Advances in Physical Organic Chemistry

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ADVISORY BOARD
W. J. Albery, FRS University of Oxford
A . L. J . Beckwith The Australian National University, Canberra
R. Breslow Columbia University, New York
L. Eberson Chemical Center, Lund
H. Iwamura University of Tokyo
G. A . Olah University of Southern California, Los Angeles
Z. Rappoport The Hebrew University of Jerusalem
P. von R. Schleyer Universitat Erlangen-Nurnberg
G. B. Schuster University of Illinois at Urbana-Champaign

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Advances in
Physical Organic Chemistry
Volume 29

Edited by

D. BETHELL
The Robert Robinson Laboratories
Department of Chemistry
University of Liverpool
P.O. Box 147

Liverpool L69 3BX

A C A D E M I C PRESS
Harcourt Brace & Company, Publishers
London San Diego New York
Boston Sydney Tokyo Toronto

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ACADEMIC PRESS LIMITED
24/28 Oval Road
London NWl 7DX
United Slates Edition published by
ACADEMIC PRESS INC.
San Diego, CA 92101

Copyright 01994 by
ACADEMIC PRESS LIMITED
AN rights reserved
No part of this book may be reproduced in any form by photostat, microfilm,
or any other means, without written permission from the publishers

A catalogue record for this book is available from the British Library
ISBN 0-12-033529-8
ISSN 0065-3160

Printed and bound in Great Britain by
Hartnolls Ltd, Bodmin, Cornwall


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Contents

Preface

vii

Contributors to Volume 29

ix

The Stabilization of Transition States by Cyclodextrins
and other Catalysts

1

OSWALD S. TEE
1
2
3
4
5
6
7

Introduction 1
Cyclodextrins 3
Transition state stabilization 9

Non-covalent catalysis 13
Covalent catalysis 22
Other catalysts 46
Future prospects 62

Crystallographic Approaches to Transition State Structures

87

ANTHONY J . KIRBY

1
2
3
4

Introduction 87
Structure-structure correlations 95
Structure-reactivity correlations 125
Extrapolation to transition state structures 173

Electron Transfer in the Thermal and Photochemical Activation
of Electron Donor-Acceptor Complexes in Organic
and Organometallic Reactions

JAY K . KOCHI

1 Introduction 185
2 Direct observation of transient ion pairs by charge-transfer
activation of E D A complexes 188

v

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185


CONTENTS

Time-resolved picosecond spectroscopic studies of
charge-transfer complexes 190
Variable charge-transfer structures of nitrosonium-EDA
complexes leading to thermal and photo-induced electron
transfer 224
Charge-transfer activation as the unifying theme in electrophilic
237
aromatic substitution-nitration
Concluding remarks 262

273

Homoaromaticity

R I C H A R D V. WILLIAMS
1
2
3
4
5
6

7

AND

HENRY A. KURTZ

Introduction 273
Cationic homoaromaticity 278
Neutral homoaromaticity 294
Anionic homoaromaticity 314
Radical homoaromaticity 316
Theoretical treatment 320
Conclusion 323

Author Index

333

Cumulative Index of Authors

351

Cumulative Index of Titles

353

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With ever increasing specialization among chemists, there is a continuing

need to ensure that research in one area is not hampered by lack of
awareness of developments in contiguous areas, expressed in language that
is understood by both groups of specialists. Over the thirty years of its
existence, such bridge-building has been a consistent aim of Advances in
Physical Organic Chemistry in relation to the physical and organic chemical
communities, and a considerable debt is owed to the many contributors who
have striven to present their material in an attractive and comprehensible
way. More recently the series has sought to reflect the relevance of the
physical organic approach to developments in the field of new materials and,
in an as yet small but it is hoped increasing way, in the burgeoning realm of
bio-organic research. The Editor and his Advisory Board continue to
encourage comments on the series, suggestions of topics that are worthy of
coverage in future volumes, and, perhaps best of all, offers to contribute
articles on any aspect of the quantitative study of organic compounds and
their reactions.

D. BETHELL

vii

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Contributors to Volume 29

Anthony J. Kirby University Chemical Laboratory, Lensfield Road, Cam-

bridge CB2 lEW, UK
Jay K. Kochi Department of Chemistry, University of Houston, Houston,


TX 77204-5641, USA
Henry A. Kurtz Department of Chemistry, Memphis State University,
Memphis, TN 38152, USA
Oswald S. Tee Department of Chemistry and Biochemistry, Concordia

University, Montreal, Quebec H3G 1M8, Canada
Richard V. Williams Department of Chemistry, University of Idaho,
MOSCOW,
ID 83844-2343, USA

viii

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The Stabilization of Transition States by
Cyclodextrins and other Catalysts
OSWALD
S. TEE
Department of Chemistry and Biochemistry, Concordia University, Montreal,
Canada

1 Introduction 1
2 Cyclodextrins 3
Effects on reactivity 7
3 Transition state stabilization 9
The Kurz approach 9
Cyclodextrin mediated reactions 11
4 Non-covalent catalysis 13
Intramolecular reactions 13

Decarboxylation 15
Bromination-debromination 17
5 Covalent catalysis 22
Ester cleavage 22
Amide cleavage 45
Deprotonation 46
6 Other catalysts 46
Acids and bases 47
Metal ions 52
Amylose 55
Micelles 55
Catalytic antibodies 56
Enzymes 60
7 Future prospects 62
Acknowledgements 63
References 63
Appendix 69

1 Introduction

Enzymes fascinate (and exasperate) chemists because they can catalyse
reactions at ambient temperatures and at modest pH, often with high
substrate selectivity, regioselectivity, and enantioselectivity . Moreover, they
do all this at rates that are 106-10” times faster than the uncatalysed
reaction. The origins of these impressive feats almost certainly lie in
supramolecular behaviour (Lehn, 1985, 1988) since enzymes invariably form
1
ADVANCES IN PHYSICAL ORGANIC CHEMISTRY

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2

enzyme .substrate complexes from which the catalysed reactions ensue.
Many static and dynamic studies of enzyme behaviour have provided ample
evidence of such complexes and great progress has been made in elucidating
many of the mechanisms by which enzymes transform their substrates into
products (Walsh, 1979; Fersht, 1985; Page and Williams, 1987; Liebman and
Greenberg, 1988; Dugas, 1989). At the same time, there have been
significant advances in understanding the factors underlying the catalytic
abilities of enzymes (Jencks, 1969, 1975; Bender, 1971; Lienhard, 1973;
Gandour and Schowen, 1978; Page, 1984; Fersht, 1985), although at times it
has seemed as though there were too many theories of enzymatic catalysis,
based on the multiplicity of ideas about the efficiency of intramolecular
processes (Page, 1984, 1987; Menger, 1985; Page and Jencks, 1987)!
The underlying principle of enzyme catalysis was expounded many years
ago by Haldane (1930) and Pauling (1946). According to them, catalysis
results from stabilization by the enzyme of the reaction transition state,
relative to that of the initial state. This view was developed by Kurz (1963)
into a quantitative approach to transition state binding, and hence of
transition state stabilization, albeit in the context of catalysis by acids and
bases (Kurz, 1963, 1972). His approach was taken up and used by
enzymologists (Wolfenden, 1972; Lienhard, 1973; Jencks, 1975; Schowen,
1978; Fersht, 1985; Kraut, 1988), so much so that it is now implicit in many
modern studies of enzyme action (see, for example: Fersht et al., 1986,

1987; Leatherbarrow and Fersht, 1987). Of particular note, Kurz’s innovation
helped to develop the use of “transition state analogues” (Jencks, 1969) as
efficient enzyme inhibitors, either for the purposes of mechanistic studies or
for possible pharmaceutical use (Wolfenden, 1972; Wolfenden and Frick,
1987; Wolfenden and Kati, 1991). In turn, the availability of transition state
analogues as haptens has been critical to the recent development of
“catalytic antibodies” (Schultz, 1988, 1989a,b).
The fascination of chemists with enzymes has led, in recent years, to many
attempts to model or mimic their action (e.g. Bender, 1971, 1987; Breslow,
1982, 1986a,b; Page, 1984; Tagaki and Ogino, 1985; Kirby, 1987; Stoddart,
1987; Schultz, 1988, 1989a,b; Dugas, 1989; Chin, 1991). The object of such
studies has been to understand enzyme action and, in a broader sense,
catalysis better, and possibly to learn how to synthesize catalysts (“artificial
enzymes”) for specific purposes (Breslow, 1982; Schultz, 1988). Many such
studies have employed model systems based on the binding and catalytic
properties of cyclodextrins (CDs) or their derivatives (Bender and
Komiyama, 1978; Breslow, 1980, 1982, 1986a,b; Tabushi, 1982; Komiyama
and Bender, 1984; Bender, 1987; D’Souza and Bender, 1987; Tee, 1989). At
the same time, CDs have commanded another, more practical and populous
audience due to their many potential applications in the food, pharmaceutical, and cosmetic industries (Szejtli, 1982; Pagington, 1987). These differing
interests in the chemistry of CDs have led to an explosion in the literature

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TRANSITION STATE STABILIZATION

3

concerning these molecules in recent years, especially now that they are

produced commercially and are available relatively cheaply.
The present review deals with a particular aspect of the chemistry of
cyclodextrins: the effects that they can have on organic reactions by virtue of
their abilities to bind to many organic and inorganic species (Bender and
Komiyama, 1978; Saenger, 1980; Szejtli, 1982). It is a considerable
expansion of an earlier work (Tee, 1989) which first showed how the Kurz
approach to transition state stabilization can be employed profitably in
discussing reactions mediated by cyclodextrins. Most of the large amount of
data that are analysed is collected in tables in the Appendix so as to avoid
breaking up the discussion in the main text too frequently.
While the main emphasis of this review is on catalysis, since this is of
greater interest, the Kurz method can also be applied to retardation. In fact,
for some of the systems discussed later, the smooth transition from
retardation, through inactivity, to full catalysis can be quantified and
analysed in relation to the structure of the species concerned.
At the end of the review there are some examples involving catalysis by
acids and bases, metal ions, micelles, amylose, catalytic antibodies, and
enzymes to give the reader a feeling for how Kurz’s approach may be
usefully applied to other catalysts. Very few of these examples, or those
involving cyclodextrins, were discussed in the original literature in the same
terms. It is hoped that the present treatment will stimulate further use and
exploration of the Kurz approach to analysing transition state stabilization.

2 Cyclodextrins

These water-soluble molecules are cyclic oligomers of a-D-glucose formed
by the action of certain bacterial amylases on starches (Bender and
Komiyama, 1978; Saenger, 1980; Szejtli, 1982). a-Cyclodextrin (cyclohexaamylose) has six glucose units joined a(1,4) in a torus [l], whereas
p-cyclodextrin (cycloheptaamylose) and y-cyclodextrin (cyclooctaamylose)
have seven and eight units, respectively.

The form of cyclodextrins (CDs) is variously described as being “conical”,
“toroidal”, “bucket shaped”, or “doughnut shaped” [2]. Regardless of the
adjective used and the finer details of their structure, the most important
feature of CDs is the cavity, because this enables them to form inclusion
complexes in solution and in the solid state. By virtue of their cavities, CDs
possess the requisite amount of preorganization and the convergent surfaces
(Cram, 1983, 1988) necessary for them to function as hosts for small
molecular guests of an appropriate size, shape, and polarity. The depths of
CD cavities are all the same (approximately 7.5 A), being determined by the
width of a glucose molecule, but the sizes of their cavities differ in diameter
(a-CD about 5.0, p-CD about 7.0 and y-CD about 9.0A) (Bender and

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4

CH;!
\
OH

Komiyama, 1978; Szejtli, 1982), giving rise to a gradation in binding affinity.
The geometrical features of CDs, plus their relative rigidity, obviously
impose constraints on their ability to form guest-host (inclusion) complexes
with organic and inorganic species (Bender and Komiyama, 1978; Saenger,
1980; Szejtli, 1982; Atwood et af., 1984). Nevertheless, CDs have been
labelled “promiscuous” for their propensity to act as hosts to a wide variety
of small- to medium-sized guests (Stoddart and Zarzycki, 1988). It is the

ability of CDs to form complexes that enables them to influence chemical
reactions through supramolecular effects (Sirlin, 1984; Lehn, 1985, 1988). In
what follows, some of the basic aspects of C D binding, relevant to the
reactions discussed later, are presented. More detailed discussions of CD
inclusion complexes can be found in the references already cited.
Broadly speaking, the cavity sizes of a-,p-, and y-CD are appropriate for
binding simple derivatives of benzene, naphthalene, and anthracene,
respectively (Sanemasa and Akamine, 1987; Fujiki et al., 1988; Sanemasa et
af., 1989). Many studies of the inclusion of aromatics, particularly of dyes
and other molecules with strong chromophores, have been reported, and
these have been useful in delineating the main features of C D binding
(Bender and Komiyama, 1978; Saenger, 1980; Szejtli, 1982; Atwood et al.,
1984; Stoddart and Zarzycki, 1988). In contrast, the affinity of small to
medium aliphatic molecules for CDs have been less well studied, most

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TRANSITION STATE STABILIZATION

5

probably for practical reasons. Nevertheless, there have been studies with
various surfactants (On0 et al., 1979; Satake et al., 1985, 1986; Diaz et al.,
1988; Palepu and Reinsborough, 1988; Palepu et al., 1989), alkanes
(Sanemasa et al., 1990), and a particularly interesting study of the binding of
many alcohols to both a- and p-CD (Matsui and Mochida, 1979; see also,
Matsui et al., 1985; Fujiwara et al., 1987).
For the most part, CDs form simple 1 : 1 host-guest complexes with
suitable guests. But it is important to note that 2 : 1 binding can be significant

with longer aliphatics (Palepu and Reinsborough, 1988; Palepu et al., 1989;
Sanemasa et al., 1990), aromatics (Sanemasa and Akamine, 1987; Fujiki et
al., 1988), azo dyes (Bender and Komiyama, 1978; Szejtli, 1982), and
aryl-alkyl guests (Tee and Du, 1988, 1992), and this can influence reactivity.
Also, there is now evidence of 1: 1 : 1 binding of C D + two guests (Hamai,
1989a,b) which has been implicated in some reactions (Ramamurthy, 1986;
Tee and Bozzi, 1990).
The ability of a C D to form inclusion complexes in aqueous solution
results from its cavity, the interior of which is less polar than water and
hydrophobic. The apparent polarity of the C D cavity seems to depend on
the probe used. Some studies have suggested a similarity to dioxane (Bender
and Komiyama, 1978; Hamai, 1982), while others favour ethanol (Cox et
al., 1984; Heredia et al., 1985). No doubt the particular observations are
affected by the presence or absence of specific interactions, such as
hydrogen bonding, between the guest and the CD host, as well as by the
depth of penetration of the guest/probe. Decarboxylation studies, to be
discussed more fully later, suggest an environment like 50% aqueous
2-propanol (Straub and Bender, 1972a,b).
Various other factors have been cited (Bender and Komiyama, 1978;
Szejtli, 1982) as contributing to the binding ability of CDs. However, the
principal factors seem to be the hydrophobicity of the guest and the
appropriateness of its size and shape in relation to that of the C D cavity
(Tabushi, 1982). These factors are evident in the binding of alcohols to CDs
(Matsui et al., 1985) and of other guests with alkyl groups (Tee, 1989; Tee et
al.. 1990b). For illustrative purposes, and because of its relevance to a later
section, the binding of alcohols will be discussed in some detail.
For linear, primary alcohols (n-alkanols) the strength of complexation
with CDs, expressed by pKs = -logKs, where Ks is the dissociation
constant of the complex, correlates strongly with their coefficients for
partition ( P , ) between diethyl ether and water (Matsui and Mochida, 1979;

Matsui et al., 1985), with slopes close to 1 ( l a and lb). It has also been
a-CD:
P-CD:

+ 1.25;
pKs = 0.94 log P, + 0.58;
pKs = 0.91 log P,

r = 0.994

(la)

r = 0.994

(lb)

noted (Tee, 1989; Tee et al., 1990b) that for these alcohols, and other linear

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6

3.0

normal
A


6 2.0

au

u"

branched
cyclic

1.0

V

2-alkanols

+

tertiary

0.0
1 .o

2.0

3.0

pK, (a-CD)

Fig. 1 Correlation between the binding of aliphatic alcohols to p-CD and to a-CD:
(-)

the least-squares line for n-alkanols; (----) pKs (p-CD) = pK, (a-CD);
above this line a given alcohol binds strongly to p-CD than to a-CD. Data
from Matsui and Mochida (1979) and Matsui et al. (1985).

aliphatics, pKs values vary linearly with N , the number of carbon atoms in
the chain. These observations are reasonable since, as remarked above, the
binding of guests to CDs is largely governed by their size and hydrophobicity
(Tabushi, 1982). Obviously, the sizes of extended n-alkyl chains increase
linearly with N , but so also do various measures of hydrophobicity, such as
the logarithms of partition coefficients, critical micelle concentrations,
solubilities (Hansch, 1971; Leo et al., 1971; Hansch and Leo, 1979; Tanford,
1980; Menger and Venkataram, 1986).
Equations (la) and (lb) represent two nearly parallel lines with a vertical
difference of about 0.7, indicating that a given linear alcohol binds about
five times more tightly to a-CD than to p-CD. This makes sense in terms of
the sizes of the a- and p-CD cavities (about 5 and about 7 & respectively)
in relation to the cross-section of methylene chains (about 4.5 A) (Sanemasa
et al., 1990). With bulkier types of alcohols (secondary, tertiary, cyclic, and
branched) there is a tendency towards stronger binding in the larger cavity
of p-CD. This feature is clearly seen in Fig. 1 which plots values of pKs for
p-CD against those for a-CD. For the linear n-alkanols there is straight-line
correlation ( r = 0.9991) with a slope of 1.10. Other, bulkier alcohols deviate
above this line, showing the tendency to a stronger affinity with p-CD.
Points for the bulkiest alcohols (branched, tertiary, cyclic >C,) lie above the
dashed line corresponding to pKs (p-CD) = pKs (a-CD), since such alcohols
are bound more strongly by p-CD (Fig. 1).
One other feature of CDs is relevant to later discussion: the acidity of
their secondary hydroxyl groups, with pK, values about 12.2 (VanEtten et

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TRANSITION STATE

STABILIZATION

7

al., 1967b; Gelb et al., 1980, 1982). The conjugate anions may function as
nucleophiles or general bases and react with substrates included in the CD
cavity (Bender and Komiyama, 1978; Komiyama and Inoue, 1980c; Daffe
and Fastrez, 1983; Cheng et al., 1985; Tee, 1989; Tee et al., 1993a).
By virtue of their complexing ability, CDs may influence the course of
chemical reactions in respect of rates and/or product selectivity. In consequence, there is a large body of data in the literature on the effect of CDs
on many types of reactions (Fendler and Fendler, 1975; Bender and
Komiyama, 1978; Szejtli, 1982; Tabushi, 1982; Sirlin, 1984; Ramamurthy,
1986; Ramamurthy and Eaton, 1988). The present review concentrates on
reactions for which sufficient kinetic data are available to allow quantification of the effects of CDs on transition state stability, in an attempt to
understand how cyclodextrins influence reactivity in either a positive or
negative sense.

EFFECTS ON REACTIVITY

The kinetics of reactions which are influenced in a simple way by CDs may
be viewed in the following manner (Bender and Komiyama, 1978; Szejtli,
1982; Tee and Takasaki, 1985). For a substrate S that undergoes an
“uncatalysed” reaction (2) in a given medium and a “catalysed” reaction
through a 1 : l substrate/CD complex (3), the expected variation of the
observed rate constant with [CD] is given by (4).
k


s-P

hc

S+CD=S-CD-

P+CD

K.

Equation (4) corresponds to saturation-type (Michaelis-Menten) kinetics
and rate constants obtained over a suitable range of [CD], sufficient to
reflect the hyperbolic curvature, can be analysed to provide the limiting rate
constant, k,, and the dissociation constant, K s (VanEtten et al., 1967a;
Bender and Komiyama, 1978; Szejtli, 1982; Sirlin, 1984; Tee and Takasaki,
1985). The rate constant ku is normally determined directly (at zero [CD]),
and sometimes Ks can be corroborated by other means (Connors, 1987).
Traditionally, data corresponding to (4) are analysed by using a
Lineweaver-Burk approach, but an Eadie-Hofstee treatment is preferable
for statistical reasons (Dowd and Riggs, 1965; VanEtten et al., 1967a;
Bender and Komiyama, 1978). With the present, widespread availability of

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cheap microcomputers and appropriate software, it is now feasible to
analyse data more directly in terms of (4), using non-linear least-squares
fitting techniques (Bevington, 1969; Leatherbarrow, 1990; Duggleby, 1991).
In our own work, we have settled on this last approach, usually keeping k ,
fixed at the measured value, and treating k, and Ks as the constants to be
fitted (Tee and Takasaki, 1985). Using such non-linear fitting gives a more
consistent approach to data analysis, particularly when one has to use
expressions more complex than (4), because of additional processes such as
non-productive 2: 1 binding or reactions with a second CD molecule (Tee
and Du, 1988, 1992).
Generally speaking, discussions of the effects of CDs on reaction rates are
given in terms of k,lk,, K s , and, sometimes, k,lKs. Most often, the ratio
k,lk, is emphasized since this quantity measures the maximal rate acceleration (or retardation) due to binding to the CD. Obviously, Ks measures the
strength of binding of S to CD, but it conveys no information whatsoever
about the mediation of the reaction by the CD or the mode of binding in the
transition state which may be very different from that of the substrate (Tee,
1989; Tee et al., 1990b). Sometimes use is made of the apparent second
order rate constant for the reaction of the substrate with the CD ( 5 ) , where
ki

S+CD-P

k2 = k,/Ks ( 3 ) , since this rate constant measures the selectivity of the CD
for different substrates. This usage is analogous to the use of kcat/KMfor
measuring the “specificity” of enzymes (Fersht, 1985). In cases of catalysis
where saturation kinetics are not observed, because binding of the substrate
to the CD is weak and K s is relatively large, k2 may be obtainable from the
linear increase of kobsdwith [CD].
Provided due attention is paid to the potential deprotonation of the
substrate, and of the cyclodextrins (VanEtten et af., 1967a,b; Gelb et af.,

1980, 1982; Tee and Takasaki, 1985), the value of Ks should not be pH
dependent. However, for many reactions, such as the widely studied ester
cleavage, k , , k,, and k2 are all dependent on the pH of the medium. This
makes direct comparisons between the observed constants for different
CD-mediated reactions either difficult or problematical. However, in
general, the ratios k,lk, and k21k, are independent of pH and so are more
useful for comparative purposes.
As remarked already, k,lk, measures the maximal acceleration at levels of
the CD sufficient to saturate complexation of the substrate. By looking
carefully at the variations of this ratio with structure one may obtain insights
into the mode of transition state binding (VanEtten et al., 1967a,b; Bender
and Komiyama, 1978). More useful is the ratio k21k, ( = k c / K s k , ) because it
takes into account the effect of substrate binding and it scales the reactivity
of S towards the CD to its intrinsic reactivity in the absence of CD.

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TRANSITION STATE STABILIZATION

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Enzymologists have used the analogous ratio k,,,lKM k, in full realization of
its significance and usefulness (Wolfenden and Kati, 1991). However, k,lk,
has been used only occasionally by chemists (Sirlin, 1984; Tee and Takasaki,
1985) without realizing that the ratio, or rather its reciprocal (k,lkl = K.rs),
has another, much greater significance. The utility of K,, is the main focus
of this review; its significance will be made apparent in the next section.

3 Transition state stabilization


Following on from the early ideas of Haldane (1930) and Pauling (1946), it
has become widely accepted that the principal factor in enzymic catalysis is
stabilization of the reaction transition state by binding to the enzyme
(Jencks, 1969, 1975; Lienhard, 1973; Schowen, 1978; Page, 1984; Fersht,
1985). Likewise, lowering of the free energy of the transition state must be
crucial in catalysis by other agents. Therefore, any method that can provide
quantitative information about the strength of such stabilization has great
potential for use in the study of catalysis, whether it be enzymic or
non-enzymic. Application of the method to different substrates and catalysts
might furnish insight into the nature of the catalysis involved and, in
particular, into the manner in which catalysts bind to transition states and
thereby stabilize them.
Thirty years ago, Kurz (1963) devised a very simple method, based on
transition state theory, whereby the energy of stabilization of transition
states by catalysts may be estimated. He used the method to probe the
transition states of acid- and base-catalysed reactions, and developed the
idea of transition state pK, values (Kurz, 1972). The approach was taken up
by enzymologists (Wolfenden, 1972; Lienhard, 1973; Jencks, 1975;
Schowen, 1978; Kraut, 1988), and it proved to be very influential in the
formulation of the ideas about enzyme catalysis referred to in the previous
paragraph and in the Introduction. It is, therefore, surprising that the Kurz
method has been ignored by most physical organic (and inorganic) chemists
studying the mechanisms of catalysed reactions. Very recently, however,
essentially the same method has been applied to organic reactions catalysed
by metal ions (Dunn and Buncel, 1989; Pregel et al., 1990; Ercolani and
Mandolini, 1990; Cacciapaglia et af., 1989, 1992), and the present author has
shown how the Kurz approach can be used in discussions of reactions
mediated by cyclodextrins (Tee, 1989; Tee et al., 1990b; Tee and Du, 1992).


THE KURZ APPROACH

Consider two reactions, one of which is “uncatalysed” (6a) and the other
of which (6b) is influenced by some “catalyst”, cat. According to simple

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transition state theory (Glasstone et al., 1941; Laidler, 1987), the rate
constant for the uncatalysed reaction is given by (7a), and that for the
catalysed reaction by (7b), where v = kBT/h, and the transition state of the
catalysed process (6b) is considered for mathematical and thermodynamic
purposes to be that of reaction (6a) bound to the catalyst (TSecat). It is
assumed that the average frequency of passage over the barrier (v) is the
same for (7a) and (7b), and that the transmission coefficients are equal for
the two processes. Kraut (1988) considers the possible consequences when
these assumptions are relaxed.

k

A+B+. . .

A +B+. . .

k'


=

+ cat

products

k'

products

k = v[TS]/[A][B] . . .

(7a)

v[TS.cat]/[A][B] . . . [cat]

(7b)

With the assumptions, just given, division of (7a) and (7b) leads to a
simple definition (8) of an apparent constant for the dissociation of TS.cat
into TS and catalyst. Obviously, KTS is a quasi-equilibrium constant, since

KTS = [TS][cat]/[TS cat] = k/k'

(8)

actual, reversible dissociation of TSscat into TS and catalyst is unlikely, if
not impossible. Nevertheless, KTs (or more accurately AG$s = -RTln KTS)
provides a useful measure of the relative energies of the transition states for
the normal and the catalysed reactions, under standard conditions, regardless of their actual structures.

It is important to note that the derivation of KTS, given above, involves
no ussumptions about the mechanisms of either the catalysed or uncatalysed
reactions. Therefore, it is possible to use values of K,rs (and
pKPrs = -log KTs) and their variations with substrate or catalyst structure
(or some other reaction parameter) as probes of transition state structure
(Kurz, 1972; Tee, 1989). Clearly, complications may arise when the
mechanisms of the catalysed and uncatalysed reactions are quite different,
but under such circumstances one can reasonably hope that trends in KPrs
and other kinetic parameters may be such as to point to the discrepancy and
that they may even suggest a resolution.
It is not the purpose of the present review to give a critical appraisal of
the Kurz approach; that can be found in the review by Kraut (1988).
Rather, it is to show how this simple method can be used in the study of
reactions influenced by cyclodextrins. Some examples involving catalysed

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TRANSITION STATE STABILIZATION

11

reactions of other types which may be of interest to a wider audience of
physical organic chemists are also presented.

CYCLODEXTRIN MEDIATED REACTIONS

Application of the Kurz approach to CD-mediated reactions, whether they
be accelerated or retarded, is straightforward (Tee, 1989), provided
appropriate kinetic data are available. From the rate constants k , for the

normal, “uncatalysed” reaction (2) and for the mediated (“catalysed”)
reaction ( k 2 = k , / K s ) as in (3), application of simple transition state theory,
in the manner shown above, leads to (9), where now KTs is the apparent
dissociation constant of the transition state of the CD-mediated reaction
(symbolized here as T S - C D ) into the transition state of the normal reaction
(TS) and the CD. This constant and its logarithm, which is proportional to a
free energy difference, is a valuable probe of the kinetic effects of CDs on
reactions.

As outlined in Section 2, discussions of catalysis (or inhibition) by CDs
are generally in terms of k,lk,, K s , and, to a lesser extent, k2 = k , / K s . This
last quantity has the same usefulness (and significance) as does kCat/KMfor
enzymes (Fersht, 1985) in that it is a measure of the substrate selectivity of
the CD (VanEtten et al., 1967b; Tee and Takasaki, 1985). With proteolytic
enzymes such as a-chymotrypsin, there is no major problem with the use of
k,,,lKM since the peptide bonds formed between different amino acids have
fairly similar intrinsic reactivities ( k , ) (Berezin et al., 1971; Dorovska et al.,
1972; Fersht, 1985), but comparisons between substrates having quite
different reactivities require some kind of scaling, and this can be achieved
by looking at k21k,. As remarked already, such ratios have occasionally
been used (Sirlin, 1984; Tee and Takasaki, 1985), but it was not recognized
at the time that k21k, is simply the reciprocal of K r s , as seen in (9).
While purists of thermodynamics may cavil that KTS is not a true
equilibrium constant, it does correspond to an energy of great interest and
importance: the free energy difference between the transition states of the
uncatalysed and catalysed reactions [(2) and (3), respectively] under
standard conditions. Alternatively, one may prefer to consider this difference as the free energy of transfer of the transition state from aqueous
solution to a 1 M solution of the catalyst, as has been done recently (Dunn
and Buncel, 1989; Pregel et al., 1990). Whatever the case, the significance of
Kvrs can most easily be appreciated by consideration of the Gibbs energy

diagram in Fig. 2. As indicated there, the relative free energies of various
species involved in reactions (2) and (3) are directly accessible from the

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0 . S . TEE

12

TS+cat
A

G

S.cat

products

Fig. 2 Relative Gibbs energies for the species involved in a reaction which is
uncatalysed (S -+ TS + P) and mediated by a catalyst (S cat --* TS .cat + P). For a
specified [cat] the free energy differences can be directly calculated from the
measurable constants k,, k, and K s , and the derived values k2 and KTs, as indicated.
pKTs = -logKTs is a measure of the stabilization of the transition state by the
catalyst.

+

measurable quantities k , , k,, and K s (or k , and k 2 ) . As long as these
constants are all measured under the same conditions, the apparent

“equilibrium constant” KTS (through its logarithm) gives a direct measure of
the binding energy of the transition state to the catalyst for those conditions,
regardless of the mechanism (Schowen, 1978).
The diagram in Fig. 2 also serves to emphasize that stabilization of the
transition state by the catalyst is primarily responsible for any rate increase.
To a considerable extent the binding of S is irrelevant, except that strong
substrate binding necessarily detracts from catalysis. In fact, according to
(9), the change in rate is determined by the strength of binding of TS,
relative to that of S (k,lk, = K s / K T s ) (Lienhard, 1973). This emphasis has
been termed the “fundamentalist view” by Schowen (1978). A much more
agnostic view of the importance of transition state stabilization has recently
been presented by Menger (1992).
Obviously, strong binding of the substrate to the catalyst may distort the
structure of S towards that of TS, thereby making reaction easier. However,
such distortion simply reflects the complementarity of the catalyst and the
transition state (Fersht, 1985). From a purely thermodynamic point of view,
the formation of a strong S.catalyst complex lowers free energy by an
additional amount that must be overcome in the process of activation of the
k, process (3) (Fig. 2). Living organisms and their enzymes have evolved so

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TRANSITION STATE STABILIZATION

13

as largely to avoid this problem by having working levels of [S] close to K , ;
thus the free energy difference between S enzyme and S.enzyme is quite
small and the cost in free energy is minimal (Jencks, 1969; Lienhard, 1973;

Fersht, 1985).
As pointed out above, values of KTS are obtainable from rate data
without making any assumptions about the reaction mechanism. Therefore,
one may use Kr.7 and its variation with structure as a criterion of mechanism,
in the same way that physical organic chemists use variations in other kinetic
parameters ( B r ~ n s t e dplots, Hammett plots, etc.). For present purposes, the
value of KTS can be useful for differentiating between the modes of binding
in the S . C D complex and the TS .CD transition state, between different
modes of transition state binding, and hence between different types of
catalysis (Tee, 1989).
According to Bender and Komiyama (1978), CDs may show two basic
forms of catalysis: “non-covalent” and “covalent”. In the former case the
C D binds to the substrate(s) and provides an environment for the reaction
that is different from the bulk solvent, whereas in the latter case there are
also distinct covalent interactions between the substrate(s) and some
functional group(s) on the C D in the rate-limiting step of the reaction.
Therefore, it seems reasonable to expect that values of KTS for these two
types of catalysis may show different sensitivities to structural change, since
the partial bonding involved in covalent catalysis will normally lead to
stronger interactions with the CD and possibly to more stringent geometric
requirements than non-covalent catalysis.

+

4

Non-covalent catalysis

In this form of catalysis, inclusion of the substrate in the C D cavity provides
an environment for the reaction that is different from that of the bulk,

normally aqueous, medium. In the traditional view, the catalytic effect
arises from the less polar nature of the cavity (a microdielectric effect)
and/or from the conformational restraints imposed on the substrate by the
geometry of inclusion (Bender and Komiyama, 1978). However, catalysis
may also arise as a result of differential solvation effects at the interface of
the CD cavity with the exterior aqueous environment (Tee and Bennett,
1988a,b; Tee, 1989).

INTRAMOLECULAR REACTIONS

A simple example of non-covalent catalysis is the intramolecular acyl
transfer [3] to [4] which is catalysed by a-CD but retarded by p-CD
(Griffiths and Bender, 1973). As seen by the constants in Table 1, the

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14

Table 1 Non-covalent catalysis of intramolecular acyl transfer [3]+ (41.”

48
0.96

7.3
0.19

LY


P

6.6
5.2

“Based on data from Griffiths and Bender (1973).

difference in behaviour of the two CDs lies in the substrate binding ( K s ) ,
and not in the transition state binding ( K T s ) . The binding of the transition
state to each CD is very similar, but the stronger binding of the reactant to
p-CD in the initial state leads to rate retardation (k,lk, < 1). Presumably,
the substrate [3] (or as [3’]) sits deeper and more tightly in the larger cavity
of p-CD so that access to the transition state geometry is made more
difficult. It is noteworthy that the “transition state analogue” [5] binds to
a-CD (inhibition constant, K I = 12 f 2 mM) with almost the same strength
as the actual reaction transition state which presumably resembles the
tetrahedral intermediate [6].
In another example of intramolecular participation, the attack of the
carboxylate ion group of mono-p-carboxyphenyl esters of substituted
glutaric acids, the rate of anhydride formation is sharply reduced by p-CD
(VanderJagt et al., 1970). Apparently, the substrates bind to p-CD in a
conformation that is unsuitable for reaction. At the same time, the large
rate reductions must also mean that the transition state of the reaction
cannot be bound by p-CD in such a way as to be significantly stabilized.

02Nd0H
- 02NwH
OCOtBu


OCOtBu

__f

131

r l

OzN

0

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t Bu
OH


TRANSITION STATE STABILIZATION

15

Several other intramolecular reactions showed only slight rate accelerations
or retardations (VanderJagt et af., 1970). Of potential synthetic use, it has
been found that both intramolecular and intermolecular Diels-Alder reactions can be catalysed by p-CD (Sternbach and Rossana, 1982; Breslow and
Guo, 1988).

DECARBOXYLATION

The rate of decarboxylation of activated carboxylate anions [e.g. (lO)],

shows strong solvent dependence. It is not surprising, therefore, that these
reactions have been used to probe the microsolvent effects of micelles and
CDs (Fendler and Fendler, 1975). In particular, it was anticipated that
complexation with a CD might result in catalysis by providing an environment for the reaction that is less polar than water.
X-Ph(CN)CHCO;

+ X-Ph(CN)CH-

+ COZ

( 10)

In keeping with this expectation, Straub and Bender (1972a) found that
the decarboxylation of phenylcyanoacetate anions (10) shows catalysis in the
presence of p-CD, albeit modest [Appendix, Table A4.11. The rate
accelerations show little variation (12-23, at 60.4”C) even though the
reactivity of the anions spans two orders of magnitude and Ks varies with
the position and size of the substituent. Consequently, the values of pKTs
vary in parallel with pKs (slope = 1.08k0.13; r = 0.957) which strongly
suggests that the binding of the transition state in the CD cavity is very
similar to that of the substrate, S.
The magnitude of the rate accelerations caused by p-CD is comparable to
that brought about by a change from water to 55% (w/w) aqueous
2-propano1, but significantly less than those in wholly organic media: 100%
2-propanol (2600); dioxane (2800). Also, the activation parameters for
reaction in the mixed solvent and for the S - C D complex in water are very
similar (Straub and Bender, 1972a). Presumably, these findings mean that
the aryl ring of S is situated largely in the C D cavity, with the anionic moiety
directed towards the exterior, so that the reaction centre is situated in a
“mixed” environment near the interface between the bulk aqueous medium

and the less polar C D cavity.
Data for the 4-chlorophenyl derivative were obtained at three temperatures (Table A4.1). At the lower temperatures, the rate acceleration is
greater because the transition state binding is strengthened more than the
substrate binding. The data may be analysed to elicit the enthalpic and
entropic contributions to the free energy of transition state stabilization,
obtainable from the variation of AC&( =AH+, - TAS+s) with temperature
(Table 2). If desired, the data may be further dissected since, from ( 9 ) ,

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16

Table 2 Thermodynamic parameters for the P-cyclodextrin-catalysed decarboxylation of the 4-chlorophenylcyanoacetate anion."

AG:

AAC'

Temp./"C

2.32
2.22
2.09
AAH* = 5.22
AAS
= 9.40


35.4
45.4
60.4

2.79
2.77
2.68
AH(' - 4.21
AY! 2 4.57

AG;~

5.11
4.99
4.77
A P ' S = 9.42
A& = 13.9

"From the data of Straub and Bender (1972a) (see Table A l ). Free energies and enthalpies are
in kcal mo1-l: entropies are in cal K-' mol-'.

-RTlnKTS = -RTln(k,/k,) -RTlnKs, and so AC;, is given by (ll),
where AAG' = (AC; - AC:) is the difference in activation free energies of
the two kinetic steps. The relationship (11) is evident in the diagram in Fig.
2. Likewise, for the enthalpy and entropy, the separate contributions are
AH!;s = AAH$ AH: and AS& = AASs + AS: (Table 2).

+

As seen in Table 2, AH;.s = 9.42 kcal mol-' and AS;, = 13.9 e.u., and so

the free energy of transition state stabilization (approximately 5 kcal mol-')
results from a favourable enthalpy change, partly offset by an unfavourable
entropy change. A similar situation pertains to binding of the substrate also
(Table 2). Thus, the similarity between transition state binding and substrate
binding, pointed out above from the correlation of pKTs with pKs, is
evident in thermodynamic parameters as well.
The decarboxylation of benzoylacetic acids in acidic solution proceeds
with intramolecular proton transfer [7] + (81. This feature of the reaction
appears to limit charge separation in the transition state since the rates in
water are very insensitive to the electronic nature of the substituents
( p = +0.03), unlike the reaction of their anions ( p = +1.42) (Straub and
Bender, 1972b). The reaction of the acids shows catalysis by p-CD, with
limiting accelerations of 2-8 (Table A4.1). Values of Ks and of KTs do not
vary greatly with the aryl substituent, probably because the hydrophilic keto
and carboxyl groups of [7] do not allow the benzoyl function to penetrate
deeply into the C D cavity in either the initial state or the transition state.
The modest catalysis presumably arises because binding to the p-CD heIps
to bring the reactive groups together and to stabilize the cyclic transition
state. It is highly unlikely that catalysis results from a microsolvent effect
since the decarboxylation reaction [7] + [8] is not particularly sensitive to
the solvent (Straub and Bender, 1972b).

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