Lecture 14 February 3, 2014
Rules for Chem. React. - Woodward-Hoffmann
Nature of the Chemical Bond
with applications to catalysis, materials
science, nanotechnology, surface science,
bioinorganic chemistry, and energy
Course number: Ch120a
Hours: 2-3pm Monday, Wednesday, Friday
William A. Goddard, III, wag@wag.caltech.edu
316 Beckman Institute, x3093
Charles and Mary Ferkel Professor of Chemistry, Materials
Science, and Applied Physics,
California Institute of Technology
Teaching Assistants:Sijia Dong <sdong@caltech.edu>
Samantha Johnson <sjohnson@wag.caltech.edu>
Ch120a-Goddard-L14
© copyright 2011 William A. Goddard III, all rights reserved
Ch120a1
Woodward-Hoffmann rules
orbital symmetry rules
Frontier Orbital rules
Certain cycloadditions occur but not others
Roald
Hoffmann
2s+2s
2s+4s
4s+4s
Ch120a-Goddard-L14
Why?
© copyright 2011 William A. Goddard III, all rights reserved
2
Woodward-Hoffmann rules
orbital symmetry rules
Frontier Orbital rules
Certain cyclizations occur but not others
conrotatory
disrotatory
disrotatory
conrotatory
3
Ch120a-Goddard-L14
Why?
© copyright 2011 William A. Goddard III, all rights reserved
2+2 cycloaddition – Orbital correlation diagram
ground state
Start with 2 ethene in GS
Occupied orbitals have SS
and SA symmetries
Now examine product
cyclobutane
Forbidden
Occupied orbitals have SS
and AS symmetry
Thus must have high energy
transition state: forbidden
reactions
GS
Ch120a-Goddard-L14
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4
Stopped L13, Feb. 11, 2013
Ch120a-Goddard-L14
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5
2+2 cycloaddition – Orbital correlation diagram
excited state
Start with 1 ethene in GS and one
in ES
Open shell orbitals have SA and AS
symmetries
Now examine product cyclobutane
Allowed
Open shell orbitals have AS and SA
symmetry
Thus orbitals of reactant correlate
with those of product
ES
Thus photochemical reaction
allowed
Ch120a-Goddard-L14
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6
Consider butadiene + ethene
cycloaddition; Diehls-Aldor
2+4 Ground State
A
A
Ground state has S,
S, and A occupied
S
Product has S, A,
and S occupied
Allowed
A
Thus transition state
need not be high
Allowed reaction
S
S
Ch120a-Goddard-L14
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7
WH rules – 2 + 4
Excited State
A
Excited state has
S, S, doubly occupied
A and S singly occupied
A
S
Forbidden
A
Product has
S, A doubly occupied
SA singly occupied
Thus transition state will
be high
Forbidden reaction
S
S
Ch120a-Goddard-L14
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8
Generalization WH rules cycloaddition
2n + 2m
n+m odd: Thermal allowed
Photochemical forbidden
n=1, m=2: ethene + butadience (Diels-Alder)
n+m even: Thermal forbidden
Photochemical allowed
n=1, m=1: ethene + ethene
Ch120a-Goddard-L14
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9
Butadiene
S
A
S
Conrotatory
Allowed
A
S
A
S
A
Rotation, C2
Ch120a-Goddard-L14
WH rules – cyclization-GS
Cyclobutene
Cyclobutene
A
A
Disrotatory
Forbidden
S
S
A
S
A
S
Reflection, s
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10
Generalization: WH rules cyclization (electrocyclic)
2n
n even: Thermal conrotatory
Photochemical disrotatory
n=2  butadiene
n odd: thermal disrotatory
Photochemical conrotatory
n=3  hexatriene
Ch120a-Goddard-L14
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11
HF_PT2
XYG3
Product: H2+CH3
H--C
Energy (kcal/mol)
20.00
2D Reaction Surface
forCCSD(T)
H + CH4  H2 + CH3
B3LYP
15.00
BLYP
SVWN
10.00
5.00
0.00
-2.00
-5.00
-1.50
-1.00
-0.50
0.00
0.50
1.00
1.50
2.00
Reaction coordinate
Energy
along
reaction
path
Reactant: H+CH4
Ch120a-Goddard-L14
H--H
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12
GVB view reactions
Reactant HD+T
H
D
T
Product H+DT
Ch120a-Goddard-L14
14
Goddard and Ladner, JACS 93 6750 (1971)
© copyright 2011 William A. Goddard III, all rights reserved
GVB view reactions
Reactant HD+T
H
D
T
During reaction, bonding orbital on D stays on D,
Bonding orbital on H keeps its overlap with the orbital on D but
delocalizes over H and T in the TS and localizes on T in the
product. Thus highly overlapping bond for whole reaction
Nonbonding Orbital on free T of reactant becomes partially
antibonding in TS and localizes on free H of product, but it
changes sign
Product H+DT
Ch120a-Goddard-L14
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15
GVB view reactions
Reactant HD+T
H
D
T
Bond pair keeps
high overlap while
flipping from reactant
to product
Transition state
nonbond orbital
keeps orthogonal,
hence changes sign
Product H+DT
Ch120a-Goddard-L14
H
D
T
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16
Changes in VB orbitals along inversion reaction path for
D+ CH4 to DCH3 + H
Initial CH
bond
D-C-H
bond TS
Initial
nonbond
on D
D-C-H
antibond
TS
Final
Final DC
nonbond
on H
Ch120a-Goddard-L14 bond
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17
Physics behind Woodward-Hoffman Rules
For a reaction to be allowed, the number of bonds must be
conserved. Consider H2 + D2
2 bonds
TS ? bonds
2 bonds
To be allowed must have 2 bonds at TS
How assess number of bonds at the TS. What do the
dots mean? Consider first the fragment
Have 3 electrons, 3 MO’s
Have 1 bond. Next
consider 4th atom, can
nonbonding
Bonding
antibonding
we Ch120a-Goddard-L14
get 2 bonds?
1 elect
2 2011
elect
© copyright
William A. Goddard
III, all rights reserved 0 elect 18
Physics behind Woodward-Hoffman Rules
Bonding
2 elect
nonbonding
1 elect
antibonding
0 elect
Have 1 bond. Question, when add 4th atom,
can we get 2 bonds?
Can it bond to the nonbonding orbital of the
TS?
Answer: NO.
Ch120a-Goddard-L14
The two orbitals are orthogonal in
the TS, thus the reaction is
19
forbidden
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A. Goddard III, all rights reserved
Summary H2 + D2  HD + DH is forbidden
the barrier is comparable to the bond energy
Bond 1
Bond 1
Bond 2
Bond 2 ? No
Orbital phases do not correlate
The bonding phases of the reactants Do NOT correlate
with those of the products
Thus the reaction is Forbidden
Ch120a-Goddard-L14
© copyright 2011 William A. Goddard III, all rights reserved
20
What about H2 + D2 + T2  HD + DT + TH?
D
D
D
H
H
T
H
D
T
H
T
T
Is this allowed? Yes
as flip green from D2 to DT and
Blue from T2 to TH get 2 phase
changes in red H as it moves to D
Next year show sequence of orbital changes
Ch120a-Goddard-L14
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21
Selection rules for reactions
Valence bond view
Selection Rules for Chemical Reactions Using the
Orbital Phase Continuity Principle
W. A. Goddard III
J. Am. Chem. Soc. 94, 793 (1972
Ch120a-Goddard-L14
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22
GVB analysis of cyclization (4 e case)
4 VB orbitals:
A,B,C,D reactant
φB
φA
φC
Move AB bond;
Ignore D;
C changes phase as
moves from 3 to 1
φD
2 3
1
φφB φφA
B
A
2 3
4
1
φφC
C
φφD
D
4
φB
Now ask how the CH2 groups 1 and
4 must rotate so that C and D retain
positive overlap.
φA
2 3
φC
Clearly this case (4n)
is conrotatory
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2011 William A. Goddard III, all1rights reserved
Ch120a-Goddard-L14
φD
4
23
Orbital analysis 4 electron cyclization (electrocyclic)
Reactant
Conrotatory
TS
Phases are
continuous
Product
Ch120a-Goddard-L14
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24
GVB analysis of cyclization (6 e case)
2ab
Flip
2ab
Hexatriene
1ab
3ab
Question
which rotation of the AB, CD
groups maintain the phase
between 1a and 1b?
Flip
3ab
Cyclohexadiene
Ch120a-Goddard-L14
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25
GVB analysis of cyclization (6 e case)
2ab
Flip
2ab
Hexatriene
1ab
3ab
Question
which rotation of the AB, CD
groups maintain the phase
between 1a and 1b?
Answer: Disrotatory
Flip
3ab
Cyclohexadiene
Ch120a-Goddard-L14
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26
Generalization: orbital phase continuity principle
rule for cyclization
2n=4: butadiene - conrotatory
2n=6: hexatriene - disrotatory
n even: conrotatory
n odd: disrotatory
Ch120a-Goddard-L14
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27
Apply GVB model to 2 + 2 cycloaddition
TS: ignore C but maintain
4 VB orbitals:A,B,C,D reactant overlap of A with B as A
delocalizes to new center
φB
φA
φB
φC
φD
φD
φC
Ch120a-Goddard-L14
φA
φD
φB
φA
\
D moves
but has
φC
Nodal
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reserved
4 VB
orbitals
product
28
1
2
1
2
Transition state for 2 + 2
3
4
3
4
Transition state: ignore C
Orbitals A on 1 and B on 2
keep high overlap as the
2
1
bond moves from 12 to 23
φA
with B staying on 2 and A
moving from 1 to 3
Orbital D must move from 3 to 1
3
4
but must remain orthogonal to
the AB bond. Thus it gets a
nodal plane
φ
φB
D
The overlap of D and C goes
from positive in reactant to
Nodal
negative in product, hence goingφ
plane
C
through 0. thus break CD bond.
Reaction Forbidden
Ch120a-Goddard-L14
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29
GVB model fast analysis 2 + 2
4 VB orbitals:A,B,C,D reactant
1
2
φA
φB
φC
3 φD
4
Move A from 1 to 3 keeping overlap with
B
Simultaneously D moves from 3 to 1 but
must change sign since must remain
orthogonal to A and B
φD
C and D start with positive overlap
and end with negative overlap.
Thus break bond  forbidden
Ch120a-Goddard-L14
φC
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φB
φA
\
30
Stopped L14, February 13, 2013
Ch120a-Goddard-L14
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31
GVB 2+4 cycloaddition
φC
φB
φD
φA
23
1
4
6
5
φF
φA
φB
φD
φC
23
1
4
6
φE
φF
5
φE
1. Move AB bond; Ignore D; C
changes phase as it moves
from 3 to 1
Ch120a-Goddard-L14
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32
GVB 2+4
2. Move EF
bond; C
changes phase
again as it
moves from 1
to 5
φA
φB
φD
φC
23
1
4
φA
φB
φD
23
6
φF
5
φE
3. Now examine overlap of D with
C. It is positive. Thus can retain
bond CD as AB and EF migrate
Ch120a-Goddard-L14
1
4
φE
φC
6
5
φF
Reaction
Allowed
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33
GVB 2+4
φC
φB
φD
φA
23
1
4
φA
φB
φD
φC
23
1
4
2. Move EF
bond; C
changes phase
again as it
moves from 1
to 5
φA
φB
φD
23
6
φF
5
6
φE
φF
5
φE
1
4
3. Examine final
φE
1. Move AB bond;
φC
overlap of D with
Ignore D; C changes
C. It is positive.
6
5
phase as it moves
Thus can retain
φF
from 3 to 1
bond CD as AB
Reaction
Allowed
Ch120a-Goddard-L14
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2011EF
William
A. Goddard III, all
rights reserved
and
migrate
34
Summary 2+4 cycloaddition
1ab
2ab
Flip 1ab
1ab
3ab
Flip 2ab
2ab
Ch120a-Goddard-L14
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35
Generalization orbital phase continuity principle
rule for cycloaddition
n=1, m=1: ethene + ethene: forbidden
n=1, m=2: ethene + butadience (Diels-Alder): allowed
n+m even: forbidden
n+m odd: allowed
Ch120a-Goddard-L14
© copyright 2011 William A. Goddard III, all rights reserved
36
What is best geometry for a forbidden reaction?
Consider 2+2 cycloaddition
Woodward Hoffmann suggested that need to orient two
ethylenes perpendicular to get them to react
Consider that bond 1ab is
moving from C12 to C23
Then the orbital 2b initially on
C3 bonding to orbital 2a on C4
Must change phase as it
delocalizes onto C1
Question: how must the AB on
C4 move to maintain phase?
Ch120a-Goddard-L14
© copyright 2011 William A. Goddard III, all rights reserved
37
What is best geometry for a forbidden reaction?
Consider 2+2 cycloaddition
Woodward Hoffmann suggested that need to orient two
ethylenes perpendicular to get them to react
Consider that bond 1ab is
moving from C12 to C23
Then the orbital 2b initially on
C3 bonding to orbital 2a on C4
Must change phase as it
delocalizes onto C1
Question: how must the AB on
C4 move to maintain phase?
Answer we must rotate the C34
bond out of the plane (~30) so
that the minus lobe of orbital 2a
can overlap the minus lobe of
2b on C1.
Ch120a-Goddard-L14
© copyright 2011 William A. Goddard III, all rights reserved
38
Sigmatropic Reactions: [1,5] H migration
3ab
1ab
2ab
Flip
2ab
2ab
Flip 3ab
Question: Can H
remain above the
plane (suprafacial)
as it moves from
bonding to C5 to C1?
3ab
Ch120a-Goddard-L14
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39
Sigmatropic Reactions: [1,5] H migration
3ab
1ab
2ab
Flip
2ab
H remains above the
plane (suprafacial) as it
moves from bonding to
C5 to C1
2ab
Flip 3ab
3ab
Ch120a-Goddard-L14
© copyright 2011 William A. Goddard III, all rights reserved
40
Sigmatropic Reactions: [1,3] H migration
Flip
1ab
2ab
1ab
1ab
Ch120a-Goddard-L14
H must go below the plane (antarafacial)
as© copyright
it moves
fromA.bonding
C3reserved
to C1
2011 William
Goddard III, allto
rights
41
Sigmatropic Reactions: [1,7] H migration
4ab
1ab
3ab
Flip
2ab
2ab
2ab
4ab
Can H
remain
above the
plane
(suprafacial)
as it moves
from bonding
to C7 to C1
Ch120a-Goddard-L14
Flip 3ab
Flip
4ab
3ab
© copyright 2011 William A. Goddard III, all rights reserved
42
Sigmatropic Reactions: [1,7] H migration
4ab
1ab
3ab
Flip
2ab
2ab
2ab
Flip 3ab
4ab
Flip
4ab
Ch120a-Goddard-L14
3ab
H must move below
the plane (antarafacial)
as it moves from
C7reserved
to C1
© copyright 2011 William A.bonding
Goddard III, allto
rights
43
Generalization orbital phase continuity principle
rule for [j,k] H migrations (sigmatropic)
j+k=1+5=6: suprafacial
j+k=1+3=4 and j+k=1+7=8 : antarafacial
j+k=4n+2 : suprafacial
j+k=4n: antarafacial
Ch120a-Goddard-L14
© copyright 2011 William A. Goddard III, all rights reserved
44
Low symmetry reactions
Cylco-octatetraene  cubane?
1ab
2ab
3ab
4ab
Flip 1ab from C12 to C23
must break 3ab bond as it
moves to C14
Flip 2ab from C34 to C47
must break 4ab bond as it
moves from C78 to C83
Thus doubly forbidden
Ch120a-Goddard-L14
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45
Butadiene + butadiene reactions
All forbidden
Ch120a-Goddard-L14
© copyright 2011 William A. Goddard III, all rights reserved
46
Can we have 2s + 2s reactions for transition
metals?
2s + 2s forbidden for organics
X
2s + 2s forbidden for organometallics?
?
Cl2Ti
Cl2Ti
Me
Me
Ch120a-Goddard-L20
Cl2Ti
Cl2Ti
Me
?
Me
Cl2Ti
Cl2Ti
Me
© copyright 2011 William A. Goddard III, all rights reserved
Me
47
Now consider a TM case: Cl2TiH+ + D2
Orbitals of reactants
GVB orbitals
of TiH bond
for Cl2TiH+
GVB orbitals
of D2
Ch120a-Goddard-L20
© copyright 2011 William A. Goddard III, all rights reserved
48
Is Cl2TiH+ + D2  Cl2TiD+ + HD allowed?
Bonding
2 elect
nonbonding
1 elect
antibonding
0 elect
when add Ti 4th atom, can we get 2 bonds?
Now the bonding orbital on Ti is d-like. Thus at TS have
Answer: YES. The two orbitals can have high overlap at the TS
orthogonal
in the TS,©thus
the reaction is allowed
Ch120a-Goddard-L20
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49
GVB orbitals at the TS for
Cl2TiH+ + D2  Cl2TiD+ + HD
Ch120a-Goddard-L20
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50
GVB orbitals for the Cl2TiD+ + HD product
Note get phase change
for both orbitals
Ch120a-Goddard-L20
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51
Follow the D2
bond as it
evolves into the
HD bond
Ch120a-Goddard-L20
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52
Follow the TiH
bond as it
evolves into the
TiD bond
Ch120a-Goddard-L20
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53
Barriers small, thus allowed
Increased d character in
bond  smaller barrier
Ch120a-Goddard-L20
© copyright 2011 William A. Goddard III, all rights reserved
54
Are all MH reactions with D2 allowed? No
Example: ClMn-H + D2
Here the Mn-Cl bond is very polar
Mn(4s-4pz) lobe orbital with Cl:3pz
This leaves the Mn: (3d)5(4s+4pz), S=3 state to bond to the H
But spin pairing to a d orbital would lose
4*Kdd/2+Ksd/2= (40+2.5) = 42.5 kcal/mol
whereas bonding to the (4s+4pz) orbital loses
5*Ksd/2 = 12.5 kcal/mol
As a result the H bonds to (4s+4pz), leaving a high spin d5.
Now the exchange reaction is forbidden
Ch120a-Goddard-L20
© copyright 2011 William A. Goddard III, all rights reserved
55
Show reaction for ClMnH + D2
Show example reactions
Ch120a-Goddard-L20
© copyright 2011 William A. Goddard III, all rights reserved
56
Summary
Generalized Valence Bond (GVB) calculations find
that during chemical reactions the localized bonding
orbitals of the reactants delocalize over 3 centers in
the TS and relocalize on the atoms of the product
bond, retaining the same phase (overlap) throughout
the reaction
This continuity of the phase leads to selection rules
for reactions identical to the Woodward Hoffmann
rules (for thermal reactions) analysis provides a very
simple orbital.
This OPCP does not need symmetry. One can do
virtual reactions of one pair at a time to analyze the
phases and derive the selection rule
Ch120a-Goddard-L14
© copyright 2011 William A. Goddard III, all rights reserved
57