Effective Molarities for
Intramolecular Reactions
ANTHONY J . KIRBY
University Chemical Laboratory, Cambridge, England
1 Introduction 184
2 The efficiency of intramolecular catalysis I85
3 Calculation of effective molarities 187
4 Effective molarity and mechanism 190
Classification of reactions 190
Nucleophilic vs. general acid-base catalysis 191
Intramolecular general acid catalysis in reactions of salicylic acid derivatives 196
Why are EM’S for general acid-base catalysed reactions so low? 198
EM and the nature of the transition state 200
The formation of small rings 205
5 Effects of substitution on the EM for ring-closure reactions 208
The Thorpelngold effect 208
Effects on the formation of larger rings 216
The relief of ground-state strain 2 17
Orbital steering 222
6 Tables of effective molarities 223
Notes on Tables A-H 224
I EFFECTIVE MOLARWIES FOR CYCLEATION REACTIONS 225
A Reactions of the carboxylic acidgroup 225
A. 1 Equilibrium data for anhydride formation 225, A.2 Intramolecular nucleophilic
catalysis of ester hydrolysis 226, A.3 Intramolecular nucleophilic catalysis of amide
hydrolysis 23 1, A.4 Lactone formation from w-halogenocarboxylates 234, A S
Intramolecular nucleophilic catalysis of phosphate and phosphonate ester hydrolysis 235,
A.6 Intramolecular nucleophilic catalysis of the hydrolysis of sulphonamides 238
B Reactions of the hydroxyl group 239
B.l Equilibrium constants for the lactonization of hydroxy acids 239, B.2 Acidcatalysed lactonization of hydroxy acids 24 1, B.3 Base-catalysed lactonization of
hydroxy esters 245, B.4 Epoxide formation from chlorohydrins 246, B.5
Base-catalysed formation of cyclic ethers 247, B.6 Intramolecular cyclization of
hydroxyalkyl phosphates 25 1
C Reactions of the surphydryl group 252
C.l Equilibrium constants for thiolactone formation from pthiolacids 252, C.2
Thiolactonization of pthiolacids, etc. 253
D Reactions of the amino-group 254
D.la Intramolecular attack by the dialkylamino-group on a neighbouring ester group 254,
D. l b Intramolecular nucleophilic attack by imidazole and pyridine 255, D.2 Intramolecular attack by the NHR group 256, D.3 The cyclization of halogeno-amines, etc.
256, D.4 Intramolecular nucleophilic attack on phosphorus 259
183
ANTHONY J
184
KIRBY
I1 INTRAMOLECULAR GENERAL BASE CATALYSIS 259
E Catalysis by the ionized carboxylgroup 259
E. 1 Intramolecular general base catalysis of ester hydrolysis 259, E.2 Intramolecular
general base catalysis of Schiffs base hydrolysis 262, E.3 Intramolecular general base
catalysis of enolization 262
F Intramolecular general base catalysis by phenolate oxygen 264
F.1 Catalysis of ester hydrolysis 264, F.2 Catalysis of enolization 265
G Intramolecular general base catalysis by nitrogen 266
G. 1 Catalysis of ester hydrolysis 266, G.2 Intramolecular general base catalysis of
enolization 269, G.3 Intramolecular general base catalysis of aminolysis by the
amino-group 270
I11 INTRAMOLECULAR GENERAL ACID CATALYSIS 271
H.l Intramolecular general acid catalysis by the carboxyl group 271, H.2 Intramolecular general acid catalysis by the hydroxyl group 273
References 274
1
Introduction
The extraordinary efficiency of enzyme catalysis has stimulated a great deal of
chemistry in recent years. Enzymes promote very fast reactions, often between
functional groups which are normally exceedingly unreactive, under the mildest
conditions of temperature and pH, by bringing the groups together under the
special conditions of the enzyme-substrate complex. These conditions may be
special in various ways, but it is clear that a major part of the very large rate
enhancements involved is due simply to the way the functional groups
concerned are brought together. Consequently it is of particular interest to
study the same reactions between the same groups in systems simple enough to
understand in detail. The first step towards unravelling the mechanism of an
enzyme-catalysed reaction is to be able to specify the mechanisms available for
the reaction concerned.
Many of these reactions are not observed at all when the relevant groups are
allowed to come together in bimolecular processes in aqueous solution. For
mechanistic work involving intermolecular reactions, therefore, it is necessary
to use activated substrates. Much of what we know about the relevant
reactions of esters, for example, comes from studies using aryl esters like
p-nitrophenyl acetate, or acyl-activated compounds like ethyl trifluoroacetate
(Bruice and Benkovic, 1966; Jencks, 1969; Bender, 1971).
An attractive alternative is to study intramolecular reactions. These are
generally faster than the corresponding intermolecular processes, and are
frequently so much faster that it is possible to observe those types of reaction
involved in enzyme catalysis. Thus groups like carboxyl and imidazole are
involved at the active sites of many enzymes hydrolysing aliphatic esters and
amides. Bimolecular reactions in water between acetic acid or imidazole and
substrates such as ethyl acetate and simple amides are frequently too slow to
185
EFFECTIVE M O L A R l T l E S
detect even under vigorous conditions. But when the catalytic and substrate
groups are brought together in the same molecule such otherwise unreactive
compounds may be hydrolysed under quite mild conditions. Mechanistic
studies of intramolecular reactions of this sort have therefore played an
important part in elucidating the chemistry of the groups involved in enzyme
catalysis and in defining the mechanisms available for particular reactions.
Though such purely mechanistic work continues, recent studies of
intramolecular catalysis have been concerned more and more with the factors
responsible for the high efficiency of enzyme catalysis. It is now possible to
write quite detailed-and quite plausible-mechanisms for certain enzyme
reactions (Fersht, 1977); it is not so easy to account for their very high rates.
Since some simple intramolecular reactions are very fast, in some cases going
at rates comparable with similar enzyme reactions (Fife, 1975), it seems
reasonable to suppose that an understanding of how efficiency depends on
structure in intramolecular catalysis will shed some light on the related
problems of enzyme catalysis. If reactivity does depend crucially on the way
functional groups are brought together it should be possible to identify the
factors involved by bringing groups together in different ways on the same
molecule and observing the effect on reactivity.
This problem has been reviewed (Page, 1973; Jencks, 1975), and the general
conclusion emerging from a great deal of work is that it is possible to account
for the efficiency of enzyme catalysis in terms of known concepts (Fersht,
1977; Fersht and Kirby, 1980).
2
The efficiency of intramolecular catalysis
If we are to examine systematically how catalytic efficiency depends on
structure we need to define a convenient measure of efficiency. One measure
commonly used is the magnitude of the rate acceleration observed for the
reaction under consideration. For example, the rate of hydrolysis of the anion
of aspirin [ 11, which is known to involve catalysis by the carboxylate group
(Fersht and Kirby, 1967), is about 50 times faster than that of phenyl acetate
under the same conditions at pH 7. This figure is easily defined because both
reactions are pH-independent over a considerable range. The same comparison
for an acetal such a 2-methoxymethoxybenzoic acid [21 on the other hand is
less straightforward. Hydrolysis is catalysed by the neighbouring COOH
group in a reaction which shows a small pH-independent region near pH 2
OCOCH,
OCH,OCH,
COOH
[ll
[21
186
ANTHONY J. KIRBY
(Capon et al., 1969). There is no such region for the hydrolysis of
methoxymethoxybenzene, which is specific acid catalysed; the relative rates
depend on the pH taken. In a case like this the practice is therefore to quote the
maximum rate enhancement, The efficiency of catalysis defined in this way has
some uses, particularly when absolute rates of reaction are important. The
values do not, however, allow the sensible comparison of efficiency in different
reactions because like is not being compared with like. The hydrolysis of
aspirin involves intramolecular general base catalysis of the attack of water by
the COO- group 131, whereas that of phenyl acetate involves water alone [41
(Kirby, 1972); so the ratio of hydrolysis rates contains, as a hidden factor, the
relative efficiencies as general bases in this particular reaction of water and the
carboxylate group of aspirin. The similar comparison for 121 is between
COOH as a general acid, in a reaction where proton transfer and C-0
bond-breaking are concerted, and a specific acid catalysed reaction where the
proton transfer is complete in the rate determining step; so a quite different
hidden factor is built in to the simple rate ratio in this case.
The solution to this problem is to compare the rate constant for the
intramolecular reaction with that for the corresponding intermolecular process.
In the case of aspirin hydrolysis [31 this would be general base catalysis of the
hydrolysis 151 of aspirin by an external carboxylate group, RCOO-, of the
same basicity as the carboxylate group of aspirin. The necessary data are
H,O:
I
/
H OPh
151
available. The first order rate constant (k,) for the hydrolysis of aspirin at 39'
is 1.1 x
s-l (Fersht and Kirby, 1967b), while that for the same reaction
catalysed by acetate ion (k2)is 1.27 x
dm3 mol-' s-' under the same
E F F ECTl V E M 0LA R I TI E S
187
conditions. The ratio k,/k, = 8.7 and has the dimensions of molarity. This
figure underestimates the true effective molarity because acetate (pK, 4.76) is
more basic than the carboxylate group of aspirin (3.69). The correction
requires a knowledge of the linear free energy relationship between the basicity
and reactivity of the general base. The Brransted /3 has been measured for this
reaction, and is 0.30 (Fersht and Kirby, 1967) so an appropriate value of k,
(8.4 x lo-’ dm3 mol-I s-l) can be calculated for the reaction with a
carboxylate group of pK, = 3.69, and the correct effective molarity calculated
as 13 M.
The effective molarity (EM) is formally the concentration of the catalytic
group (RCOO-in [51) required to make the intermolecular reaction go at the
observed rate of the intramolecular process. In practice many measured EM’S
represent physically unattainable concentrations, and the formal definition is
probably relevant only in reactions (which will generally involve very large
cyclic transition states) where the formation of the ring or cyclic transition
state per se is enthalpically neutral, or in diffusion-controlled processes. For the
formation of small and medium-sized rings and cyclic transition states the EM
as defined above contains, and may indeed be dominated by, the enthalpy of
formation of the cyclic form. This topic has been discussed briefly by Illuminati
ef al. (1977) and will be treated at greater length in a future volume in this
series.
The measurement of accurate EM’S, as defined above, clearly has very
stringent requirements. First, the mechanisms of both intermolecular and
intramolecular reactions must be known and have been shown to be the same.
Then acceptable rate measurements must be carried out under the same
conditions for both reactions. Generally it is not possible to measure the rates
of both the intermolecular reaction and the intramolecular process (thus
catalysed by the same group) under the same conditions; measurements on the
intermolecular reaction catalysed by a series of catalytic groups are necessary
to define the EM accurately.
Such stringent conditions are clearly not likely to be fulfilled by chance, and
in fact data suitable for the accurate measurement of effective concentrations
are available only for a handful of reactions. On the other hand, the range of
EM’S known is very large (from zero to 1OI6 M) and, certain specialized uses
apart, very accurate figures are not essential.
3
Calculation of effective molarities
In most cases the EM’S quoted in the tables in Section 6 are based on accurate
measurements of k,,the rate constant for the intramolecular reaction (which is
quoted for all the EM’S calculated here), and the rate constant for the closest
equivalent intermolecular reaction under conditions which are as similar as
ANTHONY J. K I R B Y
188
possible. Except where otherwise indicated, the data are for reactions followed
in aqueous solution. Comparison of rate constants at widely differing
temperatures is only attempted when the enthalpy of activation is known for
one or both reactions.
The pK,-values quoted for nucleophilic, basic or acidic groups are generally
those measured in the course of the work cited, but values have been estimated
in a few instances or taken from tables. A small error in pK, affects the
calculated EM relatively little in most cases.
In a few, but important, cases, EM’S have been calculated not from rate
constants but from product ratios. Where the effective molarity is low,
competition between intramolecular and intermolecular reactions of the same
compound may be observed, as in Freundlich’s early work on the cyclization
of w-bromoalkylamines (1) described by Salomon (1936). The interH
H
molecular reaction can be minimized by working at very low concentrations,
but where both products are observed their ratio allows the calculation of the
ratio of the rate constants for the intramolecular and the corresponding
intermolecular reaction. This ratio was defined as the cyclization constant, C,
by Stoll and Rouve (1934) and is identical to the EM as long as the
bimolecular reaction is the most suitable model available for the intramolecular process. This will generally be the case except where data have been
collected specifically for the estimation of EM’S. Thus Galli and Mandolini
(1977) found that the alkylation of 8-bromooctanoate -by n-octyl bromide was
2.4 times faster than the intermolecular reaction with a second molecule of
cubromoalkanoate, probably as a result of electrostatic repulsion. In this case
a careful investigation of a large number of similar reactions under the same
conditions produced a better intermolecular comparison. More usually such
desirable data are not available, and for the purposes of this review the EM
calculated from the product ratio in a reaction of this sort is considered
acceptable (and rated if the measurements were done accurately enough).
A second situation where EM’S can be calculated from product ratios, which
again is applicable only for reactions with low EM, is exemplified by the
cyclization of 3-chloropropanol (Richardson et al., 1971). The measured rates
of cyclization of a series of cuchloroakanols in alkali show (Table B.5) that the
formation of the four-membered ring is substantially less efficient than that of
other small rings. A careful product analysis of the cyclization of 3chloropropanol in 40% methanol-water at a range of temperatures showed a
EFFECTIVE M 0 LAR IT1 ES
LOH
40% MeOH,
H,O, NaOH
fl
+
qH
OMe
C1
50%
14%
189
+
&OH
(2)
OH
28%
constant product distribution, as indicated in (2). The relative rates of the
reaction of the substrate with the neighbouring 0-group and with methoxide
are thus 50 : 14. The concentration of MeOH in 40% aqueous methanol is 9.89
M, and the pK,-values of methanol and water are close enough that a
correction for this factor is not necessary. Thus k,ntm/kwewis 2.77 M, and the
EM (given in Table B.5 as 4 M, category p) is obtained by correcting this figure
for the (small) difference in pK, between methanol and 3-chloropropanol.
This analysis begs one question, which is essentially insoluble and which
applies to many of the calculations described in the tables. Methoxide ion is
clearly not a perfect model for neighbouring (CH,),CH,O-; but what is?
Illuminati et al. (1977) solve the problem satisfactorily for reactions in which
large rings are formed by measuring rates of reaction of a large number of
possible intermolecular models (Galli and Mandolini, 1977), finally choosing a
preferred reaction for comparison on the basis of all the available information.
But the situation is different for reactions in which smaller rings are formed.
For example, good data are available for the cyclization of chlorohydrins to
epoxides (Table B.4). If we wish to compare EM’S in the series [6al, [6bl, [6cl
[6bl
the appropriate nucleophiles for comparison might be thought to be ethoxide,
isopropoxide and t-butoxide, with progressively increasing steric hindrance.
But it is clear that steric effects in intramolecular reactions, especially the
formation of small rings, are much smaller than in the corresponding
bimolecular processes. In fact reactivity increases sharply with increasing
substitution in the series under discussion as a result of the well-known (though
not well-understood) Thorpe-Ingold effect. In this case we do not have a wide
choice of data for intermolecular reactions for comparison and so have used
the same model reaction as has been used for the formation of the oxetane.
This at least puts the two reactions on the same scale and ensures that we do
not ooerestimate the Thorpe-Ingold effect.
The tables at the end of this chapter contain nearly 400 EM’S which are
considered accurate enough to be useful. In each case the intermolecular
reaction used for comparison and the conditions used for the measurements
ANTHONY J K I R B Y
190
are specified, and any extrapolations used are described. Each figure is rated a,
y for accuracy. Values rated a refer to EM’S calculated from
measurements made for both intermolecular and intramolecular reactions
under the same conditions, or involving only a short extrapolation known to be
reliable. EM’S classified as 3/ (the majority) involve a substantial extrapolation
(data at different temperatures, in different solvents etc.), while y indicates that
the extrapolations involved are less reliable. Estimated errors are up to 10% for
a figures, which are in many cases accurate to the significant figures given, a
factor of two for category /3, and an order of magnitude for category y. These
are generally generous error limits.
The main tables are designated by a letter and a number (a full list is given in
the Contents at the beginning of this chapter). Tables in the text, which mostly
contain effective molarities taken from the main tables, are designated by a
number only. Every individual reaction is identified by a reference letter and
two numbers. Thus B.6.3 refers to the base-catalysed cyclization of cyclohexyl
2-hydroxyethyl phosphate which is the third entry in Table B.6. The EM for
this reaction is given in Table 10 in the discussion of the effects of alkyl
substitution on ring-closure, and the reference number quoted there. Full
details of the calculation of the EM, the rate constant on which it is based, the
conditions used and the authors concerned can then be found by consulting
Table B.6.
/3 or
4
Effective molarity and mechanism
The data summarized in the tables are the source of most of our current ideas
about the efficiency of ring-closure reactions (Eliel, 1962; Capon and
McManus, 1976). We know, for example, that the ease of ring-formation
generally depends on the size of the ring being formed, according to the series
3 > 4 < 5 > 6 > 7, etc. Large effects of this sort are readily apparent from
simple rate comparisons which within a series of related compounds give ratios
not very different from those obtained by comparing effective molarities. A
more likely source of new insights is the comparison of EM’S for different
reaction types, because most of the data have not previously been available in
this form. So most of the discussion below concerns comparisons of this sort.
CLASSIFICATION OF REACTIONS
Capon (1964; Capon and McManus, 1976) introduced a simple classification
for reactions involving neighbouring group participation, in which G-n
indicates participation by a nucleophilic group G in an n-membered cyclic
transition state. For present purposes an extension of this symbolism is
necessary in order that the abbreviations indicate the electrophilic centre also.
EFFECTIVE M O L A R l T l E S
191
Only a relatively small number of electrophilic centres are involved in the great
majority of the reactions listed in Section I of the tables, and to avoid confusion
they are given single letter abbreviations. For example, A, M and E indicate
carboxylic acid, amide and ester groups respectively. (The full list is given at
the beginning of the tables.) Finally the suffix x or n specifies exocyclic or
endocyclic displacement of the leaving group. For displacements at tetrahedral carbon the terminology is similar to that used by Baldwin (1976), but
for reactions at trigonal carbon his ex0 and endo refer to the initial addition
step. For displacements at carbonyl and especially phosphorus centres the EM
can depend significantly on whether the leaving group is endo- or exocyclic.
The classification is illustrated in the examples given in Table 1, and in the
tables of EM’S. The extension to general acid-base catalysed reactions presents
some complications. Here three functional groups may be involved simultaneously in the transition state, and the third group may or may not be part of
the same molecule as. the other two. When it is not, this is indicated by
enclosing the relevant group descriptor in parentheses. The size of the
transition state is also represented differently for proton-transfer processes. The
X...Y distance in X.. H.. Y is commonly about If times that in X... Y,
and, following Bell (see various references under his name), the size of cyclic
transition states containing H is designated (n + i),where n is the number of
heavy atoms (see last four examples in Table 1). This has the added advantage
that the classification defines the type of mechanism also.
. .
NUCLEOPHILIC V S . GENERAL ACID-BASE CATALYSIS
The most striking result is the contrast between the absolute magnitudes of EM
for the nucleophilic reactions in Tables A-D, and those for general acid-base
catalysis in Tables E-H. For the ring-closure reactions EM’S range up to 1OI6
M, with values of 104-108 M common for the formation of five-membered
rings from conformationally flexible systems, and higher values are readily
attained by simple structural variation. The highest EM for general base
catalysis (Tables E-G), on the other hand, is 80 M, and the great majority are
less than 10 M. In the case of acyl salicylates it is possible to make a direct
comparison of EM’S for nucleophilic and general base catalysis in the same
system. For the nucleophilic reaction (COO--E-6n) 171 the EM can be
calculated as 2.6 x lo7 M (compound A.2.35). By contrast the EM for the
general base catalysed hydrolysis (COO-(HO)E--7fn) IS1 is 13 M. Both the
absolute magnitudes and the effects on EM of structural variation are strikingly
smaller for general base catalysed reactions. Thus gem-dialkyl substitution can
have large effects on the rates of ring-closure reactions (see Table 8), but it
appears to have little effect on the efficiency of general base catalysis. For
example, intramolecular nucleophilic catalysis of ester hydrolysis is not
192
ANTHONY J. KIRBY
TABLE1
Examples of the symbolism used in the classification of reactions
COO--E-Sx
COOH-M-SX
n -n
HO
CO,H
O d = O
-d
HO-A-SX
0--C-3~
0
0
COO--P3-6n
COO-(HO)E--74n
OR
COO--H-qx
N-HN(E)-+
OH-O=C(N)-qn
EFFECTIVE M O L A R l T l E S
HO,C
193
0
A.2.35
EM = 2.6 x 107 M
0
E.1.6
EM=13M
(71
[Sl
observed for derivatives of malonic acid because this mechanism would involve
a four-membered cyclic anhydride. Consequently the general base catalysis
reaction can be observed in this system (Kirby and Lloyd, 1976b). For a
comparison with a nucleophilic reaction of a similar compound we can use the
hydrolysis of the sulphonamides A.6.1 and A.6.2.' This reaction 191 is 40 times
faster for the gern-dimethyl compound (the effect is still larger for the
formation of four-membered rings containing only first row elements: see Table
8). For the malonate reaction (E. 1.1 and 2) [ 101 the gern-dimethyl compound
reacts only half as efficiently.
A.6.1,2
R=H
R=Me
[91
E M = 4 x 106M
E M = 8 x lO'M
E.1.1,2
[ 101
EM=25M
EM=11M
A more extensive comparison is given in Table 2, where a much larger range
of effective molarities is observed as a result of alkyl substitution in a rigid
system. For the most reactive maleamic acids the relief of ground state strain is
an important driving force for cyclization, as it appears to be also for the
formation of small rings accelerated by gem-dialkyl substitution (see Section 5;
p. 208). The changes in bond angle caused by the changing pattern of alkyl
substitution are of the same order of magnitude for the maleamic acids and
the malonic esters listed in Table 2; on the other hand, the resulting changes in
It is known that four-membered rings containing phosphorus or sulphur are formed more
readily than those containing only first-row elements, and the EM'S calculated for compounds
A.6.1 and 2 allow a quantitative estimate of the importance of the effect. In this series the
four-membered ring is formed almost as efficiently as the five [the EM for the hydrolysis of
HO,C(CH,), S0,NMePh (A.6.3) is 2 x 10' MI
ANTHONY J. KIRBY
194
TABLE2
The contrasting effects of structural variation on EM for nucleophilic
vs. general base catalysis by the carboxyl group
System
Angle(48)
EM/M
118.4O
60
1100
25
106.2O
11
121.0, 121.7O
3 x 1013
126.8, 131.7O
6 x loxo
132.1, 133.4O
8 x lo3
General base catalysis
E.l.lb
70zAr
H,C a
‘COT
E. 1.4b
C0,Ar
P C O ,
Nucleophilic catalysis
A.3.17c
A*3.13
A.3.2ob
R
CONHMe
R
CO,H
Y
CONHMe
CO,H
CONHMe
CO,H
Data taken from Kirby and Lloyd, 1976b, and Tables A.3 and E.l
Angles are those for the diacid
EM for R = Me, angles for R = isopropyl. EM is not much affected
by this change in substitution
EFFECTIVE MOLARlTlES
195
effective molarity cover a range of nearly 1O'O for the hydrolysis of the
maleamic acids which involves nucleophilic catalysis (Kirby and Lancaster,
1972), but change by less than one order of magnitude for the intramolecular
general base catalysed hydrolysis of the malonate esters.
These differences in absolute magnitude are large enough and sufficiently
clear cut to make a useful criterion of mechanism. It is not always a simple
matter to distinguish nucleophilic from general species catalysis. For general
base catalysis consistent results from a series of four or five tests are conclusive
(Kirby, 1979); for general acid catalysis the simplest test, the solvent
deuterium isotope effect, is often inconclusive (Fersht and Kirby, 1971). The
magnitude of the effective molarity, which is based on a single comparison of
rate constants, is generally quite unambiguous.
If the EM is greater than 80 M the mechanism is nucleophilic.' If it is less
than 80 M the mechanism is almost certainly general acid or general base
catalysis.
These generalizations hold for reactions involving the formation of
unstrained rings (specifically, for systems where there is no more strain in the
cyclic product than in the ground state). They should not therefore be applied
to reactions in which small (three- or four-membered) or large (sevenmembered or more) rings are formed. For the great majority of reactions of
interest, however, in which five- or six-membered rings would be formed by the
nucleophilic mechanism, the rule holds. For these classes there are just three
exceptions in the Tables (neglecting the group of six compoundsZdiscussed
specifically in the next section). These are shown in (3) and (4).
- o=c)+Br(3)
-3 Br
fi
OQ
HN
N'O-
EM = 14.5 M
H N i o + x -
D.1.14 (X = SPr')
D.l.10 (X= OPh)
(4)
EM=53M
EM=13M
All three cases involve the formation of six-membered rings, as would be
expected, since the formation of five-membered rings is generally much more
efficient in conformationally flexible systems. The imidazole reactions present
no real problem since the reference reaction used in each case was the attack of
*With the important exception of acetals (and possibly certain other derivatives) of salicylic
acid (compounds H.l.6-11; see the following section), which are hydrolysed with intramolecular general acid catalysis by the carboxyl group, with EM'S of the order of lo4 M
196
A N T H O N Y J. KIRBY
imidazole on an acetyl derivative, and propionate and higher esters are
generally less reactive than acetates by factors of at least two (Kirby, 1972). So
the quoted error (a factor of two) is already biased towards a higher EM,
which brings these reactions into line.
The formation of Gvalerolactone from the 6-bromocarboxylate (A.4.5)
appears to be a genuine exception. The formation of a six-membered ring in a
reaction in which the new ring-bond is only partially formed in the transition
state is expected to have a particularly low EM (see Section 4; p 200) and so it
does.
INTRAMOLECULAR GENERAL
SALICYLIC A C I D DERIVATIVES
ACID
CATALYSIS
IN
REACTIONS
OF
Relatively few data are available (Table H) for reactions involving intramolecular general acid catalysis, but in most cases the EM’S fall in the same
range as those for general base catalysis (Tables E-G). This is expected if EM
is a characteristic transition-state property, because a general acid catalysed
reaction is always the microscopic reverse of a general base catalysed process
although in no case has the EM been measured in
as shown in equation (9,
both directions.
H.2.1
Reactions H. 1.6-1 1 therefore stand out as an important class of exceptions.
The hydrolysis of these acetals of salicylic acid (e.g. [ 111) is catalysed by the
neighbouring carboxyl group in a reaction which is certainly kinetically, and
probably also mechanistically, general acid catalysis (Craze and Kirby, 1974),
yet the effective molarities observed are far greater than any others measured
for intramolecular general acid-base catalysis, and fall in the range characteristic of nucleophilic reactions. The nucleophilic mechanism has been ruled
out for these reactions (it would require either an endocyclic displacement in a
six-membered ring, or the formation of an intermediate known not to be
reactive enough to support the reaction). It is therefore of the greatest interest
to identify the factors which make this particular system so efficient’.
Highly-efficient general acid catalysis of acetal hydrolysis is involved in the reactions of
glycosidase enzymes such as lysozyme (Dunn and Bruice, 1973)
E F F ECTlV E M 0 LA R ITI E S
197
It is clear that the high efficiency is a property of the salicylate system and is
not limited to acetal hydrolysis. Similar highly efficient catalysis is observed
also in the hydrolysis of salicyl phosphate [12l,and a similar mechanism
appears to be involved (Bromilow and Kirby, 1972). The essential structural
07p
@?
ph*
0
H. 1.7, EM = 2.9 x lo4 M
0
Salicyl phosphate (EM not known)
[111
[121
feature can be further defined as the conjugation between the carboxyl and
leaving groups by the results summarized in [131-[151. The EM for the
cOMe
q\
PMe
OMe
H
H
0
0
[131 EM = lO‘M
0
[141 EM = 2 x lo4 M
0
[151 EM
<1M
hydrolysis of methoxymethyl benzoic acid [131 is not known, since the
intermolecular reaction is not detectable in t h i s case. We therefore assume a
value similar to the other salicylic acid acetals. The tetrahydro-derivative [ 141
is actually more reactive still, but the related compound [ 151,which has similar
acetal, catalytic and leaving groups and differs only slightly in geometry, shows
only very weak catalysis, if any (Kirby and Osborne, unpublished). Thus
explanations which depend on the favourable (59ring-size can be ruled out,
and we must look to a special property of the salicylate and related systems.
It seems likely that this property is, or is related to, the strong
hydrogen-bond formed in the salicylate anion. In Section 4 (p. 202) we shall
consider the relationship between EM’s derived from rate constants and the
EM’s for the corresponding equilibrium processes. Reactions with high
“thermodynamic” EM’s generally have high kinetic EM’s also, depending upon
the position of the transition state along the reaction co-ordinate. For almost
all the reactions in Tables E-H no ring is being formed, so that the factors
responsible for high EM’s in ring-closure reactions do not apply and high
198
A N T H O N Y J. KIRBY
“thermodynamic” EM’S are not to be expected. The hydrolysis of a salicylate
derivative (6), on the other hand, has one clear advantage over the
corresponding intermolecular process (7) in the formation of a product with a
strong intramolecular hydrogen-bond in water.
0
0
0
The “thermodynamic” EM for the hydrolysis of the salicylate derivative is
therefore favoured by a factor presumably similar to that which favours the
hydrogen-bonded form of the salicylate anion. In terms of the dissociation
constant of the phenol group, which is some 3 pK units less acidic than
expected for a phenol with an ortho-carboxylate group (Eberson, 1969), a
factor of lo3,which is of the right order of magnitude to explain the observed
effect, could be involved.
This explanation is of particular interest, because it is practically certain that
general acids and bases in the active sites of enzymes can form strong
hydrogen bonds to suitably placed donors or acceptors on the protein. So the
very low EM’s normally observed for general acid-base catalysed reactions in
simple systems in water may well underestimate the EM’s available in enzyme
active sites. Consequently the abnormal values seen with salicylate derivatives
(which are clearly not ideal models for enzyme reactions since the leaving
group is actually conjugated with the general acid) may actually be a better
guide to the potential efficiency of general acid-base catalysis in enzyme
reactions.
W H Y A R E EM’S F O R G E N E R A L A C I D - B A S E C A T A L Y S E D R E A C T I O N S S O
LOW?
A question of more general importance than why the EM’S for one small group
of general acid catalysed reactions are exceptionally high, is why the EM’S for
EFFECTIVE MOLARlTlES
199
these reactions should otherwise be so low. We have already touched on one
key factor, the fact the intramolecular nucleophilic reactions involve ring
formation, so that the special factors favouring ring-closure affect the relative
rates of similar intermolecular and intramolecular processes. We now consider
these factors in a little more detail.
Page and Jencks (1971; Page, 1973) have estimated the losses of translational and rotational entropy expected for the formation of the transition state
for a typical bimolecular reaction as being of the order of 40-50 e.u. The size of
this factor for a given reaction depends on the residual entropy of the transition
state which is associated with a variable number of low frequency vibrations.
The greater this residual entropy, that is to say, the looser the transition state,
the greater and thus more favourable is the entropy of activation for the
bimolecular process, and thus the smaller is the possible advantage of the
intramolecular process.
By way of example, compare the transition state [161 for a typical general
base catalysed reaction (E.1.6) with that for the corresponding reaction
involving a nucleophilic mechanism [171 (A.2.35). We have already seen that
the EM’S for these mechanisms are 13 M and 2.6 x lo7M, respectively. In the
do?
di
)/o\H
0-
0“
[161
[171
transition state for the nucleophilic mechanism [ 171 only one sigma bond is
being broken, and the six-membered ring is almost fully formed (the rate
determining step is expected to be breakdown of the tetrahedral intermediate in
a case like this). It is clear that the transition state for the general base
catalysed reaction is altogether looser, with no less than four covalent bonds
being made and broken simultaneously, three of them u-bonds and two of
them involving bonds to hydrogen. This is a feature of every general acid-base
catalysed reaction and a significant one since partial bonds to hydrogen are
expected to involve particularly low-frequency vibrations (Bell et al., 1974). The
advantage of the intramolecular reaction, which is primarily entropic, is thus
much reduced for the general base catalysis mechanism because the transition
state is so much looser.
If this explanation is correct, the looseness of the proton-transfer part of the
mechanism is evidently crucial, both because it is part of every general
acid-base catalysed reaction, and more specifically because EM’S for reactions
200
ANTHONY J. K I R B Y
in which no other o-bonds are being broken (an example would be general base
catalysed enolization, as in [181), though relatively high for general base
catalysed reactions, are not substantially greater than those for general base
catalysis of hydrolysis.
0
E.3.18 EM = 56 M
I181
EM
A N D THE NATURE OF THE TRANSITION STATE
We have seen that the absolute magnitude of the EM may allow the assignment
of a reaction to its broad mechanistic class (nucleophilic or general acid-base
catalysis) because the tighter transition states associated with nucleophilic
reactions give rise to much higher values. There is some evidence that this
general correlation holds also within a series of nucleophilic reactions. Table 3
shows data for three cyclization reactions of carboxylic acid derivatives. In
reaction A. 1.1 bond formation is complete. In the transition state for reaction
A.2.1 the new ring-bond is more or less fully formed because the breakdown of
the tetrahedral intermediate is rate determining, while reaction A.4.4 is an
“intramolecular SN2 reaction” with the new bond only partially formed in the
transition state. The EM’S for these reactions thus refer to progressively looser
states, and it is consistent with the general correlation noted above that the
observed value of the EM decreases in the same sequence.
Reaction B.5.4, which might be expected to have a transition state similar to
that of reaction A.4.4, in fact has a higher EM, but since nucleophile, leaving
group and geometry have all changed it is difficult to assess the significance of
this. Now the coresponding “SN2” reaction shows a larger EM than attack on
an ester group (reaction B.3.1; five-membered ring formation). The difference
between this system and reactions A. 1 and A.2 is that now theformation of the
tetrahedral intermediate is rate determining (&oxide is a poorer leaving group
than phenoxide) so that the new ring-bond is only partially formed in the
transition states of both reactions. For the formation of the six-membered ring
the EM’S are equal for the two cyclizations. Reaction B.3.2 is a case where
both nucleophile and leaving group are aryloxide anions, and so the breakdown
and formation of the tetrahedral intermediate should be close to balance.
Compared with the “intramolecular SN2” reaction B.5.8, the EM is now equal
201
EFFECTIVE M O L A R l T l E S
TABLE3.
Correlation between EM and the tightness of the transition state for the formation of five- and
six-membered rings
~
_
_
Compound
A.l.l
_
_
_
_
(Transition) state
Succinic acid
EM-SIM
EMdM
1.9 x 10'
-
PhO,C(CH,),CO;A.2.1
A.2.21
n=2
n=3
5.1 x l(r
220
Br(CHJ,CO,
A.4.4
A.4.5
n=3
n=4
B.3.1
B.3.5
n=3
n=4
1.6 x 103
14.5
PhO,C(CH,),O5 x 103
280
Cl(CH,),OB.5.4
B.5.9.
n=4
n=5
B.3.2
B.3.6
n=l
n=2
6 x lo4
280
2.5 x 10'
\
B.5.8
B.5.10
n=2
n=3
5 x 104
0 1.3 x 10'
6.6 x lo3
(five-membered ring) or slightly larger (B.5.10; six-membered ring), as
expected if the transition state is somewhat tighter for reaction B.3.6.
It is interesting to attempt to extend this type of analysis in the direction of a
more quantitative assessment of the degree of bond-making or breaking in the
2 02
A N T H O N Y J. KIRBY
transition state. We may distinguish two extreme cases. For the “infinitely
loose” transition state where bond reorganization has not started (an example
would be a diffusion-controlled reaction in the thermodynamically favoured
direction), very low effective molarities are to be expected, presumably in the
region of 55/n (where n is the number of nearest neighbour molecules to the
substrate group) as suggested by Koshland (1962). For simple nucleophilic
reactions at least, the opposite extreme will be reached when reaction is
complete. So a comparison of EM’S derived from the rate constants for
intramolecular cyclization and displacement processes with the “thermodynamic EM’S” derived from the equilibrium constants for the same reactions
could be instructive.
Few relevant data are available. Both equilibrium and rate constants have
been measured for very few reaction series in solution, but comparisons are
possible for lactone and thiolactone formation, and for a few anhydrideforming reactions (Tables 4 and 5). For lactone formation (Table 4) the EM
for the rate process is of the same order of magnitude as that derived from the
equilibrium constant data, and in some cases actually exceeds it (though only
in one case by an amount clearly greater than the estimated uncertainty which
is nominally a factor of 4 for these ratios). Lactonization generally involves
rate-limiting breakdown of the tetrahedral intermediate, and the transition
state is expected to be late and thus close in structure to the conjugate acid of
the lactone.
Neutral sulphur and oxygen nucleophiles of similar structure react with
carbonyl groups at similar rates (Jensen and Jencks, 1979); the position of the
transition state for thiolactonization is therefore expected to be similar. The
comparisons of EM possible for three compounds in Table 4 show that the
EM,/EM,, ratios are somewhat smaller for thiolactonization, by factors of 3
and 9 for the two compounds where all four EM’S can be estimated.
Omitted from Table 4 are Hershfield and Schmir’s data (Tables B.l, 1&13
and B.2, 28-31) for the lactonization of substituted coumarinic acids. The
EM,/EM,, ratios calculated from their data (given in Tables B.l and B.2) fall
in the range 1 - 4 x lo-‘, and thus differ sharply from the ratios in Table 4. This
is a consequence of the surprisingly high equilibrium constants for lactonization. These were calculated (Hershfield and Schmir, 1973a,b) from rate
constants for the hydroxide-catalysed lactonization (which is apparent as a
pH-independent reaction for very reactive systems). Though the procedure
used appears to be valid, these equilibrium constants differ substantially from
those measured for the acid-catalysed reactions, although no direct comparison is possible for any one compound.
The second relevant set of data is for the formation of the anhydride from
substituted succinic acid derivatives. Equilibrium constants for the formation
of the anhydride from the acid are available for the various methyl-substituted
compounds (Table A.l) and the derived EM’S are compared in Table 5 with
those for intramolecular nucleophilic catalysis in the hydrolysis of half-esters
EFFECTIVE MOLARlTlES
203
TABLE4.
Comparison of kinetic and thermodynamic EM’S for lactonization and thiolactonization
reactions‘
x=o
Compound
n
HX
CO,H
n
HX
CO,H
x=s
EM,
EM,
EM,/EM,,
88
80
0.91
159
117
0.74
-
-
-
Data from Tables B . l , 2 and C.l, 2
EM,
3.7
X
-
lo3
EM,
EMJEM,,
384
0.1
-
-
9.5 x i(r 4.7 x 103
4.9 x
10-2
ANTHONY J . K I R B Y
204
TABLE
5
Comparison of kinetic and thermodynamic EM’S for anhydride-forming reactions‘
Anhydride
4
EMAb
EM,
EM,/EM,
EMBC
EM,/EM,
1.9 x 10’
5.1 x lo4
0.26
5.1 x 104
0.26
1.1 x lo6
1.3 x 10’
0.12
1.3 x 10’
0.12
2.7 x lo6
5.9 x 10’
0.22
1.2 x lor
1.6 x 10’
0.04
0.06
6.7 x lo6
1.2 x lo6
0.18
4.6 x 10’
0.07
3 x 10’
6.6 x lo6
0.02
3.7 x
0.01
2.0 x 1 0 7
4 x 10-3
6.7 x lo6
1.5 x 10-3
-
-
109
>o.s
0
Go
0
Go
0
6
0
0
go
go
106
0
4.6 x
109
0
~ 1 . x7 1 0 9
0
~~
a
~
Data from Tables A.l, A.2 and A.3
Derived from rates of cyclization of succinamic acids
Derived from rates of cyclization of monophenyl succinate anions
205
EFFECTIVE MOLARlTlES
and half-amides of the same succinic acids. In both cases the transition state is
thought to be the breakdown of the tetrahedral addition intermediate to form
the anhydride (8). Furthermore, the transition state is expected to be late in
(8)
0
0
0
each case, at least for the unsubstituted succinic acid derivatives (from linear
free energy relationship data and from consideration of the reverse reaction
which involves the addition of an amine or aryloxide ion to the anhydride).
Though EM ratios are given for both reactions, the data are not
independent. The EM’S for the amide hydrolysis are based on a value
(EM = 5.1 x lo4 M) for the succinamic acid reaction which is assumed
to be identical with that for the hydrolysis of monophenyl succinate
monoanion. However, both sets of data show similar behaviour. The EM’S for
the rate processes, initially smaller by less then an order of magnitude than
those for equilibrium anhydride formation, increase much less rapidly with
increasing methyl substitution, so that the EM ratios decrease with increasing
EM.
This behaviour is reasonably interpreted in terms of a gradual change in the
position of the transition state from a structure rather close to that of the
anhydride to one with the breaking of the bond to the leaving group less far
advanced. This process alone will produce a somewhat looser transition state,
but, since the effect of methyl substitution is clearly to favour ring closure, the
breakdown of the tetrahedral intermediate to regenerate starting materials must
be substantially less favourable in the tetramethylsuccinic acid derivative. In
the extreme case, therefore, a change of rate-determining step is possible to the
formation of the tetrahedral intermediate.
Although we can make some sense of EM ratios by discussing them in terms
of varying transition state structure, the data so far available do not require this
approach which must be considered only tentative at this stage. Equilibrium
and kinetic EM’S for many more reactions are required before it will be
possible to decide whether they contain useful information about transitionstate structure. It is to be hoped that it will rapidly become normal practice to
attempt an estimate of the effective molarity as part of any quantitative work
on intramolecular reactions.
THE FORMATION OF SMALL RINGS
It is well-known that three-membered rings are readily formed by the
cyclization of 2-haloalkyl derivaties of various nucleophilic species. Effective
206
A N T H O N Y J. K I R B Y
molarities for these reactions are difficult to obtain, but a useful range of data is
available for the formation of epoxides (Table B.4) and aziridines (Table D.3).
The EM'S for these two reactions are strikingly different; where direct
comparison is possible the EM for the formation of the epoxide is 100-1000
times greater than that for the corresponding aziridine.
It is likely that this factor reflects a fundamental difference in the nature of
the nucleophilic centres concerned. This difference is responsible also for the
wide differences in the relative rates of formation of three and five-membered
rings containing differing hetero-atoms noted by Bird and Stirling (1973).
These authors showed that the formation of the episulphonium ion from
2-chloroethyl p-tolyl sulphide (9) is actually faster than the formation of the
corresponding five-membered ring from p-tolyl-S(CH,),CI. The EM for the
formation of ethylene oxide from the 2-chloroethoxide anion, on the other
hand, is 24 times smaller than that for the formation of tetrahydrofuran from
Cl(CH,),O-, and for the formation of the corresponding nitrogen heterocycles
the ratio is nearly 500 (Table 6).
The ready formation of the episulphonium compound is reasonably
explained in terms of the directionality and polarizability of the non-bonded
electron-pairs of sulphur, a soft nucleophile which naturally forms bonds at
angles close to 90". We may presume that the directional requirements of the
nucleophilic orbitals of first-row elements (N, 0) are stricter, and that this
factor shows up most clearly in a situation (the formation of a three-membered
ring) which makes extreme demands on orbital flexibility.
A similar explanation allows us to rationalize the differences in EM for the
formation of epoxides and aziridines (Table 6). The three covalent bonds to
neutral nitrogen define the orientation of the non-bonded electron-pair so that
an amine nucleophile has rather specific directional requirements. An alkoxide
anion, on the other hand, has three degenerate orbitals on the oxygen atom,
which makes for much greater directional flexibility in cases where this is
needed.4 The need is clearly greatest during the formation of a three-membered
ring and presumably disappears entirely for intermolecular nucleophilic attack.
Thus a simple prediction arising from this explanation is that the effect will
diminish with decreasing demands on directional flexibility, for example, with
increasing size of the ring formed.
'Compare the flexibility of the geometry of hydrogen-bonding to the non-bonding
electron-pairs of neutral oxygen elicited by the demands of crystal forces (Donohue, 1968)
207
EFFECTIVE M 0 LAR I TI ES
TABLE6
EM’S for the cyclization of cuhalogenoamines and alkoxides
EM
Compound
B.4.1
D.3.1
B.5.1
D.3.14
B.5.4
D.3.17
B.5.9
D.3.22
Ring
size, n
3
3
4
CI(CH,),- ,O- Br(CH,),- ]NH,
2.5 x 103
6
6
03
15
170
0.2
20
7 x 103
8.6
100
2.8
4
4
5
5
EM,-/EM,,,
6 x lo4
280
1’
I, Since EM’S are based on a common intermolecular reaction for each series,
for which EM is defined as 1 (1 M standard state) this ratio is unity by
definition. In fact EM’S for the formation of very large rings have been
measured for both series and approach 5 x lo-, in each case, though with
considerable fluctuations for particular ring sizes (Tables B.5, compounds
24-34, and D.3.24-27)
The data available for the cyclization of cuhalogenoalkoxides and amines
(summarized in Table 6) show clearly that the superior reactivity of 0-over
neutral N is indeed a function of the size of the ring formed; it falls off
monotonically as angle strain in the product, and thus also in the transition
state, decreases. These results are thus consistent with an explanation in terms
of the differing directionality of the orbitals of the nucleophilic centre.
Other relevant data are the rates of the base-catalysed cyclizations of
N-o-halogenoalkylsulphonamides, p-CH,C,H,SO,NH(CH,),CI,
where the
nucleophile is a nitrogen anion having only two covalent bonds to the
nucleophilic centre. Although accurate EM’S for these reactions cannot be
calculated, the relative rates of cyclization (1 :7.4 x lo-’ :4.4 x
for the
formation of three-, four- and six-membered rings respectively) indicate that the
formation of the three-membered ring is relatively more efficient than for
neutral amine cyclizations (Bird ef al., 1973). For cyclizations where the
nucleophile is a carbanion the three-membered ring is also formed more rapidly
than the five, at least in some cases (Knipe and Stirling, 1967, 1968). Here the
electron-pair involved occupies the n-bonding molecular orbital of the
delocalized a-keto or a-sulphonyl carbanion and cannot directly be compared
with the harder, localized oxygen and nitrogen cases.
It would be interesting to assess the relative effects of alkyl substituents vs.
protons on the directional flexibility of amine nucleophiles. Data are available
208
ANTHONY J KIRBY
(Table D.3) for aziridine formation from dialkyl 2-chloroalkylamines. The EM
for the cyclization of Me,N(CH,),CI (D.3.4) for example is 1.3 M,
significantly smaller than that for the reaction of the parent compound (D.3.1).
The corresponding figure for the diethylamine derivative (D.3.6) is much
greater (200 M), however; clearly, much larger effects come into play here.
The influence of alkyl substitution on the efficiency of cyclization is a complex
subject and is discussed in the next section.
5
Effects of substitution on the E M for ring-closure reactions
When a cyclic compound is in equilibrium with an open-chain derivative it
appears to be the almost invariable rule that alkyl substitution favours the ring
form (Hammond, 1956; Eliel, 1962). Many of the EM'S given in the tables (see
in particular Tables A.l and B.l) support this conclusion, and many more
show that it extends also to transition states leading to cyclic compounds
because the generalization is almost as strong for the effects of alkyl
substitution on the rates of ring-forming reactions (see Tables A.2, A.3, B.2,
B.4, B.5 and B.6 for examples). As a rule effective molarities based on
equilibrium constants are larger than those derived from rate constants for the
formation of a given cyclic compound (see Tables 4 and 5) as expected if the
relative stabilities of ground states and products are the dominant factor.
However, the effects of alkyl substitution on rates and equilibria clearly parallel
each other in most cases. With the considerable number of relevant EM'S
available in the tables which allow direct comparisons of the efficiency of
cyclization reactions of different types, it is of interest to examine the effects of
alkyl substitution on ring-closure reactions in the light of the explanations
currently available.
T H E THORPE-INGOLD
EFFECT
Historically the first of these explanations has become known as the
Thorpe-Ingold effect (Beesley ef al., 1915; Ingold, 1921). The external angles
between bonds on the carbon atoms of small rings are increased over the
normal tetrahedral value, leading to decreased non-bonded interactions
between geminal exocylic groups compared with the situation in open-chain
compounds. The point is illustrated by the x-ray crystallographic data shown
in Table 7 (taken from Kirby and Lloyd, 1976b). The angle between the two
bonds to the carboxyl carbons of malonic acid is l l O o , close to the normal
tetrahedral angle of 109'28'. When this angle is external to a three-membered
ring, as in cyclopropane-1,l-dicarboxylic acid, it is increased to 118.4'.
Conversely, the corresponding angle in dimethylmalonic acid is only 106.2'.
Apparently the two methyl groups force the carboxyl groups into closer
proximity, presumably by occupying space into which they would otherwise
spread out.
EFFECTIVE M O L A R I T I E S
209
TABLEI
Effects of gemdialkyl substitution
on bond angles'
Compound
,CO,H
CH, a
'CO,H
Angle a
1100
'Taken from Kirby and Lloyd,
1976b
Consider now what happens when the two carboxyl groups react to form a
small ring, for example the anhydride. The angle between the carboxyl carbons
must be reduced much further, perhaps to around 90°, in the product and in
the transition state leading to it. Compared with malonic acid itself, this
process has less far to go in the dimethyl compound because the two alkyl
groups have already forced the carboxyls part of the way towards each other.
The observed diminution in bond angle caused by the introduction of the two
alkyl substituents thus specifically favours the formation of the small ring.
The Thorp-Ingold effect is expected to operate specifically in reactions in
which small rings are formed. There is no reason why diminution of a potential
internal angle of a ring should assist ring-formation when the ring angles are
normal. Yet alkyl substitution favours the formation of five- and six-membered
rings also. The presumption is that different factors are dominant in these cases
(see below), so presumably a different sensitivity to alkyl subsitution is to be
expected for the formation of smaller compared with larger rings. Specifically,
we should expect the Thorp-Ingold effect to be particularly evident for the
formation of three- and four-membered rings. Futhermore, because the
energies involved in changing bond angles (vibrational) are greater than those
involved in changing conformation (rotational), it is a reasonable expectation
that the effects of alkyl substitution on the formation of smaller rings should be
larger than those for the formation of rings with little or no angle strain. Bird et
al. (1973) could find no evidence that the effect is greater for the formation of a
three- compared with a five-membered ring but the data in Table 8 suggest
exactly this.
N
A
..
0
TABLE8
The gem-dialkyl effect as a function of ring size: relative EM'S for the formation of small rings
Ring
size
Reaction and relative EM"
LC'
&Cl
0-
O--2
l(2.5 x l@M)
4 x l(r(1VM)
400 (lo6M)
2.8 x i(r (7 x 109 M)
3-L
425 (1700 M)
D
1
z
VOh
0
03 OAr
i (5.1 x 10' M)
2.3 (1.2 x 1oJ M)
131 (6.7 x 106 M)
W
<
5’
Succinic acid
$ anhydride
i(i.9 x 1 0 5 ~ )
HO,C )(/CO,H
2 4 x 10‘ (4.6 x lo9M)
14 (2.7 x lo6M)
18 (2.1 x 103 M)
3.6 (800 M)
With one exception (see note d) the figures quoted for each series are EM’s relative to the unsubstituted compound. The actual EM’s are given
in parentheses
* Data from Table B.4, cornpounds I, 5,6 and 9
Data from Table B.5.1-3
Data of Brown and van Gulick (1956). The figures quoted in this case are relative rate constants, as given by the authors. These were measured
in two different buffer solutions at three different buffer ratios altogether, and data for different compounds do not always refer to the same conditions. The rate constants have been corrected by the authors for pH differences, but no values of pH are given, nor have pK,-values been measured.
The data are not therefore adequate for the calculation of EM’s even of the lowest category of accuracy, and the figures given cannot be relied on
to give more than an indication of relative orders of magnitude of reactivity
Data from Table A.2, compounds 1,4 and 9
’Equilibrium data for the formation of the succinic anhydride from the acid; Table A.l, compounds I, 3 and 6. The 2,2dimethylsuccinic acid could
react either way with the electrophilic CO,H group either the one next to the tertiary centre or the other. It is assumed that the latter will be attacked
more readily by the neighbouring carboxyl group
8 Data from Table A.2, compounds, 21,22 and 27
212
A N T H O N Y J KIRBY
Table 8 contains the available data on the gem-dimethyl effect on EM’S for
the formation of small rings. Some results of Brown and van Gulick (1956) on
the cyclization of 4-amino- 1-bromobutanes have been included, although they
are not considered accurate enough for EM calculations because of the lack of
suitable data for the formation of a saturated five-membered ring. The data
have been arranged vertically according to the size of the ring formed and
horizontally according to the position of substitution relative to the
nucleophilic centre. Thus the first column lists the unsubstituted (reference)
reaction, the second column compounds with the gem-dimethyl group next to
the nucleophilic centre, and the last column compounds where it is next to the
electrophilic centre. (A trivial exception is the 3,3-dimethylglutarate ester
which should in principle occupy a separate column but does not simply to
save space.)
Arranged this way, the data show that the effect of introducing two geminal
methyl groups into any given position relative to the nucleophilic centre (read
down any column) has the largest effect on the formation of the smallest ring.
The arrangement of the data is intended to be strictly logical rather than to
prove the point in question, but almost any alternative arrangement would lead
to the same conclusion. This is that the introduction of two geminal methyl
groups can have a very large effect on the formation of an epoxide, a fairly
large effect on the formation of a four-membered cyclic ether, and relatively
smaller effects on the rates of formation of five- and six-membered rings.
Apart from this generalization, the point which emerges most clearly is that
the magnitude of the gem-dimethyl effect depends very much on the position of
substitution. If the two methyl groups are p to the electrophilic centre, which
thus becomes a neopentyl position, the effect may be sharply reduced. Thus the
formation of the pyrrolidine from 4-amino-2,2-dimethyl-1-bromobutane (Table
8) is actually slower than that of the unsubstituted compound, and the
formation of the symmetrical dimethyloxetane is only twice as efficient as that
of oxetane itself. A similar comparison is possible for the cyclization of
Me,NCH,CMe,CH,CI which is only nine times faster than that of
Me,N(CH,),CI at 5 6 O in 80% aqueous ethanol (Grob and Jenny, 1960). On
the other hand, the fact that it has the configuration of a neopentyl halide does
not prevent the corresponding /3-chloroethoxide (B.4.5) from forming the
epoxide very rapidly. So we may conclude that intramolecular nucleophilic
attack on the neopentyl centre becomes progressively less unfavourable as the
size of the ring being formed decreases.
For amine cyclizations it is possible to introduce gem-dialkyl substitution at
the nucleophilic centre, and the data in Table 9 suggest that a similar but
reduced effect may operate in this position also. The accuracy of the EM’S
given in Table D.3 is not such that absolute magnitudes are very significant,
but the relative magnitudes in this series are reliable since the rate constants on
213
EFFECTIVE M O L A R l T l E S
TABLE
9
The effect of N,N-dialkyl substitution on the efficiency of aziridine
formation
Amine
EM/M
D.3.1 H,N
*. -2
D.3.4 Me,N
1.3
owBr
D.3.6 Et,N -cl
D.3.8
15
2000
1.5
which they are based come from the same source. The pattern of reactivity is
very much that observed for substitution on carbon in similar cyclizations with
the exception that the dimethylamino-compound is less reactive than
2-chloroethylamine. It is normal [see Tables A.l and A.2, and Brown and van
Gulick (1956)l for the effects of alkyl substitution to increase with the size of
the group concerned, and there is no doubt (see footnote to Table D.3) that the
high EM for the diethylamino-compound is genuine. The data also illustrate the
well-known decrease in the steric effects of two geminal ethyl groups when they
are linked together in a six- and especially a five-membered ring. If the data of
Table 9 represent a further manifestation of the Thorpe-Ingold effect, it must
presumably be operating on the angle between the N-C bond and the axis of
the lone pair orbital on nitrogen.
There is nothing in the data to suggest that the effect of two alkyl groups is
greater than would be expected for the combination of the effects of two single
substituents or indeed that geminal substitution is necessarily more effective
that vicinal dialkyl substitution. This could be the case for the formation of
three- or four-membered rings but we cannot be sure because sufficient data
are not available. It clearly is not the case for the formation of some
five-membered rings (Table 10). Although the data are again too few to
support a generalization, the vicinal dimethylsuccinic acid derivatives cyclize at
A N T H O N Y J. KIRBY
21 4
TABLE10
Effect of geminal vs. vicinal substitution on EM'S for ring-closure reactions
Ring size
Reaction and relative EM
Lcl
&CI
O
0-
-
d
320 (8 x lo5 M)
s (4 x
I
I (5.1 x 104 M)
104
4 x l(r ( lo8 M)
400 ( lo6 M)
M)
2.5 (1.3 x l o 5 M)
Hydrolysis of
succinamic acid
0-
2.4 (1.2 x 105 M)
CONHPh
HO,C
I(5.1 x 1 P M )
Succinic acid
+ anhydride
&C02H
H02C
5.8(1.1 x 106M)
1
n
2.5 (1.3 x l o 5 M)
P
O- o P 0 2 - O R
I (1.2 x 1 0 4 ~ )
a
1.9(2.5 x 104M)
Data from Table B.4, compounds 1,3-6
Data from Table A.2, compounds 1-7
Data from Table A.3, compounds 1-5
Data from Table A . l , compounds 1 - 4
Data from Table B.6, compounds 3-6
280 (3.6 x lo6 M)
215
EFFECT1VE M OLA A IT1ES
Reaction and relative EM
C0,Ar
-0 ,c&Co2Ar
3.1 (1.6 x lo5M)
-0,c
A C O N H P h
HO,C
12 (5.9 x 105 M)
H02C
14 (2.7 x lo6 M)
+
9.0 (4.6 x 105 M)
9.0 (4.6 x los M)
CON HPh
HO,C
B ( 1 . 2 x 106M)
5.7 (2.9 x 105 M)
HO,C+/02H
35 (6.7 x 106 M)
6.1 (8 x IVM)
216
ANTHONY J KIRBY
least as efficiently as the gem-dimethyl compounds in most cases. The lower
EM’S for the cyclization of derivatives of meso-dimethylsuccinic acid are
expected because of the eclipsing interactions between the vicinal methyl groups
which develop in the transition state and the anhydride, and the same factor
may account for the low EM for the hydrolysis of cyclohexyl erythro3-hydroxy-2-butyl phosphate (Brown and Usher, 1965).
EFFECTS ON THE FORMATION OF LARGER RINGS
The magnitude and direction of the effects of alkyl substituents on the
efficiency of formation of six-membered rings are generally satisfactorily
explained by the proposals of Allinger and Zalkow (1960). The enthalpy of
ring-closure is more favourable for alkyl-substituted n-hexanes because of the
increased number of gauche interactions in the open-chain compared with the
cyclohexane product. The entropy of ring-closure is more favourable also,
because branching reduces the rotational entropy of the open-chain form
significantly more than that of the ring which has built-in restrictions to
internal rotation. Calculations of the expected magnitude of these effects for a
group of methyl-substituted cyclohexanes gave good agreement with the
known free-energy differences between open-chain and cyclic forms in the gasphase. These differences are large enough to account for all the effects of
methyl substitution on the EM’S for the formation of five- as well as sixmembered rings calculated in Tables 8 and 10.
There remain to be explained cases where very large effective molarities are
observed for the formation of five-, six- or seven-membered rings. Most of
these cases involve more or less rigid systems and are readily explained in
terms of relief of ground-state strain (see below). A small number, however,
involve conformationally mobile systems. Eliel (1962) notes cases where two
gem-dimethyl substitutions lead to dramatic effects on the equilibrium constant
for the formation of the anhydride from certain dicarboxylic acids. Quantitative information is available for one of these reactions; the formation of
tetramethylsuccinic anhydride from the acid has an EM 2.4 x 10‘ times
greater than that for the formation of succinic acid itself (Table 8). The rate
constants for the formation of the anhydrides from the aryl ester and amide
show similar effects (A.2.9 and A.3.7, respectively), and there is some
preparative evidence that the four methyl groups of ay&,d-tetramethyladipic anhydride confer similar remarkable stability on the seven-membered
ring (Farmer and Kracovski, 1927). It is possible that hydrophobic forces may
come into play for heavily alkylated systems in water, favouring, for example,
the fully eclipsed tetramethylsuccinic anhydride because the more compact
hydrocarbon part of the system disrupts the water structure less than in the
EFFECTIVE M O LA A IT1ES
217
diacid. Hydrophobic forces will of course be superimposed on the factors
considered by Allinger and Zalkow, whose calculations refer to the gas phase,
and probably also account for the surprisingly high EM’S for the formation of
very large rings (see the last entries in Tables B.5, D.l and D.3.27).
In fact there is some evidence that the effect of four methyl substituents can
be explained without invoking special effects. Blagoeva et al. (1979) have
shown that the rate and equilibrium constants for the formation of
dihydrouracils from Pureidopropionic acids ( 10) are correlated by steric strain
energies estimated from the enthalpies of formation of model hydrocarbons.
The steric strain energies P (or AP, representing the strain between two
fragments of the hydrocarbon) were obtained by a procedure due to Istomin
and Palm (1972). The correlation with AP is fairly good (r 30.965) for the
rates of cyclization of ten Pureidopropionic acids, and holds also for the data
of Tables A.l and A.3 for the formation of succinic anhydrides and the
hydrolysis of succinanilic acids ( r = 0.992 and 0.993, for five and six data
points respectively). The latter set includes the hydrolysis of tetramethylsuccinanilic acid (A.3.7), which would be expected to show a substantial
positive deviation from the correlation line if a hydrophobic effect were
superimposed on other effects in this case.
THE RELIEF OF GROUND-STATE STRAIN
The large effects of gem-dialkyl substitution on the efficiency of formation of
three- and four-membered rings were attributed above to the diminution in
bond angle caused by the introduction of the two alkyl substituents into the
chain. Ring formation is favoured because the two alkyl groups have in effect
forced the reacting groups part of the way towards each other in the ground
state. The extra driving force is presumed to result from non-bonded
interactions both between the cyclizing groups and the two alkyl substituents
and also between the two alkyl groups themselves, all of which are reduced
when a small ring is formed with its naturally small internal angle. Thus strain
in the ground state is relieved in the product and in the transition state leading
to it.
Similar effects are observed on the formation of larger rings in rigid systems.
A system where the interpretation leaves little room for doubt is di-
218
A N T H O N Y J. KIRBY
methylmaleic acid, which exists in acid solution predominantly as the cyclic
anhydride [191. The EM for reaction (1 1) is estimated as 2.7 x 1OI2 My and
0
[ 191
similar extraordinarily high EM'S are found for the rates of formation of the
anhydride from the half-esters (Table A.2) and half-amides of this acid.
Comparative data for several related amides are summarized in Table 11.
The unsubstituted maleamic acid is already a very reactive system, with an
EM almost identical to that found for the hydrolysis (via the anhydride) of
phthalamic acid (A.3.9). The introduction of one and then two methyl groups
increases the EM by factors of 30 and 1.5 x lo4 respectively, but linking the
substituents in a ring (compounds A.3.18-20) dramatically reduces the effect,
by a factor of over lo9 for the cyclobutene derivative. Since all the groups
involved lie in the same plane, conformational effects are excluded. The clue to
these large difference in reactivity, which reflect differences in the enthalpy of
activation (Kirby and Lancaster, 1972), is found in the angles (labelled a a n d P
in Table 11) between the double bond and the reacting groups. These are much
larger in the trisubstituted olefin than the normal 120" angle expected for
sp*-hybridized carbon, presumably because non-bonded repulsion between the
carboxyl and amide groups is relieved by increasing these angles, the carboxyl
group in particular moving into closer proximity to the vinylic hydrogen atom.
In a dialkylmaleic acid derivative this position is already occupied by an alkyl
group which has its own steric requirements, and angles a and P are both
sharply reduced to little more than 120O. Since the corresponding angles in the
anhydride are smaller still, the non-bonded interactions between the two alkyl
groups are reduced still further by ring-formation since bond angles exocyclic
to the five-membered ring are closer to 130" (cf. compound A.3.19). So the
picture for a dialkylmaleic acid is of considerable strain in the ground state
[evident from a close inspection of the three-dimensional structure (Roberts
and Kennard, 1973) as significant deviations from planarity about the double
bond, including a dihedral angle of 8" between the bonds to the carboxyl and
amide groups1 which is relieved in the cyclic product and the transition state
leading to it.5
In compounds A.3.19 and especially A.3.20 angles a and B open out and are even larger
than in the monomethyl derivative (A.3.13). Larger changes of bond angle are thus required to
effect cyclization which has now become even less favourable because the expansion of the
incipient exocyclic angles is inhibited by the small ring already present.
219
EFFECTIVE MOLARlTlES
TABLE11
Comparative data for the hydrolysis of substituted maleamic
acids
Compound
EM/M
Angles&$
A.3.12 L O N H M e
‘gO,H
2 x 109
A.3.13 Y C O N H M e
\CO,H
A.3.17 R
R
x
6 x 1O1O
126.8, 131.7O
3 x 1013
121.0, 121.70b
CONHMe
CO,H
A.3.18 e C O N H M e
u C 0 , H
1 X 10’’
127.7, 131.5O
A.3.20
dCONHMe
‘CO,H
sx
103
132.1, 133.40e
Data given by Kirby and Lloyd ( 1976)
EM for R = Me, artgles for R = isopropyl; the EM is not
much affected by the substitution
Angles are for the diacid (Bellus et al., 1974)
Similar explanations almost certainly account for the very large effective
rnolarities found for lactonization of the hydroxy acids B.1.13, B.2.16 and
B.2.25 (Table 12). All these compounds have the basic tetrasubstituted
ethylene (here o-phenylene) structure found in the dialkylmaleic acid system
further destabilized by substituents in the 3 and 6 positions of the benzene ring
which also act to prevent bond angle spreading of the two inner substituents.
(The effects of 3- and 6-substituents on this type of cyclization reaction are
well known, and are shown for example by the range of EM’S for compounds
ANTHONY J. KIRBY
220
TABLE
12
Effects of alkyl substitution on EM'S for lactonization of hydroxy
acids
Substituted compound
B.1.13
&02H
\
Model compound
B.1.9
\
/
H
EM 2 x 1 0 1 3
B.2.16 H : &
m
0
H
,
/
EM 3.7 x 10"
B.2.9
ErH
EM > l o 1 *
EM 9 x 104
EM 4 x lo4
EM 7 x 10"
B.2.9-12.) The interaction between an o-methyl group and an qa-dimethyl-substituted chain is particularly severe, and undoubtedly leads to
restricted rotation about the ring-chain bond (see Lomas and Dubois, 1978).
This is not itself a major source of high effective molarities, however, as shown
by the moderate EM'S for compounds like [20l and [211 which have naturally
restricted conformations (Danforth et al., 1976).
In lactonization of B.2.25 and the related compounds B.2.24 and 23, ground
B.2.26
B.2.21
EM 8 x lo6
EM 5.3 x lo8
I201
[211
EFFECTIVE MOLARITIES
22 1
state strain is implicated by force-field calculations (Winans and Wilcox, 1976)
and by the observation of a large steric isotope effect (Danforth ef al., 1976).
Thus when the geminal cr-methyl groups of B.2.23 (EM 1.2 x 10") are
replaced by CD, groups (12), the rate of lactonization is reduced by nearly
10%. The x-ray structure of the alcohol derived from B.2.25 also shows
Q02H
d
CD, CD,
mo
\
kh6/kd6= 1.09
(12)
CD, CD3
B.2.23-dG
severe distortions of bond lengths and angles. For example, the benzene ring
has internal angles ranging from 114.3 to 125O, and bond lengths as high
as 1.428 A, compared with the normal value of 1.39 A. There is a severe van
der Waals interaction between one a-methyl and the methyl group in the
ortho-position (C-C distance as small as 2.86 A), and the a-carbon bearing
the two methyl groups is 0.17 A out of the plane of the ring, All these
distortions, though they do not all disappear, are substantially relieved on
cyclization, as shown by an x-ray study by the same authors (Karle and Karle,
1972)of the corresponding lactone.
Thus in two systems showing very high effective molarities for the formation
of five- and six-membered rings there is strong structural evidence for
substantial strain in the ground state. The other two most reactive systems
(B.1.13 and B.2.16) are intermediate in structural type, and undoubtedly owe
their high reactivity to similar factors.
Such high EM'S (> 1OloM)are scarcely to be expected for the formation of
three-, or especially four-membered rings, because of the angle strain associated
with the small ring of the product, and they are not found in any system where
the open-chain form has significant conformational flexibility. An effective
molarity of 1O'O M or more may therefore be taken as prima facie evidence for
strain in the ground state which is relieved in the cyclic product.
An important question is how far these very large EM'S are relevant to the
problem of the high efficiency of enzyme catalysis. Ground state strain is built
into a molecule when it is synthesized, and organic chemists are very adept at
making highly strained compounds. The equivalent process in an enzyme
reaction is the formation of the enzyme-substrate complex, and the possibility
222
A N T H O N Y J. KIRBY
that reacting groups might be forced closer together than the sum of their van
der Waals radii, or that bond angles of the substrate might be deformed on
binding, might appear to open up exciting possibilities for the theory of enzyme
catalysis.
Recent opinion, for example calculations by Levitt (1974), does not
generally support this idea. Proteins are not rigid structures, and from
estimates of the maximum force an enzyme can be expected to exert on a
substrate he concludes that “small distortions of substrate . . that cause large
increases in strain energy cannot be caused by binding to an enzyme”. There is
little doubt that this conclusion is correct, and that enzyme-substrate binding
cannot cause substantial strain of the sort described in this section (Fersht and
Kirby, 1980).
.
ORBITAL STEERING
A great deal of interest was stimulated by Koshland’s suggestion (Koshland et
af., 1971) that the high efficiency of enzymic and some intramolecular
reactions depends on the correct orientation of the reacting orbitals. The
chance of a random collision producing this correct alignment of orbitals was
considered small, giving the prealigned reaction an advantage estimated to be
of the order of lo4 (Storm and Koshland, 1972a,b). The concept of “orbital
steering’’ has been extensively critized (for a concise history, see Gandour,
1978), generally because the potential effects have been considered to be
overestimated. Certainly some reactions do have reasonably specific orientational requirements: an example is the S,2 reaction-there are no examples of 0or N-C-6n in the tables, no doubt because the nucleophile cannot get close
enough to an “in-line” relationship with the leaving group when they and the
central carbon atom all have to be accommodated in a six-membered ring. On
the other hand the ease of epoxide formation shows that one of the components
is allowed a great deal of latitude in this reaction.
The data in the tables can generally be interpreted satisfactorily without
invoking such orientation effects. This is not to say that they do not exist at all,
but simply that they must be relatively small. The major difficulty in identifying
any small effect is the elimination of all other possibilities. Storm and Koshland
(1972ab) have made the best attempt to do this in their discussion of the
relative rates of lactonization of the series of hydroxy and thioacids B.2.1-9
and C.2.1-5, but these rates were found to parallel the equilibrium constants
for the lactonization, and it seems probable that the dominant effect controlling
reactivity in these systems-and not corrected for-is the relief of groundstate strain discussed above.
EFFECTIVE MOLARlTlES
6
223
Tables of effective molarities
As we have seen (Section 4, p. 19 1) the range of effective molarities associated
with ring-closure reactions is very much greater than that characteristic of
intramolecular general acid-base catalysis; the main classification is therefore
in terms of mechanism. By far the largest section (I, Tables A-D) gives EM’S
for intramolecular nucleophilic reactions. These can be concerted displacements (mostly at tetrahedral carbon), stepwise displacements (mostly
addition-elimination reactions at trigonal carbon), or additions, and they have
been classified in terms of the nucleophilic and electrophilic centres.
Intramolecular general base catalysed reactions (Section 11, Tables E-G)
present less difficulty. A classification similar to that of Table I is used, but
since the electrophilic centre of interest is always a proton substantial
differences between different general bases are not expected. This section
(unlike Section I, which contains exclusively unimolecular reactions) contains
mostly bimolecular reactions (e.g. the hydrolysis of aspirin [41). Where these
are hydrolysis reactions, calculation of the EM still involves comparison of a
first order with a second order rate constant, because the order with respect to
solvent is not measurable. The intermolecular processes involved are in fact
termolecular reactions (e.g. [51), and in those cases where solvent is not
involved directly in the reaction, as in the general base catalysed aminolysis of
esters, the calculation of the EM requires the comparison of second and third
order rate constants.
One class of reaction, conventionally designated as intramolecular general
base catalysis, which is actually unimolecular is enolization catalysed by a
neighbouring basic centre [221. It might be thought that this reaction has as
[221
1231
L241
much in common with an intramolecular nucleophilic substitution [231 as with
other intramolecular general base catalysed reactions [241, but the important
factors are that cyclization cannot occur and that displacements at a hydrogen
centre fall naturally into the same class.
Section I11 (Table H), intramolecular general acid catalysis, is the smallest
because this mechanism is less common and because where it is observed
(mostly in acetal chemistry) the corresponding intermolecular reactions often
cannot be detected.
224
ANTHONY J. KIRBY
NOTES O N TABLES A-H
Abbreviations
A = carboxylic acid group
E = ester group
M = amide group
C =tetrahedral carbon
P" = tetrahedral phosphorus bearing (4 - n) oxygens bound only to P (e.g.
diester phosphorus is P2).
EM = effective molarity of neighbouring group
Conditions Data refer to reactions in buffered aqueous solution unless
otherwise indicated.
Rate constants These are the ones given in the reference cited, converted if
necessary to s-l.
Temperature P C .
EM Details of calculations (see text) are given in full except where these are
given by the original authors.
Accuracy Maximum estimated errors are:
a, +lo%;
p, within a factor of 2;
y, within an order of magnitude.
EFFECTIVE MOLAR IT1ES
225
I EFFECTIVE MOLARITIES FOR CYCLIZATION REACTIONS
(TABLES A-D)
A
REACTIONS OF THE CARBOXYLIC ACID GROUP
A. 1 Equilibrium data for anhydrideformation: from succinic, maleic and phtha lic acids"
Y
0
Acid
A.l.l
A.1.2
A.1.3
A.1.4
A. 1.5
A.1.6
A.1.7
A.1.8
A.1.9
A.l.10
A.l.ll
A.1.12
A.1.13
A.1.14
A.1.15
A.1.16
K
T
7 x 10-6
60
4.2 x 10-5 60
1.0 x 10-4 60
2.5 x 10-4 60
60
(0.01
0.17
60
dl-2,3-Diethyl-2,3-dimethylsuccinic 3.4
60
meso-2,3-Dkhyl-2,360
1.o
dimethylsuccinic
Tetraethylsuccinic
10
60
dl-2,3-di-isopropylsuccinic
(0.1
60
6
dl-2,3-di-t-butylsuccinic
60
1,2,-Diethyl-cis-cyclopropane(0.01
60
dicarboxylic
1,2-Di-isopropyl-cis-cyclo60
0.30
propanedicarboxylic
0.60
Norbornane-endo-cis-2,360
dicarboxylic
2-Methylnorbornane-endo-cis0.60
60
2,3dicarboxylic
0.30
Bicyclo[2.2.2loctane-cis-2,360
dicarboxylic
Succinic
Methylsuccinic
2,2-Dimeth y lsuccinic
dl-2,3-Dimethylsuccinic
Trimeth ylsuccinic
Tetramethylsuccinic
A.1.17
A.1.18
A.1.19
A. 1.20
PhthalicC
3,6-Dimethylphthalic
3,6-Diethylphthalic
3,6-Di-iodophtalic
( 5 x 10-3
0.20
1.5
(0.1
25
60
60
60
A.1.21
A.1.22
A.1.23
A.1.24
A.1.25
A. 1.26
Dimethylrnaleic
Methylethylmaleic
Diethylmaleic
Cyclohexene-1,2-dicarboxylicd
Di-isopropylmaleic
Di-t-butylmaleic'
5.3
4.3
3.2
4.7
25
ca. lo2
20
20
20
20
20
25
EMb
Accuracy
1.9 x 105
1.1 x 106
2.7 x lo6
6.7 x lo6
(3 x 10'
4.6 x 109
9.1 x 1O1O
2.7 x 1O1O
a
a
a
a
a
a
a
a
2.7 x 10I1
(3 x 109
1.6 x loL1
<3 x 108
a
a
a
a
8 x 109
a
1.6 x 1O1O
a
1.6 x 1O1O
a
8 x 109
a
x
x
x
x
109
109
1O1O
109
B
B
B
B
2.7 x 10"
2.2 x 10'2
1.6 x lo1,
2.4 x 10I2
6.7 x 1O1I
3 x 1013
B
B
B
B
B
(1.7
5.4
4.0
(2.7
Y
226
ANTHONY J. K I R B Y
, Eberson and Welinder, 197 1
bThe reference reaction used is the formation of acetic anhydride from acetic acid in water.
From the known values of AGO (15.70 kcal mol-’) measured by Jencks et al. (1966) and
A H o (14 kcal mol-I) determined by Conn et al. (1942) and Wadso (1962) for its hydrolysis,
the equilibrium constant for the formation of acetic anhydride can be calculated to be
2.0 x lo-’, at 20°, 3.1 x lo-” at 25O and 3.7 x lo-” at 60°
See also Hawkins, 1975
Eberson, 1964
Aldersley and Kirby, unpublished
A.2
Intramolecular nucleophilic caiuiysis of ester hydrolysis by the carboxyl group
~~
~~~
Ester
Ref.
COO--E-Sx:
pK,
kOb8
T
EM’
Accuracy
Monoaryl succinates
A.2.1
4.30
-
1.42 x
1.42 x lo-’
25
25.3
5.1 x 10‘
-
P
4.3
1.55 x lo-’
25.3
5.1 x lo‘
P
4.3
4.0 x lo-’
25.3
1.3 x 10’
P
4.3
3.7 x 10-3
25.3
1.2 x 10’
P
e
5.9
5.33 x lo-’
30
1.6 x lo5
P
c*d
4.3
1.40 x lo-’
25.3
4.6 x 10’
P
e
&Ph
coo0
A.2.2
A.2.3
A.2.4
A.2.5
A.2.6
C0,Ar
c,d
XooC0,Ar
cad
xooC0,Ar
c.d
LooC0,Ar
EFFECTIVE M O L A R l T l E S
227
~~
Ester
A.2.7
A.2.8
A.2.9
Ref.
1.38 x lo-'
25.3
4.6
10'
B
C*d
4.3
0.11
25.3
3.7 x lo6
P
=*d
4.3
0.21
25.3
6.7 x lo6
P
3.5
0.17
0.87
177
24.5
30
30
2.4 x 10'
1.3 x 10'
2.5 x lo9
Y
a
24.5
3 x lo9
Y
kcooC0,Ar
Accuracy
4.3
c.d
C0,Ar
EM"
kob.
LooC0,Ar
T
pK,
X
xooA.2.10
f
r.h
COOAr
-
Y
&oo-g
COO--E-Sx:
Monoaryl maleates andphthalates
0
A.2.12
.2.68
[LIlAr
a
3.3 x lo-'
COOH-E-Sx: Monoalkyl hydrogen maleates andphthalates
A.2.13
COOMe
'*'
3.37
2.7 x lo-'
3.3
6.7 x lo-'
100
109
Y
OZH
A.2.14
61.7
8 x 1Olo
Y
A N T H O N Y J. K I R B Y
228
Ester
Ref.
pK,
koba
T
EMa
Accuracy
39.5
1.5 x 10"
Y
Y
A.2.15
n
3.0
1.6 x
A.2.16
1.P
-
4.7
10-5
60
3 x 109
P
-
6.3 x lo-'
60
6 x 1O'O
-
2.2 x 10-2
39
4 x 10l2
-
1.8 x
39
5 x 10"
-
9.9 x lo-'
39
(5 x 1012)
A.2.17
A.2.18
C0,Et
A,,,,
C0,Me
0
x C O z H
)rOzH
'
C0,Me
A.2.19a
COO--E--Sx
Anion of A.2.19
Y
Y
COW-E-6x:
Monoaryl glularates'
A.2.21
I
A.2.22
-0,c &CO,Ar
6.22
5.95
7.4 x lo-'
5.6 x lo-'
30)
30
220
B
6.20
2.7 x lo-'
30
800
B
EFFECTIVE MOLARlTlES
Ester
A.2.23
229
Ref.
R, = H, R, = Me
pK,
A.2.26
A.2.21
A.2.28
A.2.29
A.2.30
A.2.3 1
A.2.32
A.2.33
EM'
Accuracy
30
910
P
30
30
730
1.9 x lo3
P
P
1.9 x 10-3
30
3.4 x 103
B
Y
6.34
6.63
6.77
6.54
6.21
1.3 x
1.0 x
1.0 x
1.5 x
1.8 x
lo-,
lo-,
lo-'
30
30
30
30
30
2.1 x
8.2 x
6.0 x
1.5 x
3.9 x
Y
6.55
1.2 x lo-,
30
1.2 x lo4
Qj-5
3.3 x lo-,
25
I
Y
A.2.24
A.2.25
T
k,,,
R, = H,R, = Ph
R, = H,
R, = n-Pr
R, = H,
R, = i-Pr
R, = R, = Me
R, = R, = Et
R, = R, = n-Pr
R, = R,= Ph
R, = Me,
R, = Ph
R, = Me,
R, = i-Pr
Me
I
Y
Y
Y
Y
Y
Y
'
6.23
6.04
6.08
6.14
3.2 x
2.1 x
2.5 x
7.3 x
6.29
4.26
lo-'
10-4
lo-'
10-
lo-)
lo-,
lo3
lo3
lo3
lo4
lo3
9 x loL1
Y
POPh
0
COO--Edn: Acyl salicylates
&lo
=
%y
4.41 x lo-'
39
>13
B
qcoo-
25
2.6 x 10'
P
A.2.34
-2.4
OAc
COOH
3.11,4.6
1.62 x lo-,
2 30
ANTHONY J
Ester
Ref.
pK,
-
kobs
4.3 x
KIRBY
T
EMa
Accuracy
30
9.2 x 10'
B
The reference intermolecular reaction is the nucleophilic attack of acetate on phenyl acetate,
calculated by Page (1973) from the data of Gold et al. (1971) by extrapolation (from
measurements on aryl acetates which show measurable nucleophilic catalysis). But see notes g
and h
* Gaetjens and Morawetz, 1960
In 11% acetonitrile (Eberson and Svensson, 1972)
Ar = 2-hydroxyphenyl (Eberson and Svensson, 1972)
Ar =p-bromophenyl in 50% dioxan-water. EM calculated from kobs for p-bromophenyl
succinate measured under the same conditions
'Ar = p-methoxyphenyl (Bruice and Pandit, 1960). Calculated from kobs for p-methoxyphenyl
succinate measured under the same conditions and corrected for the observed pK, using B = 1.0
Bruice and Turner, 1970. Results were obtained from direct comparison of the intramolecular
and intermolecular reactions under the same conditions, but without allowing for the difference
in pK, from acetate or the fact that the intermolecular reaction in water is predominantly general
base catalysed. (The two factors largely cancel out.)
In dimethyl sulphoxide containing one mole of water. Both reactions are probably nucleophilic
under these conditions
'Thanassi and Bruice, 1966
for
'Corrected for the difference in pK, from acetate using /3 = 1.0, and by a factor of 8.7 x
the lower reactivity of phenyl benzoate compared with phenyl acetate. This calculation is that of
Page (1973) and appears to be the best that can be done
k A r =pmethoxyphenyl (Bruice and Pandit, 1960). The calculation (Page, 1973) is similar to
is used for the lower
that for phenyl phthalate (note J), except that a factor of 6.3 x
reactivity of the unsaturated ester
EM is assumed to be lo9 M for all phthalate esters, and 3 x lo9 M for all maleate esters
Eberson, 1964. The reaction is eighty times faster than that of methyl phthalate under these
conditions (using activation energy = 23 kcal mol-')
" Hawkins, 1975a. The reaction is 150 times faster than for trifluoroethyl phthalate at 39.5'
[using data of Thanassi and Bruice (1966))
for ethyl maleate = 3.07 x lO-'s-'
Pekkarinen, 1957; khyd
Lancaster, 1971
'Aldersley et al., 1974a
EM is on the same scale as for aryl succinates (above), corrected for the increased pK, of
substituted glutarates using p = 1.0
Ar =p-bromophenyl in 50% dioxan-water (Bruice and Pandit, 1960)
" Conditions and leaving group as in f (Bruice and Bradbury, 1968)
'
EFFECTIVE MOLARlTlES
23 1
" In 20% dioxan (Hegarty et al., 1974). The reference reaction is nucleophilic attack by alkoxide
ions on phenyl N-methyl-N-phenylcarbamate at 25O in water (Hutchins and Fife, 1973). The
rate constant for bimolecular attack by an oxyanion of pK, 4.26 (3.6 x
dm3 mol-I s-') is
obtained by a long extrapolation of a two point Brmsted plot (which has the reasonable slope of
0.90)
"Reference reaction is attack on 2,4-dinitrophenyl acetate by RCOO- of pK, 2.4
(k2= 3.3 x lo-' s-' based on a short extrapolation using p= 1.0: Jencks and Gilchrist, 1968).
The reaction measured is the subsequent hydrolysis of the mixed anhydride; the observed value
thus sets only a lower limit for EM (Fersht and Kirby, 1967b, 1968a)
Fersht and Kirby, 1968b. Formation of the anhydride is rate determining here. The reference
reaction is that of phenyl acetate with a carboxylate anion of pK, 3.11 (see note a )
Kemp and Thibault, 1968. The reference reaction is that of RCOO- with phenyl benzoate (see
notej]
'pK not measured. A value of 3.7, equal to that measured for aspirin, is assumed for the
calculation
A.3 Intramolecular nucleophilic catalysis of amide hydrolysis by the carboxyl group
-iy
'C0,H
Amide
COOH-M-5x:
T
Accuracy
B
Succinamic acids
4.54
3.1 x
65
-
-
2.1 x 10-5
6.5 x lo-'
60
25
5.1 x 104
1.3 x
25
1.3 x lo5
p
C
4.1 x
25
2.9 x lo5
p
C
1.8 x
25
1.2 x lo6
/3
CONH,
A.3.1
EM"
N
H02C
CONHPh
m
H02C
A.3.2
c
A C O N H P h
-
-
HO,C
A.3.3
HO,C L C O N H P h
A.3.4
CONHPh
HO,C
ANTHONY J KIRBY
232
Ref.
Amide
A.3.5
PK,
kb'
T
EMa
Accuracy
c
-
7.6 x 10-6
25
5.9 x 105
p
c
-
2.3 x
25
6.6 x
lo6
p
)(/CONHPh
H02C
A.3.6
CONHPh
H02C
A.3.1
lo-'
c
-
8.2 x
d
-
8.2 x 10-3
25
2.0 x 10'
fi
H02CV O N H P h
A.3.8
50
5x
108
y
CONHPh
HO,C
COOH-M-Sx:
Phthalamic acids
CONHR
E
A.3.9
C
0
2
H
3.1
R= H
b
A.3.10
R = Ph
n
A.3.11
-
3.60
f
3.0
2.35 x
1.3 x
1.5 x
lo-'
2.4 x 10'
47.3
65
65.8
25
109
4x
lo9
Y
p
CONdN
a
C
0
2
COOH-M-Sx:
A.3.12
H
Maleamic acids'
CONHMe
Rx
'C02H
CONHMe
A.3.13-16
C02H
I
4.0
6.5 x 10-5
39
2 x 109
Y
233
EFFECTIVE M O L A R l T l E S
Amide
A.3.13
A.3.14
A.3.15
A.3.16
R =Me
R = Et
R = i-Pr
R = t-Bu
EM"
39
39
39
39
6 x 10"
7 x 1010
9 x 10'"
I x 1011
1.13
39
3x
3.5
3.5 x 10-2
39
I x 10'2
4.2
2.7 X
2.3 x lo-'
39
100
-
8 x 10'
Y
2.2 x 1W6 100
8 x lo3
y
?. 109
Y
PK,
I
I
3.2
3.2
3.6
3.7
l.1
4.2
I
I
1
kohl
T
Ref.
2.0
2.1
2.9
4.4
x lo-)
x 10-3
x
x 10-3
Accuracy
y
7
y
y
1013
Me
A.3.20
CONHMe
3.65
y
COOH-CN-SX
'
3.30
1.26 x lo-*
60
* EM for cyclization of succinamic acid assumed equal to that for cyclization of succinic esters
(Table A.2; see text). Direct rate comparisons give EM'S for substituted succinamic acids at
25'. No corrections for pK,
Bruylants and Kezdy, 1960
Higuchi er al., 1966. Activation energy 19.5 kcal mol-I for A.3.1
Kluger and Lam, 1978. Comparison with the rate constant calculated for succinamic acid at
50' gives EM = 5 x 10'. Correction for the better leaving group uses the ratio of rates for
maleamic and maleanilic acids measured by Aldersley el al. (1974b) at 39'
eBender 1957; Bender e l al., 1958. EM assumed equal to the value found for cyclization of
phthalate esters (Table A.2)
'In 20% dioxan (Hawkins, 1976)
I Smith, 1976. Reference reaction is acetic acid catalysed hydrolysis of benzimidazole. Smith
calculates EM = 8 x 104 from this comparison. Correction for the (estimated) lower pK, of
the neighbouring carboxyl using /3= 1.7 (Oakenfull and Jencks, 1971) raises this to 4 x lo9 M
Reference for maleamic acids is N-methylphthalamic acid, for which EM is taken as 1.0 x lo9
M (A.3.9, above) and k,,, has been measured as 4.67 x lo-' s-I at 39' (ref. i). A small
"
ANTHONY J . K I R B Y
234
correction (1.46) is also made for the slightly higher intrinsic reactivity of the benzamide
[k, for N-methylbenzamide is 6.0 x loT5dm’ mol-I s-l (Bunton et al., 1972), compared with
4.12 x lo-’ dm’ mol-I s-l for N-methylacrylamide (Lancaster, 1971)l
Kirby and Lancaster, 1972
Aldersley et al., 1974b
Capon el al., 1978. No reference bimolecular reaction is available, but o-cyanobenzoic acid
is hydrolysed over 10 times faster than phthalamic acid (A.3.9), although benzonitrile is less
reactive than benzamide towards acid hydrolysis. [Rate constants for hydrolysis are
(1-2) x
s-l for benzonitrile in 1 M acid (Hyland and O’Connor, 1973) and 3.5 x 1C4
dm’ mol-I s-l for benzamide (Bender et al., 1958), both measured at lOO01
‘
A.4
Lactoneformation from the cyclization of w-halogenocarboxylatees
n
A.4.1
A.4.2
A.4.3
A.4.4
A.4.5
A.4.6
A.4.7
A.4.8
A.4.9
A.4.10
A.4.11
A.4.12
A.4. I 3
A.4.14
A.4.15
A.4.16
3
3
4
5
6
7
8
9
10
11
12
13
14
15
18
23
pK,
kobs
T
‘
‘
2.86
-
‘
‘
‘
‘
‘
-
I x 10-5
2.41 x lo-]
2.6
3.1 x lo2
2.9
1.08 x
1 . 1 1 x 10-4
1.24 x 10-4
3.72 x
9.45 x 10-4
1.18 x lo-’
3.57 x 10-1
4.65 x lo-’
5.77 x lo-’
5.68 x
6.70 x lo-’
45
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
Ref.
‘
‘
‘
‘
‘
‘
‘
‘
-
-
-
-
EMa
0.29
1.23 x
13.5
1.60 x
14.5
5.51 x
5.66 x
6.33 x
1.90 x
4.82 x
6.02 x
1.82 x
2.37 x
2.94 x
2.90 x
3.42 x
lo-’
10’
lo-’
lo-‘
lo4
lo-’
lo-’
lo-’
lo-’
lo-’
lo-’
lo-’
Accuracy
B
/3
a
a
a
a
a
a
a
a
a
a
a
a
a
a
The reference intermolecular reaction for all the compounds listed, except A.4.1,
is the S2,
reaction between potassium butanoate and n-butyl bromide measured
under the same conditions: 99 :1 v/v dimethyl sulphoxide-water at 50° (Galli et al.,
a
1973)
* Data
for chloroacetate ion in water (Smith, 1943). The reference reaction is the
intermolecular esterification of the chloroacetate anion by itself
‘Galli et al., 1977. pK,-values not measured
235
EFFECTIVE MOLARlTlES
A S Intramolecular nucleophilic catalysis by the carboxyl group of the hydrolysis ofphosphate
andphosphonate esters
Ester
A.5.2
Ref.
CH,=C
CH,=C
2.92
lo-’
Accuracy
1.2 x
25
1.5 x 106
Y
(4.35)
3.8 x 10-3
35
(1.6 x
loJ)
Y
d
4.35
3.2 x 10-4
35
1.6 x
loJ
Y
e~f
3.15
3.44 x
lo-’
39
1.8 x 105
B
e.8
3.5
4.21 x 10-4
39
1.8 x
lo5
P
/OP\Ph
\
A.5.4
2.6 x
EM’
Y
d
4.2
T
3 x 106
‘I,,,
0
II ,OCHzPh
kob.
25
/PO(OEt),
A.5.3
PK.
CO,H
OPO(OCHzPh)2
/
\
CO,H
COOH-P3-6n
A.5.5
A.5.6
e.8
3.15
3.5
8.6 x
6.3 x
39
39
1.8 x 10J
1.8 x 105
P
P
e.h
3.5
4.7 x 10-4
39
1.8 x 10J
B
e*f
COO--P’-6x
A.5.6
nOPO(OPh),
ANTHONY J. K I R B Y
236
~~
Ester
hf. PK.
k0bl
T
EMa
Accuracy
\
COi
COO--P'an
A.5.5
A.5.6
3.15
3.5
1.38 x lo4
1.2 x lo-'
39
39
1.8 x lo'
1.8 x 10'
/3
ae**
1
3.91
2.0 x lo-'
35
3.6 x 10'
/3
k
-
1.43 x lo-'
75
2.4 x 10'
/3
39
6 x 10'
/3
a*e
/3
COo--P'-Sx
fy
-PO-
A.5.9
>'
0
CH,CH(
02 - O -
COO--P'-6x
A.5.10
COPh
I
,o-PO-
\O
A.5.11
I
0
4
4.0 x
EFFECTIVE M O L A R l T l E S
237
Calculation of EM. The reference intramolecular reaction is nucleophilic attack by the anion of
a carboxylic acid of pK, 3.15 on 2-phenoxy-l,3,2dioxaphosphorinan-2-oxide.
The rate constant
for this reaction can be calculated as 7.67 x
dm’ mol-’ s-’ at 39O using the formula
derived by Khan and Kirby (1970), and allows the direct calculation of the EM for the
corresponding intramolecular reaction (COO--P3-6n of A.5.5). The EM is assumed to be the
same for the corresponding endocyclic reaction of the diphenyl ester anion (A.5.6), and has
been shown not to differ significantly for endocyclic and exocyclic displacements (Bromilow
el al., 1972)
This now allows the calculation of EM for A.5.7 and A.5.8 using a correction factor of 10
for the decrease in reactivity expected when one “spectator” aryloxy group of a phosphate
triester is replaced by an alkoxy group (Bromilow el al., 1972)
The calculation for dibenzylphosphoenolpyruvate assumes that the enol dibenzyl phosphate
will have the same reactivity towards bimolecular attack by RCOOH as the dialkyl phosphate
group of A S S . The comparison between A.5.3 and A.5.4 shows that the substitution of an
alkoxy group by phenyl increases the reactivity by an order of magnitude towards COOH, and
this factor allows us to put the phosphonate A.5.1 on the scale. The intrinsic reactivity of
A.5.1 and A.5.2 are assumed the same
Gordon el al., 1964; Blackburn and Brown, 1969
van Holst el al., 1974
dSchray and Benkovic, 1971. The pK, and EM for A.5.3 are assumed to be the same as for
A.5.4. The rate constants are not corrected for exocyclic vs. endocyclic displacement
Bromilow el al., 1972
’Corrected for 20% endocyclic displacement
Corrected for 13% endocyclic displacement
* Corrected for 96% endocyclic displacement
Simons, 1974
’Steffans el al., 1973, 1975. The reference reaction is the attack of the anion of a carboxylic
acid of pK, 3.91 on methyl 2,4-dinitrophenyl phosphate at 39O (Kirby and Younas, 1970). The
intramolecular reaction is corrected for the better leaving group using ,3,/ = 1.26 (Khan
el al., 1970), and to 39O using the activation energy measured for the intermolecular reaction
with acetate (Kirby and Younas, 1970).
‘Steffens el al., 1975. The rate of the same reference reaction (note/? was extrapolated from
60° to 75O using an activation energy of 22 kcal mol-I (Kirby and Younas, 1970), and the
same correction for leaving group applied as inj. The pK, of the substrate carboxyl group was
estimated to be 4.4
‘Khan el al., 1970. The intramolecular and reference reactions are now at the same temperature, and the leaving group correction is applied in the series for which BL0 was measured
(note 57. The major remaining uncertainty concerns the comparison of an intramolecular
reaction of a diary1 phosphate with an intermolecular reaction of a methyl aryl phosphate.
This is not a large factor; the second order rate constant for the reaction of pyridine with
bis-2,4-dinitrophenyI phosphate is less than three times greater than for the same reaction with
methyl 2,4dinitrophenyl phosphate (Kirby and Younas, 1970). For the 2-carboxylatophenyl
group a factor of two is a good estimate
a
ANTHONY J. KIRBY
238
A.6 Intramolecular nucleophilic catalysis by the carboxyl group of the hydrolysis of
sulphonamides"
Ref.
PK,
k0b*
T
EMb
Accuracy
C00H4-4~
A.6.1
A.6.2
2.49
2.78
2.26 x
1.74 x
75
75
4 x lo6
8 x 10'
Y
Y
d
3.44
-
5.32 x 10-4
4.5 x 10-3
75
75
-
c
2 x 107
Y
Y
2.5 x lo-'
75
3x
lo6
Y
HO,CCH,SO,NMePh
HO,CCMe,SO,NMePh
COOH-S-SX
A.6.3
HO,C(CH,),SO,NMePh
A.6.4
3.67
A.6.5
3.63
1.29 x
lo-)
75
3 x lo6
Y
3.64
1.62 x 10-3
75
2 x 103
Y
2.01
2.78 x
75
-
Y
1.0 x 10-2
75
4 x 10'0
Y
4.79 x lo-)
8.0 x
75
75
1 x 10'
Y
Y
Y
A.6.6
I-!:
d
aCO,H
A.6.7
(,02NMeph
C02H
A.6.8
A.6.9
c
-
2.67
aI;e'"
c
S0,NMePh
-
lo-'
2.51
7.2 x
lo-'
75
3 x 10)
3.90
1.3 x
lo-*
75
2 x lo3
Y
4.88
3.3 x
75
6 x 10'
Y
CO,H
COOH-S--6~
A.6.10
A.6.1 I
HO,C(CH,),SO,NMePh
SO,NMe,
E F FECTl VE M 0 LAR IT1ES
239
Data are from Graafland et al., 1979
No intermolecular counterpart to this reaction is available. The EM's are assumed to be the
same for compound A.6.4 and A.6.5 as for the corresponding phosphonate ester (A.5.1),
which involves a similar mechanism and almost identical geometry. EM's for other sulphonamides are then calculated by direct rate comparison with A.6.4 or A.6.5 after correction for
the difference in pK.. The correction is based on /3= 0.72 for the COOH group, calculated
from the measured pcooH = -0.54 for the hydrolysis of ring-substituted derivatives of A.6.5 and
p = 0.75 2 0.05 for the pK,-values of the same compounds (Graafland et al., 1979)
Measured in 50% aqueous ethanol
In water
a
B
REACTIONS OF T H E H Y D R O X Y L G R O U P
B. 1 Equilibrium constantsfor the lactonization of hydroxy acids
Hydroxy acid
B.l.l
B. 1.2
rn
yHydroxybutyric
HO
B.1.3
0
,,+
B.1.5
B.1.6
T
EM"
Accuracy
e
6.15
11.13
25
25
88
159
P
P
28 10
25
4 x 104
P
25
1.8 x 105
P
30
1.6 x 10'
P
C
C
Co2H
CH,OH
.Pi
HO
Kb
CO,H
"o,,
6.1.4
Ref.
1.27 x lo'
CO,H
0.621
*02H
\
240
A N T H O N Y J KIRBY
Hydroxy acid
Ref.
Kb
T
EM"
Accuracy
d
>99
30
>2.6 x 107
B
30
3.7 x 10"
/?
30
2.0 x 1013
p
1.42 x
f
lo6
7.51 x 107
,,Reference reaction is the formation of ethyl acetate from ethanol and acetic acid at 25O
(Gerstein and Jencks, 1964)
Data at 25O in 2096 ethanol-water
Storm and Koshland, 1972a
Milstien and Cohen, 1972. Reference reaction is the formation of phenyl acetate from phenol
and acetic acid at 25 O in water
Hershfield and Schmir, 1973a For reference reaction, see note d
'Hershfield and Schmir, 1973b.For reference reaction, see note d
24 1
EFFECTIVE MOLAR IT1E S
B.2
Acid-catalysed Iactonization of hydroxy acids
kob;
T
EM”
4.72 1.43 x lo-’
- 2.12 x 10-3
5.09
0.12
5.44
18.7
25
25
25
25
80
117
6.62 x lo3
1.03 x lo6
a
d
-
25
6.5 x lo4
a
d
-
d
-
1.78
25
9.8 x lo4
a
B.2.8
d
-
2.53
25
1.4 x 13’
a
B.2.9
C
-
-
25
45
25
9 x 104
-
p
C
45
1.4 x lo6
p
Hydroxy acid
HO-A-5x:
B.2.1
B.2.2
B.2.3
B.2.4
Ref.
c
C
C
e
B.2.5
1.58 x lo-’
25
87 1
a
CO,H
f
B.2.10
a
CO,H
B.2.7
HO
1.18
a
a
CO,H
B.2.6
HO
Accuracy
pHydroxy acids
B.l.l
B.1.2
B.1.3
B.1.4
HO
pK,
e
-
5.73 x 10-3
2.25 x lo-,
4.88 x lo-’
0.349
242
p:H
Hydroxy acid
B.2.11
B.2.13
Ref.
e
pK,
-
q:H
ANTHONY J. K I R B Y
kobt
T
EM"
1.19
45
5 x 106
Accuracy
p
13.3
25
2.5 x 10'
B
-
48
25
109
Y
-
h
I
-
8
8
Me Ph
B.2.14
Me Me
B.2.15
33.9
3 x 10'
y
8
15.5
3 x 10'
y
250
15.5
10'O
Y
Ph Ph
B.2.16 H:&
B.2.17
K
B.2.18
Me
Me
o
H
H
J,k
-
1.1
-
EFFECTIVE M O L A R l T l E S
2 43
Ref.
Hydroxy acid
pK,
kobsb
T
EM"
5.9 x lo-'
30
4.0 x 10'
7.0 x lo-'
30
4.7 x 10.'
4 x 10-5
30
2.7 x lo5
Accuracy
~
SHydroxy acids
HO-A-6x:
B.2.19
B.2.20
3.2 x 106
B.2.21
2.6 x lo-.
30
1.7 x 10'
2.8 x
30
1.9 x 10'
B.2.22
9.85 x
30
6.6 x lo8
B.2.23
(5.0 x 10')
30
26.2
30
B.2.24
(1.5 x lo6)
B.2.25
(2.0 x lo6)
q
B.2.26
C
0
.
H
i~
1.7 x 10"
Y
5 x 10"
Y
30
30
-
7 x 10"
1.18 x 10-3
30
8.0 x lo6
244
A N T H O N Y J. KIRBY
Hydroxy acid
Ref.
pK,
kob;
T
EMa
Accuracy
30
5.2 x 10'
B
30
6.9 x l@
B
B.2.27
B.2.28
3.7
B.2.29
3.25
P
B.2.30
z
0.103
H
bozH
\
B.2.3 1
O
7.78 x
3.84 6.82 x
30
4.5 x 10'
B
4.50 3.75 x
30
2.5 x 10'
p
/
The reference intermolecular reaction for the aliphatic compounds is the formation of ethyl
acetate from ethanol and acetic acid measured under the same conditions (20% ethanolwater, ionic strength 0.4 M) by Storm and Koshland (1972a). The esterification of benzoic
acid in methanol at 25' is 290 times slower than that of acetic acid (Kirby, 1972), so this factor
is used to correct the EM'S, calculated otherwise in the same way, for the hydroxybenzoic
acids. For the phenolic acids see notes rn and n
Rate constants are in units of dm' mol-I s-'
Storm and Koshland, 1972a
,I Storm and Koshland, 1972b
Bunnett and Hauser, 1965
'Chiong er al., 1975; in water containing 3.2% ethanol
'Weeks and Creary, 1970. Estimated from observed rate constant of 8.37 x lo-' s-' at
33.9', pH 3, for B.2.14. The measured rate constant at 20' is 33.3 dm' mol-I s-' (Milstien
and Cohen, 1972)
2.9 times slower than B.2.14, above
.
Probably faster than compound B.2.25 (Hillery and Cohen, 1972)
Kirby and McDonald, unpublished
a
EFFECTIVE M O L A R l T l E S
245
33 times less reactive than B.2.18 at pH 3.25
'Calculated from k,,, = 0.14 SKI
at pH 3.25, using A H t = 15 kcal mol-'
In 20% dioxan-water (Milstien and Cohen, 1972). The reference reaction is the formation
of phenyl acetate from phenol and acetic acid at 25O (rate constant estimated at 1.5 x
dm' mol-' s-l). These authors' very high rate constants for the lactonization of compounds
B.2.23-25 (data in parentheses) which lead to much quoted EM'S in the region of 10l6M, appear
to be too high by several orders of magnitude (Caswell and Schmir, 1980)
" In 20% dioxan-water (Caswell and Schmir, 1980). Reference reaction as in note m
'EM from direct rate comparison with B.2.19, using Milstien and Cohen's data
EM from direct rate comparison with B.2.23, using Milstien and Cohen's data
q Measured under the same conditions as B.2.19-25
Danforth ef al., 1976. For reference reaction see note m
Hershfield and Schmir, 1973a. For reference reaction see note m
Hershfield and Schmir, 1973b. For reference reaction see note m
B.3
Base cafalysed lacfonization of hydroxy esters
Ester
Ref.
PK,
k0bl
T
EM
Accuracy
3.5 x lo8
B
280
P
O---E-Sx
B.3.1
B.3.2
B.3.3
B.3.4
9.0
Me
2.23
25
C0,Ph
0-
c
0--E-6~
B.3.5
C0,Ph
0-
*** (15.9)
f
29.8
246
ANTHONY J. K I R B Y
Ref'
Ester
PKa
kobs
(10.0)
8
T
25
EM"
Accuracy
5 x 10'
3/
C0,Ar
0Capon er al., 1973
bThe pK,-value is estimated in order to allow the calculation of the first order rate constant
for cyclization of the anion from k,,, and the reference reaction is the attack of methoxide ion
on phenyl acetate (Bender and Glasson, 1959)
cThe pK,-value is estimated. The reference reaction is the attack of phenolate anion on
phenyl acetate (Bender and Glasson, 1959)
dFife and Benjamin, 1973. The reference reaction is attack by alkoxide on ethyl benzoate
estimated from the known second order rate constant for attack by hydroxide in water at
25O (Bender, 1951) and allowing a factor of 10 for the higher reactivity of aIkoxides (Gilchrist
and Jencks, 1960). The pK,-value is taken as that of benzyl alcohol (Takahashi et al., 197 1)
Hutchins and Fife, 1973. The reference reaction is the attack of the anion of a phenol of pK,
9.0 on phenyl N-methyl-N-phenylcarbamate under the same conditions
f 18 times slower than B.3.1
'Ar = 2-naphthyl. This ester is about 5 times less reactive than 2-naphthyl 2-hydroxyphenylacetate in 20% dioxan-water
B.4
Epoxide formation from chlorohydrins
Compound
Ref.
pK,
kObS(I
T
EMb
14.31
2 x lo-,
25
2.5 x lo3
y
Accuracy
0--C-3~
B.4.1
-cl
c
0-
1.05 x lo-' 18
B.4.2
13.64
0.24
25
3 x 104
y
B.4.3
dre
15.5
3.42
18
8 x 10'
y
B.4.4
d.e
14.5
9 x lo-'
18
2 x lo4
y
B.4.5
d.e
16.5
410
18
108
Y
EFFECTIVE MOLARlTlES
247
Ref
PK,
kobsD
T
d.e
14.5
4.1
18
B.4.7
d. e
16.7
3.5 x 103
18
B.4.8
d. e
15.7
530
18
16.7
3.0 x 104
18
Compound
-
B.4.6
0i-X"'
B.4.9
EMb
Accuracy
Rate constants are calculated from the observed second order rate constant for hydroxidecatalysed cyclization and the pK, given
Effective rnolarities are based on the calculation for the formation of oxetane (see reaction
B.5.1) and are derived by direct rate comparisons
Knipe, 1973
Data of Nilsson and Smith, 1933
pK, estimated by the method of Takahashi et al. (197 1)
'There is no satisfactory intermolecular counterpart to these reactions. No corrections have been
made for the effects of the methyl substituents in these compounds
B.5 Base-catalysedformation of cyclic ethers
Alcohol
Ref.
pK,
kobt
T
EM
Accuracy
~
0--C-4~
b*c
b*c*d
15.23 3.74 x
30
4
P
16.5
30
1700
P
8
P
1.58 x
A N T H O N Y J. KIRBY
248
Alcohol
Ref.
pK,
kobaa
T
EM
Accuracy
15.56
0.104
30
6 x lo'
y
7
25
390
B
30
280
Y
O--C-~X
B.5.4
HO(CH3,CI
O--C--6x
b.c*d
15.70
5.0 x
249
EFFECTIVE M O L A R l T l E S
Alcohol
Ref.
pK,
kesa
T
EM
Accuracy
-
1.92
50
6560
a
-
1.55
50
3880
a
I
1.1
0- Br
B.5.14
m
-
0.237
30
6.6 x
lo3
/I
m
-
1.65
30
4.6 x l(r
/I
736
30
2.0 x 10'
/I
30
5.7 x
B.5.15
m
B.5.17
m
-
-
2.05 x
loJ
lo9
/I
250
ANTHONY J. KIRBY
Alcohol
cyclization of
Ref.
kObP
pK,
uo[a1
B.5. I8
B.5.19
[a], n = 7
[bl, n = 7
I
B.5.20
B.5.21
[a], n = 8
[bl, n = 8
I
B.5.22
B.5.23
J
B.5.26
B.5.27
[a], n = 9
[bl, n = 9
[a], n = 10
[bl, n = 10
[a], n = 11
[bl, n = 11
B.5.28
B.5.29
[bl, n = 12
[b], n = 13
1
B.5.30
B.5.31
[a], n = 14
[bl, n = 14
[a], n = 16
[bl, n = 16
[bl, n = 24
J
B.5.24
B.5.25
B.5.32
B.5.33
B.5.34
T
EM
Accuracy
a
a
a
a
a
a
a
a
a
a
a
a
[bl
3.45 x
1.45 x lo-*
50
50
118
36.3
1.03 x lo-‘
6.61 x lo-‘
50
50
0.352
1.66
1.63 x lo-’
1.23 x lo-‘
50
50
5.57 x
0.308
1.46 x lo-’
6.07 x
50
50
4.99 x lo-*
0.152
I
3.96 x
I
1.85 x lo-’
50
50
4.64 x
2.27 x lo-’
1.50 x lo-’
50
50
5.69 x
3.76 x
3.35 x
8.89 x
50
50
1.14 x
2.23 x
4.75 x
9.07 x
2.56 x lo-’
50
50
50
1.62 x
2.28 x
6.42 x
1
1
I
I
1
I
1
J
I
1
1.35 x
a
a
a
a
a
“Rate constants calculated from the observed second order rate constant for hydroxidecatalysed cyclization, and the pK,-value given
bEM’s based on the observed product ratio for the base-catalysed cyclization of 3-chloropropanol in 40% methanol-water (Richardson et al., 1971). Over a range of temperatures the
amounts of cyclic ether (14%) and 3-methoxypropanol(50%) were constant within experimental
error. From the known molarity of methanol in the solvent the EM of the neighbouring group
is readily calculated as 2.77 M, and a small correction for the difference in pK, between
3-chloropropanol (15.23) and methanol (15.09) gives a value of 3.82 M for the EM of the 0group of 3-chloropropoxide relative to intermolecular attack by methoxide
In 40% methanol-water (Richardson et al., 1971)
Rates at 30° extrapolated from Arrhenius parameters given. pK, estimated using linear free
energy relationship given by Takahashi et al. (1971)
Richardson et al., 1971. EM based on comparison with the reaction of 3-chloropropanol under
the same conditions, corrected for change of solvent from the figure given in B.5.1 (kobs=
6.8 x
dm3 mol-’ s-l in water) on the basis of the results of Stevens et nl. (1948) [Compare
8.1 x lo4 M calculated independently by Page (1973)l
’Coward et al., 1976
25 1
EFFECTIVE MOLARlTlES
The EM refers to the pH-independent reaction which is compared to the attack of water on the
dimethyl p-nitrophenyl sulphonium cation
Irie and Tanida, 1979
'Capon and Thornson, 1977. The reference reaction is attack by phenolate anion on an
epoxide "of this type"
'Illuminati et al., 1974, 1975, 1977. The reference intermolecular reaction is the alkylation of
o-ethylphenolate anion by n-butyl bromide under the same conditions. Reactions were run
using the fully ionized substrate in 75% ethanol-water
kBeU el al., 1974. The reference intermolecular reaction is of the anion of p-hydroxyacetophenone with EtCOCH,Br under the same conditions
As for note j except that the reference reaction is alkylation of the guaiacol anion
'"Borchardt and Cohen, 1972. EM's based on relative rates assuming equal EM's for the
bromide and mesylate, B.5.10 and B.5.12
8
'
B.6
Intramolecular cyclization of hydroxyalkyl phosphates
Ester
Ref.
pK,
k,,,,,"
T
EM
Accuracy
25
1 x 10'
y
B.6.1
15
B.6.2
330
O--P'-Sx
B.6.3
B.6.4
B.6.5
C.d
14
1.4 x
100
1.3 x lo4
y
15
2.6 x
100
2.5
lo4
y
8.5 x
100
8 x lo4
y
xo'po/oR
c,d
0-
15
X
2 52
A N T H O N Y J. KIRBY
Ester
B.6.6
Ref
14
,OR
,OPh
kob,"
T
3.7 x lo-'
100
6.0
50
PK,
13.92
EM
3.6
X
Accuracy
lo6
y
3 x 107
0For intramolecular reaction of anion
Gay and Hamer, 1970. The reference intermolecular reaction is the attack of hydroxide on
the methyl ether of B.6.1, corrected (factor of 10) for the expected higher reactivity of an
alkoxide anion
eBrown and Usher, 1965a. R = cyclohexyl. The EM'S are calculated by comparison of data
for one phenyl ester (B.6.4; R = Ph; Brown and Usher, 1965b), extrapolated to 2S0, with the
intermolecular attack of hydroxide on diphenyl phosphate (k,= 1.56 x lo-' dm' mol-I s-l at
25O; Kaiser and Kudo, 1967). Hydroxide deviates little from the Brmsted plot for a series of
oxyanion nucleophiles attacking methyl 2,4-dinitrophenyl phosphate, so the only correction
made is a factor of 2 for the increased reactivity of a diary1 phosphate compared with an
alkyl aryl phosphate anion. The EM can thus be calculated directly for B.6.4 (assumed not
to change with the leaving group) and B.6.7, and for the other cyclohexyl esters by rate
comparisons with B.6.4
pK,-Values estimated by the method of Takahashi et al. (197 1)
Usher et al., 1970
c
REACTIONS OF T H E S U L P H Y D R Y L G R O U P
C. 1 Equilibrium constants for thiolactoneformationfrom y-thiolacids
HS
Acid
C. 1.1
s-co
CO,H
Ref.
y-Thiolbutyric
c.1.2
SH
Ka
T
EMb
Accuracy
2.44
25
3.7 x 10'
P
1.10
25
1.7 x 10'
P
2 53
EFFECTIVE M O L A R l T l E S
4cozH
Acid
C.1.3
K"
Ref.
63
T
EMb
Accuracy
25
9.5 x 104
P
SH
C.1.4
" Determined in 0.1 M HCI
The reference reaction is the formation of ethyl thiolacetate from ethanethiol and acetic
acid (Gerstein and Jencks, 1964)
Storm and Koshland, 1972b
C.2
Thiolactonization of y-thiol-acids. etc.
Acid
pK,
Ref.
kob;
T
EMb
2.05 x
4.80 x
2.50 x lo-'
4.38 x
25
25
25
25
384
90
4700
8.21 x loJ
24
25
1.6 x 10'
Accuracy
HS-A-SX
c.2.1
c.2.2
C.2.3
C.2.4
4.80
5.42
5.06
c.1.1
c.1.2
C.1.3
C.1.4
b*e
b*e
U
U
a
u
C.2.5
S--E-Sx
C.2.6
Me
8.7
d
" Acid-catalysed reaction measured in the range pH 1-4. Units dm'
a
mol-I s-l
The reference intermolecular reaction is the esterification of acetic acid by ethanethiol under
the same conditionse
Storm and Koshland, 1972b
dFife ef al., 1975. The reference reaction is attack by 2-arninoethanethiolate anion @K,
8.3) on p-nitrophenyl N-methyl-N-phenylcarbamate,corrected to pK 8.7
ANTHONY J. KIRBY
254
D
REACTIONS OQ THE AMINO-GROUP
D. la Intramolecular attack by the dialkylamino-group on a neighbouring ester group
Solvent
k,","
k,",,,
N-E-4n
D.1.1'
Et,N,?S,
+u7
Et,N-CH,-S-
I
Ac
Nitromethane
Acetonitrile
Chloroform
Acetone
MeOCH,CH,OMe
n-Hexane
a
-
T
EM
Et,NAc
+ (CH,S),
1.44 x
3.06 x
6.39 x lo-'
2.72 x
1.36 x
1.94 x lo-'
5.0 x lo-'
1.39 x lo-'
1.72 x
3.33 x
1.36 x
6.94 x lo-'
27
27
50
50
50
50
0.029
22
0.037
0.8
1.o
0.28
0.17
0.55
9.7
358
-
20
20
20
20
1260
1080
1700
5400
6.5 x lo-,
0.33
4.25
167
-
20
20
20
20
490
650
750
2330
Accuracy
B
P
B
B
P
B
N-E-SX
a
a
a
a
N-E-~x
D.1.6'
D.1.7'
D.1.8'
D.1.9'
Ar = Ph
Ar =p-CIC6H4
Ar = m-NO,C,H,
Ar =p-NO,C,H,
a
a
a
a
Both intermolecular and intramolecular reactions can be measured for this reaction. EM is
calculated as the ratio of the rate constants for the intramolecular (s-l) and intermolecular
reactions (dm' mol-I s-l). Data of Searles and Nukina, 1965
'Bruice and Benkovic, 1963. The reference reaction is the attack of trimethylamine on the
corresponding aryl acetate under the same conditions
a
255
EFFECTIVE MOLARlTlES
D.1b Intramolecular nucleophilic attack by imidazole and pyridine
Ester
Ref.
PK,
kobs
T
EM
Accuracy
6.91
6.69
6.79
6.24
4.3 x lo-,
0.17
2.4
33.3
25
25
25
25
-
73
P
7.55
8.8 x
lo-,
30
53
B
N-E-~x
4
H N ,N:-0Ar
D.l.10
D.1.1 1
D.1.12
D.1.13
Ar=Ph
Ar = p-CIC,H,
Ar = m-NO,C,H,
Ar =p-NO,C,H,
(I
O
a
O
D.1.14
N-E-ttt~
D.1.1SE
CH,NH(COCH,NMe),COCH~CH,CO#NP
I
25
For m = 25-100 EM falls from
2.5 x lo-,
- 4 x 10-3
to
D.1.16d
CH,CH,O(CH,CH,O),COCH~CH,CO~NP
I
EM is maximum near m = 32-33 (n = 7)
EMfdsoffasm+100to
25
-6 x lo-’
-2 x lo-’
a
4Bruice and Sturtevant, 1959. The EM’S are complicated by a mechanism change for the
substituted compounds (see footnote b) and are based on the reaction of the phenyl acetate
with imidazole
Bruice, 1959
Sisido et al., 1976.Reference reaction is of the substrate with pyridine
Sisido et al., 1978.Reference reaction is of the substrate with pyridine
ANTHONY J. KIRBY
256
D.2 Intramolecular nucleophilic attack by the NH, group
Ref.
pK,
T
kobs
EM
Accuracy
Fife et al., 1975. The EM is based on an estimated lower limit for the rate of the reaction
of cyclohexylamine with p-nitrophenyl N-methyl-N-phenylcarbamate(aniline does not react at
all) and requires a long extrapolation from pK, 10.7 to 2.7, using /3 = 0.8
(I
D.3
The cyclization of halogeno-amines, ere.
Amine
PK,
Ref'
k b s
T
EMa
Accuracy
N-C--3~
D.3.1
8.8c 1.74 x
25
15
Y
D.3.2
8.65
5.6 x lo-'
25
15
Y
8.97
8.0 x
75
15
Y
-0s0,
D.3.3
HZN
D.3.4
D.3.5
D.3.6
'
MeZNl-'
Me,N
mBr
Et,N -cl
d
d*g
D.3.7
Me2N/Yc1
2.88 x lo-'
25
1.3
Y
10-2
25
-
Y
8.80
9.33 x lo-'
25
2000
Y
8.31
1.62 x lo-'
25
9
Y
8.2
-
D.3.8
d*h
8.9
2.0 x
25
D.3.9
d*h
8.6
7.9 x
25
6
Y
25
30
Y
D.3.10
7.6
1.81 x lo-'
1.5
Y
EFFECTIVE M OLARl TI E S
257
-
b~J
3.29 x 10"
25
1
15
N-C--4~
D.3.14
D.3.15
D.3.16
H,N(CH,),Br
Me,N(CH,),CI
H,N(CH,),OSO,
m
-
8.3 x lo-,
1.08 x lo4
9.08 6.5 x lo-'
25
56
75
0.2
-
Y
0.2
Y
9=
N-C-SX
D.3.17
D.3.18
H2N(CH2),Br
H2N(CH2),CI
9 3
-0.5
9.58 5.84 x lo-'
25
25
7000
3000
Y
Y
D.3.19
Ph
8.45 5.44 x lo-)
25
6000
Y
3.57 2.74 x 10-3
10.28 3.55 x lo-'
2s
75
3000
3000
I
25
73
73
73
73
73
73
100
100
1.7
2 x lo-,
9 x 10-2
4 x lo-'
0.15
0
D.3.20
D.3.21
-
C
I
PhNH(CH,),CI
H,N(CH,),OSO,
b
Y
N-C-(616)x
D.3.22
H,N(CH,),Br
9.8c
n
D.3.23
D.3.24
D.3.25
D.3.26
D.3.27
H,N(CH,),Br
H,N(CH,),,Br
H,N(CH,),,Br
H2N(CH2),,Br
H,N(CH,),,Br
-
10.w
n
n
-
n
-
R
-
n
-
8.3 x
3.3 x
5.5 x
6.7 x
1.2 x
lo-'
10-2
10-4
lo-,
10-5
1.3 x lo-'
2.5 x lo-'
Y
B
B
B
B
B
A N T H O N Y J. K I R B Y
258
Amine
D.3.28
Me
I
Ref.
0
PK,
-
koba
1.2 x 10-3
T
EM4
Accuracy
25
3 x 10-3
u
'The reference reaction is the S,2 reaction of the closest amine (trimethylamine, triethylamine for dimethyl and diethylamino-compounds, ethylamine for the primary amines) with the
chloroacetate anion in water at 25O [data of Moore el al. (1912)l. The reference reactions are
not expected to involve participation by the COO- group (Gacek and Undheim, 1973), but
may underestimate rate constants for an ideal intermolecular reaction because of the aniondipole interaction, thus overestimating EM. Page's value of EM = 1.4 x 10' for D.3.17 is
actually based on data for the reaction of Et3N with EtI, not EtBr, with both temperature and
solvent extrapolations (Page, 1973). Where an independent estimate of EM is possible (D.3.22)
the value calculated by the above method is in agreement (see note n). The data are corrected
for pK, differences, using = 0.27 (Dixon and Bruice, 1971)
In 50% dioxan-water (Bird ef al., 1973)
=The value of pK, is estimated from the linear free energy relationship given by Takahashi
et al. (197 1)
Hansen, 1962,1963a
Dewey and Bafford, 1967. EM is assumed for D.3.3 which is used to calculate EM'S for D.3.16
'Simonetta er al., 1950
'Et,N reacts with chloroacetate almost 80 times more slowly than does Me3N yet the intramolecular reaction of the diethylamino-compound is 32 times faster than that of D.3.5. Most of
the difference in EM is therefore probably real
* Reference reaction is of Me3N, since the ring N shows much less steric hindrance than Et3N
pK, is based on that of D.3.19 and standard effect of b-Cl
'EM'S are assumed the same as D.3.1-3 and D.3.18 respectively. These are certainly underestimates, but by how far is difficult to say
'Hutchins and Rua, 1975. Based on Me,N(CH,),CI (D.3.4); rate constant 6.22 x lo-' s-l
at Oo, and EM = 1.3 M
Freundlich and Kroepelin, 1926
In 80% ethanol (Grob, 1969); safe extrapolation to aqueous solution at 25O is not possible
"Data of Salomon (1936) at 73.35O in 30% aqueous isopropyl alcohol. No pK,-values are
available. The EMS quoted are derived independently of those above from comparison of the
rates of the intramolecular and intermolecular reactions of these compounds [the so-called
cyclization constants of Stoll and Rouve (1934) referred to on page I881
In dioxan (Lok and Coward, 1976). The reference intermolecular reaction is demethylation by
piperidine under the same conditions
'
2 59
EFFECTIVE MOLARlTlES
D.4
Intramolecular nucleophilic attack on phosphorus
Ester
-
PK,
kobs
T
EM
Accuracy
4.2
3.5 x 10-4
60
1.1 x 103
fi
b
9.4
2.7 x 10-3
35
1.5 x lo6
p
C
-1
>2 x 10-2
22
> 109
Y
Ref.
N-P'--Sx
D.4.1
\ o,
-0,p
GOpNP
D.4.2
EtNH
POT-OpNP
D.4.3
r " v pQ
OA
'O
' Ph
-
Loran and Williams, 1977. The reference intermolecular reaction is the attack of pyridine
on methyl o-nitrophenyl phosphate (Kirby and Younas, 1970). Corrections for the conversion
to a diary1 ester and a p-nitrophenyl leaving group are assumed to cancel out. Temperature
correction uses E, = 14.8 kcal mol-', as measured for the reference reaction
Lazarus et al., 1980
CRiley et al., 1957. Reference reaction is nucleophilic attack of ethyl glycine on methyl
2,4-dinitrophenyl phosphate (Kirby and Younas, 1970), corrected for the leaving group using
,3,/ = 1.0 and for pK of the nucleophile using B = 0.3 1
a
I1 INTRAMOLECULAR GENERAL BASE CATALYSIS
E
CATALYSIS B Y THE IONIZED CARBOXYL GROUP (TABLES E-G)
E. 1 Intramolecular general base catalysis of ester hydrolysif'
Ester
~~~
Ref.
PK,
kobs
T
EM
Accuracy
~
COO-(HO)E-qx
0-3H-0
/H
OAr
E.l.l
Ph02CCH2CO;
3.15
1.43 x
39.6
25
a
260
E.1.2
E.1.3
ANTHONY J. K I R B Y
Ester
Ref.
PK,
kb.
T
EM
Accuracy
PhO,CCMe,CO,
ArO,CCEt,COr
b*c
3.11
3.2
3.2
6.67 x
2.90 x
3.48 x lo-'
39.6
39.6
39.6
11
0.3
60
a
a
3.03
1.33 x lod
80
24
a
3.39
7.42 x lo-,
7.43 x lo-*
25
25
15
-
a
6.69 x
25
13
a
b*c
b~C
E.1.5
PhCO,CH,CO,
dpc
0
C OO-(HO)E--74n
II
h
E'1*7
~
~
~
C
a
H
C
-
l
@
,
3.52
EFFECTIVE MOLAR IT1ES
Ester
E.l.10
a
C
O
7
261
Ref.
PK,
kohl
T
EM
8
3.70
9.06 x lo-,
25
18
3.42
6.65 x lo-'
25
Accuracy
a
OCOCHCI,
E.l.ll
P
C
O
i
1.4
a
OCOCHCI,
E.1.12
E.1.13
X=OMe
X = NHCONH,
'
3.38
3.38
25
25
1
23
P
P
For notation see pages 191-2
Kirby and Lloyd, 1976b; Ar(E.1.3) =p-nitrophenyl
CThe reference intermolecular reaction is general base catalysis of the hydrolysis of phenyl
acetate by the anion of a carboxylic acid of pK, 3.1
Arcelli and Concilio, 1977
The reference intermolecular reaction is the observed general base catalysis of the hydrolysis
of the substrate by external carboxylate
'Fersht and Kirby, 1967b
'Gandour el al., 1979. The reference reaction is general base catalysis of the hydrolysis of
phenyl dichloroacetate at 25O by external carboxylate of the given pK,. Rate constants
calculated from a two point Brensted plot using the data of Fersht and Kirby (1967)
Minor and Schowen, 1973
St. Pierre and Jencks, 1968. The reference intermolecular reaction is the carboxylate-catalysed
aminolysis of phenyl acetate, corrected for the pK, of the general base
262
ANTHONY J K I R B Y
E.2 Intramolecular general base catalysis of S c h i r s base hydrolysisa
k,,,
T
E.2.1
3.68 x lo-*
25
30
E.2.2
2.0 x 10-3
25
1
3.20 x lo-*
25
31
PK.b
Compound
EM' Accuracy
coo-(so,c=~-~",
7f.
E.2.3
2.09,
3.86
0
Kayser and Pollack, 1977
pK,-Values estimated by authors
Reference intermolecular reaction is external general base catalysis by the anion of a
carboxylic acid of the same pK,
E.3 Intramolecular general base catalysis of enolization
Ketoacid
E.3.1
E.3.2
E.3.3
CH,COCH,CH,CO,H
C H,COCH2CHMeC02H
CH3COCH2CMe2CO2H
Ref.
bre
'x
b-e
PK,
4.61
4.57
4.69
kobs
3 x lo-'
5 x lo-*
7 x lo-'
T
25
25
25
EM" Accuracy
0.1
0.1
0.3
P
a
EFFECTIVE M O L A R IT1ES
263
Ketoacid
4.72
4.67
1.05 x lo-'
8.4 x lo-'
25
25
EM" Accuracy
a
0.5
a
2.3
b.c
4.73
4.77
1.80 x
1.30 x lo-'
25
25
9
50
P
b*c
4.73
4.83
8.3 x lo-'
9.0 x lo-'
25
25
0.5
4.5
a
a
4.61
4.57
4.69
4.58
2.5 x lo-'
2.6 x lo-'
5 x lo-"
1.87 x lo-'
25
25
25
25
0.9
0.7
0.2
1.0
a
a
a
a
Ref.
PK,
kobs
T
~
E.3.4
E.3.5
Bu'COCH~H,CO,H
PhCOCHFH,CO,H
brc
COO--H-qx
C O
0
E.3.6
E.3.7
CHlCOCH2(CH,),C0,H
PhCOCHz(CHJ2CO2H
b*c
a
COO--H-6fx
E.3.8
E.3.9
CHlCOCH~CH2)lC02H
PhCOCH2(CH,)lC0,H
COO--H-6fn
E.3.10
E.3.11
E.3.12
E.3.13
C H K 0(CH ,),C 0,H
CHKOCH,CHMeCO,H
CHXOC H,CMe,CO,H
CHKOCMe,CH,CO,H
b*c
b-c
b,c
E.3.14
Y
0
E.3.15
q?
'*d
3.45
cad
3.65
3.3 x lo-'
25
2.6
P
25
>20'
y
CO,H
E.3.16
0
2.65 x
ANTHONY J. K I R B Y
264
Ketoacid
E.3.18
0
Ref.
c,d
f
PH,
3.68
T
kobs
5.02 x
25
5 x
25
EM“ Accuracy
>2oC
56‘
a
p
The reference intermolecular reaction is general base catalysis of the enolization of the
substrate by external acetate
Bell and Covington, 1975
pK,-Values given are the “true” pK, calculated from rate constants for nitramide decomposition where necessary. Observed pK,-values are complicated by lactol formation
Bell el al., 1976
For these more efficient reactions the rate of the intermolecular reaction (acetate-catalysed
detritiation) is too slow relative to that of the intramolecular reaction to be measured accurately.
These EM’S are therefore based on estimated upper limits for the rates of the reference reactions
f Harper and Bender, 1965. The reference intermolecular reaction is the benzoate-catalysed
enolization of PhCOCHMe,
F
INTRAMOLECULAR G E N E R A L B A S E CATALYSIS BY PHENOLATE OXYGEN
F. 1 Catalysis of ester hydrolysis
Ester
0-(HO)E-qx
Ref.
PK,
kobs
T
EM Accuracy
EFFECTIVE MOLARlTlES
Ester
265
Ref.
PK,
kobs
T
EM Accuracy
Capon and Ghosh, 1966. No appropriate reference intermolecular reaction rate has
been measured for an aryl benzoate. The reference used is the intramolecular general
base-catalysed hydrolysis of salicyl salicylate (Kemp and Thibault, 1969) which has
khvd= 2.89 x
s-l in water at 30°. If the EM is assumed to be the same as for
aspirin (13 M) this corresponds to an intermolecular reaction of an aryl benzoate
catalysed by benzoate with k, = 2.22 x lo-’ dm’ mol-l s-l. The correction from the
pK-value of salicyl salicylate (3.6) to the pK, of the substrate uses 8=0.5 (cf. 0.52
for the aspirin reaction). The temperature sensitivity is also taken to be equal to that of
the aspirin reaction
bHansen, 1963b, c. The reference intermolecular reaction is calculated, in the way
described in note a from data for aspirin
a
F.2
Catalysis of enolization
Ester
Ref.
PK,
kobs
10.27 2.4 x lo-’
T
EM
Accuracy
25
(1.3), 14c
y
Bell and Earls, 1976. The reference intermolecular reaction is that of the substrate with itself
Bell el al., 1976
CThe reference intermolecular reaction is that of a base of pK, 8.05 (reckoned to be the
appropriate figure for the non-H-bonded OH of an o-hydroacetophenone) and either the
substrate (1.3 M, which underestimates k, because it is negatively charged) or acetophenone,
which may overestimate it, though less seriously. Estimated values of k , are based respectively
on enolization of the substrate catalysed by (CF,),CHO- and of acetophenone catalysed by
hydroxide; they are extrapolated to the correct pX using B = 0.8
G INTRAMOLECULAR GENERAL BASE CATALYSIS BY NITROGEN
G. 1
Catalysis of esfer hydrolysis
,/&
Ester
N(HO)E--4ln
Ref.
PK,
kb.
T
EM Accuracy
No observed catalysis.’
C0,Ph
H
N(HO)E-qx
G. 1 . 1
G.1.2
I
Me,N(CH,),CO,Ph
Me,N(CH,),C0,C6H,N0,-p
G.1.3
bpc
bsc
CO,C,H,NO,-p
8.87 2.75 x lo-’
8.86 3.23 x lo-,
20.6 >20
20.6 >0.5
y
4.01 8.82 x lo-‘
39.6
0.25
y
y
o N M e 2
G. 1.4
e*f
4.26
4.4 x
30
13
p
-
2.5 x lo-’
30
2
p
6.1
8.5 x
50
70
p
y
C0,Ph
G. 1.5
p-nitrophenyl ester of G.1.4
e
N(HO)E-qx
G.1.6
9ii
HN
N(HO)E-@n
G.1.7
Cp
CH,COO
N(H0)E- 7411
G.1.8
/
qi
N
H
h
‘*’
3.09
4.37 x 10-4
55
Y
6.50
1.67 x
50
0.38
Ester
G.1.9
f
Ref.
QK,
k,,,
T
EM Accuracy
1.1
6.90 4.33 x
50
0.63
p
‘-1
4.57 2.67 x
50
4.9
/3
‘-1
4.85
5.17 x
50
7.0
p
‘*I
5.62 4.83 x
50
2.8
p
OAc
G.l.10
iOAC
G.l.ll
(OAC
H
G.1.12
H
a*‘*k
5.6
3.5 x lo-’
30
18
p
‘*’
6.8
6.4 x lo-’
60
1.7
p
H
N(HO)E--~)II
G.1.14
H
268
ANTHONY J K I R B Y
Ester
Ref.
G.1.15
PK,
kobs
T
EM Accuracy
6.8
1.8 x 10-7
60
0.3
B
6.25
2.3 x
25
1.0
/3
N(H0)E-1 l4n
G.1.16
ZNH
0
CONH,
Felton and Bruice, 1969
Kirby and Lloyd, 1976
The reference intermolecular reaction is between trimethylamine and the corresponding aryl
acetate at 20° (Bruice and Benkovic, 1963). This gives an upper limit for k, because the
mechanism is nucleophilic
The reference intermolecular reaction is between trimethylamine and p-nitrophenyl quinoline-6carboxylate (Bruice and Bruice, 1974). It is not corrected for basicity because the Me,N
group must be rotated out of plane in the transition state for the intramolecular reaction.
(Datum in 20% ethanol)
In 20% acetonitrile (Bruice and Bruice, 1974). The reference intermolecular reaction is with
quinuclidine and is corrected for pK, using /3 = 0.47
'Rate constant estimated from a Hammett plot for a series of substituted compounds
@ = 0.97)
#Fife et al., 1978. Compare G.1.7 for the calculation of EM on the same scale. The correction
used for conversion to benzoyl is the same as for cinnamoyl since k,, is almost the same for
this ester and for G. 1.14
Felton and Bruice, 1969. pK, (3.64 at 30°) is the same as that of aspirin. A direct rate
comparison would give EM = 116 M (based on 13 M for aspirin), but G.1.7 reacts with
hydroxide some 5 times faster than does aspirin, and intramolecular general base catalysis is
more sensitive to the leaving group [p,, = 0.55 for HO- attack on aryl acetates (Bruice
ef al., 1962) compared with 0.96 for the intramolecular general base catalysed hydrolysis of
substituted aspirins (Fersht and Kirby, 1967a)l. Taking these factors into account, the intrinsic
reactivity of G. 1.7 is estimated to be 13 times greater than that of aspirin
The reference intermolecular reaction is general base catalysis by imidazole of the hydrolysis
of N,O-diacetylserinamide at 100° (Anderson et al., 1961). The second order rate constant for
this reaction (1.83 x lo-' dm' mol-' s-' at looo) is compared with the rate constant for the
269
EFFECTIVE MOLARlTlES
intramolecular reaction of compound G.1.8 extrapolated to 100' using the enthalpy of activation
measured by the authors and corrected for the different pK, of imidazole (7.05) using /3 = 0.47
and for the poorer leaving group (pK estimated as 15.6, compared with 13.6 of N-acetylserinamide) using p= 0.27. This comparison gives an EM for G.1.8, and those for other
compounds in this series were calculated by comparing the rate constants given, after correction
for the pK, of the imidazole using p = 0.47. The cinnamoyl (and benzoyl) esters-see note gwere placed on the same scale by allowing a factor of 2.23 for the lower reactivity of the
ester of the unsaturated acid (this is the ratio of the second order rate constants for the alkaline
hydrolysis of 0-acetyl and 0-cinnamoyl-N-acetylserinamide[data of Anderson ef al. (196 1) and
Bender ef al. (1962), respectively]
'Utakaef al., 1976,1977
EM based on aspirin (EM 13 M) by comparison of rates which had been corrected for the
higher pK of the general base using p= 0.52 (Fersht and Kirby, 1967b)
I Komiyama ef ab, 1977
Boudreau ef al., 1978; Z = PhCH,OCO
G.2 Intramolecular general base catalysis of enolizafion
Aminoketone
G.2.1. Me,N(CH,),COCH3
G.2.2 Et,N(CH,),COCHj
Ref.
(I
PK,
k0b*
T
EM Accuracy
9.0 1.32 x lo-)
10.14 3.35 x lo-,
30
25
0.05
0.45
p
a
10.01 7.80 x lo-'
25
0.10
a
N-H-4n
G.2.3 Et,N(CH,),COCHj
Coward and Bruice, 1969. The reference intramolecular reaction is the enolization of acetone
catalysed by trimethylamine
Bell and Timid, 1973. The reference intramolecular reaction is the enolization of the substrate
conjugate acid catalysed by ethanolamine (pK, 9.50), and EM is corrected for the different
pK, using /?= 0.8 and for the effect of the protonated nitrogen
270
ANTHONY J K I R B Y
G.3 Intramolecular general base catalysis of aminolysis by the
amino-group
Reaction
Ref.
N-HN(E)-+
R'-C
EM" Accuracy
/!
/ \OR
.PH\
HzNUNH
G.3.1
G.3.2
G.3.3
+
NH,CH,CH,NH,
acetyl imidazole
methyl formate
phenyl acetate
b
C
d. e
a
0.55
0.5
-1
P
P
0.94
0.6
-1
1
B
P
P
0.20
-1
P
0.25
1
P
-1
P
N-HN(E)--Sf
G.3.4
G.3.5
G.3.6
NHz(CHz)Wz +
acetyl imidazole
methyl formate
phenyl acetate
G.3.7
p-nitrophenyl acetate
b
C
d .e
e
a
N-HN(E)-q
G.3.8
G.3.9
NH,(CH,),NH,
acetyl imidazole
phenyl acetate
+
b
d.e
a
N-HN(E)-74
NHz(CH2)JHz +
G.3.10 acetyl imidazole
G.3.11 phenyl acetate
b
d ,e
a
N-HN(E)-q
G.3.12 NHz(CH,)6NH,
phenyl acetate
+
d. e
~
EM'S calculated by comparing the second order rate constant for
aminolysis by the diamine with the third order rate constant for
aminolysis by a monoamine of the same pK,
Page and Jencks, 1972
Blackburn and Jencks, 1968
Bruice and Willis, 1965
Gilchrist and Jencks, 1966
a
EFFECTIVE MOLAR I TI E S
27 1
111 INTRAMOLECULAR GENERAL ACID CATALYSIS
H. 1
Intramolecular general acid catalysis by the carboxyl group
Compound
Ref.
PK,
kobs
T
EM
Accuracy
4.09
1.24 x lo-*
25
(0.2
Y
6.7 x lo-)
15.5
>I
Y
3 x 10-3
15.5
20
P
4.49 x 10-3
25
3.5
a
1.83 x lo-,
10
2.2
a
CO,H-O=C-Sfx
H.l.l
&
H,O:
H
0
COZH-N(CO)-Sfx
H. 1.2
COzH-O(CO)-Sfx
H.1.3
c.d
0
7
0
~
-
0
$22
0
H.1.4
;o;4
HO
HO
4.3
9 H
HO
03
H.1.5
0 ’
/
0-P- 0
HOH&>P
0-
-
2 72
ANTHONY J K I R B Y
Compound
H.1.6
qi?
Ref.
PK,
k,,,
T
EM
Accuracy
*
5.72
4.72
2.71 x lo-,
0.89
15
39
6500
4600
P
P
I
3.77
4.11
3.83
3.63
3.33
1.04 x
1.00 x
7.6 x
8.9 x
2.46 x
10,
10,
lo3
lo'
lo4
25
25
25
25
25
1
3.77
2.05 x lo3
25
9500
P
3.68
4.38 x
65
<lo-'
Y
5.56
6.31 x
30
38
a
0
phYoEt
H.1.7
H.1.8
H.1.9
H.l.10
H.l.ll
X=Y=H
'
X = Me, Y = H
X = H, Y = Me
X = H, Y = OMe
X = H.Y = CI
H.1.12
'
2.9 x
2.7 x
2.5 x
1.9 x
1.8 x
lo4
lo4
lo4
lo4
lo4
p
p
p
p
p
C02H(0)CO--6fx
H.1.14
CI
EFFECTIVE M O L A R I T I E S
273
Bell and Page, 1973. Reference intermolecular reaction is the acetic acid catalysed enolization
of the corresponding methyl ester. The EM is not corrected for the pK, difference (correction
would reduce EM) because there is some uncertainty about the mechanism in this comparison
*Kirby et al., 1974. The external general acid catalysed reaction becomes independent of
catalyst concentration at about 1 M as is the intramolecular reaction
This rate constant contains the equilibrium constant for the formation of the tetrahedral
intermediate shown
Kirby and Rao (unpublished). The reference reaction is the H,O+-catalysed hydrolysis of the
methyl ester (Aldersley el al., 1974a) corrected for the pK, of the neighbouring group (taken
as that of pmethoxypropionic acid) using /3 = 0.5
CCapon and Walker, 1971. The reference intermolecular reaction is the mutarotation of Dglucose, catalysed by a carboxylic acid of pK, 4.3
'Bailey el al., 1970. The reference intermolecular reaction is the phosphate-catalysed mutarotation of D-glucose under the same conditions
8 Data in 50% dioxan-water (Fife and Anderson, 1971). The reference intermolecular reaction is
the hydrolysis of 2-phenoxytetrahydropyranat 50° catalysed by formic acid (pK,4.64 under
these conditions). The EM given by the authors (580 M) is a lower limit because no corrections
were made for T or pK,. Applying both corrections (a= 0.5, AH$ = 10-15 kcal mol-I) gives
EM 4-9 x 103
* In 3096 dioxan (Glenn and Kirby, unpublished). The reference intermolecular reaction is the
hydrolysis of the methyl ester catalysed by a general acid (RC0,H) of pK, 4.72
Buffet and Lamaty, 1976. The pK,-values quoted are for the Corresponding methoxymethoxybenzoic acids. The reference intramolecular reaction is the acetic acid catalysed hydrolysis of the
methyl ester in each case corrected for differences in pK, using a= 0.5 (Capon and Nimmo,
1975)
'Fife and Anderson, 1971. The reference intermolecular reaction is the hydrolysis of the methyl
ester catalysed by formic acid (pK, of the substrate assumed the same as for H1.7)
kCapon and Page, 1972b. Reference reaction is the acetic acid catalysed hydrolysis of the
substrate corrected for the pK, difference using a= 1 (Capon and Page, 1972a)
'In 50% dioxan (Fife and Przystas, 1977). The reference intermolecular reaction is the
hydrolysis of the acetal group of the corresponding methyl ester by a carboxylic acid of
pK, 5.56. The value of k, was calculated from the buffer catalysis data given for three carboxylic
acids using buffer pK,'s measured in 50% dioxan (at SO0) by Fife and Brod (1970)
a
'
H.2
Intramolecular general acid catalysis by the hydroxyl group
Compound
H.2.1
PhNHNH9I
Ref.
a
PK,
10.4
k0bl
T
EM Accuracy
1.83 x lo-'
25
0.1
y
ANTHONY J. K I R B Y
274
Compound
Ref.
PK,
kobs
T
EM Accuracy
Data of Alves e f a/. (1978), in 20% ethanol. The intermolecular reference reaction is the
general acid catalysed addition of phenylhydrazine to the methyl ether, calculated from
kH,O+
using a = 0.35 and determined for the reaction with o-methoxybenzaldehyde (Bastos and
do Amaral, 1979). The EM, which is in some doubt because of possible mechanistic complications, is determined by comparison of the rate constant given (dm3 mol-I s-I) with the third
order rate constant for the reference reaction
Capon and Walker, 1974. The reference intermolecular reaction is the phenoxide-catalysed
mutarotation of the 6-O-phenoxy-compound, corrected for pK,
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