explain regioselectivity we look at the
coefficients of the atomic orbitals in the more important pair of frontier orbitals. We should perhaps remind
ourselves that the sign of the lobe that is overlapping with another lobe is a much more important factor in
determining the energy change than is the second-order effect of its size, but from now on we shall ignore the
sign because we shall only be looking at allowed (and hence observed) reactions.
OMe
OMe
CHO
OMe
CHO
+
and not
CHO
6.194
6.190
6.202
6.203
We already know from the data in Fig. 6.25, and from the arguments used to create Fig. 6.26, that the
important interaction in a case like this with normal electron demand will be between the HOMO of the diene
and the LUMO of the dienophile, shown on the left in Fig. 6.29 (Er – Es ¼ 8.5 eV), not the other way round
shown on the right (Er – Es ¼ 13.4 eV). We see that the two larger atomic orbitals overlap (dashed line) in
forming the observed product 6.202.
It is not self evident that the choice of the large-large interaction in Fig. 6.29 is better than two largesmall interactions. Here is a simple theorem which proves that it is right. Consider two interacting
molecules X and Y in Fig. 6.30: let the square of the terminal coefficients on X be x and xþn, and let the
square of the coefficients on Y be y and yþm. For the large-large/small-small interaction (Fig. 6.30a), the
contribution to the numerator of the third term of the Salem-Klopman equation, Equation 3.13, will be:
xyþ(xþn)(yþm). For the large-small/small-large case (Fig. 6.30b), the contribution will be:
x(yþm)þ(xþn)y. Subtracting the latter from the former gives nm. In other words, the former interaction
is greater so long as n and m are of the same sign; that is, xþn and yþm are either the two large (as shown)
OMe
OMe
CHO
CHO
LUMO
HOMO
ELUMO – EHOMO = 8.5 eV
LUMO
HOMO
ELUMO – EHOMO = 13.4 eV
Coefficients of the frontier orbitals of methoxybutadiene and acrolein
Fig. 6.29
x
x
y+m
y
y
y +m
x+n
x+n
(a) Large-large
small-small
(b) Large-small
large-small
Fig. 6.30
(c) Large-large
small-small
(d) Large-small
large-small
Large-large/small-small pairing of frontier orbitals compared with large-small/large-small
304
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
or the two small lobes. Pictorially, this conclusion can be even less rigorously demonstrated by Fig. 6.30c
and 6.30d, which shows that overlap develops earlier with the large-large/small-small combination. The
implication of a large-large interaction leading over the small-small interaction, as in Fig. 6.30c, is that
the transition structure of an unsymmetrical Diels-Alder reaction is itself unsymmetrical, having the two
bonds being formed to different extents. The reaction is still concerted, with both bonds forming at the
same time, but it is not synchronous, with them both formed to an equal extent in the transition structure.
Secondary deuterium isotope effects, which are so successful in confirming that Diels-Alder reactions
are concerted cycloadditions, have also been applied to asynchronous reactions, where they match the
calculated values allowing for the asynchronicity.776
You may feel that we have laboured hard to justify an example of regioselectivity which experienced
organic chemists would have predicted would go this way round. They would have drawn curly arrows 6.204
(or 6.205 creating the canonical structures 6.206) to express the feeling that C-4 of the diene is a nucleophilic
carbon and C-30 of the acrolein an electrophilic carbon. This reasoning is fine, but it cannot be applied to all
cases.
OMe
1
O
2'
OMe
O
H
OMe
O
H
H
3'
3'
4
4
6.204
6.205
6.206
For example, it would not work in the case of the reaction between butadiene carboxylic acid 6.208 and
acrylic acid 6.209. The curly arrows 6.207 establish that C-4 of the diene carboxylic acid can be expected to
be electrophilic, just like C-30 of the acrylic acid. The partial positive charges ought to repel each other and
the adduct expected would be the ‘meta’ adduct 6.211. In contrast, the reaction gives mainly the ‘ortho’
adduct 6.210.777
O
OH
O
O
OH
OH
O
OH
+
CO2H
CO2H
150°
+
3'
4
6.207
CO2H
6.208
CO2H
6.209
6.210
90:10
6.211
Clearly this valence bond argument is not good enough, whereas the frontier orbital argument does work.
Taking the orbitals and the energies from Fig. 6.25, we get Fig. 6.31, in which the usual HOMO(diene)/
LUMO(dienophile) combination has the smaller energy gap. These orbitals are polarised with the marginally
Z
Z
Z
HOMO
Z
LUMO
ELUMO – EHOMO = 9.5 eV
Fig. 6.31
LUMO
HOMO
E LUMO – E HOMO = 10.4 eV
Frontier orbitals for a Z-substituted diene and a Z-substituted dienophile
6 THERMAL PERICYCLIC REACTIONS
305
higher coefficient in the HOMO of the diene on C-4, which stems from the hexatriene-like character of the
conjugated system (see p. 313). As a result, the counter-intuitive combination with bonding between C-4 and
C-30 wins. The somewhat less favourable LUMO(diene)/HOMO(dienophile) combination has little effect on
regiochemistry, because the HOMO of the dienophile is barely if at all polarised.
The anions of these acids also undergo a Diels-Alder reaction. The contribution of a carboxylate ion group
(CO2) to the frontier orbitals will be even more like that of a simple C-substituent and less like that of a
Z-substituent. The prediction from the frontier orbitals is therefore the same—an ‘ortho’ adduct—but this
time the negative charges will strongly repel each other, favouring the ‘meta’ adduct. The observation778 of a
50:50 mixture of ‘ortho’ and ‘meta’ adducts shows how powerful a directing effect the orbital contribution
must be. Another example, in which the simple curly arrow argument would not have predicted the right
answer, is the reaction between the azoniaanthracene cation 6.196 and acrylonitrile 6.197c. The electrophilic
carbon atoms (*) have become bonded to each other in both adducts, which differ in stereochemistry but not
in regiochemistry.
There are 18 possible combinations of C-, Z- and X-substituted dienes and C-, Z- and X-substituted
dienophiles. The ‘ortho’ adduct is predicted (and found) to be the major product for eight of the nine
possible combinations with 1-substituted dienes, and the ‘para’ adduct predicted (and found) for eight
of the nine possible combinations of 2-substituted dienes. The reactions of Z-substituted dienophiles
with the 1-X-substituted diene 6.194 (see p. 303) and with the 1-Z-substituted diene 6.208 (see
p. 304) illustrate two of these combinations, and here are examples of most of the rest which obey the
‘ortho-para’ rule.
Z-substituted dienophiles:779,780
1-C-Substitued diene
Ph
2-C-Substitued diene
Ph
CHO
CHO
Ph
+
Ph
Ph
+
CN
+
CN
CN
80:20
only adduct
2-X-Substituted diene
2-Z-Substituted diene
MeO
MeO
(RO)2B
+
(RO)2B
+
CHO
CHO
CHO
only adduct
X-substituted dienophiles:781
1-Z-Substituted diene
CO2Me
MeO2C
N
CHO
only adduct
N
+
only adduct
306
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
C-substituted dienophiles:782
1-Z-Substituted diene
CO2H
2-Z-Substituted diene
CO2H
CO2H
Ph
Ph
+
NC
NC
+
+
Ph
NC
CN
86:14
only adduct
1-C-Substituted diene
Ph
2-C-Substituted diene
Ph
Ph
Ph
Ph
+
Ph
Ph
+
Ph
+
Ph
Ph
+
Ph
Ph
95:15
89:11
The two exceptions to the ‘ortho-para’ rule are the reactions between an X-substituted diene, with the
X-substituent at C-1 or C-2, and an X-substituted dienophile. The frontier orbitals in Fig. 6.32, taken from
Fig. 6.25, indicate that the preferred combination, whichever pair of frontier orbitals and whichever diene,
1-substituted or 2-substituted, is taken, will lead to the ‘meta’ adduct.
X
X
X
X
X
X
X
HOMO LUMO
LUMO
ELUMO – EHOMO
= 11.5 eV
ELUMO – EHOMO
= 11.5 eV
HOMO
(a) A 1-X-Substituted diene with an Xsubstituted dienophile
Fig. 6.32
X
HOMO
LUMO
ELUMO – EHOMO
= 11.7 eV
LUMO
HOMO
ELUMO – EHOMO
= 11.3 eV
(b) A 2-X-Substituted diene with an Xsubstituted dienophile
FOs for the combination of X-substituted dienes with an X-substituted dienophile
Neither frontier orbital interaction is between orbitals close in energy (>11 eV in all combinations), with
the result that these reactions can be expected to be very slow, and they are in practice exceedingly rare.
The most revealing are two reactions which take advantage of aromatisation of the diene to make them
feasible: the combination of the (vinylogous) 2-X-substituted diene 6.212 and ethyl vinyl ether 6.213 gives
more of the ‘meta’ adduct, and so does the combination of the 1-X-substituted diene 6.214 and propyne
6.215.783 Neither reaction is usefully regioselective, partly because they take place at quite high temperatures, necessary to open the benzocyclobutene precursors of the dienes, but the direction of the effect
is clear.
6 THERMAL PERICYCLIC REACTIONS
307
MeO
180°
OEt MeO
MeO
+
+
OEt
6.212
2d
OEt
6.213
61:39
190°
+
+
7d
6.214
6.215
65:35
In summary, we predict the regioselectivity of a Diels-Alder cycloaddition by the following sequence:
1. Estimate the energies of the HOMO and the LUMO of both components.
2. Identify which HOMO/LUMO pair is closer in energy.
3. Using this HOMO/LUMO pair, estimate the relative sizes of the coefficients of the atomic orbitals
on the atoms at which bonding is to take place.
4. Match the larger coefficient on one component with the larger on the other.
An alternative explanation for regioselectivity to that based on the molecular orbitals has been the
diradical theory, in which the major adducts correspond to those which would be obtained if a diradical
intermediate were to be involved.784,785 Thus, taking a 2-substituted diene, the intermediate diradical
6.216 leading to the ‘para’ adduct 6.217 can be expected to be better stabilised than either of the diradicals
6.218 or 6.219 leading to the ‘meta’ adduct 6.220, given that any substituent, C, Z or X, stabilises a radical
(Section 2.1.5). This explanation works for the majority of cases but not for the combination of
X-substituted diene and X-substituted dienophile, which is therefore telling support for an orbital-based
explanation.
X,Z,C
X,Z,C
X,Z,C
C,Z,X
C,Z,X
C,Z,X
6.216
X,Z,C
6.217
C,Z,X
a
C,Z,X
X,Z,C
a
b
X,Z,C
6.218
C,Z,X
b
a
X,Z,C
C,Z,X
b
6.220
6.219
308
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
A special case is the effect of a sulfur lone pair. On its own, this is clearly an X-substituent but a curious
feature of its influence on regioselectivity in Diels-Alder reactions is that it appears to be a more powerful
X-substituent than an alkoxy group. A sulfur lone pair is higher in energy than an oxygen lone pair, and any
inductive effect towards sulfur will be less than towards oxygen. Both factors should make sulfur a better
p donor, but a sulfur atom is too large to allow good overlap between its lone pair and a p orbital on carbon.
On balance, the latter appears to be usually more important, and an alkyl- or arylthio substituent is less
effective at stabilising a cation than the corresponding oxygen substituent. In contrast, Trost found that the
2,3-disubstituted diene 6.221 reacted with methyl acrylate to give the two adducts 6.222 and 6.223 in a ratio
of 4:1. His calculation for the HOMO coefficients, shown on 6.221, nicely agreed with this result, but in more
detail frontier orbital explanations were not effective on their own in accounting for all his observations.786
–0.292
MeO
CO2Me
MeO
CO2Me MeO
+
+
PhS
PhS
CO2Me
PhS
0.512
6.221
6.222
6.223
80:20
Another special case is the effect of a boron substituent. Since it is electropositive and has an empty p orbital,
it will be a donor and a p acceptor. If the effect in the p system overrides that in the system, it should be
like a Z-substituent activating a dienophile by lowering the LUMO energy. It almost certainly does, as shown
by the easy reaction of vinyl-9-BBN 6.224 with butadiene, which takes place at room temperature, 200 times
faster than the corresponding reaction with methyl acrylate.787 The energy calculated for the LUMO is –0.08
eV, close to that of acrylic acid (0.07 eV at the same level of calculation). Vinyl boronic acids and esters, in
which the empty p orbital is conjugated to oxygen lone pairs, have a higher energy LUMO (0.82 eV at the
same level of calculation), and they are in practice much less reactive.788,789 Vinylboranes also show
unexpected regioselectivity, giving mainly (>98:2) the ‘meta’ adduct 6.225 with trans-piperylene, in spite
of the large difference in the coefficients of the LUMO suggesting that the ‘ortho’ adduct should, as usual, be
the major product. This appears to be a steric effect, since the reaction with the piperylene is significantly
slower than the reaction with butadiene, which is not the normal pattern, and the less sterically hindered
vinyldimethylborane is no longer selective for the ‘meta’ isomer. Furthermore, if the vinyl group has a
trimethylsilyl group at the other end, that provides the major steric interaction, and the regioselectivity
changes to be ‘ortho’ (88:12) with respect to the boron substituent. All the reactions of vinylboranes are
remarkably endo selective (92:8), which we shall discuss in Section 6.5.2.4.
B
25 °C
0.64
0.37
+
B
B
–0.62
LUMO –0.08 eV
6.224
6.225
A number of other examples of regioselectivity in Diels-Alder reactions are less straightforwardly categorised.
Thus, citraconic anhydride 6.226 and l-phenylbutadiene react to give the ‘ortho’ adduct 6.227.790 This might
be described as the combination of a 1-C-substituted diene with an X-substituted dienophile, since the two
carbonyl groups make the dienophile symmetrical with respect to the Z-substituents. If we ignore the carbonyl
groups for the moment and treat the dienophile simply as an X-substituted alkene, the LUMO of the diene and
the HOMO of the dienophile would be the closer pair of frontier orbitals in energy, from which we would
6 THERMAL PERICYCLIC REACTIONS
309
predict the ‘ortho’ adduct, as observed. However, appearances are misleading. With two carbonyl groups on
the dienophile, the correct HOMO and LUMO to take in this case is HOMO(diene) and LUMO(dienophile), from
which the prediction would be the ‘meta’ adduct. It is obviously unreasonable to ignore the carbonyl groups.
One simple-minded way of looking at it, similar to the discussion on p. 191, is to say that the hyperconjugation
6.228 of the methyl group, through the double bond, with the carbonyl group attached to C-3 will reduce the
electron-withdrawing effect of that carbonyl group. The result is that the carbonyl group attached to C-2 is
more important in guiding the reaction: the C¼C orbital is more polarised by the C-2 carbonyl than by the C-3
carbonyl, and this reaction thus becomes another example of a Z-substituted dienophile.791
Ph
Ph
O
H
O
H
+
O
O
H
O
6.226
H
O
O
H
2
O
O
3
2
H
O
O
3
H
O
6.228
6.227
An unfortunate consequence of this regiochemistry was a set-back to a steroid synthesis. 2,6-Xyloquinone
6.230 reacted with the diene 6.229 to give the adduct 6.231, and not the adduct which would have been useful
for a steroid synthesis. The polarisation of the LUMO of citraconic anhydride deduced using the same
arguments as for citraconic anhydride, and the HOMO of a 1-substituted diene, explain the observed
regioselectivity. Evidently the 2-aryl substituent has not changed the relative sizes of the coefficients,
although it might have been expected to boost the coefficient at C-2. Substituents at C-2 are usually less
effective in polarising a frontier orbital than those at C-1. For a sequel to this set-back, see p. 319.
O
O
H
HOMO
+
2
H
1
LUMO O
MeO
O
MeO
6.229
6.230
6.231
Another special case, in which the unsymmetrical diene is part of a conjugated system which cannot easily be
placed in any of the categories, C-, Z- or X-substituted, is tropone 6.232 when it reacts as a diene. On account
of its symmetry, we have to work out the coefficients of the atomic orbitals by some other means than by the
simple arguments used above and in Chapter 2 (see pp. 70–76). The coefficients of the HOMO and LUMO
are shown in Fig. 6.33.241 The numbers for the HOMO are not easily guessed at, and we must be content, in
this more complicated situation, to accept the calculation which led to them.
0.653
HOMO
–0.187
–0.393
–0.093
0.326
O
0O
0
–0.521
LUMO
0.232
0.418
Fig. 6.33 The frontier orbital coefficients of tropone
310
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
With this pattern in mind, we can see that the regioselectivity shown when tropone reacts as a diene to give
the adduct 6.233 with styrene792 and the major adduct 6.234 with acrylonitrile793 is readily explained,
whichever pair of frontier orbitals we take in the second case.
LUMO
O
O
HOMO
6.232
O
Ph
Ph
6.233
O
O
LUMO
O
HOMO
HOMO
CN
6.232
6.234
LUMO
CN
CN
6.232
6.234
CN
6.5.2.3 The Regioselectivity of Hetero Diels-Alder Reactions. In a few cases, carbonyl, nitrosyl, cyano, and
a few other double bonds with one or more electronegative heteroatoms have acted as dienophiles in Diels-Alder
reactions.794 The carbonyl group has the HOMO and LUMO shown in Fig. 1.66 (see p. 58). The energies of both
orbitals are relatively low, and most of their Diels-Alder reactions will therefore be guided by the interaction
between the HOMO of the diene and the LUMO of the carbonyl or similar compound. The examples with
formaldehyde 6.235, the dithienium ion 6.236 and p-chloronitrosobenzene 6.237 illustrate that this works.795
O
+
H
O
S
+
H
S
S
6.235
S
6.236
R
+
R = Ph,
CO2Me or OAc
O
O
N
N
Cl
+
H
Cl
O
6.190
CHO
6.190
O
CHO
6.238
6.237
There are also Diels-Alder reactions in which the heteroatom is part of the diene system.796 The most notable
of these is the dimerisation of acrolein 6.190 giving the adduct 6.238.797 This reaction had been a longstanding puzzle. As in the reaction of butadienecarboxylic acid 6.208 with acrylic acid 6.209 (see p. 304), the
‘electrophilic’ carbon atoms, labelled , are the ones which have become bonded.
The first calculations of the frontier orbitals for acrolein gave the larger HOMO coefficient to the carbon
of the C¼C double bond of acrolein. This failed to explain the regiochemistry, but only because the simple
Hückel theory that was used is notoriously weak in dealing with electron distribution in heteroatom-containing
systems. Later calculations798,799 gave a better set of coefficients, one of which375 is shown in Fig. 6.34.
6 THERMAL PERICYCLIC REACTIONS
311
0.59
0.58
0.58
0.38
2.5
–0.48
0.48
O
0.51
LUMO
–14.5
–14.5
–0.30
CHO
0.59
0.48
O
2.5
–0.38
CHO
–0.58
HOMO
H O MO
LUMO
Frontier orbital energies and coefficients for acrolein
Fig. 6.34
Both LUMO(diene)/HOMO(dienophile) and HOMO(diene)/LUMO(dienophile) interactions have to be considered, because both energy separations are the same for dimerisations. The former interaction is
directly appropriate for the formation of the observed product, as shown on the left of Fig. 6.34,
but the latter interaction, as shown on the right, has no obvious polarisation in the diene—the C and
O atoms have accidentally identical coefficients. However, the resonance integral, , for the formation of a C—O bond is smaller than the resonance integral for the formation of a C—C bond. (This is
only true when the atoms are more than 1.75 Å apart, but no one has suggested that the transition
structure is likely to have a shorter distance than this, though several people have used longer
distances.) Thus the (c)2 term of Equation 3.13 is smaller at oxygen than at carbon in this orbital,
and consequently this interaction also explains the regioselectivity. The regioselectivity in this
reaction is delicately balanced,800 but it also matches several cycloadditions between ,-unsaturated
aldehydes, ketones and imines with C-, Z- and X-substituents on the dienophile, although some of the
reactions may be stepwise, and not pericyclic.801
6.5.2.4 The Stereoselectivity of Diels-Alder Reactions. One of the most challenging stereochemical
findings is Alder’s endo rule for Diels-Alder reactions. The favoured transition structure 6.239 has the
electron-withdrawing substituents in the more hindered environment, under the diene unit, giving the
kinetically more favourable but thermodynamically less favourable adduct 6.240. Long heating
eventually equilibrates this isomer with the thermodynamically favoured exo adduct 6.241, by a
retro-cycloaddition re-addition pathway. The endo rule is also obeyed by open-chain dienes like
diphenylbutadiene 6.242, which gives the adduct 6.243 with all the substituents cis on the cyclohexene ring as the major adduct (90:10).802 This too equilibrates on heating with the minor isomer 6.244
with the carboxylic acid substituent trans to the two phenyl substituents. Any reaction in which a
kinetic effect overrides the usual thermodynamic effect on reaction rates is immediately interesting,
and demands an explanation.
H
r.t.
O
H
O
H
O
6.239
6.240
6.241
Ph
Ph
r.t.
Ph
HO2C
O
O
H
O
O
H
H
O
O
Ph
HO2C
Ph
H
H
Ph
CO2H
CO2H
100°
H
Ph
6.242
190°
6.243
Ph
6.244
312
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
4
70°
O
S
Ph
MeN
24 h
O
6.245
S
N
Me
Ph
6.246
The usual explanation is based on the signs of the coefficients in the frontier orbitals—the HOMO of the
diene and the LUMO of the dienophile. As a model, we use 2 of butadiene for the former, and 3* of
acrolein as the latter. If we place these orbitals in the appropriate places for the endo reaction (Fig. 6.35a), we
see that there is the usual primary interaction (solid bold lines), with overlap of orbitals with matching signs,
consistent with the rules, but there is an additional bonding interaction (dashed line) between the lower lobe
of the p orbital on C-2 of the diene and the upper lobe on the carbonyl carbon of the dienophile, since they
have the same sign. This interaction, known as a secondary orbital interaction,803 does not lead to a bond, but
it might make a contribution to lowering the energy of this transition structure relative to that for the exo
reaction, where it must be absent. It is equally effective in explaining the endo selectivity of a reaction
showing inverse electron demand 6.245 ! 6.246,804 although there is some doubt whether this example is
actually pericyclic—it could so easily be stepwise. The frontier orbitals are now the LUMO of the diene and
the HOMO of the dienophile, for which the secondary interaction shown in Fig. 6.35b is again attractive,
because the lobes have the same sign.
HOMO
2
LUMO
1
4
O
O
S
Ph
H
LUMO
(a) HOMO(diene)/LUMO(dienophile)
Fig. 6.35
R2N
HOMO
(b) LUMO(diene)/HOMO(dienophile)
Secondary interactions and the endo rule for the Diels-Alder reaction
Secondary orbital interactions have also been invoked to explain regiochemistry as well as stereochemistry.
Whereas 1-substituted dienes sometimes have only a small difference between the coefficients on C-1 and
C-4 in the HOMO, they can have a relatively large difference between the coefficients on C-2 and C-3.
Noticing this pattern, Alston suggested that the regioselectivity in Diels-Alder reactions may be better
attributed, not to the primary interactions of the frontier orbitals on C-1 and C-4 that we have been using so
far, but to a secondary interaction with the orbital on C-2 (Fig. 6.36a) being stronger than the secondary
interaction with the smaller lobe on C-3 (Fig. 6.36b), even though it is not forming a bond.331,799
We can easily enough estimate the relative sizes of the coefficients on C-2 and C-3, using the same
analogies that we used to estimate the coefficients on C-1 and C-4. The presence of a larger (in absolute
magnitude) coefficient in the HOMO on C-2 than on C-3 for 1-C-substituted dienes is unambiguous:
hexatriene has coefficients of 0.418 and 0.232 on these atoms (Fig. 1.42). 1-X-Substituted dienes are
also unambiguous: the pentadienyl anion has coefficients in the HOMO of 0.576 and 0 on these atoms.
6 THERMAL PERICYCLIC REACTIONS
HOMO
313
C,X,Z
2
HOMO
3
C,X,Z
2
3
O
R
R
LUMO
LUMO
O
(a) Transition structure f or
f ormation of an 'ortho' adduct
Fig. 6.36
(b) Transition structure f or
f ormation of a 'meta' adduct
Secondary interactions as an influence on the regioselectivity of a Diels-Alder reaction
However, the crude way we have handled the problem does not immediately demonstrate this for 1-Zsubstituted dienes, which we need to explain the reaction of butadiene carboxylic acid 6.208 and acrylic acid
6.209: thus we can see in Fig. 6.37 that the contribution of the triene-like character and the pentadienyl
cation-like character have opposite effects on the coefficients on C-2 and C-3. However, the differences in
the coefficients on each component are noticeably large, and it is therefore easy to accept that C-2 and C-3
could have quite different coefficients if either contribution should dominate. Alston’s calculation gives the
values 0.384 and 0.314; it seems that, the triene-like character is more important than the pentadienyl
cation-like character, and the arrangement giving the ‘ortho’ adduct (Fig. 6.36a) has a larger secondary
interaction than that leading to the ‘meta’ adduct (Fig. 6.36b). As it happens, Alston’s calculation gives the
opposite polarisation to C-1 and C-4 (0.483 and 0.460) to the generic picture for a Z-substituent in Fig. 6.25
from Houk. Experimental support for this theory is the formation of the adducts 6.247 and 6.248 from
piperylene with fumaric acid, with the former the major,805 perhaps because it can benefit from secondary
overlap with the larger coefficient in the HOMO of the X-substituted diene on C-2. Similar results have been
reported for 1-acetoxybutadiene with dimethyl fumarate806 but see the diene 6.251 for a contrasting
observation.
CO2H
0.418
HOMO
–0.418
+
0.232
0
–0.384
=
HOMO
0.314
0.500
0.521
Fig. 6.37
–0.483
–0.500
0.500
0.460
Crude estimate of the coefficients on C-2 and C-3 of a l-Z-substituted diene
HO2C
CO2H
+
CO2H
+
CO2H
CO2H
6.247
75:25
CO2H
6.248
314
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
O
O
H
O
H
H
Me
H
O
6.249
Me
H
H
6.250
OMe
OMe
ClOC
+
OMe
COCl
+
COCl
COCl
COCl
COCl
6.251
6.252
28:72
6.253
Explanations for stereochemistry and regiochemistry based on secondary orbital interactions, like frontier
orbital theory itself, have not stood the test of higher levels of theoretical investigation.807 Calculations, low
level808 and high level,809,810 produce transition structures which have an endo preference, and a substantial
degree of asynchronicity, with the bond from C-4 of the diene to the carbon of the acrolein 0.3 Å shorter
than the bond from C-1 to the carbon. One consequence of this is that the atoms which would be involved in
any secondary overlap are too far apart, at about 2.8 Å, for their orbitals to have any significant overlap.811 A
few experimental observations also call secondary orbital interactions into question. Whereas acrolein
unexceptionally gives mainly (74:26) the adduct 6.249 with the formyl group endo, methacrolein gives
mainly (83:17) the adduct 6.250, in which the methyl group is endo rather than the formyl group.812
Furthermore, in contrast to the reaction of piperylene giving the adduct 6.247, 1-methoxycyclohexadiene
6.251 and fumaroyl chloride give more of the adduct 6.253 which, if secondary overlap were important,
would benefit from secondary overlap with the orbital with the smaller coefficient on C-3 than of the adduct
6.252 which would benefit from secondary overlap with the p orbital on C-2.813 1-Phenylbutadiene and 2methoxycyclohexadiene give 50:50 mixtures of adducts with fumarates, even though the frontier orbitals
have significantly different coefficients on C-2 and C-3, implying insignificant secondary orbital
effects.814,815 Also, there is a substantial solvent effect on endo:exo ratios, with the preference for the
endo adduct significantly increased in polar solvents,816 implying that electrostatic interactions are playing
some part.
H
HH (+) repulsion
O
H (+) repulsion
O
(+) H
6.254
O (–)
attraction
O
(+) H
6.255
(+)
6.256
One possibility for an electrostatic effect is a repulsion in the exo transition structure.807 Since H—C bonds
are polarised towards the carbon, hydrogen atoms carry a partial positive charge, and therefore the inhydrogens and the carbonyl carbon, which also carries a partial positive charge, will repel each other 6.254.
There will be even greater repulsion from the methylene group of cyclopentadiene 6.255 than from the inhydrogens of butadienes, which agrees with the greater propensity for forming the endo isomer with this
diene. There will be a similar Coulombic repulsion in the methacrolein reaction between the methyl group
and the methylene group of cyclopentadiene, and an attraction, a weak hydrogen bond, between the methyl
group and C-2. Working in the opposite direction—a Coulombic attraction favouring exo attack—the
oxygen atom of a furan, carrying a partial negative charge, will be attracted to the carbonyl group of
6 THERMAL PERICYCLIC REACTIONS
315
cyclopropenone 6.256, and an exo adduct is, unusually, kinetically as well as thermodynamically
favoured.817
The unusually high endo selectivity shown by vinylboranes has led to an alternative explanation. The
boron substituent with its empty p orbital is not part of a double bond, and so its effect on the frontier orbitals
will not be the same as that of a Z-substituent like a carbonyl group—a vinylborane is even more like an allyl
cation, with a more highly polarised LUMO than a Z-substituted alkene. This explains the high reactivity of
vinylboranes, but the highly polarised LUMO does not account for the low levels of regioselectivity. An
explanation for the endo selectivity is based on the calculated transition structure 6.257 for the endo reaction
of vinylborane with butadiene.818 It has C-1 of the diene closer to the boron atom than to C-10 of the
vinylborane, and with negligible overlap between the boron atom and C-2 of the diene, the normal atom
invoked for secondary interactions. This matches the LUMO coefficients (see p. 308): the coefficient on the
boron is larger than that on C-10 , and they have the same sign. The exo transition structure 6.258 still has
some bonding to the boron atom, but C-1 is now closer to C-10 than to the boron atom, and the energy is not as
low. In both cases, the reaction is concerted and asynchronous, with the leading bond from C-4 to C-20 , which
are the atoms in the starting materials with the larger coefficients in the HOMO and LUMO, respectively.
The transition structure is somewhere in between the usual transition structure for a [4 þ 2] Diels-Alder
reaction and the transition structure for a diene reacting with an allyl cation to give a cyclohept-4-enyl cation.
2.27Å
1 2.53Å
2.05Å
H
4
H
B
2'
6.257
2.45Å
1
2.06Å
2.67Å
4
H
1'
1'
2'
B
H
6.258
This explanation also accounts for the low electronic component to the regioselectivity. The LUMO
coefficients that are important are not just those at C-10 and C-20 , they must also include the coefficient at
the boron atom, since it is close to C-1 of the diene. Since the coefficients at the boron and at C-20 are
comparable, the regioselectivity is low. In detail, the calculations suggest that the transition structure for the
‘ortho’ adduct from piperylene and the unsubstituted vinylborane should be slightly lower in energy than that
for the ‘meta’ adduct, which would be in line with the frontier orbital predictions. They also suggest that the
two methyl groups in dimethylvinylborane introduce enough of a steric effect to reduce the regioselectivity
to zero, and, as we saw earlier, makes vinyl-9-BBN selective for the formation of the ‘meta’ adduct. The
frontier orbitals of a normal dienophile like acrolein, especially when it is coordinated to a Lewis acid, are
similar in magnitude and sign to those for a vinylborane. There ought therefore to be a strong attraction
between C-1 of the diene and the carbonyl carbon of a dienophile in the endo transition structure, just as there
is for the vinylborane, and maybe this is the explanation for the endo rule.
Yet another approach to explaining the endo rule draws attention to some of the details in a transition
structure calculated for the dimerisation of cyclopentadiene (Fig. 6.38).819 As usual this reaction is
kinetically in favour of the formation of the endo adduct 6.260, and thermodynamically in favour of the
exo adduct. Old bottles of the dimer usually contain more of the exo adduct, and so, if you want to use the
endo adduct for a synthesis, it is necessary first to crack the dimer, and then allow the monomer to dimerise.
The transition structure 6.259 calculated for the dimerisation shows a high degree of asymmetry in the
formation of the two bonds. The leading bond between C-1 and C-10 is 1.96 Å long, whereas the C—C bond
that is still to form between C-4 and C-20 is 2.90 Å. The interesting feature of the transition structure is that
the C—C distance between C-2 and C-40 is also 2.90 Å, and the reaction can continue in two equally probable
directions, one closing the bond from C-4 to C-20 and the other closing the bond from C-2 to C-40 . The
products 6.260 and 6.261, whichever of the two bonds develops, have the same structure. These products are
316
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
C-4—C-2'
2
3
4'
2.90Å
1
6.260
1.96Å
4
1.64Å
1'
2' 2.90Å
3'
6.259
6.262
C-2—C-4'
6.261
The transition structure for the dimerisation of cyclopentadiene
Fig. 6.38
also connected by a Cope rearrangement, but the transition structure for that reaction 6.262 is different,
having a full bond between C-1 and C-10 , and is slightly lower in energy than the transition structure 6.259 for
the Diels-Alder reaction. In another calculation, the bonding from C-1 to C-10 in the transition structure is
estimated to be half the strength of a full bond, and the bonds between C-2 and C-40 and between C-4 to C-20
are one-quarter as strong as the bond between C-1 and C-10 .820
That the two bonds in a cycloaddition may not form to the same extent is what we have been assuming in
matching the large coefficients with the large coefficients in unsymmetrical Diel-Alder reactions, and we
have called such reactions asynchronous. The idea was first suggested by Woodward and Katz821 when they
examined the rearrangement of the tricyclic diene 6.263 to its isomer the tricyclic diene 6.265, in both of
which the hydroxy substituents are stereochemical labels. This rearrangement might reasonably take place
by either of two pathways: retro-cycloaddition and readdition, or a single Cope rearrangement. They
observed that the diastereoisomeric alcohol 6.266 gave the diastereoisomeric product 6.268, which showed
that the retro-Diels-Alder pathway was not being followed, and that it must be a Cope rearrangment. This is
easier to see from the bold lines, which identify the 1,5-diene system undergoing the Cope rearrangement,
redrawn without moving the atoms in 6.264 and 6.267. At the time, the Cope rearrangement was barely
known, and they identified the transition structure for the rearrangement as that of an asynchronous DielsAlder reaction. We can now see that the transition structures for the asynchronous Diels-Alder reaction 6.259
and the Cope rearrangement 6.262 are subtly different, but this work was significant historically, because it
established the idea of concerted but asynchronous reactions.
HO
heat
OH
OH
6.263
6.264
6.265
OH
heat
HO
6.266
HO
6.267
6.268
6 THERMAL PERICYCLIC REACTIONS
317
Another way of looking at the bonds in the transition structure for the dimerisation of cyclopentadiene is to
see that they develop from the best frontier orbital overlap: the leading bond comes from overlap between the
large lobes on C-1 and C-10 in both the HOMO/LUMO interaction marked in bold in the drawing 6.269 and the
equally effective LUMO/HOMO interaction marked in bold in the drawing 6.270. The two partly formed bonds,
marked with dashed lines, come from overlap between a large lobe on C-4 and a small lobe on C-20 and between
a large lobe on C-40 and a small lobe on C-2,822 either of which can develop into the full bond of the product.
2
HOMO
1
LUMO
4
LUMO
4'
1'
HOMO
2'
6.269
6.270
The traditional secondary orbital interaction drawn in Fig. 6.35, first suggested by Woodward and Hoffmann,
and redrawn with the orientation and numbering we are using here as 6.271, is effectively between C-3 and C-30 .
Both of these atoms have small lobes in the frontier orbitals, whereas now, at least in this case with two identical
partners, the secondary orbital interaction between C-2 and C-40 , as in the drawing 6.272, uses one large and one
small lobe. This whole picture is dependent upon the dienophile being s-cis, which it must be in a cyclic diene. It
may not apply to open-chain dienophiles, where the energetic penalty of having an s-cis conformation in the
component acting as a dienophile may not lead it to be in the transition structure with the lowest energy.
2
3
secondary
overlap
primary
overlap
secondary
overlap
primary
overlap
4'
3'
6.271
6.272
With butadiene itself, the two lowest-energy transition structures are one similar to that in 6.259, and the
other leading to an exo adduct.823 The difference in energy is small and this is in agreement with experimental results showing that the endo selectivity with butadiene itself, only measurable when there are
deuterium substituents, is small.824 The reason for the lower degree of stabilisation for the endo transition
structure is probably that the ends of the diene are further apart in butadiene than in cyclopentadiene, and the
two diene fragments in the transition structure are both twisted a great deal more than in the drawing 6.259 to
try to overcome this problem.
One exceptional endo rule is found in the triazoline dione reaction on p. 285, which shows a strong
preference for the endo transition structure. This can be ascribed to the presence of the lone pairs on the
dienophile—it is known as the exo lone pair effect. A lone pair, if it were in the endo orientation, meets an
antibonding interaction with the diene orbitals, and is strongly repelled. Sadly, this has no synthetic
usefulness, since the two nitrogen atoms are not stereogenic centres, and the endo and exo transition
structures, although very different in energy, give the same product.
In conclusion, the standard textbook secondary orbital interaction depicted in Fig. 6.35 is not fully
accepted, yet it remains a simple and much cited explanation for many observations.825 It would be wise
to be cautious in using it, for there are several other possibilities.
318
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
6.5.2.5 The Effect of Lewis Acids on Diels-Alder Reactions. Diels-Alder reactions are, as we know, little
influenced by polar factors, such as changing the solvent from a nonpolar to a polar one, yet Lewis acids exert
a strong catalysing effect. Furthermore, Lewis-acid-catalysed Diels-Alder reactions are not only faster but
also more stereoselective and more regioselective than the uncatalysed reactions. For this reason, catalysed
reactions are of great synthetic importance. An early example was the use of cupric ion to catalyse the DielsAlder reaction of the 5-substituted cyclopentadiene 6.275 to make the 7-substituted intermediate 6.276 in
Corey’s prostaglandin synthesis. The rate constants k1 for the 1,5-hydrogen transfers, which interconvert the
cyclopentadienes 6.273–6.275, is unaffected by the Lewis acid, but the rate constant k2 for the Diels-Alder
reaction is increased considerably. In the absence of the Lewis acid, the other dienes, which have an extra Xsubstituent on the diene, are more reactive than the isomer 6.275.826
MeO
OMe
OMe
OMe
+
5
k1
6.273
6.274
7
k2
Cl
2+
CN Cu
Cl
6.275
CN
6.276
The effects of Lewis acids on regioselectivity is illustrated by the reaction of piperylene and methyl acrylate
giving mainly the ‘ortho’ adducts 6.277, as usual, but this preference was increased with Lewis acid
catalysis.827 Similarly, isoprene and 3-methylbut-3-ene-2-one gave the ‘para’ isomer 6.279 as the major
product in the synthesis of a natural product, but it could only with great difficulty be separated from the
unwanted ‘meta’ isomer. The synthesis of the ‘para’ isomer alone was achieved by adding stannic chloride to
the reaction mixture.828 Similarly, the effects of Lewis acids on stereoselectivity are illustrated by the
reaction of cyclopentadiene with methyl acrylate giving endo-6.280 as the major product, with the proportion of this isomer higher when aluminium chloride was present.829 A similar increase in endo selectivity was
seen in the reaction of piperylene giving the ‘ortho’ products 6.277. The unsymmetrical fumarate 6.281, with
a soft and hard site for coordination by the Lewis acid, has the hard site endo with the hard Lewis acid boron
trichloride, and the soft thiocarbonyl endo with the soft Lewis acid copper(II) triflate.830
CO2Me
CO2Me
+
+
SnCl4
+
CO2Me
6.277
without AlCl3
with AlCl3
O
6.278
O
90 : 10
98 : 2
MeO2C
+
CO2Me
+
CO2Me
endo-6.280
MeO2C
+
without AlCl3 at 0 °C
with AlCl3 at 0 °C
with AlCl3 at –80 °C
CSOMe
+
CSOMe
CO2Me
6.283
6.282:6.283
with BCl3
with Cu(OTf)2
CSOMe
6.282
endo:exo
88 : 12
96 : 4
99 : 1
exo-6.280
CO2Me
6.281
6.279
4 : 96
89:11
6 THERMAL PERICYCLIC REACTIONS
319
All the features of Lewis acid catalysis can be explained by the effect of the Lewis acid on the LUMO of
the dienophile.375,331,831 The Lewis acid forms a salt, which is the more active and selective dienophile. For
simplicity, protonated acrolein is used as a model dienophile for calculations instead of the Lewis salt. When
we were trying to estimate the energies and polarities of the frontier orbitals of acrolein itself (see p. 72), we
added to the orbitals of a simple diene a contribution from the allyl cation-like character of acrolein. The
effect of adding a proton to acrolein is to enhance its allyl cation-like character (see p. 187). For the frontier
orbitals of acrolein, we add a larger contribution from the allyl cation. The results are: (i) both HOMO and
LUMO are even lower in energy; (ii) the HOMO will have the opposite polarity at the C¼C double bond, the
contribution from the allyl cation now outweighing the contribution from butadiene-like character; and (iii)
the LUMO will have even greater polarisation, the -carbon carrying an orbital with an even larger
coefficient, and the -carbon carrying an orbital with an even smaller coefficient. The calculation we used
earlier in Section 4.5.2375 sets values on these energies and coefficients, repeated in Fig. 6.39. The lowering
in energy of the LUMO makes the ELUMO(dienophile)–EHOMO(diene) a smaller number and therefore increases
the rate. The increased polarisation of the LUMO of the C¼C double bond increases the regioselectivity.
Finally, the increased LUMO coefficient on the carbonyl carbon makes the secondary orbital interaction
(Fig. 6.35a) and the electrostatic repulsion 6.254 greater, accounting for the greater endo selectivity
whichever of those explanations we adopt for endo selectivity.
0.51
O
X
X
O
H
–0.48
HOMO
–0.70
–0.39
–0.09
0.59
0.60
LUMO 2.5 eV
Without acid catalysis
Fig. 6.39
0.37
H OMO
LUMO –7 eV
With acid catalysis
Frontier orbitals showing increased regioselectivity for acid-catalysed Diels-Alder reactions
We can conclude this section on Lewis acid catalysis with a striking example of its use in solving a problem
in steroid synthesis. We saw, on p. 309, how 2,6-xyloquinone 6.230 added to the diene 6.229 with
inappropriate regioselectivity for steroid synthesis. When boron trifluoride was added to the reaction
mixture, it formed a salt 6.284 at the more basic carbonyl group, the one conjugated to the two methyl
groups, which is also the less hindered. The result was that the polarisation of the LUMO of the C¼C double
bond was reversed, the major adduct was the isomer 6.285, appropriate for a steroid synthesis.832,833
O
O
+
H
H
O
MeO
6.229
6.284
BF3
O
MeO
6.285
6.5.2.6 The Site Selectivity of Diels-Alder Reactions. Site selectivity is another kind of regioselectivity, in which a reagent reacts at one site (or more) of a polyfunctional molecule when several sites are,
320
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
in principle, available. In cycloadditions, site selectivity usually involves a pair of sites; thus, butadiene
reacts faster with the quinone 6.286 at C-2 and C-3 than at C-5 and C-6,834 and Diels-Alder reactions of
anthracene 6.287 generally take place across the 9,10-positions rather than across the 1,4 or 3,9a.835
The familiar explanation for this example of site selectivity is that reaction at the 9,10-position creates two
isolated benzene rings, whereas reaction at the 1,4-position would create a naphthalene nucleus, which is a
less stable arrangement of two benzene rings. This explanation relies on the influence of product-like
character in the transition structure, but we may also note that the same product is accounted for by looking
at the frontier orbital coefficients of the starting materials: the largest coefficients in the HOMO of 6.287 are
at the 9,10-positions (see p. 174).
O
O
6
2
CN
5
3
CN
O
CN
CN
+
+
O
6.286
O
9
CN
CN
O
O
1
9a
O
+
O
O
3
10
O
80:20
4
O
6.287
In cycloadditions, the frontier orbital interactions are almost always between orbitals well separated in
energy, and consequently they are second order and follow the form of the third term of Equation 3.13. As
long as only the frontier orbitals are being considered, we can ignore the Er–Es term when assessing site
selectivity, because, for any particular pair of reagents, it is always the same, whichever way they combine.
Furthermore, as long as the atoms at the reaction sites in each component are the same (for instance, if they
are both carbon atoms in one reagent, and both carbon atoms or both oxygen atoms in the other) then we can,
as a first approximation, also ignore the 2 term. Thus all we have left is the Sc2 term. The dimerisation of
hexatriene, in which the dimer formed is 6.288 and not 6.289, will serve as an example.836
–0.418
–0.418
–0.232
+
0.521
HOMO
+
0.521
–0.418
0.418
0.521
LUMO
6.288
H O MO
LUMO
6.289
The former, which retains a conjugated diene system, is likely to be lower in energy than the latter, which has
lost all conjugation; the product 6.288 is therefore thermodynamically favoured. In this example, the frontier
orbitals also suggest that this will be the major product. Thus we have the coefficients for the HOMO and
LUMO from Fig. 1.42. The Sc2 term for the observed reaction is given by:
Sc2 ¼ (0.418 0.232)2 þ (0.521 0.521)2 ¼ 0.083
and for the reaction which is not observed by:
Sc2 ¼ (0.418 0.418)2 þ (0.521 0.418)2 ¼ 0.078
6 THERMAL PERICYCLIC REACTIONS
321
The former reaction is unsymmetrical, like many Diels-Alder reactions, and the transition structure will
also be unsymmetrical. This will make , which is distance-dependent, different for each of the C—C bonds
being formed, and will effectively increase the difference between the Sc2-values calculated above.
Asynchronicity involving initial overlap of the two largest lobes will also be enhanced by the stabilisation
of whatever radical character the transition structure has, and hence will augment the frontier-orbital
explanation for the site selectivity in several other conjugated systems.
For example, heptatriene 6.290 and 1-cyanobutadiene 6.294 react with maleic anhydride and isoprene
6.293 to give mainly the lower-energy adducts 6.291 and 6.295, respectively, rather than the alternatives
6.292 and 6.296.837 These reactions are similarly governed both by the formation of the thermodynamically
favoured products and by the initial overlap with the larger frontier orbital coefficient in each component
leading to the unsymmetrical transition structure.
O
O
O
O
+
O
+
O
O
O
O
6.290
6.291
CN
6.292
75:25
CN
CN
and not
+
6.293
6.294
6.295
6.296
Frontier orbital theory, however, comes into its own when we consider the dimerisation of 2-phenylbutadiene. In this case, the less stable dimer 6.297 is obtained.838 Furthermore, its formation involves attack at the
more crowded double bond, so that neither a product-stability, which would favour the conjugated product
6.298, nor a steric argument works. The frontier orbitals have the coefficients shown, and the major pathway
has the leading bond formed between the two larger coefficients (0.625) and a much higher Sc2-value
(0.178) than the minor pathway (0.103). Another example of the same kind of site selectivity can be found in
the dimerisation of 2-cyanobutadiene on p. 306, indicating that orbital control does have some importance in
site selectivity.
Ph
+
Ph
0.625
HOMO
–0.475
–0.337
0.625
LUMO
+
Ph
Ph
6.297
Ph
Ph
Ph
–0.475
–0.256
0.475
0.625
HOM O
LUMO
Ph
6.298
The formation of Thiele’s ester 6.302839 is a remarkable example of several of the kinds of selectivity that we
have been seeing in the last few sections, all of which can be explained by frontier orbital theory. The particular
pair of cyclopentadienes which do actually react together 6.301 and 6.300 are not the only ones present. As a
result of the rapid 1,5-sigmatropic hydrogen shifts (see p. 267), all three isomeric cyclopentadiene carboxylic
322
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
esters are present, and any combination of these is in principle possible. As each pair can combine in several
different ways there are, in fact, 72 possible Diels-Alder adducts.
The regioselectivity is a vinylogous version of the combination of a 2-Z-substituted diene with a Zsubstituted dienophile, for which the ‘para’ isomer is expected, and for which we had the earlier example of
2-cyanobutadiene on p. 306 without discussion. The HOMO and LUMO energies of the three isomeric
dienes will be close to the representative values used in Fig. 6.25, and these are repeated under the structures.
The isomer 6.299 ought to be the most reactive diene, because it has the highest-energy HOMO, but it is
known to be present only to a very small extent—evidently too low a concentration to be a noticeable source
of products. Leaving this isomer out of the account, the smallest energy separation is between the HOMO of
6.301 and the LUMO of 6.300. These isomers, therefore, will be the ones to combine, and they can react in
either of two main ways: 6.301 as the diene and 6.300 as the dienophile or 6.301 as the dienophile and 6.300
as the diene. The second of these suffers from steric hindrance, because two fully bonded carbon atoms
would have to be joined, always a difficult feat. This leaves the combination of 6.301 as the diene and 6.300
as the dienophile, the reaction actually observed. The endo selectivity is normal. Now, knowing about the
site selectivity of the reaction with 1-cyanobutadiene 6.294, we finally see that the terminal double bond of
6.300 will be the double bond to react.
CO2Me
MeO2C
MeO2C
6.299
1.0
LUMO
MeO2C
6.300
–0.5
MeO2C
6.301
–0.3
9.2
–9.1
HOMO
–9.5
–9.3
6.300
6.302
CO2Me
–0.5
8.8
–9.5
There is a further addition to this argument, because 2-Z-substituted dienes in general are unusually reactive
as dienes, in spite of their having low-energy HOMOs.840 It may be that the isomer 6.301 is actually a more
reactive diene than the isomer 6.299. One explanation is that the asymmetry in the transition structure,
especially pronounced in cyclopentadiene dimerisations (Fig. 6.38), puts a premium on the initial bonding
between the two large coefficients, marked with a heavier dashed line between 6.301 and 6.300. As a result,
the transition structure like that in Fig. 6.38 has radical character in the incompletely bonded fragments,
which a Z-substituent can stabilise, an explanation moving towards the position adopted by those in favour of
an explanation based on diradical intermediates without actually losing concertedness in the bond forming
processes. Another way of looking at this phenomenon is based on the perception in Fig. 6.23: the
importance of the HOMO(dienophile)/LUMO(diene) interaction in advancing the bonding between C-2 and C3 in the diene component of the transition structure may make a Z-substituent on C-2 of the diene as good as
having a 2-X-substituent.753 Further evidence that a Z-substituent at C-2 is rate-accelerating is found in the
reactions of dienes with a boron substituent in this position. They are unusually reactive in Diels-Alder
reactions in spite of boron, with its empty orbital, being a powerful Z-substituent.780
6.5.3 1,3-Dipolar Cycloadditions684
The range of possible 1,3-dipolar cycloadditions is large, as we saw with the generic dipole 6.37 and the
generic dipolarophile 6.38. We are not restricted to carbon atoms in the five atoms that form the ring; we can
6 THERMAL PERICYCLIC REACTIONS
323
have an allyl-like or allenyl-like conjugated system in the dipole, and a double or triple bond in the
dipolarophile. Fig. 6.40 shows the parent members of the most important 1,3-dipoles, and gives their names.
CH N CH2
nitr ile ylids
CH N NH
nitrile imines
CH N O
nitr ile oxides
CH2 N N
diazoalkanes
NH N N
azides
N N O
nitr ous oxide
H
H
H
N
CH2
CH2
azomethine ylids
N
CH2
NH
azomethine imines
N
CH2
O
nitrones
H
H
H
N
NH
NH
azimines
N
NH
O
azoxy compounds
N
O
O
nitr o compounds
O
CH2
CH2
carbonyl ylids
O
NH
CH2
carbonyl imines
O
O
CH2
car bonyl oxides
O
NH
NH
nitr osimines
O
O
NH
nitr osoxides
O
O
O
ozone
Fig. 6.40
The parent members of the most important 1,3-dipoles
6.5.3.1 The Rates of 1,3-Dipolar Cycloadditions. Some 1,3-dipoles, like diazomethane, have high-energy
HOMOs, and react faster with alkenes carrying electron-withdrawing substituents. In this context these
alkenes are called dipolarophiles, and they have low-energy LUMOs, just as they had when we called them
dienophiles. 1,3-Dipoles like diazomethane can be described as nucleophilic in character, and the frontier
orbital interactions resemble those of a normal Diels-Alder reaction. In support of this picture, the rates of the
cycloadditions of diazomethane with alkenes correlate well with estimates of the difference in energy of the
HOMO of diazomethane and the LUMOs of the dipolarophiles.841 Other 1,3-dipoles, like azomethine
imines, have low-energy LUMOs, and react faster with dipolarophiles carrying electron-donating substituents, which have high-energy HOMOs. They can be described as electrophilic in character, and their
frontier orbital interactions resemble those of a Diels-Alder reaction with inverse electron demand.
Attaching electron-donating or electron-withdrawing substituents to a dipole can change this pattern. For
example, a diazoketone is an electrophilic dipole, reacting faster with X-substituted alkenes instead of with
Z-substituted alkenes. Putting an acyl group, a Z-substituent, onto the diazoalkane lowers the energy of the
LUMO in the usual way, changing the balance of frontier orbital interactions.842
A few dipoles, like phenyl azide 6.303, are neither particularly nucleophilic nor particularly electrophilic.
Like tetracyclone 6.200 in its Diels-Alder reactions with styrenes, phenyl azide reacts more slowly with
simple alkenes than with alkenes having either an electron-withdrawing group or an electron-donating
group. Sustmann843 has plotted the rate constants for this reaction against the energy of the HOMO of a wide
variety of alkenes, and obtained a U-shaped curve (Fig. 6.41), showing that orbital energies are key factors in
determining rates. An upwardly curved plot like this is characteristic of a change of mechanism (as distinct
from a change of rate-determining step). The change of mechanism in this case is the change from a
dominant HOMO(dipole)-LUMO(dipolarophile) interaction on the left, where we assume, reasonably enough,
324
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
N
N
Ph
CO2Me
N
N
+
N
N
Ph
N
6.303
log k
CO2Me
E HOMO of the dipolarophile
Fig. 6.41
Correlation between the energy of the HOMO of a range of dipolarophiles and the rates of their reaction with
phenyl azide
that a low-energy HOMO implies a low-energy LUMO, to a dominant LUMO(dipole)-HOMO(dipolarophile)
interaction on the right.
C-, Z- and X-Substituents will affect the energies of the molecular orbitals of both dipoles and dipolarophiles in the same way that they affect the orbitals of dienes and dienophiles, but it is not possible to
estimate the energies of the frontier orbitals of the parent dipoles in the crude but easy way that it was
possible for dienes. To begin with, there are so many kinds of dipole. Even if we restrict ourselves to the
elements carbon, nitrogen and oxygen, we still have many possible types of unsymmetrical dipole (Fig.
6.40), and with very few of them can we find simple arguments from which to deduce the relative energies of
the frontier orbitals. Fortunately, Houk has calculated representative energies for the HOMOs and LUMOs
of a wide range of dipoles, with and without C-, Z- and X-substituents. They are presented in Table. 6.2,
together with Houk’s calculations of ‘coefficients’ needed for the discussion of regioselectivity in the next
section.844,845
We can see that diazoalkanes have a high-energy HOMO, and that azomethine imines have a low-energy
LUMO, matching the assertions above. Also, phenyl azide has neither a particularly high-energy HOMO nor
a particularly low-energy LUMO, explaining the pattern of its reactivity with alkenes seen in Fig. 6.41. The
data in the two columns labelled HOMO refer to the 4-electron p orbital taking part in the reaction, and not to
any nonbonding lone pairs that might in some cases be higher in energy. Likewise the important unoccupied
orbital for cycloadditions is not, in a number of cases, strictly the lowest in energy of the unoccupied orbitals,
which in several cases is an orbital at right angles to the reaction plane. The data in the two columns labelled
LUMO therefore refer to the lowest of the unoccupied orbitals which is in the reaction plane, and therefore
capable of participating in a 1,3-dipolar cycloaddition.
6.5.3.2 The Regioselectivity of 1,3-Dipolar Cycloadditions. Regiochemistry in a 1,3-dipolar cycloaddition can be illustrated by the reaction of diazomethane 6.304 with methyl acrylate, in which the first-formed
intermediate 6.305 undergoes tautomerism to give the better conjugated product 6.306.846 There is no
guessing the regiochemistry by just looking at the reagents. If we draw the resonance structures 6.304a and
6.304b, they show that both the C and the N termini are simultaneously nucleophilic and electrophilic, as the
6 THERMAL PERICYCLIC REACTIONS
Table 6.2
Dipole
325
Energies and ‘coefficients’ of 1,3-dipoles
HOMO
(c )2/15
Energy (eV)
–7.7
Nitrile ylids
CH
N
1.07
PhC
N
CH2
N
NH
CH
N
–11.0
PhC
–10.0
N
O
–9.0
CH
N
–11.5
N
N
Nitrous oxide
CH2
N
–6.9
Ar
RO2CCH
N
HN
N
Azomethine imines
PhCH
CH2
N
N
NPh
NCOR
Nitrones
–5.6
–9.7
PhCH
H
N
Ar(NC)C
O
(NC)2C
CH
N
1.18
O
0.17
1.8
CH2
N
0.66
0.1
N
0.56
HN
N
0.37
N
0.76
N
N
CH2
O
–1.1
1.33
H
N
CH2
N
N
0.96
1.4
1.28
CH2
O
0.19
H
N
0.73
CH2
0.73
–0.6
CH2
H
N
1.15
NH
1.24
–0.3
–1.4
CH2
H
N
0.87
NH
0.49
–0.4
CH2
H
N
O
–0.5
1.06
CH2
H
N
0.98
–8.7
0.3
–8.0
–0.4
O
0.32
O
–7.1
O
CH2
1.29
CH2
0.4
1.29
–6.5
–0.6
C(CN)2
–9.0
–1.1
–8.6
O
CH2
1.04
Carbonyl oxides
–10.3
–13.5
–0.2
1.34
O
CH2
0.82
NH
O
O
CH2
0.82
C(CN)Ar
Carbonyl imines
Ozone
NH
0.36
O
Carbonyl ylids
O
N
–0.2
1.11
N
N
–9.0
R
CH2
N
–7.7
–8.6
–0.5
0.72
1.28
CHCO2R
CH
0.92
0.85
0.67
Azomethine ylids
O
–9.5
–12.9
CH2
0.64
–1.0
1.55
PhN
0.1
1.24
1.57
Azides
N
–0.5
0.81
Diazoalkanes
NH
1.45
–7.5
Nitrile oxides
CH
0.69
0.6
0.90
PhC
0.9
1.50
–6.4
–9.2
Nitrile imines
CH2
LUMO
(c )2/15
Energy (eV)
O
CH2
1.06
–0.9
1.25
–2.2
NH
0.49
O
CH2
1.30
CH2
0.82
O
0.24
326
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
arrows show. It is an ambident reagent. If we were to think only of the total charge distribution, we might
guess that the electronegative end of the dipole, the nitrogen, will have more negative charge than the carbon
atom. However, as an ambident nucleophile, diazoalkanes are known to react with electrophiles like
carbonyl groups at the carbon end. Neither of these considerations offers a safe way of predicting the
regioselectivity of a cycloaddition. Until Houk introduced frontier orbital theory to explain the regioselectivity of 1,3-dipolar cycloadditions, they remained an outstanding mystery.847 Both sets of arrows 6.304a
and 6.304b are reasonable, both describe what happens, but they do not reveal which atom, C or N, will bond
to the electrophilic carbon of the dipolarophile.
N
6.304a
CO2Me
N
CO2Me
N
N
N
6.304b
–H+
+H+
N
CO2Me
HN
CO2Me
6.305
N
6.306
Turning to the frontier orbitals, we already have a picture of the polarisation of the dipolarophile: it is the
same as a dienophile with a Z-substituent, as shown in Fig. 6.25. What we need is a corresponding picture for
the dipole, and this is not easy to estimate, any more than it was easy to estimate the energies of the parent
dipoles. Furthermore, in most cases, the bonds being made are no longer always C—C bonds, as they are in
the common Diels-Alder reactions. Just as with heterodienes and heterodienophiles, we must include an
estimate of the appropriate resonance integral, , as well as the coefficients of the atomic orbitals, c.
Fortunately, all this work has been done for us by Houk, and we shall take his figures in Table 6.2 on
trust.844 Instead of straightforward coefficients for the atomic orbitals, as we had for dienes and dienophiles,
he has calculated (c)2 values in their place, and divided them by 15 to bring the numbers close to 1. They are
calculated assuming that the new bonds are being made to carbon atoms in the dipolarophile from the carbon,
nitrogen or oxygen atoms of the dipole. They would need to be changed if the bond forming is between two
heteroatoms. Because contains S, the overlap integral, it is a distance-dependent function, which is also
dependent upon whether the element is C, N or O, as we saw in Section 1.7.2 (see p. 54). The values chosen
by Houk involve a guess about the distance apart of the atoms in the transition structure. Table 6.3 gives some
values for for the different combinations of C, N and O, where we can see that the choice of distance is
critical: Houk used a representative distance of 1.75 Å on the basis that cycloaddition reactions show large
negative activation volumes and sizeable steric effects. If more detail were needed, the (c)2 values would
Table 6.3 -Values (in eV) as a function of distance (in Å) calculated for overlap between all combinations of 2p
orbitals of C, N and O
Å
CC
CN
CO
NN
NO
OO
1.50
1.75
2.00
2.50
3.00
6.97
6.22
5.00
2.63
1.20
7.20
5.83
4.35
2.14
0.78
7.05
5.38
3.77
1.53
0.55
7.18
5.35
3.65
1.40
0.45
6.92
4.81
3.02
1.04
0.28
6.63
4.19
2.45
0.68
0.17
6 THERMAL PERICYCLIC REACTIONS
327
have to be adjusted to take account of unsymmetrical transition structures, but such detail is inappropriate for
the general discussion we need here.
To account for the regioselectivity of 1,3-dipolar cycloadditions, we must first assess whether the reaction
that we are looking at has a smaller separation between the HOMO of the dipole and the LUMO of the
dipolarophile or between the LUMO of the dipole and the HOMO of the dipolarophile. The former is called
dipole-HO controlled and the latter dipole-LU controlled. We can do this simply by taking the energies of the
dipoles in Table 6.2, and the energies of the representative dipolarophiles in Fig. 6.25, and transferring them
to a diagram like that in Fig. 6.42. Here we see that diazomethane has frontier orbital energies with the
smallest separation in energy of all of the possible frontier orbital interactions (the double-headed arrows) for
the reaction between diazomethane and a Z-substituted alkene, for which ELUMO(dipolarophile)–EHOMO(dipole) is
9 eV. Reactions of diazomethane with electron-deficient alkenes are the fastest and most often encountered
of the cycloaddition reactions of diazoalkanes, and we can now see that the strong frontier orbital term for
this particular combination accounts for the chemoselectivity. This reaction is therefore dipole-HO-controlled, and we can now look at the ‘coefficients’.
X
3
0.56
LUMO
N
1.8
N
1
C
LUMO
0.66
0
10.8
10
Z
12
12.7
9
9.8
X
–8
0.85
HOMO
N
–9
–9
C
HOMO
N
1.57
–10.9
Fig. 6.42
Z
Frontier orbitals for diazomethane and representative dipolarophiles
In this case they will be the (c)2 values for the HOMO of the dipole from Table 6.2 and the coefficients of
the LUMO of the dipolarophile from Fig. 6.25. Regioselectivity should follow in the usual way from the
large-large/small-small interaction 6.307, which we can see has the carbon end of the dipole bonding to the carbon of the Z-substituted alkene, as observed, and used as an example at the beginning of this book in
posing the problem of how we should explain such selectivity.
0.85
CO2Me
N
N
HOMO
LUMO
N
CO2Me
N
N
CO2Me
HN
1.57
6.307
6.305
6.306
328
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
The reactions of diazomethane with C- and X-substituted alkenes are much slower, and consequently there are
fewer known examples. The slower rate of reaction is explained easily by the larger energy separation in the frontier
orbitals (10 and 9.8 eV, respectively, in Fig. 6.42). The regioselectivity, however, is the same: Dl-pyrazolines like
6.309 and 6.311 with the substituent at C-3 are obtained with both C- and X-substituted dipolarophiles.848 This at
first sight surprising observation can be explained by the change from dipole-HO control in the cases of the Z- and
C-substituted alkenes 6.307 and 6.308 (supported, incidentally, by the positive Hammett -value for the latter) to
dipole-LU control 6.310 in the case of the X-substituted alkene ethyl vinyl ether.849
R
0.85
R
N
N
0.56
3
N
N
OEt
N
N
OEt
N
N
1.57
3
0.66
LUMO
HOMO
HOMO
6.309
6.311
LUMO
6.308
6.310
In general, substituents present on a dipole will modify the energies and coefficients shown for the
unsubstituted cases in Table 6.2, but it should be an easy matter, at least qualitatively, to predict how
these substituents will affect the energies and (c)2/15 values, which we shall call ‘coefficients’, by taking
advantage of our qualitative understanding of the effects of C-, Z- and X-substituents on alkenes. Table 6.2
shows the effect of a few of the commonly found substituents on the energy of the frontier orbitals—phenyl
groups do indeed raise the HOMO and lower the LUMO energy, and ester and cyano groups lower both the
HOMO and the LUMO energy.
The effect of substituents on the diazoalkane can be accounted for using such reasoning. X-Substituents raise
both the HOMO and the LUMO energies, and will speed up reactions with Z-substituted alkenes. In agreement,
alkyl diazomethanes are more reactive than diazomethane in cycloadditions.850 Z-Substituents, which lower both
the HOMO and the LUMO energies of the dipole, speed up the normally slow reactions with X-substituted
alkenes like enamines. Furthermore, with a Z-substituent on the carbon atom of the diazomethane, the coefficient
on the carbon atom will be reduced in the LUMO, just as it is in the LUMO of an alkene with a Z-substituent.
Since the (c)2/15 terms for the LUMO of diazomethane are rather similar 6.312, the Z-substituent is enough to
polarise them decisively in the opposite sense 6.313. This reaction is now dipole-LU-controlled, and the
regioselectivity changes to that shown in the pyrazole 6.314, where the methyl substituent has served as a
marker to show that the nitrogen end of the dipole has bonded to C-2 of the enamine.851
0.56
N
N
N
N
N
N
0.66
LUMO
6.312
Z
LUMO
X
HOMO
6.313
H
N
2
+
N
N
EtO2C
EtO2C
6.314
The following discussion is limited to a few other dipoles, in order to illustrate some of the less straightforward cases. The balance of factors leading to a particular chemo- and regioselectivity is often close—the
choice of which pair of frontier orbitals to take is sometimes difficult, the fact that some frontier orbitals are
not strongly polarised forces us to judge each case carefully on its merits, and the outcome is not quite always
in agreement with the experimental results. There is more discussion of these and all the other cases in
Houk’s papers.843
6 THERMAL PERICYCLIC REACTIONS
329
X
3
0.76
1
N
0.1
N
N
C
Z
0
–0.2
12.5
N
0.37
H N
Ph
LUMO
N
8.8
10.7
10.5
9.5
7.8
X
–8
N
N
C
HOMO
N
N
0.72
–9
–9.5
–11.5 Ph
Z
–10.9
N
1.55
H N
Fig. 6.43
Frontier orbitals for phenyl azide and representative dipolarophiles
Let us look at azides so popular in ‘click’ chemistry,852,853 although that chemistry largely uses a coppercatalysed version of azide cycloadditions,854 and not the simple thermal 1,3-dipolar cycloadditions discussed
here. The parent hydrazoic acid is not the usual dipole of this class; a frequently used one is phenyl azide. The
phenyl group is a C-substituent, which will raise the energy of the HOMO and lower that of the LUMO. We
can see from Table 6.2 that in the HOMO of hydrazoic acid the nitrogen carrying the substituent (H in
hydrazoic acid, Ph in phenyl azide) has the larger coefficient, and that in the LUMO of hydrazoic acid it has a
smaller value. The consequence of this is that the phenyl group is more effective in raising the energy of the
HOMO than in lowering the energy of the LUMO. The result, taking the values from Table 6.2, is shown in
Fig. 6.43. The smallest energy separation (7.8 eV) is with X-substituted dipolarophiles, which implies that
they will be dipole-LU-controlled reactions. The orientation should therefore be that shown as 6.315. The
reactions with C- and X-substituted alkenes 6.316 and 6.318 should be, and are, fast. Orientation like this has
often been observed, as in the formation of the triazolines 6.317 and 6.319 with the C- and X-substituent at
the 5-position.855,856
N
N
C,X
N
Ph
HOMO
LUMO
6.315
N
N
N
Ar
N
N
+
Ph
N
N
Ph
Ph
Ph
6.316
N
N
5
6.317
N
N
+
O
5
N
Ar
6.318
6.319
O
330
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
However, when the dipolarophile is phenylacetylene 6.320 instead of styrene 6.316, the regioselectivity is
sharply reduced, and nearly equal amounts of the 1,5-diphenyltriazole 6.321 and the 1,4-diphenyltriazole
6.322 are obtained.857 This puzzling observation can be explained, by the frontier orbitals. The second p
bond of an acetylene is stronger than the first, because it is made between two atoms held close together by
the first p bond. The overlap of the p orbitals on carbon is therefore stronger, and an acetylene has a lowerenergy HOMO than ethylene.
N
Ph
N
N
N
N
+
5
N
N
Ph
+
Ph
Ph
6.320
6.321
55:45
N
Ph
4
N
Ph
6.322
This argument is supported by photoelectron spectroscopy, where the HO level is generally found to be 0.4 to 0.9
eV lower than that of the corresponding alkene. We can also relate this observation to the familiar notion that
alkynes are less reactive towards electrophiles like bromine than are the corresponding alkenes. Curiously, the
LUMO is not raised for alkynes relative to alkenes. This is shown by UV spectroscopy, where phenylacetylene
(lmax 245 nm) and styrene (lmax 248 nm) would appear to have rather similar separations of their HOMOs and
LUMOs. Thus, with a LUMO also lowered in energy, it is not unexpected to find that acetylenes with
Z-substituents are more reactive towards nucleophiles than are the corresponding alkenes. The effect of going
from styrene to phenylacetylene is therefore to lower both the HOMO and the LUMO by about, say, 0.5 eV.
This makes what was clearly a dipole-LU-controlled reaction into one which is affected by both interactions
(Fig. 6.44). Since dipole-HO control leads to the opposite regioselectivity, it is not so surprising that both
orientations are now observed. The poor regioselectivity in the reaction of azides with terminal acetylenes is
overcome in the copper-catalysed version, which gives cycloaddition exclusively in the sense 6.322.
1
N
C
C
0.5
–0.2
N
Ph
N
N
8.8
10.5
–9
–9.5
9.3
10.0
C
C
(–9.5)
N
Ph
Fig. 6.44
N
Frontier orbitals for phenyl azide, styrene and phenylacetylene
With Z-substituted dipolarophiles and phenyl azide, the situation is again delicately balanced and only just
dipole-HO-controlled (9.5 eV against 10.7 eV from Fig. 6.43). For the dipole-HO-controlled reaction, we
should expect to get adducts oriented as in Fig. 6.45a. However, a phenyl group reduces the coefficient at the
neighbouring atom both for the HOMO and for the LUMO, and this will reduce the polarisation of the
6 THERMAL PERICYCLIC REACTIONS
331
Z
N
N
N
Ph
N
N
HOMO
LUMO
LUMO
Z
N
Ph
HOMO
ELUMO – E HOMO = 9.5 eV
E LUMO – E HOMO = 10.7 eV
(a) Dipole-HO-controlled regiochemistry
(b) Dipole-LU-controlled regiochemistry
Fig. 6.45 Regioselectivity for phenyl azide reacting with a Z-substituted alkene
HOMO. Conversely, it will increase the polarisation for the LUMO and hence increase the effectiveness of
the interaction of the LUMO of the dipole with the HOMO of the dipolarophile, as in Fig. 6.45b. The
difference in energy for the two cases is small enough that firm prediction is not possible. In practice, dipoleHO control appears to be dominant, as shown by the formation of the adduct 6.323 from methyl acrylate, but
it only needs the addition of an -methyl group, for some dipole-LU control to become evident in the
formation of some of the adduct 6.324 from methyl methacrylate, in addition to the aziridine 6.326 derived
from the normal regioisomer 6.325.858 Perhaps the methyl group has raised the energy of both the HOMO
and the LUMO of the dipolarophile, making the HOMO/LUMO separations still more nearly equal.
CO2Me
N
+
N
Ph
CO2Me
N
N
N
N
Ph
6.323
N
N
Ph
N
N
N
CO2Me
+
N
N
CO2Me
+
N
CO2Me
CO2Me
Ph
N
N
Ph
Ph
6.324
25:75
6.325
6.326
Turning now to azomethine imines, the commonly used reagents have at each end aryl groups, which
raise the energies of the HOMOs and lower the energies of the LUMOs relative to the unsubstituted
system. Because the ‘coefficients’ at the terminal atoms of the dipole are smaller in the LUMO than
they are in the HOMO, the phenyl groups do not lower the energy of the LUMO as much as they
raise the energy of the HOMO. These effects on the energy are included in Table 6.2, and are
reproduced in Fig. 6.46.
With simple conjugated dipolarophiles like styrene, the reaction is only just dipole-HO-controlled
(6.6 and 7.6 eV), and mixtures can be expected. Styrene does, in fact, give both regioisomers 6.328
and 6.329 in not very different amounts, but with the major product that corresponding to dipole-HO
control.684 With an acetylenic dipolarophile, phenylacetylene, the lowering of the energy of the
HOMO of an acetylene relative to that of the corresponding alkene should make the reaction more
predominantly dipole-HO-controlled. The experimental observation is, in fact, the opposite of what
we would expect: phenylacetylene with the same azomethine imine 6.327 gives only the adduct
332
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
X
3
H
0.49
N
N
–0.3
N
C
Z
0
–1.4
LUMO
N
H
0.87
1
Ph
H
H
Ph
6.6
Ph
N
H
1.24
N
5.6
9.5
8.6
–5.6
–8.6
H
X
–9
HOMO
C
Ph
H
6.6
–8
N
N
1.15
7.6
Z
–10.9
H
Frontier orbitals for azomethine imines and representative dipolarophiles
Fig. 6.46
6.330.684 The dipole-HO has very similar ‘coefficients’ on nitrogen and carbon, and other factors,
such as steric and dipole repulsions, are more likely to make themselves felt.
Ph
+
N
N
N
N
Ph
Ph
N
dipole-LU-control
6.328
6.327
Ph
N
6.330
N
36:62
dipole-HO-control
6.329
N
Ph
However, with Z-substituted dipolarophiles, the reaction ought to be even more decisively dipoleHO-controlled, and the regioselectivity observed is easily and correctly accounted for: the reaction
with acrylonitrile gives only the adduct 6.331.684 Placing an acyl group on the nitrogen end of the
dipole 6.332 lowers the energy of both the HOMO and the LUMO relative to the unsubstituted
azomethine imine (to 9 and 0.4 eV). Reaction with conjugated alkenes like styrene will now
change to dipole-LU control (8.6 eV as against 10 eV). The LUMO has a large difference between
the (c)2 terms, which will be enhanced by the acyl substituent, explaining the regioselectivity in the
formation of the adduct 6.333 actually observed.859
6 THERMAL PERICYCLIC REACTIONS
N
HOMO
333
N
N
LUMO
N
NC
6.331
NC
O
N
O
Ph
N
LUMO
N
HOMO
Ph
N
Ph
Ph
6.332
6.333
Placing an acyl group on the carbon atom end of the dipole also lowers the energy of the LUMO and leads to
dipole-LU control 6.334, but this time the acyl group will reduce the difference between the coefficients. An
overwhelming preference for one orientation is not to be expected, but all three kinds of dipolarophile should
give adducts of the type 6.335.
O
LUMO
O
N
N
N
N
HOMO
X,Z,C
X,Z,C
6.334
6.335
This is exactly what has been observed for the cycloaddition reactions of sydnones 6.336 with all three kinds
of dipolarophile. An intermediate is produced in the first instance with the general structure 6.337; this loses
carbon dioxide in a retro 1,3-dipolar cycloaddition, followed by tautomerism giving the 3-substituted
pyrazolines 6.338 as the major products.860
Ph
Ph
Ph
N
R
–CO2
O
R = Me, CN or Ph
N
N
O N
N
6.337
6.336
6.338
Ph
MeO2C
N
N
R
O
O
–H
+H+
R
R
N
Ph
+
Ph
N
N
N
+
N
–CO2
MeO2C
CO2Me
6.339
76:24
6.340
334
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
X
3
0.17
O
1
C
Z
0
–0.5
N
1.18
LUMO
C
8.5
H
12
10.4
11
7.5
14
–9
1.24
0.81
C
O
N
X
–8
Z
–10.9
–11
HOMO
C
H
Fig. 6.47
Frontier orbitals for a nitrile oxide and representative dipolarophiles
In the reaction of the same sydnone with an acetylenic dipolarophile, slightly more dipole-HO control can be
expected, and this has been observed. Propiolic ester still gives mainly the 3-substituted pyrazole 6.339, but
also a substantial amount of the 4-substituted pyrazole 6.340.861
Two dipoles especially important in organic synthesis are nitrile oxides and nitrones. In both cases
cycloaddition to an alkene makes a C—C bond, and the N—O bond in the product can be easily cleaved by
reduction to establish heteroatom functionality with a 1,3-relationship. The frontier orbital picture for a simple
nitrile oxide is shown in Fig. 6.47, where we can see that the easy reactions ought to be decisively dipole-LUcontrolled, and fast with C- and X-substituted alkenes. This matches well with the reactions of benzonitrile
oxide with styrene, terminal alkenes, enol ethers and enamines which all give only the 5-substituted
isoxazolines 6.341. In the reactions with Z-substituted alkenes, however, the frontier orbitals are not strongly
in favour of either of the pairings, and the polarisation gives opposite predictions, with dipole-LU control
marginally in favour of the isoxazoline 6.342 and dipole-HO control strongly in favour of the isoxazoline
6.343. In practice, the regiochemistry with Z-substituted alkenes is delicately balanced, and it may be that the
decisive factor is simply steric, since the two ends of the nitrile oxide are very different in their steric
demands.862 Methyl acrylate gives largely the isoxazoline 6.342 (R ¼ H), but when the -position has two
methyl groups, the regiochemistry is completely inverted in favour of the isoxazoline 6.343 (R ¼ Me).863
O
N
R
+
N
HOMO
Ph
LUMO
R
R
HOMO
R = Ph, alkyl, OEt
Ph
6.341
CO2Me
+
R
N
Ph
LUMO
O
5
O
CO2Me
O
N
O
R
N
+
R
Ph
R
6.342
Ph
HOMO
6.342:6.343
R
R
O
R
N
CO2Me
LUMO
Ph
6.343
CO2Me
R = H 96:4
R = Me 0:100
6 THERMAL PERICYCLIC REACTIONS
335
X
3
C
1
0.32
R
O
0.3
0.58
C
Z
0
N
LUMO
H
9.3
H
9.7
8.7
11.2
13.9
8.3
X
–8
1.15
R
O
–8.7
C
–9
HOMO
N
C
1.11
Z
–10.9
H
H
Fig. 6.48
Frontier orbitals for a nitrone and representative dipolarophiles
The frontier orbital picture for a simple nitrone is shown in Fig. 6.48, where we can see that the easy reactions
will be dipole-LU-controlled with X-substituted alkenes and dipole-HO-controlled with Z-substituted
alkenes. In practice, phenyl, alkoxy and methoxycarbonyl substituents speed up the cycloadditions. Any
substituent on the carbon atom of the dipole introduces a steric element in favour of the formation of the 5substituted isoxazolidines 6.344. The usual selectivity with monosubstituted alkenes is in favour of this
regioisomer, decisively so with C- and X-substituents, but more delicately balanced with Z-substituents,
since the HOMO of the dipole is not strongly polarised.864 With methyl crotonate, having one X- and one Zsubstituent, the adducts are stereoisomers with the same regiochemistry 6.346, having the methyl group on
the 5-position and the ester group on the 4-position.865
R
O
Ph
+
N
C
H
LUMO
R
O
Ph
5
N
+
O
Ph
N
4
Ph
R
Ph
HOMO
Ph
6.344
6.345
O
N
Ph
O
+
N
CO2Me
6.344:6.345
98:2
R = Me
R = Ph
100:0
R = CO2Et 70:30
Ph
5
4
CO2Me
6.346
Dipolarophiles with electronegative heteroatoms such as carbonyl groups, imines and cyano groups also
show an orientation in agreement with frontier orbital theory. Because these heterodienophiles all have lowenergy LUMOs, they will more often than not be involved in dipole-HO-controlled reactions. The orientation observed will therefore depend upon the LUMO of the dipolarophile, which will have the large
coefficient on the carbon atom. The reaction of diazomethane 6.304 with benzylidine aniline 6.347 giving
one regioisomer 6.348 fits this pattern.
336
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
N
HOMO
N
Ph
6.304
N
N
N
Ph
Ph
N
Ph
LUMO
6.347
6.348
Another example is the third stage of the ozonolysis sequence; the first step 6.349 has no regiochemistry, the
second step 6.350 is a cycloreversion, but the third stage 6.351, the cycloaddition of a ketone oxide to a carbonyl
group, is highly regioselective and just one representative of many others that might have been chosen.856,866
HOMO
O
O
O
O
O
+
O
O
O
H
O
O
6.349
6.350
O
O
LUMO
H
6.351
We are far from exhausting the subject of regioselectivity in dipolar cycloadditions with these few examples.
Frontier orbital theory, for all its success in accounting for most of the otherwise bewildering trends in
regioselectivity, is still fundamentally defective. We must keep in mind that the frontier orbitals used here
must reflect some deeper forces than those that we are taking into account in this essentially superficial
approach. Nevertheless, no other easily assimilated theory, whether based on polar or steric factors, or on the
possibility of diradical intermediates,683 has had anything like such success. It is plain that, as so often
happens in science, a large body of data has been reduced to an amenable set of principles.
6.5.3.3 The Stereoselectivity of 1,3-Dipolar Cycloadditions. The exo or endo stereochemistry of 1,3dipolar cycloadditions is not as straightforward as it is for Diels-Alder reactions. Stereoselectivity, more
often than not, is low, as shown by the nitrone reactions that we saw on p. 335 when we were looking only at
regiochemistry. We now see that the major regioisomer 6.344 from the reaction of C,N-diphenylnitrone with
methyl acrylate is a mixture of exo and endo isomers, exo- and endo-6.344. Similarly, the only regioisomer
6.346 from the reaction of N-benzyl-C-ethylnitrone with methyl crotonate is a mixture of exo-6.346 and
endo-6.346. In both cases, the reaction is a little in favour of the exo product.867
Ph N
O
Ph
CO2Me
exo
Ph N
Ph N
O
Ph
CO2Me
exo-6.344
Bn N
O
Et
CO2Me
exo
Bn N
Ph
57:43
Et
O
Ph
MeO2C
O
Et
MeO2C
77:23
Ph N
endo-6.344
Bn N
exo-6.346
endo
MeO2C
O
CO2Me
O
endo
Bn N
O
Et
MeO2C
endo-6.346
However, 1,3-dipolar cycloadditions are sometimes highly stereocontrolled in the exo sense, as in the
cycloaddition 6.352 of a cyclic nitrone to a vinyl ether giving largely (97:3) the exo adduct exo-6.353.868
6 THERMAL PERICYCLIC REACTIONS
337
In contrast, other reactions are endo selective, as in the cycloaddition 6.354 of an azomethine ylid to dimethyl
maleate giving largely (80:20) the endo adduct endo-6.355.869,870 Thus the stereoselectivity depends in a not
always predictable way upon the dipole, the dipolarophile and their substituents, in contrast to Diels-Alder
reactions, which more often than not obey the endo rule. It is advisable, when planning a synthesis, to look up
close analogies before relying upon the exo or endo stereoselectivity of a 1,3-dipolar cycloaddition.
O
N
N
exo
N
O
O
+
O
O
O
major
6.352
H
97:3
exo-6.353
Ph
N
endo
MeO2C
MeO2C
MeO2C
major
6.354
H
Ph
N
MeO2C
MeO2C
MeO2C
endo-6.355
endo-6.353
Ph
N
H
H
+
H
MeO2C
CO2Me
CO2Me
80:20
exo-6.355
In trying to explain these results, we can look at the generic secondary orbital interactions in Fig. 6.49. The
HOMO of the dipole will be similar to the HOMO of an allyl anion (see p. 27), which has a zero coefficient
on the central atom. In unsymmetrical dipoles it will still only have a small coefficient, which could be either
way up, depending upon the relative electronegativity of X and Z. We would therefore predict that dipoleHO-controlled reactions can only have small secondary orbital interactions, and low endo-exo selectivity.
However, we can predict that the endo mode might be favoured for dipole-LU-controlled reactions, since
there is potentially a favourable secondary orbital interaction. This does not match the observations. Nitrone
reactions are likely to be dipole-LU-controlled, especially the reaction 6.352 with the X-substituted alkene,
yet this is one of the most exo selective. The reaction 6.354 of the azomethine ylid with dimethyl maleate is
likely to be dipole-HO-controlled (7.7 eV as against 10.3 eV), and yet this is the one that is endo selective. In
reactions like these, the nature of the substituents changes the orbital energies, making the assignment of HO
or LU control less certain than the numbers used above imply. It is not even clear in every case what the
geometry of the dipole is (Z or E), or whether the results are kinetically or thermodynamically controlled.
Nevertheless, we may conclude that the theory of secondary orbital interactions is not well supported by the
evidence from 1,3-dipolar cycloadditions, although it is still invoked, for want of a better, in trying to explain
their stereochemistry.
LUMO
HOMO
Y
weak interaction,
could be bonding
or antibonding
X
X,Z,C
LUMO
(a) Dipole-HO control
X
Y
Z
Z
stronger bonding interaction
X,Z,C
HOMO
(b) Dipole-LU control
Fig. 6.49 Possible secondary orbital interaction in 1,3-dipolar cycloadditions
338
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
6.5.3.4 The Site Selectivity of 1,3-Dipolar Cycloadditions. The site selectivity of 1,3-dipolar cycloadditions is the same as for the Diels-Alder reactions in Section 6.5.2.6. To give just two examples, the
unsaturated ester 6.356 reacts with diazomethane at the 4,5-double bond, to give the adduct 6.357,871
and diazoacetic ester adds to the terminal double bond of l-phenylbutadiene 6.358, giving the pyrazoline
6.359, with the product actually isolated after the loss of nitrogen being the corresponding
cyclopropane.872
CO2Me
CO2Me
N
N
N
N
+
N
N
6.356
Ph
Ph
6.357
N
+
EtO2C
N
6.358
EtO2C
6.359
6.5.4 Other Cycloadditions
6.5.4.1 [4 þ 6] Cycloadditions. Secondary orbital interactions have been cited as an explanation for the
stereochemistry of [4 þ 6] cycloadditions such as that between cyclopentadiene and tropone 6.45 ! 6.46,
which favours the exo transition structure 6.360. The frontier orbitals have a repulsive interaction (wavy
lines) between C-3, C-4 on the tropone and C-2 on the diene (and between C-5 and C-6 on the tropone and C3 on the diene) in the endo transition structure 6.361. However, in this reaction the exo adduct is thermodynamically favoured, the normal repulsion between filled orbitals in the endo transition structure is an
adequate explanation, and the electrostatic explanation given in Section 6.5.2.4 works just as well. There is
no real need to invoke secondary orbital interactions.
LUMO
3
O
O
4
2
3
6.360
HOMO
6.361
6.5.4.2 Diyl Cycloadditions. Trimethylenemethane is a reactive intermediate, usually drawn as a diradical
6.362, which can exist in singlet and triplet states. The triplet shows the properties of a radical, but the singlet
is better thought of as a cross-conjugated system of four p orbitals which can participate in pericyclic
reactions. The p molecular orbitals of trimethylenemethane in Fig. 6.50 are 1, bonding across the whole
system, then higher in energy a formally degenerate, nonbonding pair 2 and 3, and finally a fully
antibonding combination 4*. If the degeneracy can be lifted, one of the middle pair will be the HOMO
and the other the LUMO.
For example, the singlet trimethylenemethane 6.365 can be produced by heating the strained bicyclic
hydrocarbon 6.363 or the diazene 6.364, or by photolysis of the latter. It dimerises to give a mixture of at least
three hydrocarbons out of the eight possible, of which one stereoisomer of the fused-bridged product 6.366 is
the major. The exocyclic methylene carbon is the unique carbon, and can be assigned to be the one with the
large coefficient in 2 and a zero coefficient in 3. The experimental result can then be explained if the
former is the HOMO and the latter the LUMO.873
6 THERMAL PERICYCLIC REACTIONS
339
4*
2
3
6.362
1
Fig. 6.50
The p molecular orbitals of trimethylenemethane
heat
LUMO
6.363
h or
heat
6.365
H
HOMO
N
6.366
N
6.364
When the same intermediate is generated in methyl acrylate, only the four possible fused products
6.367 are formed, and no bridged products. This regioselectivity corresponds to that expected if 2 is
the HOMO.
CO2Me
6.365
LUMO
CO2Me
HOMO
CO2Me
6.367
The same reaction in cyclopentadiene gives a mixture of two of the fused products 6.368 and a single
bridged product 6.369. The fused products are similar to those from the reaction with acrylate, and the
bridged product is allowed, whether one takes the frontier orbitals as HOMO(trimethylenemethane)/
LUMO(cyclopentadiene) or the other way round as illustrated. One hint that the other way round is important
is the endo-like selectivity, which might follow from the secondary interaction shown as dashed
lines.873,874
340
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
HOMO
LUMO
+
and
6.365
6.368
6.369
LUMO
HOMO
The oxyallyl system, another reactive intermediate usually written with two charges 6.370 instead of
as a diradical, has a similar conjugated system, except that the coefficients will be different, and the
central carbon atom, although close to a node in 2 and 3, will not have a node exactly through it.
When generated on its own, it dimerises with different regioselectivity from trimethylenemethane,
giving the 1,4-dioxan 6.371.875
LUMO
HOMO
O
O
Cr(II)
R=Me
O
O
O
O
O
6.370
O
Br
R
6.371
LUMO
HOMO
Br
R
O
HOMO
LUMO
O
O
O
Cr(II)
and
R=H
6.372
6.373
HOMO
LUMO
This looks as though each of the C—C bonds is independently the result of both HOMO/LUMO
interactions, with an endo selectivity as well. In the presence of dienes, these species behave as allyl
cations (see p. 259) and undergo clean [4 þ 2] cycloadditions, as in the reaction of the oxyallyl 6.372
giving the tricyclic ketone 6.373, which is similar to the diene 6.369. Normally, oxyallyls are in
equilibrium by disrotatory electrocyclic ring closures with cyclopropanones and with allene oxides,
but the presence of the five-membered ring in these particular examples makes these pathways
counter-thermodynamic.
6.5.4.3 Ketene Cycloadditions As we saw in Section 6.3.2.7, ketenes undergo cycloadditions to
double bonds 6.149 (repeated below) to give cyclobutanones. In practice, the reaction is faster and
cleaner when the ketene has electron-withdrawing groups on it, as in dichloroketene, and when the
alkene is relatively electron-rich, as in cyclopentadiene. The product from this pair of reagents is the
cyclobutanone 6.374.876
6 THERMAL PERICYCLIC REACTIONS
341
2a
2a
O
O
O
+
Cl
Cl
Cl
2s
Cl
6.374
6.149
Already we can see that the effects of substituents on rate follow the same pattern as in the Diels-Alder
reaction, and we can explain them in the same way, using the interaction between the LUMO of the ketene
and the HOMO of the ketenophile. The conjugation of the C—Cl bonds with the carbonyl group of the ketene
will lower, by negative hyperconjugation, the energy of the LUMO, which is more or less p*CO. A C- or Xsubstituent on the alkene will raise the energy of its HOMO, and the energy separation between the frontier
orbitals is reduced. This interaction contributes to the bonding represented by the left-hand bold line in the
transition structure 6.149. The other pair of frontier orbitals may also be important. The HOMO of the ketene
is more or less the p-bonding orbital of the C¼C double bond conjugated to the lone pair on the oxygen atom,
which is an X-substituent raising its energy. The LUMO of the ketenophile will be lowered by the Csubstituent, and this frontier orbital interaction may also contribute to the bonding represented by the righthand bold line in the transition structure 6.149. The orbital contribution from a lone pair is not present in
keteniminium ions, which are highly reactive in cycloadditions to alkenes and show similar
regioselectivity.877
The energies and coefficients of the frontier orbitals of ketene are shown in Fig. 6.51.878 The
regioselectivity in the reaction between cyclopentadiene and dichloroketene giving the cyclobutanone
6.374 is explained by the overlap from the large LUMO coefficient on the central atom of the ketene
and the larger coefficient in the HOMO of the diene at C-1. Evidently this pair of frontier orbitals is
the more important. The same regiochemistry is seen with a Z-substituted ketenophile 6.375 (actually
a doubly vinylogous Z-substituted ketenophile),879 and with the X-substituted ketenophiles 6.376 and
6.377.880
3.8
O
LUMO
–12.4
HOMO
Fig. 6.51
O
Energies and coefficients of the frontier orbitals of ketene
A rather special case is presented by the reaction of ketenes with enamines, such as that between the
enamine 6.378 and dimethylketene. This reaction between a strongly nucleophilic alkene and the
inherently electrophilic ketene seems more likely to be stepwise than the other reactions of ketenes,
with the regioselectivity largely determined by the formation of the well stabilised zwitterionic
intermediate 6.379. The formation of this intermediate is also consistent with frontier orbital control,
in that the atoms with the large coefficients in the HOMO of the enamine and the LUMO of the
ketene are the first to become bonded. However, the interesting aspect of this reaction is that the ring
closure to give the cyclobutanone 6.380 ought not to be easy because it would be 4-endo-trig at the
enolate end (6.379 arrows) (see pp. 218–222). It may well be that this pathway, even though the
342
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
O
O
Ph
Ph
6.375
O
+
Ph
O
Ph
Ph
O
O
O
+
O
Ph
Ph
O
+
O
Ph
Ph
Ph
OEt
6.376
Ph
Ph
EtO
Ph
Ph
6.377
zwitterion 6.379 is formed, is sterile. There is in fact evidence that this reaction at least in part takes a
concerted pathway directly to the cyclobutanone 6.380, in which case it is another obedient case of the
regioselectivity shown by an X-substituted alkene with a ketene.881
O
O
O
?
+
N
N
N
6.379
6.378
6.380
When the two substituents on the ketene are different, as in methylketene 6.381, the stereoselectivity is
usually in favour of the product 6.382 with the larger substituent in the more hindered endo position.882 This
follows from the approach 6.383, in which the ketene is tilted so that both bonds can develop simultaneously
(dashed lines), and tilted in the direction with the larger substituent, the methyl group, up and away from the
C¼C bond, and the smaller substituent, the hydrogen atom, tilted down towards the C¼C bond. As the bonds
develop further, the methyl group moves down into the more hindered environment, but this must only
become perceptible after the transition structure has been passed.726,883
O
O
Me
H
O
H
+
Me
Me
H
6.381
6.382
98:2
6.383
The cycloaddition of ketenes to carbonyl compounds also shows the expected regioselectivity. In this
case, both HOMO(ketone)/LUMO(ketene) and LUMO(ketone)/HOMO(ketene) interactions may be important,
but they lead to the same conclusions about regioselectivity, with the carbonyl oxygen atom bonding
to the carbonyl carbon atom of the ketene as in the reactions of the quinone 6.384 and formaldehyde
6 THERMAL PERICYCLIC REACTIONS
343
6.385.884 Lewis acid catalysis is commonly employed in this reaction; presumably the Lewis acid
lowers the energy of the LUMO of the ketene (or that of the ketone) in the same way that it does
with dienophiles (see pp. 318–319).885
O
O
O
Ph
Ph
O
+
Ph
O
O
O
Ph
H
O
O
ZnCl2
+
H
H
O
H
6.385
6.384
Ketenes also dimerise with ease, since they are carbonyl compounds, and the regiochemistry, whether it is
forming a -lactone 6.386 or a 1,3-cyclobutanedione 6.387, is that expected from the frontier orbitals of
Fig. 6.51.886
O
O
O
O
+
+
H
H
O
O
H
O
H
O
6.386
6.387
The reaction of the imine 6.388 with the ketene 6.389,887 one of many Staudinger reactions, is more
plausibly stepwise. The imine is nucleophilic enough to attack a ketene carbonyl group directly from the
lone pair on the nitrogen atom,888 just as the enamine 6.378 was probably nucleophilic enough to attack
from the carbon. In the case of the imine, however, the ring closure of the intermediate 6.390 to give the
-lactam 6.391, even though it is 4-endo-trig at both ends, will not be difficult, because it is an electrocyclic reaction. Electrocyclic reactions do not seem to suffer unduly from the strictures of Baldwin’s rules
(see p. 220).
O
Ph
Ph
N
Ph
6.388
Ph
O
N
Ph
Ph
6.389
O
N
Ph
Ph Ph
6.390
Ph
Ph
Ph
6.391
When the imine is ,-unsaturated, a [4 þ 2] cycloaddition is in competition with the -lactamforming reaction, but the latter usually wins.889 The imine 6.392 and methoxyketene give the
intermediate 6.393 from attack anti to the methoxy group, and the conrotatory electrocyclic step
then places the methoxy and the vinyl groups cis in the product 6.394. In this case the s-cis
conformation 6.395 is easily accessible, making the disrotatory electrocyclic closure to a six-membered ring 6.396 a plausible alternative. That only the four-membered ring is formed is in fact
because of the nature of the substituents at the termini, a methoxy group and a substituted vinyl group
in this case. The methoxy group on the outside and the vinyl group on the inside in 6.393 leads to a
344
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
low energy transition structure, because the torquoselectivity (Section 6.5.7) is favourable for this
arrangement. When the substituents are changed to those found in 2-chloro-2-methylketene, the
two intermediates, also in rapid equilibrium, have more evenly balanced torquoselectivity forces at
work in the two conformations of the intermediate, and both the four- and six-membered rings are
formed.
O
Me
Me
N
Me
O
N
H
O
N
OMe
OMe
Ph
H
OMe
Ph
Ph
6.393
6.392
6.394
fast
Me
O
O
N
N
OMe
OMe
Ph
Ph
6.395
6.396
Site selectivity in ketene cycloadditions is also explained by the frontier orbitals. Diphenylketene reacts with
isoprene 6.397 mostly at the more substituted double bond to give the cyclobutanone 6.398 as the major
product.890 In contrast, it reacts with cis-piperylene 6.399891 and with cis-butadiene-l-nitrile 6.400890 at the
less substituted double bond. In all three cases the site of attack is the double bond having the largest
coefficient in the HOMO.
O
O
O
–0.614
+
Ph
+
–0.420
Ph
0.506
Ph
Ph
0.348
6.397 HOMO
O
Ph
Ph
70:30
6.398
O
O
O
–0.534
+
Ph
Ph
+
–0.350
CN
CN
0.531
0.456
6.399 HOMO
Ph
Ph
Ph
Ph
Ph
Ph
6.400
In the [p8þp2] cycloaddition of the bromoketene 6.402 to the pyridinium betaine 6.401 giving the lactone
6.403, the oxygen atom has the highest coefficient in the HOMO, and the next highest is the pyridinium 2position, which is the other site of attack when the group R is not large.892
6 THERMAL PERICYCLIC REACTIONS
0.32
O
345
–0.67
HOMO
O
O
O
–HBr
O
+
O
0.55
N
N
Br
Ar
R
6.401
HBr
R
6.402
N
Ar
R
Ar
6.403
6.5.4.4 Allene Cycloadditions. As we saw in Section 6.3.2.7, allenes undergo cycloadditions similar to those of
ketenes, except that allenes react faster if they have X-substituents and the alkene has Z-substituents. The HOMO
and LUMO of allenes are higher in energy than those of ketene, and they are polarised with larger coefficients on the
terminal atoms in the degenerate HOMOs (Fig. 6.52).893 The degenerate LUMOs are essentially unpolarised.
0.77
–0.78
–0.78
0.77
8.7
LUMO
–8.8
HOMO
0.66
Fig. 6.52
0.56
0.56 0.66
Energies and coefficients of the frontier orbitals of allene
The regiochemistry of the cycloadditions of allenes is not easily explained by these frontier orbitals. Penta2,3-diene and acrylonitrile give the adducts Z- and E-6.404 in which the central carbon of the allene, with the
smaller HOMO coefficient, has bonded to the carbon of the Z-substituted alkene.894 Equally unexplained
is the regiochemistry of the reaction between allene itself and diazomethane, which gives more of the adduct
6.405 than of its regioisomer 6.406.893
2
H
4
+
+
H
NC
Z-6.404
NC
+
N
NC
E-6.404
+
N
N
N
N
N
6.405
97:3
6.406
Energetically this reaction can be expected to be dipole-HO-controlled (ELUMO – EHOMO ¼ 15.5 eV), but this
should have little regiocontrol since the LUMO of the allene is so little polarised. The LUMO(dipole)/
HOMO(allene) interaction (ELUMO – EHOMO ¼ 16.75 eV) might come into play, since the allene HOMO is
polarised, but the orbitals do not match up to explain the high level of regioselectivity, since the larger
‘coefficient’ in the LUMO of diazomethane is on carbon. Finally, the hydroboration of allenes gives mainly
the product with the boron on the central carbon 6.407.895 With boron as the electrophilic atom, frontier
346
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
orbitals ought to have directed it to the terminal carbon. It is possible that steric effects play a major part.
Steric effects are manifestly important when enantiomerically enriched penta-2,3-diene is used in the
reaction with acrylonitrile—both adducts 6.404 have the absolute configuration corresponding to attack
on the allene from the lower surface, as drawn, approaching C-2 from the opposite side from the methyl
group on C-4.
H
+
H
BH2
H
BH2
6.407
Similarly, in the Diels-Alder reaction between 1,1-dimethylallene and tetracyclone 6.200 giving the product
6.408 which loses carbon monoxide to give the triene 6.409, attack has taken place on the double bond
carrying the methyl groups, but orthogonal to them 6.410, avoiding the steric clash which would have taken
place had it attacked the less substituted double bond 6.411.896 However, this result may be an anomaly,
perhaps because phencyclone is so large, because maleic and fumaric esters predominantly attack the lesssubstituted double bond in [2 þ 2] reactions (see p. 282).
Ph
O
Ph
O
Ph
Ph
Ph
Ph
Ph
Ph Ph
Ph
Ph
6.200
Ph
6.408
phencyclone
6.409
phencyclone
H
Me
Me
Me
H
H
H
6.410
Me
6.411
This raises the question of the direction of twist in the methylene group not undergoing attack, and for that we
need to return to the picture 6.150 on p. 282. A revealing reaction is the dimerisation of buta-1,2-diene
6.412.897 The stereochemistry in the major product 6.414 is comfortably accounted for using the
[p2sþp2sþp2s] picture, with the [p2s] component at the bottom in 6.413 approaching the upper allene from
the side opposite to the methyl group on C-3 (bold lines), but with its own methyl group orthogonal, just as
the two methyl groups were in the Diels-Alder reaction 6.410. The direction of rotation at C-3, determined by
the dashed curve, brings the methyl group towards the viewer, and into the inside position of the diene in the
product making it a Z-alkene.725 The corresponding product with the E-double bond will be lower in energy,
yet it is a relatively minor product (18%). The direction of rotation at C-1 in the lower component will be
conrotatory, but that is not detectable in this isomer. The next most abundant product is that from the reaction
6.415 ! 6.416 in which both methyl groups are orthogonal to the bonds forming at C-3. The C-3 atoms will
approach each other to minimise steric interactions by having the methyl groups mutually in the sectors
between the hydrogen and methyl groups, which leads to the trans arrangement of the methyl groups in the
product 6.417.
6 THERMAL PERICYCLIC REACTIONS
Me
1
347
Me
3
H
H
3
H
H
H
Me
H
Me
Me
Me
H
1
H
6.412
H
Me
3
H
H
Me
6.414 37%
6.413
H
3
Me
H
Me
Me
Me
H
6.415
6.417 25%
6.416
The picture of allene cycloadditions as [p2sþp2sþp2s] reactions is by no means proved but it does provide an
explanation for most of the puzzles in these remarkable reactions.
6.5.4.5 Carbene Cycloadditions. Carbene and carbenoid cycloadditions show substantial and orderly
regioselectivity. The carbenoid Simmons-Smith reaction with isoprene (6.418 þ 6.397) takes place on
the double bond with the highest coefficient in the HOMO.898 Dichlorocarbene, an electrophilic
carbene, reacts at the terminal double bond of cycloheptatriene 6.419,899 and at the central double
bond of heptafulvalene 6.420.900 In both cases the site of attack is the double bond having the largest
coefficient in the HOMO. In the former, the Sc2-values would lead one to predict attack at the central
double bond [(0.4182 þ 0.4182) is a little larger than (0.5212 þ 0.2322)], but it is likely that the
asymmetry of carbene cycloadditions (see pp. 284 and 288) makes the single largest coefficient
disproportionately important.
–0.614
IZn
I
+
+
–0.420
+
0.506
0.348
6.418
6.397
0.521
0.521
Cl2C: +
Cl
0.232Cl
0.232
–0.418 –0.418
6.419
64:32:4
HOMO
0.253
Cl2C: +
–0.300 –0.199 –0.199–0.300
0.253
0.336
0.253
–0.300
Cl
Cl
0.336
0.253
–0.199 –0.199
–0.300
6.420
Nucleophilic carbenes, which might show a different site selectivity, rarely undergo cycloadditions (see
p. 199), but methoxychlorocarbene adds to the exocyclic double bond of 6,6-dimethylfulvene 6.422, to give
the cyclopropane 6.421, whereas dichlorocarbene adds to one of the ring double bonds to give the
cyclopropane 6.423. These match the sites with the largest coefficients in the LUMO and HOMO,
respectively.901
348
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
OMe
Cl
MeOClC:
0.72
0
–0.27
0
–0.42
–0.42
0.35
6.421
LUMO
–0.56
0.56
–0.38
0.35
Cl2C:
6.422
Cl
0.38
6.423
HOMO
Cl
6.5.4.6 Epoxidations and Related Cycloadditions. The so-called K-region of polycyclic hydrocarbons is
implicated in the carcinogenicity of these compounds. It is believed that these hydrocarbons are epoxidised
at a site called the K-region; for example the benzanthracene 6.424 gives the epoxide 6.425, which is then an
electrophilic species capable of alkylating the pyrimidines and purines of nucleic acids. On the whole, but
only very approximately, the more nucleophilic the K-region (i.e. the larger the coefficients and the higher
the energy of the HOMO), the more carcinogenic the hydrocarbons prove to be, presumably at least partly
because they are epoxidised more readily. Epoxidation is like a cycloaddition, in that the new bonds to the
oxygen atom are formed simultaneously from each of the carbon atoms. In cycloaddition reactions in
general, in which both bonds are being made to more or less the same extent in the transition structure,
the highest single coefficient is not the most important, as it was in the less symmetrical reactions of
carbenes. Instead, it is the highest adjacent pair of coefficients, which is often found in the K-region. Thus if
benzanthracene 6.424 is to take part in a cycloaddition in which it provides the 2-electron component, a high
value of Sc2 is found in the K-region. (0.2982 þ 0.2882 is larger than 0.1942 þ 0.3242 or any other sum of
adjacent coefficients not involving the angular carbons; reaction at the angular carbon atoms presumably
involves the loss of too much conjugation.) This is also the site of attack by osmium tetroxide,902 which
probably reacts in a cyclic process to give the ester 6.426 as an intermediate, and it is also the site of attack by
ethoxycarbonylcarbene, derived from diazoacetic ester, giving the cyclopropane 6.427.903
biological
oxidation
O
HOMO coefficients
0.203
–0.003
–0.301
0.393
0.095
–0.204
–0.236
–0.100
0.078
0.194
–0.047
–0.154
0.324
–0.445
6.425
–0.160
–0.167
OsO4
0.288
0.298
K-region
6.424
O
O OsO2
6.426
:CHCO2Et
6.427
CO2Et
6 THERMAL PERICYCLIC REACTIONS
349
The same idea accounts for the site selectivity in the reactions of the carcinogenic hydrocarbons 6.428 and
6.429, both of which react with osmium tetroxide in the K-region. The contrast is with the behaviour of these
hydrocarbons with other oxidising agents, like lead tetraacetate, chromic acid and sulfuryl chloride, which
react only at one site at a time: none of the hydrocarbons 6.424, 6.428 or 6.429 reacts in the K-region with
these reagents.904 Instead, reaction takes place at the site with the highest single coefficient in the HOMO,
just as we would expect for an electrophilic substitution (see p. 174).
0
–0.054
–0.368
0.368
–0.164
0.164
0.296
–0.340
–0.296
K-region
0.296
–0.296
–0.164
0.164
–0.368
OsO4
:CHCO2Et
O3
0.320
0.294
–0.275
0.180
–0.275
K-region
0.368
0
OsO4
0.434
CrO3
SO2Cl2
0.175
0.235
–0.268
–0.088
6.428
6.429
CrO3
SO2Cl2
Pb(OAc)4
6.5.5 Other Pericyclic Reactions
It is more difficult to explain the effect of substituents on the rates, and on the regio- and stereoselectivities of the unimolecular pericyclic reactions. We cannot strictly look at the HOMO and
LUMO of each component, as we could with bimolecular reactions, and therefore cannot properly use
frontier orbitals to explain the effects of electron-donating and electron-withdrawing substituents on
the rates.905 The effects are profound, sometimes even strong enough to override the WoodwardHoffmann rules.906
6.5.5.1 [3,3]-Sigmatropic Rearrangements. Cope and Claisen rearrangements may take place with a
chair-like transition structure, chair-6.125 (see p. 276), or with a boat-like transition structure, boat6.125, both of which are allowed. The stereoselectivities like those seen in the Ireland-Claisen rearrangements 6.106 ! 6.107 (see p. 269) show that, other things being equal, the chair-like transition structure is
favoured. Doering had elegantly proved a few years earlier that the Cope rearrangement showed the same
preference.907 However, when other things are not equal, a boat-like transition structure 6.108 is easily
adopted. We cannot strictly define the secondary orbital interactions that might explain the preference for
the chair-like transition structure, which may simply be a steric effect. Nevertheless, we can pretend to,
and it works. The orbitals can be divided artificially into two groups: one is an isolated p bond (between
C-20 and C-30 ) and the other a p bond conjugated to a bond (C-10 , C-1, C-2 and C-3). If we ignore the
fact that they are connected, we can assign to the former the role of LUMO and to the latter the role of the
HOMO (with a node between the p and the bond, just as there is between the two p bonds in the HOMO
of butadiene). While the primary interaction between the lobes on C-3 and C-30 is bonding in both
conformations 6.430 and 6.431, the secondary interaction between the atoms on C2 and C-20 in the boatlike conformation 6.431 is out of phase, and the repulsion should make the chair even more favourable
than it already was from the normal steric repulsion between the filled orbitals. This is not convincing,
but it illustrates how far we can extend, some would say distort, frontier orbital theory if we have a
mind to.
350
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
2
1
1
1'
1'
2
3
3
3'
3'
2'
6.430
antibonding
2'
6.431
There are however, important substituent effects that do need explaining. The most striking example
of a rate acceleration in an allowed reaction is that of an anionic substituent on the periphery of a
[3,3]-sigmatropic rearrangement. The bold lines in the drawings of the dienes 6.432 and 6.435
identify the 1,5-hexadiene systems undergoing Cope rearrangements, and the bold lines in the
drawings of the first-formed products 6.433 and 6.436 identify the same six carbon atoms. The
extraordinary feature of the first reaction is that the oxyanion substituent in 6.432 increases the rate
enormously relative to the corresponding reactions without the oxyanion substituent.908 The rate is
increased even further when the potassium counterion is completely removed from the oxygen atom
by 18-crown-6, and yet more again in the gas phase.909,910 Similarly, in the second reaction, although
the tosylate 6.434 is a stable compound, with the Cope rearrangement taking place only at 140 °C,
the cation 6.435 derived from it by solvolysis rearranges rapidly at 95 °C to give the cation
6.436.37,911 The effect is even more dramatic when a related iodide is treated with silver ion, when
the cation rearranges at –15 °C. In each case, a charged substituent attached to the periphery of the
rearranging system dramatically increases the rate.
H
OM
MeO
OM
≡
MeO
MeO
6.432
OM
H
M
k rel
H
K
K + 18-C-6
1
1012
1017
6.433
TsO
≡
6.434
6.435
6.436
The oxyanion —OM in 6.432 is an X-substituent, and the carbocation in 6.435 is a Z-substituent (but
without having any double bond character in the way that a carbonyl group does). Any explanation of the
substituent effect must be able to encompass this change from a strong electron donor to a strong electron
withdrawer. One approach to explaining the substituent effect has been suggested by Carpenter.912 It uses
simple Hückel molecular orbitals, and avoids the need to rely on frontier orbitals. The basis of the idea is to
return to the picture of a pericyclic transition structure as having aromatic character (see p. 286). Let us use
the Cope rearrangements as an example, for which the starting material has two independent p bonds, and
the transition structure, with six electrons in motion, has some of the character of a benzene ring.
To provide a baseline from which to compare the substituted system, we first compute the p energy of the
unsubstituted starting material on the left in Fig. 6.53a and the fully aromatic version of the corresponding
transition structure on the right. The starting material will have the p energy of two independent p bonds,
6 THERMAL PERICYCLIC REACTIONS
351
2
3
1
–4.00
(a) Unsubstituted
4
8
–4.72
(b) Substituted by
X- or 'Z'-substituent
4
8.72
–4.43
(c) Substituted by
C-substituent
6
Fig. 6.53
10.43
p-Energy changes for a Cope rearrangement with a substituent on C-3
each doubly occupied, 4 below the level (Figs. 1.31 and 1.33), and the transition structure will have the p
energy of benzene, 8 below the level (Fig. 1.44). If there is an anionic substituent on C-3, the starting
material in Fig. 6.53b, will still have the p energy of two independent p bonds, 4 below the level, but the
aromatic version of the transition structure will have the p energy of a benzyl anion, 8.72 below the level
(Fig. 4.9). The presence of the substituent lowers the energy barrier between the starting material and the
transition structure by 0.72 relative to the unsubstituted case. As it happens, the p energy of a benzyl cation
is the same as the benzyl anion, because the highest of the orbitals in the anion is on the level, and makes no
contribution to the p energy. The calculation for having a cationic substituent is therefore the same as for the
anionic substituent.
An empty orbital is a crude model for the usual Z-substituents, although it was appropriate for the cation
6.435, so we ought to do the comparison again with a vinyl group as a model for a C-substituent, and we can
then guess that the usual Z-substituents will have an effect somewhere in between the two. The starting
material in Fig. 6.53c has three independent p bonds, 6 below the level, and the transition structure is
modelled by styrene, 10.43 below the level. The difference therefore is 0.43 relative to the unsubstituted
case, not quite as effective as an isolated p orbital, whether filled or empty.
A substituent on C-2 will have a different effect. The unsubstituted system is the same as in Fig. 6.53a, and the
empty or filled p orbital will again be equally effective, as shown in Fig. 6.54a. The starting material will have p
energy of one isolated p bond, 2 below the level and one allyl system, 2.83 below the level, making a total
of 4.83. The transition structure will be modelled by a benzyl system, 8.72 below the level, and the overall
stabilisation is 3.89, which is less than the change of 4 seen in the unsubstituted case. A donor or withdrawing
substituent on C-2 might therefore be expected to slow the rearrangement down. The corresponding calculation
for a C-substituent in Fig. 6.54b makes it 0.06 less than the unsubstituted case, and so it ought to be rather less
rate-retarding. In practice a phenyl substituent on this position is mildly rate accelerating,913 but this has been
explained as a substituent stabilising a transition structure with radical character on C-2. The main point to be
seen here is the dramatically greater effectiveness of a substituent on C-3 than on C-2.
Claisen rearrangements are in general faster than the corresponding Cope rearrangements, and this has
been explained using frontier orbitals, by counting the oxygen atom as a substituent on the sigmatropic
rearrangement divided into two arbitrary parts in the same way as we saw on pp. 349 and 350 in explaining
the preference for a chair transition structure in the Cope rearrangement.914 The experimentally observed
effect of donor and withdrawing substituents on Claisen rearrangements are summarised in 6.437 and 6.438.
352
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
(a) Substituted by
X- or 'Z'-substituent
–3.89
4.83
8.72
(b) Substituted by
C-substituent
–3.96
6.47
Fig. 6.54
10.43
p-Energy changes for a Cope rearrangement with a substituent on C-2
Claisen rearrangements introduce the complication of oxygen lone pairs within the rearranging system,
rather than as substituents on the perimeter. They may be ignored and the transition structure treated as
benzene-like, or they may interrupt the conjugation, and the transition structure is then like a heptatrienyl
anion.915 Predictions based on the simple theory above, whichever of these models is taken, match most of
the substituent effects, and more elaborate treatments with calculations account for the anomalous accelerating effect of a donor substituent at C-6.916
faster
X
O
faster
2
4 5
faster
1
6
faster
Z
faster
slower
6.437
O
slower
2
4 5
1
6
faster
slower
faster
6.438
This simple way of explaining substituent effects is effective, and even gives quite good quantitative
correlations for electrocyclic reactions and sigmatropic rearrangements.917 It can also be applied
to cycloadditions, although the latter are usually explained by the frontier orbitals discussed in
Section 6.5.3.
The same is true for Cope rearrangements in general, which can be accounted for by accepting the
chameleon-like918 nature of substituents.919 Most substituents at C-1 and C-3 accelerate the reaction, and
with more than one of them, their effects are cooperative. Substituents at C-2, however, shift the balance of
the transition structure towards a biradical-like intermediate in which the new bond is formed ahead of the
old one breaking. Substituent effects at this site are not cooperative with substituent effects at C-1 and C-3,
because they change the nature of the transition structure rather than contribute to it in the same way. Some
substituents, like an amide ion at C-3920 and a thio group at C-6,921 can tip the reaction close to or actually
into being stepwise ionic or stepwise radical.
6.5.5.2 [1, n]-Sigmatropic Rearrangements. [1,5]-Sigmatropic shifts have another kind of selectivity—
the migratory aptitude of the groups that are migrating. It is clear that hydrogen migrates exceptionally
easily, as we have seen in cyclopentadienes; carbon groups are more reluctant. The ease with which
hydrogen atoms migrate is easily understandable—it is related to the ease with which their bonds to
electronegative heteroatoms are made and broken in acid-base chemistry. At the extreme, a proton in
between two fluoride ions is in the transition structure for the transfer from one to the other. Thus hydrogen
6 THERMAL PERICYCLIC REACTIONS
353
bonding (see pp. 118–121) is a paradigm for the exceptional properties of hydrogen, and, although much
stronger when the hydrogen atom sits between electronegative atoms, it is not restricted to them. Another
factor is the relative ease with which bonding can develop in any direction towards an s orbital. Carbon
atoms, with bonding made from s and p orbitals has much stricter limits on the direction from which a bond
can be made. In [1,5]-sigmatropic rearrangements, hydrogen does not have to obey the constraints of
retention or inversion, but can lean over towards the carbon atom it is bonding to, and start to form a bond
(Fig. 6.12, top). Likewise with antarafacial [1,7]-sigmatropic rearrangements, their is no difficulty for the
hydrogen atom moving from the top surface at one end to the bottom surface at the other (Fig. 6.12,
bottom), to develop overlap so that it sits half way between, making a nearly linear connection between the
two ends.
When a migrating group R is based on carbon they vary in their willingness to migrate, and there
appears to be some correlation to the LUMO energy of the migrating group, with vinyl migrating
faster than alkyl, and acyl faster than vinyl.922 Clearly a double bond allows overlap to develop to
the p orbitals, before the bond breaks, in a way that an alkyl group cannot. Similarly, a boryl
group, with an empty p orbital orthogonal to the migrating bond, can undergo suprafacial [1,7]shifts, formally forbidden, but made possible by the new bond forming before the old one has
broken.923
In the most simple of sigmatropic carbon shifts, the [1,2]-shift in a carbocation, or the related
Beckmann, Curtius and Baeyer-Villiger reactions, major factors are the capacity of the migrating carbon
to carry partial positive charge, together with the capacity of the carbon atom from which it is migrating
to take up the developing positive charge—the [1,2]-shift is accelerated when either or both are capable
of supporting an electron deficiency, because both are electron deficient in the transition structure 6.439
with two half-formed bonds. However, other things being equal, phenyl and vinyl groups migrate more
easily than alkyl, even though phenyl and vinyl are less stabilised cations than alkyl. They do so by
participation in a stepwise event—the new bond forms from the empty p orbital to the p bond to give a
cyclopropylmethyl cation 6.440 with two full bonds, which then breaks the old bond to give the product.
When the overlap creating the bond in the intermediate 6.440 is geometrically impossible, phenyl
and vinyl groups are much slower to migrate than alkyl, because they do not easily support positive
charge.
R
R
R
6.439
6.440
For example, the oxime tosylate 6.441, in which an alkyl group, the bridgehead, migrates, undergoes
Beckmann rearrangement rapidly when warmed above room temperature in ethanol; in contrast, the
isomer 6.442 can be distilled at 200°C largely unchanged.924 In this case, the rigidity of the bicyclic
system prevents the vinyl group from bonding in the sense 6.440—the p orbitals are orthogonal to the
bond between the nitrogen atom and the tosylate group, directly behind which the new bond must
start to form.
354
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
200 °C
r.t.
EtOH
HN
N
6.441
N
O
OTs
N
H
O
TsO
6.442
6.5.5.3 Electrocyclic Reactions. The benzocyclobutyl oxide 6.443 is a reactive intermediate obtained by
trapping benzyne with the lithium enolate of acetaldehyde. It opens rapidly, even at 0 °C, to give the diene
6.444, which is trapped in situ by another molecule of benzyne to give the anthracene hydrate 6.445, and
hence anthracene itself.925 In contrast, a benzcyclobutene 6.446 without the benefit of the oxyanion
substituent has to be heated in refluxing decane (bp 174 °C) for 30 h before it gives the aromatic product
6.448 by an intramolecular Diels-Alder reaction,926 and there is evidence that it is the ring opening 6.446 !
6.447 that is rate-determining, not the intramolecular Diels-Alder reaction 6.447 ! 6.448.927
O
O
O
0 °C
6.443
6.444
O
6.445
O
O
174 °C
6.446
6.447
6.448
To explain the increase in the rate of an electrocyclic ring opening like 6.443 ! 6.444, we need to remember
that the conrotatory pathway will have a Möbius-like aromatic transition structure, not the antiaromatic
Hückel cyclobutadiene that we saw in Fig. 1.46. We have not seen the energies for this system expressed in terms, nor can we do it easily here, but the numbers are in Fig. 6.55, where we can see that a donor, a
withdrawing group, and a C-substituent on C-3 can each accelerate the reaction—the numbers on the right,
4.29 and 4.06, are more negative than for the unsubstituted system, 3.66.
2
3
–3.66
(a) Unsubstituted
1
2
5.66
(b) Substituted by
X- or 'Z'-substituent
–4.29
2
6.29
(c) Substituted by
C-substituent
–4.06
4
Fig. 6.55
8.06
p-Energy changes for a conrotatory cyclobutene opening with a substituent on C-3
6 THERMAL PERICYCLIC REACTIONS
355
6.5.5.4 Alder ‘Ene’ Reactions. Like the Diels-Alder reaction, Alder ‘ene’ reactions usually take place
only when the enophile has a Z-substituent, the regiochemistry is that expected from the interaction of the
HOMO of the ‘ene’ and the LUMO of the enophile, and Lewis acids increase the rate. All these points can be
seen in the reaction of -pinene 6.449 with the moderately activated enophile methyl acrylate, which takes
place at room temperature in the presence of aluminium chloride,928 but which would not have taken place
easily without the Lewis acid. The lowering of the LUMO energy of the methyl acrylate accounts for the
increase in the rate of reaction. Similarly, the rates of diimide reductions of alkenes show some correlation
with ionisation potential and hence orbital properties.929
LUMO
CO2Me
HOMO
CO2Me
AlCl3
H
6.449
6.5.6 Periselectivity
Periselectivity is a special kind of site-selectivity. When a conjugated system enters into a pericyclic reaction, a
cycloaddition for example, the whole of the conjugated array of electrons may be mobilised, or a large part of it,
or only a small part of it. The Woodward-Hoffmann rules limit the total number of electrons (to 6, 10, 14, etc., in
all-suprafacial reactions, for example), but they do not tell us which of 6, 10 or 14 electrons would be preferred if
they were all geometrically feasible. Thus in the [4 þ 6] reaction of cyclopentadiene with tropone 6.45 !
6.46,686,930 there is a possibility of a Diels-Alder reaction, leading to the [2 þ 4] adduct 6.450 (Fig. 6.56). The
products 6.46 and 6.450 are probably not thermodynamically much different in energy, so that will not be a
compelling argument to account for this example of periselectivity, although it may be a factor.
HOMO
HOMO
–0.371
0.371
–0.600
O
0.600
–0.371
0.371
–0.600
0.600
O
O
–0.232
–0.521
0.232
O
–0.521
0.418
–0.232
6.46
–0.418
0.418
0.521
–0.418
0.521
0.232
6.450
LUMO
LUMO
(a) [4+6] Favoured path
Fig. 6.56
(b) [2+4] Less-f avoured path
Frontier orbitals of cyclopentadiene and tropone
The frontier orbitals, however, are clearly set up to make the longer conjugated system of the tropone more
reactive than the shorter. The coefficients of the frontier orbitals of tropone were given in Fig. 6.33. The
largest coefficients of the LUMO of tropone are at C-2 and C-7 (Fig. 6.56a), with the result that bonding to
these sites lowers the energy more than bonding to C-2 and C-3 (Fig. 6.56b), when this frontier orbital is the
356
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
more important, as it usually is. In general, the ends of conjugated systems carry the largest coefficients in
both frontier orbitals, and we can therefore expect pericyclic reactions to use the longest part of a conjugated
system compatible with the Woodward-Hoffmann rules, regardless of which frontier orbital is the more
important. This proves to be true up to a point, with the important qualification that the reactions have also to
be geometrically reasonable. Some examples of this pattern come from the cycloadditions of heptafulvene
6.451 and hexatriene 6.452,931 from electrocyclic reactions of an octatetraene 6.453 and a heptatrienyl anion
6.454,932 and from a sigmatropic rearrangement of a pentadienyl phenyl ether 6.455,933 to which we can add
several reactions illustrated earlier: 6.42 þ 6.43 ! 6.44 to the cycloadditions, and 6.9 ! 6.10, 6.112 !
6.113 and 6.114 ! 6.115 to the sigmatropic rearrangements. All these cases show the largest possible
number of electrons being mobilised, when smaller, but equally allowed numbers might have been used
instead.
CO2Me
CO2Me
+
CO2Me
CO2Me
6.451
SO2
+ SO2
SO2
6.452
6.453
6.454
OH
O
OH
OH
[5,5]
+
+
major
6.455
50%
7%
27%
However, carbenes react with dienes 6.457 to give vinylcyclopropanes 6.458, avoiding the symmetryallowed [2 þ 4] cycloaddition with a linear approach giving cyclopentenes 6.456. Almost the only
exceptions to this pattern are the reaction of difluorocarbene with norbornadiene, where a [2 þ 2 þ 2]
reaction is in competition with the [2 þ 2],934 and the [2 þ 4] pathway taking place in the opposite
direction in the easy loss of carbon monoxide from strained cyclopentenones as in the decarbonylation
6.408 ! 6.409.
6 THERMAL PERICYCLIC REACTIONS
357
Cl
Cl
:CCl2
:CCl2
Cl
Cl
6.456
s-cis-6.457
6.458
s-tr ans-6.457
We have seen that the cyclopropane-forming reaction is allowed when it uses a nonlinear approach 6.161,
but we need to consider why the nonlinear approach is preferred when the linear approach giving a
cyclopentene could profit from overlap to the atomic orbitals with the two large coefficients at the ends of
the diene. One factor which must be quite important is the low probability that the diene is in the s-cis
conformation s-cis-6.457 necessary for overlap to develop simultaneously at both ends. Since the cyclopropane-forming reaction can take place in any conformation, it goes ahead without waiting for the diene to
change from the s-trans-6.457 to the s-cis conformation. Cyclic dienes like cyclopentadiene, fixed in an s-cis
conformation, also react to give cyclopropanes, probably because the alternative would create a strained
bicyclo[2.1.1]hexene ring system. Cyclic dienes in larger rings also form the cyclopropanes, but they have
the two ends of the diene held so far apart that they cannot easily be reached from the one carbon atom of the
carbene. All these factors may be enough to account for the periselectivity leading to cyclopropanes, but it
has been found from a calculation that even when the 1,4-addition is forced on the s-cis diene, there is an
unexpected repulsion embedded in the transition structure, whereas the nonlinear approach of a carbene to an
alkene meets virtually no barrier. The barrier in the linear approach can be ascribed to repulsion between the
subjacent orbital NHOMO with the filled orbital of the carbene (Fig. 6.57a) counteracting the attractions
from the frontier orbitals themselves (Fig. 6.57b and c).935
LUMO
HOMO
NHOMO
1
Fig. 6.57
*
HOMO
2
(a) Repulsion
HOMO
(b) Attraction
LUMO
(c) Attraction
Frontier orbital interactions in the 1,4-addition of a carbene to an s-cis diene
Ketenes also seem to be avoiding the higher coefficients in their reactions with dienes. We have already seen
on pp. 281 and 341 that they can undergo [2 þ 2] cycloadditions in an allowed manner giving adducts like
6.374, but we also have to account for why they do so, even when [2 þ 4] reactions are available. The [2 þ 4]
reactions giving the adduct 6.459 or 6.460 would involve the higher coefficients in the HOMO of the diene,
which seemingly ought to make these reactions faster.
The reason why the C¼C double bond of a ketene does not react as the p2s component of a [p2sþp4s]
reaction, giving the adduct 6.460, is that the orbital localised on the C¼C double bond is at right angles to the
O
O
O
or
Cl
Cl
6.459
Cl
Cl
6.460
[2+4]
O
[2+2]
+
Cl
Cl
Cl
6.374
Cl
358
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
p orbitals of the C¼O double bond. Consequently, the C¼C p bond does not have a low-lying LUMO. Its
LUMO is raised in energy by the conjugation with the lone pair on the oxygen atom, and it is not, therefore, a
good dienophile. In the [2 þ 2] reaction, however, it is the LUMO of the C¼O p bond that is involved in
forming the leading C—C bond, and this is low-lying in energy, especially as it is in this case conjugated to
two C—Cl bonds.936 The [4 þ 2] isomer in which the carbonyl group is the dienophile, giving the ether
6.459, is presumably unfavourable just as any other Diels-Alder with a carbonyl group is unfavourable
(Section 6.5.2.3), but a [4 þ 2] cycloaddition of this type is known for diphenylketene, which gives the
adduct 6.461 at low temperature. On warming, this adduct undergoes a [3,3] Claisen rearrangement to give
what looks like a [2 þ 2] adduct 6.462. 1-Methoxybutadiene works the other way round, giving initially the
[2 þ 2] adduct 6.463, which undergoes a [3,3] Claisen rearrangement to give what looks like a [4 þ 2] adduct
6.464.937 Periselectivity is evidently delicately balanced, and the direct [4 þ 2] pathway is probably seen
only because cyclopentadiene is inherently in the s-cis conformation. The fact that the Claisen rearrangement
interconverts the two isomers makes it possible that other apparent [4 þ 2] and [2 þ 2] reactions may actually
be a consequence of rearrangements.
O
+
[4+2]
O
[3,3]
O
–20 °C
0 °C
Ph
Ph
Ph
Ph
Ph
Ph
6.461
MeO
6.462
OMe
MeO
O
Ph
[2+2]
Ph
O
[3,3]
Ph
Ph
+
Ph
0 °C
25 °C
O
Ph
6.464
6.463
Another example where the longest possible conjugated system is not used is the dimerisation (see p. 320) of
hexatriene 6.465, and of many similar compounds. This takes place in a Diels-Alder manner to give the
cyclohexene 6.288, not only for the trans isomer but also for the cis, which might, in principle, have undergone
a [4 þ 6] dimerisation to give the cyclodecatriene 6.466. Presumably the hexatriene is rarely in the right planar
conformation to be a p6 component, even though this would be preferred on frontier orbital grounds.
In open-chain and in some cyclic systems, therefore, reactions often take the path which uses the longest
part of the conjugated system consistent with a symmetry-allowed reaction, but several other factors, spatial,
entropic, steric, and so on, have obviously to be taken into account. Thus various sesquifulvalenes, with
HOMO coefficients in the parent system 6.467, react in a variety of ways. The reaction giving the [8 þ 2]
adduct 6.468 finds the sites with the highest Sc2 value, but the three reactions with tetracyanoethylene giving
the adducts 6.469–6.471 show different selectivities, for no obvious reason. These examples serve to
emphasise the pitfalls of a too easy application of frontier orbital theory.
–0.418
–0.418
–0.232
+
0.521
HOMO
–0.521
+
0.521
6.465
0.521
LUMO
6.288
0.521
HOMO 6.465
LUMO
6.466
6 THERMAL PERICYCLIC REACTIONS
359
–0.426
0.183
HOMO
NC
0.531
CN [8+2]
+
–0.064
CN
CN
–0.284
NC
–0.098
CN
CN
CN
0.228
6.468
6.467
Ph
Ph
Ph
Ph
Ph NC
+
CN
NC
CN
[4+2]
Ph
Ph
Ph
CN
CN
CN
CN
6.469
But
H
But
NC
CN
NC
CN But
But
CO2Me
But
CO2Me
CO2Me
CN
CN
CN
CN
[12+2]
CO2Me
But
[4+2]
H
6.470
6.471
More readily identifiable geometrical factors probably outweigh the contribution of the frontier orbitals in the
remarkable reaction 6.47 between tetracyanoethylene and heptafulvalene giving the adduct 6.49 (see p. 261).
The HOMO coefficients for heptafulvalene 6.420 (see p. 347) are highest at the central double bond, but a
Diels-Alder reaction, with one bond forming at this site is impossible. The best reasonable possibility for a
pericyclic cycloaddition, from the frontier orbital point of view, would be a Diels-Alder reaction across the
1,4-positions (HOMO coefficients of –0.199 and 0.253), but this evidently does not occur, probably because
the carbon atoms are held too far apart. This is well-known to influence the rates of Diels-Alder reactions:
cyclopentadiene reacts much faster than cyclohexadiene, which reacts much faster than cycloheptatriene (see
p. 302). The only remaining reaction is at the site which actually has the lowest frontier-orbital electron
population, the antarafacial reaction across the 1,10 -positions, which have HOMO coefficients of 0.199.
Dimethylfulvene 6.422, which we have already seen on p. 348 showing different site selectivity in its
reactions with electrophilic and nucleophilic carbenes, also shows a variety of different periselectivities in
which the longest conjugated system available is not always the one involved in cycloadditions, but this time
frontier orbital theory is rather successful in accounting for the experimental observations. The frontier
orbital energies and coefficients are illustrated again in Fig. 6.58.938,939 The result of there being a node
through C-l and C-6 in the HOMO is that when a relatively unsubstituted fulvene might react either as a p6 or
as a p2 component with an electron-deficient (low-energy LUMO) diene or dipole, it should react as a p2
component because of the zero coefficient on C-6 in the HOMO. This is the usual reaction observed
with electrophilic dienes like the nitrile 6.473, derived from the benzcyclobutene, and
360
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
0
+2
0.72
–1
–0.42
1
–0.49
–0.42
0.35
5
NLUMO
–0.27
LUMO
6
0
0.49
0.74
–0.74
0.35
2
4
3
0
–8.6
6.422
HOMO
–0.56
–0.38
Fig. 6.58
–0.44
0
0.56
–9.5
NHMO
–0.54
–0.03
–0.03
0.38
0.40
0.40
Energies and coefficients of the frontier orbitals of 6,6-dimethylfulvene
dimethyldiphenylcyclopentadienone 6.474, and with dichloroketene 6.477 and electrophilic dipoles like
benzonitrile oxide 6.478 giving adducts 6.472, 6.475, 6.476 and 6.479, respectively. 940–942
Ph
O
H
Ph
CN
6.473
Ph
6.474
CO
Ph
H
CN
6.472
O
6.476
Cl
Cl
6.475
O
Cl
Cl
6.422
O
N
Ph
Ph
O
6.478
NH +
6.477
39%
Ph
N
31%
O
6.479
Equally, when it reacts with tropone 6.480 as a p4 component, it does so at C-2 and C-5 to give the tricyclic
ketone 6.481, because the coefficients in the HOMO are large at these two positions.943
O
HOMO
LUMO
+ O
6.422
6.480
6.481
In contrast, if the important frontier orbital in the cycloaddition is the LUMO of the fulvene, and if the
fulvene is to react as p2 or p6 component, it will now react as a p6 component, because the largest coefficients
are on C-2 and C-6. For this to be feasible, its partner must have a high-energy HOMO, since it does not itself
have a particularly low-energy LUMO. This pattern of periselectivity is found with the electron-rich diene
6 THERMAL PERICYCLIC REACTIONS
361
1.8
1
LUMO
LUMO
–1
LUMO
10.4
9.6
8.0
8.1
–8.6
–9
HOMO
HOMO
–9.1
HOMO
N
N
Fig. 6.59
Frontier orbital interactions for dimethylfulvene, diazomethane and butadiene
6.483 and with diazomethane.944,945 The LU(fulvene)/HO(diazomethane) interaction is probably closer in energy
than the HO(fulvene)/LU(diazomethane) (Fig. 6.59), and this explains the formation of the adduct 6.484. The
regiochemistry is also appropriate for this pair of frontier orbitals.
HOMO
O
N
6.483
O
N
N
N
[4+6]
[4+6]
H
NH
–H+
N
+H+
LUMO
6.482
6.422
6.484
Similarly, although reaction with a simple diene ought also to be dominated by the LU(fulvene)/HO(diene)
interaction (Fig. 6.59), the observed product 6.485 from the reaction of dimethylfulvene with cyclopentadiene has the fulvene acting as a p2 component rather than as a p6 component.941 This anomaly has
been explained by invoking the next-lowest unoccupied orbital (NLUMO) of fulvene (Fig. 6.58).938 This
orbital has zero coefficients on C-l and C-6, and hence relatively large coefficients on C-2 and C-3. The
interaction of this orbital with the HOMO of cyclopentadiene is apparently large enough to tip the
balance in favour of the [2 þ 4] adduct 6.485. This result is in contrast to the result with the diene 6.483
having the higher energy HOMO, for which the interaction with the LUMO of the fulvene is proportionately greater than that with the NLUMO. The same change to a [4 þ 6] reaction is also seen with 1aminobutadienes, which also have higher level HOMOs.946 These examples come as another useful
reminder that the frontier orbitals are not the only ones to be interacting as the reaction proceeds. They
usually appear to be the most important orbitals but they can never be assumed to be decisive.
6
1
5
2
4
3
6.422
[2+4]
6.485
6-Dimethylaminofulvene 6.486 has a powerful X-substituent on C-6, raising the energy of the HOMO and
losing the symmetry, so that the coefficient on C-6 is no longer zero and the coefficient on C-2 is raised. The
362
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
reaction with a Z-substituted diene 6.487 now leads to a mixture of regioisomers of the hydroazulenes 6.488,
in both of which the new bonds are to C-2 and C-6 on the fulvene from C-1 and C-4 on the diene. The result
was an expeditious synthesis of the azulenes 6.489.947
Me
Me2N
Me(Et)
Me2N
O2S
6.487 Et
O2S
[4+6]
H
Et(Me)
6.488
6.486
Me(Et)
Et(Me)
6.489
This section on periselectivity has been disproportionately long. It is one of those subjects which frontier
orbital theory has rationalised reasonably well, for all its inherent limitations. It is a fitting close to this
section to reflect upon the bewildering variety of cycloadditions shown by dimethylfulvene, and to reflect
upon how difficult it would be to explain the pattern of their reactions without frontier orbital theory.
6.5.7 Torquoselectivity
Torquoselectivity applies only to electrocyclic ring openings and closings, and refers to which of the two possible
senses in which an electrocyclic ring opening can take place is the faster. In a conrotatory ring opening with a
total of (4n) electrons, the two outer substituents R in the drawing 6.71 can follow each other to the right in a
clockwise rotation, as illustrated in Fig 6.3, or they can follow each other to the left in an anticlockwise rotation.
If the two groups R are the same, there is no difference in the energies, since the transition structures are
enantiomeric. If they are different, there is a remarkable level of torquoselectivity determining which substituent
shall turn up on the cis double bond and which on the trans. The observation is that X-substituents selectively
move outwards to be on the trans double bond. The benzcyclobutene opening 6.443 ! 6.444 on p. 354 might
have been put down to a purely steric effect, but torquoselectivity is not driven only by steric effects, for the more
powerfully electron-donating the X-substituent is in the cyclobutenes 6.490, the stronger is the preference for the
formation of trans-6.491.948 The activation energy for ring opening is lower when electron-donating substituents
are rotating outwards than it is for the ring opening of cyclobutene itself, with a methyl group and an ethoxy
group lowering the energy by 3.8 kJ mol1 (0.9 kcal mol1) and 38 kJ mol1 (9.0 kcal mol1), respectively. The
activation energy for ring closing is similarly lower when there is a methoxy group in the outside position of a
diene as we saw earlier when it determined the ease of the cyclisation of the intermediate 6.393 on p. 344.
Furthermore, the activation energy for ring opening is raised if an electron-donating substituent is forced to rotate
inwards. Dramatically, the better X-substituent moves outwards in the ring opening of the cyclobutene 6.492,
even though this places the tert-butyl group in the more hindered position in the diene 6.493.949
R
R
heat
+
6.490
tr ans-6.491
R
R = EtO > AcO > Cl > Me
cis-6.491
MeO
MeO
heat
6.492
tr ans:cis
6.493
6 THERMAL PERICYCLIC REACTIONS
363
Even more remarkable, Z-substituents move inwards to be on a cis double bond. Examples are the
formation of the cis,cis-diene 6.495, in which the trifluoromethyl groups have moved inwards from
the trans-3,4-disubstituted cyclobutene 6.494,950 and the formation of the cis-butadienal 6.497 from the
cyclobutene 6.496, in which the aldehyde group has moved inwards.951 Steric effects are not absent, since
the corresponding methyl ketone 6.498, with a larger Z-substituent, gives the trans-butadienyl ketone trans6.499, but in the presence of Lewis acids, when coordination to the carbonyl group makes it into a more
powerfully electron-withdrawing substituent, the ring opening gives the cis-butadienyl ketone cis-6.499 in
spite of the fact that the substituent is larger when coordinated to the Lewis acid.952
F
F
CF3
F
heat
F
CF3
F
COMe
F
CF3
heat
CF3
F
COMe
F
6.495
6.494
trans-6.499
CHO
heat
CHO
heat
COMe
6.498
Lewis acid
6.496
cis-6.497
cis-6.499
Houk has explained this pattern in two ways.953 The most simple is to note that the transition structure
for conrotatory opening with a filled p orbital inside 6.500 has a three-atom, four-electron conjugated
system (ignoring the electrons of the p bond for the moment), which will be antiaromatic, whereas an
empty orbital inside 6.501 has a three-atom, two-electron conjugated system, which will be aromatic.
His calculations indicate that there is very little involvement of the p orbitals of the p bond in the
transition structure, but even if they are included, the conjugated system is then of the Möbius kind and
the systems are still antiaromatic and aromatic, respectively. Furthermore, an orbital outside, whether
filled or unfilled, is becoming part of a longer conjugated system as the reaction proceeds, and this will
lower the p energy. The net result is that there is a preference for X-substituents to rotate outwards, and a
weaker preference for Z-substituents to rotate inwards, as observed. The formation of cis,cis stereochemistry in the perfluorohexa-2,4-diene 6.495 is driven more by the fluoro substituents on C-2 and C-5,
which are p donors, moving outwards, than by the trifluoromethyl groups, which are p acceptors, moving
inwards.
6.500
6.501
The second explanation is a more thorough dissection, which will only be summarised here, of what amounts
to the same perception. The frontier orbitals of the transition structure for an unsubstituted cyclobutene
undergoing conrotatory opening are approximately and * in the centre of Fig. 6.60, related to the original
and * orbitals of the bond, and having so little interaction with the p bond at the back that we can neglect
that complication. The effect of the substituent can be estimated by looking at how a filled p orbital on
oxygen will interact with these orbitals when it is held one bond away from the left-hand atom, either on the
inside, on the left, or on the outside, on the right. In both cases, the interaction of the p orbital with and *
will have a bonding combination, largely resembling the original p orbital, but lowered in energy.
364
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
O
O
*
O
O
O
Fig. 6.60
Orbital interactions in conrotatory opening of a 3-substituted cyclobutene
The interactions in an antibonding combination will create orbitals raised in energy. The difference between
inside and outside is that, on the inside, on the left, there is an extra antibonding interaction, marked with a
wavy line, with the atomic orbital of the more distant atom, raising the energy of more than when the p
orbital is on the outside, where that interaction is missing. In addition, the interaction with * is less
antibonding on the left, because there is a small attraction, marked with a dashed line, which is absent on
the right. These orbitals are empty, and have no direct effect on the energy of the transition structure, but
these same interactions have consequences on the p orbital energy, which is pushed lower on the right just as
* is pushed higher. The net result is that the overall energy of the filled orbitals is lower in the arrangement
on the right than on the left.
A trimethylsilyl group is a weak Z-substituent, because the Si—Me bonds are polarised away from silicon
towards the carbon. Weak though its p electron-withdrawing properties are, the silyl group in the cyclobutene 6.502 moves predominantly inwards in spite of the steric crowding in the product cis-6.503.
Furthermore, the presence of the silyl group accelerates the electrocyclic opening relative to the rate for
the corresponding cyclobutene lacking the silyl group, just as a methoxy group accelerates the opening when
it is moving outwards.954 An Si—C bond is polarised towards the carbon atom of the cyclobutene ring,
making the silyl group like an anion; this perception is matched by the torquoselectivity for the electrocyclic
opening of a 3-azacyclobutene, in which the lone pair has been predicted to move inwards, just as the silyl
group does, and the substituent on the nitrogen to move outwards.955
n-C8H17
140 °C
n-C8H17
n-C8H17
+
SiMe3
SiMe3
SiMe3
6.502
cis-6.503
83:17
tr ans-6.503
The Nazarov reaction, in which the key electrocyclic step is the conrotatory process 6.505, has one more
atom in the ring but the same number of electrons. The question with respect to torquoselectivity now, since
this reaction is taking place in the opposite direction, namely ring-closing, is which reacts faster, a dienone
6 THERMAL PERICYCLIC REACTIONS
365
with an X- or a Z-substituent inside, or with an X- or a Z-substituent outside? In the absence of chirality, there
is no torquoselectivity as such in a cyclisation, but there is by implication, in that the reverse reaction, were it
to take place, would have torquoselectivity. Nothing much is known about substituent effects, but calculations have predicted that the same pattern as that found in cyclobutene openings obtains—a silyl group
should accelerate the ring closure if it is inside 6.504, but a methyl group, a weak X-substituent, should slow
it down if it is inside 6.506.956
OH
OH
OH
predicted to
be faster than:
SiH3
6.504
predicted to
be faster than:
H
Me
6.505
6.506
Another silicon-assisted kind of torquoselectivity is in the allylsilane-type of Nazarov cyclisation. Now there
is chirality, and there is a high level of torquoselectivity in the sense shown by the allylsilane 6.507,
determined by the chirality.957
Me3Si
Me3Si
O
O
FeCl3
O
H
FeCl3
H
6.507
H
6.509
6.508
It is perhaps more simple to note that both the vinylsilane reaction 6.504 and the allylsilane reaction
6.507 are showing the normal pattern of stereochemistry for their reactions with electrophiles: a
preference for retention of configuration in the double bond geometry for a vinylsilane, and anti for an
allylsilane, where anti refers to the side of the double bond to which the new bond is formed relative to
the side on which the silyl group resides. In the product 6.509, the new C—C bond has formed to the
lower surface of the left-hand double bond, while the silyl group was conjugated to the top surface in the
allylsilane 6.508.
With two more electrons, the disrotatory ring opening of a hexatriene, with a total of (4nþ2) electrons,
has the two upper substituents R in 6.69 able to move outwards, as illustrated for the reaction going from
right to left in Fig. 6.3, or able to move inwards. In general, steric effects seem to dominate, and the larger
substituents move outwards. More usually, the reaction seen is in the other direction, and the question is
then: which reacts faster, a hexatriene with one substituent on a cis double bond and the other on a trans,
or to have them both on a trans double bond. The former leads to a cyclohexadiene with the two
substituents trans to each other, which is usually the lower in energy. Nevertheless the ring closure
cis-6.510 ! anti-6.511 is slower than the ring closure trans-6.510 ! syn-6.511 by a factor of
about 20.958
Ph
Ph
Ph
Ph
cis-6.510
anti-6.511
Ph
20
slower
than
Ph
Ph
tr ans-6.510
Ph
syn-6.511
366
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
Houk has explained this by pointing out that the same considerations apply as in cyclobutene openings,
but, with two more electrons, an X-substituent on the inside will contribute to an antiaromatic transition
structure, and a Z-substituent on the inside will contribute to an aromatic transition structure.959 In both
cases the effect will be less than it was for the conrotatory opening and closing in cyclobutenes,
electronically because the orbitals in a disrotatory process 6.512 and 6.513 will be less well aligned for
overlap, whether energy-raising as in 6.512 or energy-lowering as in 6.513. Furthermore, a transition
structure looking like 6.514 must have a substantial steric clash between two of the substituents, which
makes the steric component deterring any substituent from occupying the inside position more severe than
it was for a conrotatory process. The prediction is that the electronic nature of the substituents will have
only a small contribution, and that steric effects are likely to be more important than they were in
cyclobutene openings.
6.512
6.513
6.514
Torquoselectivity of a different but more powerful kind is found in the ring opening of cyclopropyl halides.
These reactions are formally related to the disrotatory opening of a cyclopropyl cation to give an allyl cation,
but the opening is concerted with the loss of the leaving group. Cyclopropyl cations themselves are high
energy species, and are not intermediates, as can be seen in the reactions of the stereoisomeric halides 6.515–
6.517, which give the stereoisomeric cations 6.518–6.520, respectively.141 These cations are configurationally stable at the low temperatures used. If the free cyclopropyl cation had been involved the cyclopropyl
halides 6.515 and 6.516 would have given the same allyl cations instead of one giving the W-shaped cation
6.518 and the other giving the U-shaped cation 6.519. In all three cases, although only the first and second
prove it, the torquoselectivity is such that the chloride ion leaves from the same side as that in which the
substituents move towards each other.
H
H
Cl
H
6.515
H
Cl
H
6.516
6.517
–100 °C
SbF5SO2ClF
6.518
H
Cl
6.519
6.520
The most simple explanation is that if the substituents on the same side as the leaving group, the methyl
groups in the cyclopropyl chloride 6.516, are moving towards each other, and the substituents on the
opposite side are moving apart, as they do in forming the allyl cation 6.519, then the bulk of the electron
population from the breaking bond is moving downwards 6.521 (arrow) through a transition structure
6.522 to the allyl cation 6.523, effectively providing a push from the backside of the C—Cl bond.
6 THERMAL PERICYCLIC REACTIONS
367
Torquoselectivity in this series is a powerful force, overriding any steric clash of the two methyl groups
moving towards each other.
Cl
Cl (–)
Cl
Me
Me
Me
Me
(+)
Me
H
H
H
H
Me
H
H
6.521
6.523
6.522
It is powerful enough to lead the cyclopropyl bromide 6.524 to give the trans-cyclooctenol 6.526, in spite of
the strain from having a trans double bond in a ring of this size.960 The arrow on the drawing 6.524 is like that
in 6.522 showing the electrons moving in behind the C-halogen bond, and creating in the disrotatory opening
a W-shaped cation 6.525. No matter which end of the cation is attacked by the nucleophile, a trans double
bond must be formed.
H
H2O
Br
H
H
H2O, dioxan
H
H
reflux, 28 h
6.524
t
HO 6.526
6.525
The isomeric cyclopropanes 6.527 and 6.529 lose fluoride and chloride, respectively, in spite of the much
better nucleofugal properties of the latter. The sense of torquoselectivity is determined because only a Ushaped cation can be formed in the six-membered ring leading to the products 6.528 and 6.530, and this in
turn determines which of the halide ions leaves.961
F
Cl
F
150 °C
Cl
150 °C
Cl
F
Cl
6.527
6.528
F
6.529
6.530
The reverse reaction of this general class—an allyl cation giving a cyclopropyl cation—is found in
Favorskii rearrangements. The diastereoisomeric cis and trans -chloro enolates 6.531 give the cis and
trans cyclopropanones 6.532, respectively, with the cis and trans designation referring to the relationship
between the nucleophilic enolate carbon C-20 and the resident methyl group on C-2 that is acting as a
stereochemical label. Thus the reaction is stereospecific with inversion of configuration at C-1, at least in a
nonpolar solvent. Evidently the allyl cation is not formed, otherwise the two chlorides would give the same
product or mixture of products. The cyclisation step is presumably disrotatory with the torquoselectivity
determined by which side of the allyl system the chloride leaves from. The cyclopropanone is not isolated,
because the alkoxide attacks the carbonyl group with subsequent cleavage of the bond towards the methyl
group giving the esters cis and trans 6.533.962
368
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
O
2'
2'
2'
–
Et2O
1
Cl
O
cis-6.531
OBn
CO2Bn
cis-6.532
cis-6.533
O
CO2Bn
Cl
1
O
Et2O
–
2'
OBn
2'
2'
tr ans-6.531
trans-6.532
tr ans-6.533
In a more polar solvent, Favorskii reactions cease to be stereospecific,963 and presumably take place by
ionisation of the chloride to give the same cation from each diastereoisomer. Whether the reaction takes
place by way of the cation, when it is 3-endo-trig at both ends, or with concerted loss of the chloride ion,
when it is 3-endo-trig at the enolate carbon, this reaction presented a serious puzzle before its pericyclic
nature was recognised. The overlap of the p orbital on C-20 of the enolate with the p orbital at the other end
of the allyl cation 6.534 (or with the orbital of the C—Cl bond 6.535) looked forbiddingly unlikely. We can
now see that it is made possible by its pericyclic nature, where the tilt of the orbitals can begin to sense the
development of overlap, even though it is not at first in character, and is a further illustration of the extent to
which Baldwin’s rules do not apply in pericyclic reactions. The torquoselectivity in the development of
overlap 6.535, however improbable it looks, corresponds to the usual inversion of configuration at the carbon
atom from which the chloride departs.
Cl
O
O
2'
2'
6.534
6.535
With two more electrons, and rather more complicated structures, the Nazarov-like reactions of the
carbamates 6.536 and 6.538 are conrotatory, with the torquoselectivity determined, as in the Favorskii
reactions, by which side of the conjugated system the nucleofugal group departs from, clockwise as drawn
for the carbamate 6.536 and anticlockwise for its diastereoisomer 6.538.964 The topological sense of the
event in the left-hand allylic system corresponds to an anti SN20 reaction in both cases.
OCONPri2
Br
OLi
Ph
Pri2NCOO
Br
O
6.536
But
OLi
Ph
Ph
H
Br
6.537
O
But
Ph
t
Bu
Br
H
6.538
But
6.539
Notice how the two starting materials 6.536 and 6.538 differ from each other stereochemically in two
respects: the configuration at the carbon atom carrying the carbamate group and the configuration of the
allenolate system. Likewise, the products 6.537 and 6.539 differ in two respects: the configuration of the
carbon atom carrying the phenyl group and the geometry of the exocyclic double bond. The stereospecificity
is shown by the absence of the other pair of diastereoisomers in the product mixtures.
7
Radical Reactions
Much of the selectivity seen in radical reactions may be explained by frontier orbital theory, in contrast to
ionic reactions, where it makes a relatively small contribution. Frontier orbital theory may not be well
founded as a fundamental treatment, but it is appropriate that it might come to the fore with radicals, where
Coulombic forces are usually small, orbital interactions likely to be strong, and the key steps usually
exothermic. Most of the discussion in this chapter will use frontier orbital theory, and will seem to do so
uncritically.965 It is important to remember that it is not as sound as its success in this area will make it seem.
7.1
Nucleophilic and Electrophilic Radicals
We saw in Chapter 2 that all substituents, C-, Z- or X-, stabilise radicals, that carbon-based radicals are
usually pyramidal, with a low barrier to inversion of configuration, and that the energy of the singly occupied
molecular orbital (SOMO) was inherently close to the nonbonding level, unchanged by C-substitution,
lowered by Z-substitution and raised by X-substitution. In contrast to the frontier orbitals in ionic and
pericyclic reactions, the SOMO can interact with both the HOMO and the LUMO of the reaction partner to
lower the energy of the transition structure (Fig. 7.1).966,967 Plainly the interaction with the LUMO will lead
to a drop in energy (E3 in Fig. 7.1b) but so does the interaction with the HOMO, and, for that matter, with
each of the filled orbitals. Because there are two electrons in the lower orbital and only one in the upper, there
will be overall a drop in energy (2E1 – E2) from this interaction. We can combine these effects in the frontier
LUMO
E2
SOMO
SOMO
E1
(a) SOMO-HOMO
Fig. 7.1
LUMO
SOMO
E3
HOMO
HOMO
(b) SOMO-LUMO
(c) SOMO-HOMO/LUMO
The interaction of the SOMO with the HOMO and the LUMO of a molecule
Molecular Orbitals and Organic Chemical Reactions: Reference Edition
© 2010 John Wiley & Sons, Ltd. ISBN: 978-0-470-74658-5
Ian Fleming
370
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
orbital picture in Fig. 7.1c. Radical reactions are consequently fast, and, in favourable cases, are even
diffusion controlled, having little or no activation enthalpy.
Radicals are soft: most of them do not have a charge, and in most chemical reactions they react with
uncharged molecules. Thus the Coulombic forces are usually small while the orbital interactions remain
large. This is borne out by such well-known reactions as the attack of radicals at the conjugate position of
,-unsaturated carbonyl compounds like methyl methacrylate 7.1, rather than at the carbonyl group, and the
attack by the ambident -carbonylmethyl radical 7.2 from the carbon atom, not from the oxygen atom. The
clean and industrially important polymerisation giving poly(methyl methacrylate) (PMMA) demonstrates
both of these typically soft patterns of behaviour.
R
OMe
R
OMe
O
7.1
OMe
O
7.2
O
OMe etc.
R
CO2Me
O
7.1
Highly reactive species like radicals are not usually expected to show high levels of selectivity (the reactivityselectivity principle), and so it had always been something of a puzzle why they did, nevertheless, have
nucleophilic and electrophilic character—some radicals showing higher reactivity with reagents normally
thought of as electrophilic, and others higher reactivity with reagents normally thought of as nucleophilic.
These observations are easily explained by frontier orbital theory. Radicals with a high-energy SOMO (Fig. 7.2a)
will react fast with molecules having a low-energy LUMO, characteristic of electrophiles, and radicals with a
low-energy SOMO (Fig. 7.2b) will react fast with molecules having a high-energy HOMO, characteristic of
nucleophiles. The former are therefore the nucleophilic radicals and the latter are the electrophilic radicals.
LUMO
LUMO
SOMO
SOMO
HOMO
HOMO
(a) High-energy SOMO—a nucleophilic radical (b) Low-energy SOMO—an electrophilic radical
Fig. 7.2
Frontier orbital interactions for a nucleophilic and an electrophilic radical
This insight is strikingly illustrated by the observation of alternating copolymerisation from a 1:1 mixture of
dimethyl fumarate 7.3 and vinyl acetate 7.5.968,969 The radical-initiated polymerisation takes place largely970
to give a polymer in which the fragments derived from the two monomers alternate along the chain. In this
case it is evident that a growing radical such as 7.4 attacks vinyl acetate rather than fumarate; but the new
radical 7.6, so produced, attacks fumarate rather than vinyl acetate. The radical 7.4, because it is flanked by a
carbonyl group, in other words by a Z-substituent, will have a low-energy SOMO (see p. 81), and will be an
electrophilic radical. It therefore reacts faster with the molecule having the higher energy HOMO, namely
the X-substituted alkene 7.5. Furthermore, the coefficient in the HOMO of the X-substituted alkene 7.5 will
be particularly large (see p. 76) at the terminal carbon atom where bonding takes place The new radical 7.6 is
7 RADICAL REACTIONS
371
next to an oxygen atom, in other words an X-substituent, and will have a high-energy SOMO (see p. 81). It
will be a nucleophilic radical, closer in energy to a low-lying LUMO. Of the two alkenes 7.3 and 7.5, the
fumarate, because it is a Z-substituted alkene, has the lower energy LUMO (see p. 73), and it is therefore this
molecule which reacts with the radical 7.6—and so on, as the polymerisation proceeds. This explanation for
alternating polymerisation satisfyingly avoids the vague terms, such as ‘polar factors’, which had been used
in the past.
CO2Me
CO2Me
OAc
R
R
CO2Me
CO2Me
7.3
OAc
MeO2C
CO2Me MeO2C
7.4
OAc
CO2Me
etc.
R
R
CO2Me
7.5
CO2Me
7.6
CO2Me
CO2Me
7.3
In general: radicals with a high-energy SOMO show nucleophilic properties and radicals with a
low-energy SOMO show electrophilic properties.
Radicals show three types of reaction: substitution 7.7, addition to double bonds 7.8, and radical-with-radical
combination 7.9, and the reverse of each of these reactions. We shall now look at these in turn to see how the
various kinds of selectivity in each of them can be explained.
R
X
R
R
RX +
7.7
7.2
R
R
7.8
R
R
7.9
The Abstraction of Hydrogen and Halogen Atoms
7.2.1 The Effect of the Structure of the Radical
Substitution 7.7 most commonly takes place by the radical abstracting a hydrogen atom (X ¼ H), a chalcogen
substituent (X ¼ SR or SeR), or a halogen (X ¼ Br or I). Most work on the effect of the structure of the radical
has been carried out for hydrogen atom abstraction. At first glance the story is simple: the less-stabilised the
radical the faster it abstracts a hydrogen from such reagents as tributyltin hydride. Thus methyl, ethyl,
isopropyl and tert-butyl radicals have relative rates of 5.6, 1.2, 0.8 and 1, respectively, more or less reflecting
the exothermicity of the reaction.971 The story is actually more complicated because different radicals
abstract different hydrogen atoms from butyrolactone 7.11: alkoxy radicals selectively abstract the hydrogens from the methylene group adjacent to the oxygen atom, whereas a boryl radical abstracts the hydrogens
from the position to the carbonyl group.972 The bond dissociation energies of the two kinds of C—H bond
are about the same, and both product radicals, 7.10 and 7.12, are stabilised. There must be some extra kinetic
factors not included in the simple thermodynamics of the overall event.
t
O
BuO
H
H
O
O
7.10
H2B-NEt3
O
O
7.11
O
7.12
372
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
The frontier orbitals are the SOMO of the radical and the local or * orbitals of the C—H bonds (Fig. 7.3).
The tert-butoxy radical, based on an electronegative element, will have a low-energy SOMO, and will have a
stronger interaction D with the orbital which is high in energy for having an adjacent X-substituent. In
contrast, the boryl radical, based on an electropositive element, will have a high-energy SOMO, and it will have
a stronger interaction A with the lower-energy * orbital of the C—H bond adjacent to the Z-substituent. The
interaction A is more effective than C for the boryl radical, and D more effective than B for a butoxy radical. If
A and D are the dominant interactions, then the observed pattern of reactivity is explained.
H
LUMO
O
O
H
LUMO
A
O
Et3N-BH2 SOMO
O
B
C
t
BuO
SOMO
H
D
HOMO
O
O
H
HOMO
O
O
Fig. 7.3 Interactions for the attack of tert-butoxy and boryl radicals on butyrolactone
Another example of this type of selectivity, more muted but still easily measurable, is the different
selectivities shown by methyl radicals and chlorine atoms for the methylene and methyl groups of propionic
acid 7.14. Methyl radicals abstract the hydrogen atoms on C-2 5.2 times faster than the hydrogen atoms on
the methyl group C-3. However, chlorine atoms abstract the hydrogen atoms on the methyl group 50 times
faster than the hydrogen atoms on C-2.973
Me
H
Me
H
k rel 1
2
3
CO2H
k rel 5.2
7.14
CO2H
CO2H
7.13
Cl
k rel 50
k rel 1
H
Cl
H
2
3
7.16
CO2H
7.14
From the picture of C—H bonding in Chapter 1, we can deduce that the SOMO of a methyl radical is close
to half way between the local and * orbitals of a C—H bond, or, to put it another way, at the level of
Hückel theory. The interactions should be more or less equally the SOMO of the methyl radical with the
HOMO and with the LUMO of a simple C—H bond.974 In this case, the lowering of the LUMO for the C—H
7 RADICAL REACTIONS
373
bond adjacent to the carbonyl group makes it closer in energy to the SOMO of the methyl radical, and there
must be a small contribution from the greater stability of the radical produced 7.16 than of the primary alkyl
radical 7.13. The chlorine atoms, however, will have a much lower energy SOMO, and will be relatively
electrophilic in character, selecting the C—H bonds that are not conjugated to the carbonyl group.
A number of radicals abstracting the hydrogen atom from p-substituted toluenes have been studied, and
Hammett -values from the relative rates of these reactions plotted against the SOMO energy, as measured by
the ionisation potential (Fig. 7.4). The -value for a methyl radical in this reaction is only –0.2, confirming that
it is if anything slightly electrophilic. Other radicals give larger values, but they are all fairly small compared
with the -values found for many ionic reactions. Some radicals give larger negative -values, indicating that
the attack is by a more electrophilic species, and others give positive values indicating attack by a nucleophilic
species. Although agreement among the numbers is not perfect, the trend seems to suggest that those radicals
with high-energy SOMOs, like the triethylsilyl and substituted alkyl radicals, show nucleophilicity (with
positive -values), whereas the oxy and halogen radicals, with low-energy SOMOs, are distinctly electrophilic.
The alkyl series shows a reasonably good correlation between SOMO energies and -values.975
1.0
H
0.8
0.6
0.4
H
H
R
But
C5H11
C9H21
0.2
SiEt3
X
0
Me
–0.2
Ph
ButO
–0.4
OOBut
–0.6
Cl
–0.8
CH2CO2H
–1.0
–1.2
–1.4
Br
–1.6
–13
–12
CCl3
–11
–10
–9
–8
–7
–6
Ionisation potential (eV) (SOMO energy)
Fig. 7.4
-Values for hydrogen abstraction from p-substituted toluenes
When the SOMO/HOMO interaction is the more important, and assuming, as is usually true for hydrogenabstraction reactions, that the SOMO energy lies between that of the HOMO and the LUMO, the radical with
the higher-energy SOMO will be less reactive than the one with the lower-energy SOMO (because 2E1 – E2
in Fig. 7.1 will be smaller). This explains why the ButOO • radical is 10 000 times less reactive in hydrogen
abstraction than the ButO • radical.976 Here we see the -effect making an electrophilic radical less reactive,
whereas it made a nucleophile more reactive (see p. 155); the cause is the same, namely the raising of the
energy of the HOMO. It may be that the lower reactivity of the ButOO • radical makes it more selective than
the ButO • radical, and similar factors may explain the other anomalous entries in Fig. 7.4.
7.2.2 The Effect of the Structure of the Hydrogen or Halogen Source
7.2.2.1 Selectivity Affected by the Nature of the Radical. Selectivity is also seen in which atom is
abstracted when there is more than one to choose from, as we have seen already in the reactions of the lactone
7.11 and propionic acid 7.14. When the tributyltin radical has a choice of a C—S, a C—Se, or a C—halogen bond,
374
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
they are selected, other things being equal, in the order I > Br > SeAr > Cl > SAr > SMe. This is roughly in the
order of the strengths of the Sn—X bond being made, and is again explained simply as a consequence of the
most exothermic reaction being the most rapid (see p. 135). Furthermore, these reactions are faster than attack on
a C—H bond, since the halogens and Se and S are soft sites, and can accept bonding to a radical ahead of the bond
breaking—the interaction of the SOMO with the nonbonding, lone-pair orbitals is likely to be stronger than with
or * of a C—H bond, as well as forming a stronger bond. The relatively less nucleophilic methyl radical,
however, abstracts a hydrogen atom from benzyl chloride rather than the chlorine atom. Even more subtle
examples of selectivity come when it is a question of which kind of C—H bond is attacked.
Most radicals attack hydrogen atoms in the order: allylic > tertiary > secondary > primary. The most
important factor here is again that the faster reactions are producing the product with the lower energy.
In addition, the more neighbouring groups a C—H bond has, the more overlap (hyperconjugation) can be
present. Since such overlap is between filled orbitals and filled orbitals, the effect is to raise the energy of
the HOMO. This effect therefore puts the energy of the HOMOs of the C—H bonds in the same order as their
ease of abstraction.977 More quantitatively, Fukui showed that it is possible to calculate a parameter, called
the delocalisability D(R), for different kinds of hydrogen atom attached to carbon, from the coefficient on the
hydrogen atom cri of the atomic orbital on atom r in each molecular orbital i, having energy Ei, when the
SOMO of the attacking radical has energy (Equation 7.1).978
occ
DðRÞ
r ¼ S
i
unocc
c2ri
c2ri
ðÞ
ðÞ þ S
i
Ei
Ei 7:1
This parameter correlates well with the rate constant for abstraction of the different kinds of hydrogen atoms,
primary, secondary and tertiary in hydrocarbons and in alkyl fluorides. It works, both for a relatively neutral
radical like methyl, and for electrophilic radicals like trifluoromethyl, because it takes into consideration
both SOMO/OMO and SOMO/UMO interactions.979
Selectivity between hydrogen atom abstraction and addition to an alkene (Section 7.3) is very dependent
upon the structures of the radical and of the substrate. Tin radicals abstract halogen atoms even when there is
a double bond to add to, but that is probably because of the strong bond being formed. Simple alkyl radicals
attack H—Sn bonds competitively with their conjugate addition to Z-substituted alkenes, showing that there
is a fairly delicate balance, even though the H—Sn bond is notably weak. tert-Butoxy radicals remove allylic
hydrogens faster than they add to the terminus of simple alkenes, but quite small changes, to perfluoroalkoxy
radicals for example, reverse this selectivity.980
One of the complications in assessing the selectivity between atom abstraction and addition to an alkene is
that one or the other might be reversible. The best known case where this appears is in two well-known
reactions of bromine atoms. One of these is the allylic bromination of alkenes 7.16 ! 7.18 using
N-bromosuccinimide (NBS). Radical brominations using NBS are known to take place by the NBS slowly
releasing bromine, since the same results can be obtained using bromine in low concentration. This detail is
irrelevant here, but it is well known. In the key step of the allylic bromination using NBS, a bromine atom
derived from the bromine molecule abstracts an allylic hydrogen atom 7.16, and the allylic radical produced
7.17 then abstracts a bromine atom from another molecule of bromine to give the allylic bromide 7.18,
together with a bromine atom which can continue the chain reaction. Unsymmetrical allyl systems give
mixtures of products, because the allyl radical is ambident.
Br
Br
Br
Br
H
7.16
7.17
+ HBr
7.18
7 RADICAL REACTIONS
375
The other reaction is the peroxide-catalysed addition of HBr to alkenes 7.19 giving the anti-Markovnikov
product 7.21. The peroxide generates a bromine radical by abstracting the hydrogen atom from the HBr. The
key step is the addition of the bromine atom to the double bond 7.19, which takes place to give the moresubstituted radical 7.20, and this in turn abstracts a hydrogen atom from another molecule of HBr to give the
primary alkyl bromide 7.21.
Br
Br
Br
H
Br
7.20
7.19
7.21
It seems that the bromine atom can show different selectivity, allylic abstraction 7.17 or addition 7.19,
depending upon its source, but this is an illusion. One of these reactions, 7.16 or 7.19, must be reversible, and
the second step must be proceeding slowly enough to allow the alternative pathway to dominate. The better
candidate for the slow second step is the bromination 7.17 ! 7.18, since the concentration of bromine
is so low.
7.2.2.2 Selectivity Affected by Stereoelectronic Effects. Molecules with a more or less rigid relationship
between a lone pair and a C—H bond can be used to probe the effect of conjugation between the two. Ethers,
acetals and orthoesters show a range of reactivity towards hydrogen atom abstraction by tert-butoxy radicals,
with some telling stereochemical features. The acetal 7.22 shows a selectivity between the three different
kinds of hydrogen atom that matches the energy of the radicals produced. The most stable is the tertiary
radical 7.23 flanked by two oxygen atoms, which is produced nearly seven times faster than the secondary
7.24, which is flanked by only one. It is normal to correct for the statistical factor that there are four times as
many hydrogens that can produce the secondary radical as the tertiary, and so the selectivity for tertiary is
actually 27 times the secondary. The third possibility would be the primary radical, with no lone pair
stabilisation, produced by abstraction from the methyl group, which is not observed at all. However, the rigid
acetal 7.25 loses a hydrogen atom only from the secondary position to give the radical 7.26, which
is stabilised by syn overlap with one of the lone pairs, whereas the tertiary radical that would be created at
the bridgehead 7.27 would not be stabilised, because the singly occupied orbital would be gauche to all the
lone pair orbitals.981
OBut
O
O
H
O
O
+
H
O
7.22
7.23
H
O
87:13
7.24
H
O
OBut
O
O
+
O
O
O
H
7.25
7.26
100:0
7.27
Orientation affects not only the stability of the radicals being produced, but also the energies of the orbitals of
the C—H bond. If the angles are right, a lone pair will raise the energy of the local HOMO and LUMO of a
C—H bond. Thus the axial hydrogen atom in the acetal 7.28 is selectively removed by tert-butoxy radicals,
partly because it gives a well stabilised tertiary radical 7.29, similar to 7.23. More significantly, the axial
hydrogen atom in the acetal 7.28 is removed more than 10 times faster than the equatorial hydrogen atom in
376
MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS
its diastereoisomer 7.30.982 Since they give the same radical 7.29, and the same final products, this is an
effect from the nature of the C—H bonds, and not just an effect from the stability of the radical. The SOMO/
HOMO interaction will be the most important, since the butoxy radical, based on an electronegative atom,
will have a low-energy SOMO, which will select the higher energy HOMO of the C—H bond conjugated to
the X-substituent. Similar effects have been seen with nitrogen lone pairs.983
H
k rel 11
O
H
O
O
7.28
7.3
k rel 1
O
O
O
7.29
7.30
The Addition of Radicals to p Bonds
7.3.1 Attack on Substituted Alkenes
There is a great deal of information available about the addition of radicals to p bonds, since it is such an
important step in radical polymerisation, as we have already seen.969 The regioselectivity in a lot of these
reactions is easily explained: the more stable ‘products’ 7.2, 7.6, 7.20, 7.31984 and 7.32,985 with the radical
centre adjacent to the substituent are almost always obtained, and the site of attack usually has the higher
coefficient in the appropriate frontier orbital. With C- and Z-substituted alkenes, the site of attack will be the
same regardless of which frontier orbital is the more important—both have the higher coefficient on the
carbon atom remote from the substituent (Figs. 2.2 and 2.5).
25
Br
75
CCl3
Br
Cl3C
Cl3C
Br
+ Cl3C
Cl3C
7.31
25:75
Et
B
O
Et
Et
O Et
Et
H
OBEt2
Et
+
Et
H
7.32
With