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 

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 woW-equilibrium constant, since 

It is important to note that the derivation of KTS, given above, involves no assumptions about the mechanisms of either the catalysed or uncatalysed reactions. Therefore, it is possible to use values of KT s (and pKrs = —log/fxs) 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 Krs 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 

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 A u for the normal, uncatalysed reaction (2) and for the mediated ( catalysed ) reaction (k2 = kJKs) as in (3), application of simple transition state theory, in the manner shown above, leads to (9), where now Krs is the apparent dissociation constant of the transition state of the CD-mediated reaction (symbolized here as TS CD) 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. 

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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. 

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. 

From the rate constant kc2 and that for reaction of S-CD complex (kc), application of the Kurz approach leads to K s = kcikc2 for dissociation of the second CD molecule from the transition state in (19). Values of K rs are remarkably similar for the C6, C7, C8 and 4MeC5 esters (45, 59, 49 and 48 mM, respectively), providing strong evidence that the second CD stabilizes the transition state by binding to the aryl group of an ester molecule already bound by its alkanoate chain to the first CD [27] (Tee and Du, 1992). 

Further analysis of the rate constants in Tables A5.13 and A5.14 can be made using the Kurz approach, particularly regarding the structural dependence of the transition state stabilization. For the Pi-mediated reaction, we define /fTS by (25), where now TS stands for the transition state in reaction (3) and TS-PI is that in reaction (21) [or (24)]. As indicated in (25), KTS may also be derived from the rate constants for the second order process in (3 = 5) and the third-order process involving PI, since k2 = kc/Ks and k3 = kJKs [see (21)]. 

The primary literature now contains a very large body of kinetic data for the catalysis of enolization and ketonization, not only of ketones and aldehydes but also of )3-diketones, )3-keto esters, and dienones, much of which could be treated by the Kurz approach. Also, data exist for third-order enolization, due to combined general acid and base catalysis, that could also be analysed. Such treatment is beyond the scope the present review. However, one study of metal ion catalysis of enolization is discussed later in this section. 

In principle, reactions which are subject to electrophilic catalysis by protons can be catalysed by metal ions also (e.g. Tee and Iyengar, 1988 Suh, 1992). However, metal ions may function in other ways, such as to deliver a hydroxide ion nucleophile to the reaction centre (e.g. Dugas, 1989 Chin, 1991), and it is often difficult to decide between kinetically equivalent mechanisms without resorting to extensive (and intensive) model studies. Use of the Kurz approach may help to resolve such ambiguities, as shown below. 

The effects observed in a given case depend on the reaction type, its charge type, and the nature of the surfactant (cationic, anionic, or neutral) forming the micelles. One recent study of ester cleavage (37) in cationic micelles affords data that are amenable to treatment by the Kurz approach. 

As mentioned in the Introduction, various authors have been influenced (directly or indirectly) by the Kurz approach in their discussions of enzyme behaviour (e.g. Wolfenden, 1972 Lienhard, 1973 Jencks, 1975 Schowen, 1978 Fersht, 1985 Kraut, 1988 Wolfenden and Kati, 1991). Also, as noted earlier, the concepts of transition state binding and stabilization were crucial to the development of transition state analogues as enzyme inhibitors and hence as chemotherapeutic agents (Jencks, 1969 Wolfenden, 1972 Wolfenden and Frick, 1987 Wolfenden and Kati, 1991). 

This review will have been of service if it exposes the Kurz approach to a broader audience and particularly if it stimulates other researchers to utilize... 

The author has been made aware of several more references which treat transition state stabilization by metal ions in the Kurz manner (Rudakov et al., 1974 Illuminati et al., 1983 Ercolani et al., 1983 Mandolini and Masci, 1984 Galli and Mandolini, 1984) and that the Kurz approach was discussed briefly in the second edition of Hammett s famous book (Hammett, 1970). In another area, a recent special issue of Accounts of Chemical Research (vol. 26, 8, pp. 389-453 (1993)), which is devoted to Chemistry and Immunology , has several articles on catalytic antibodies. 

The object of this review was to show how Kurz s approach to quantifying transition state stabilization is useful in the discussion of the kinetic effects of cyclodextrins on organic reactions, while at the same time pointing out its comparable utility for various other types of catalyst. It is hoped that the approach gains wider acceptance and employment since it provides a framework for the discussion of factors affecting transition state stability in both catalysed and retarded reactions. 

J.L. Kurz, The Relationship of Barrier Shape to Linear Free Energy Slopes and Curvatures, Chem. Phys. Lett., 1978, 57, 243 J.C. Harris J.L. Kurz, A Direct Approach to the Prediction of Substituent Effects in Transition-state Structures, J. Am. Chem. Soc., 1970, 92, 349 R.P. Bell, Proc. Roy. Soc. London, 1936, 154A, 414. 

Joswig [1990] combined the STA/LTA trigger with a sonogram analysis of the seismic signal. This approach has been tested by Kurz [2006] on acoustic emissions and was found to be acceptable for acoustic emissions. 

In the domain of acoustic emissions, Kurz et al. [2005] applied the principle of the autoregressive AIC picker in an automatic onset detection procedure. The results of the autoregressive AIC picker were then compared to manual picks and to an auto picker based on the Hinkley criterion, developed for acoustic emissions by Grosse and Reinhardt [1999]. Details about these approaches and the results can be found in Kurz et al. [2005]. In the following, only a short summary will be given. 

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