Transition state theory isotope effects

Garret, B. C. and Truhlar, D. G. Generalized transition state theory. Quantum effects for collinear reactions of hydrogen molecules and isotopically substituted hydrogen molecules, JPhys.Chem., 83 (1979), 1079-1112... 

Garrett B. C. and Truhlar D. G. (1979) Generalized Transition State Theory. Quantum Effects for Collinear Reactions of Hydrogen Molecules and Isotopically Substituted Hydrogen Molecules, J. Phys. Chem. 79, 1079-1112. 

Generalized Transition State Theory. Quantum Effects for Collinear Reactions of Hydrogen Molecules and Isotopically Substituted Hydrogen Molecules. 

We now carry the argument over to transition state theory. Suppose that in the transition state the bond has been completely broken then the foregoing argument applies. No real transition state will exist with the bond completely broken—this does not occur until the product state—so we are considering a limiting case. With this realization of the very approximate nature of the argument, we make estimates of the maximum kinetic isotope effect. We write the Arrhenius equation for the R-H and R-D reactions... 

Transition state theory has been useful in providing a rationale for the so-called kinetic isotope effect. The kinetic isotope effect is used by enzy-mologists to probe various aspects of mechanism. Importantly, measured kinetic isotope effects have also been used to monitor if non-classical behaviour is a feature of enzyme-catalysed hydrogen transfer reactions. The kinetic isotope effect arises because of the differential reactivity of, for example, a C-H (protium), a C-D (deuterium) and a C-T (tritium) bond. 

Tetrahedral intermediates, derived from carboxylic acids, spectroscopic detection and the investigation of their properties, 21, 37 Topochemical phenomena in solid-state chemistry, 15, 63 Transition state structure, crystallographic approaches to, 29, 87 Transition state structure, in solution, effective charge and, 27, 1 Transition state structure, secondary deuterium isotope effects and, 31, 143 Transition states, structure in solution, cross-interaction constants and, 27, 57 Transition states, the stabilization of by cyclodextrins and other catalysts, 29, 1 Transition states, theory revisited, 28, 139... 

Transition stale structure, secondary deuterium isotope effects and, 31, 143 Transition states, structure in solution, cross-interaction constants and, 27, 57 Transition states, the stabilization of by cyclodextrins and other catalysts, 29, 1 Transition states, theory revisited, 28, 139... 

Since the discovery of the deuterium isotope in 1931 [44], chemists have long recognized that kinetic deuterium isotope effects could be employed as an indicator for reaction mechanism. However, the development of a mechanism is predicated upon analysis of the kinetic isotope effect within the context of a theoretical model. Thus, it was in 1946 that Bigeleisen advanced a theory for the relative reaction velocities of isotopic molecules that was based on the theory of absolute rate —that is, transition state theory as formulated by Eyring as well as Evans and Polanyi in 1935 [44,45]. The rate expression for reaction is given by... 

There have been numerous kinetic studies of the deuterium isotope effect for proton and hydrogen atom transfer where values for EH — Ev greatly exceed 1.4kcal/mol and the ratio of A factors, AD/AH, are significantly >1.4 values >10 are very common [4]. These observations directly challenge the classical model for proton transfer based upon transition state theory that neglects contributions from k. 

Transition state theory, a quasi-thermodynamic/statistical mechanical approach to the theory of reaction rates was developed in the early 1930s by a number of workers including H. Eyring, E. R Wigner, and J. C. Polanyi and was very quickly applied to the consideration of isotope effects on rates of simple molecular reactions. 

Isotope Effects on Equilibrium Constants of Chemical Reactions Transition State Theory of Isotope Effects... 

Isotope effects on rates (so-called kinetic isotope effects, KIE s) of specific reactions will be discussed in detail in a later chapter. The most frequently employed formalism used to discuss KIE s is based on the activated complex (transition state) theory of chemical kinetics and is analogous to the theory of isotope effects on thermodynamic equilibria discussed in this chapter. It is thus appropriate to discuss this theory here. 

In earlier sections of this chapter we learned that the calculation of isotope effects on equilibrium constants of isotope exchange reactions as well as isotope effects on rate constants using transition state theory, TST, requires the evaluation of reduced isotopic partition function ratios, RPFR s, for ordinary molecular species, and for transition states. Since the procedure for transition states is basically the same as that for normal molecular species, it is the former which will be discussed first. 

Kinetic Isotope Effects Continued Variational Transition State Theory and Tunneling... 

Abstract Some of the successes and several of the inadequacies of transition state theory (TST) as applied to kinetic isotope effects are briefly discussed. Corrections for quantum mechanical tunneling are introduced. The bulk of the chapter, however, deals with the more sophisticated approach known as variational transition state theory (VTST). 

To begin we are reminded that the basic theory of kinetic isotope effects (see Chapter 4) is based on the transition state model of reaction kinetics developed in the 1930s by Polanyi, Eyring and others. In spite of its many successes, however, modern theoretical approaches have shown that simple TST is inadequate for the proper description of reaction kinetics and KIE s. In this chapter we describe a more sophisticated approach known as variational transition state theory (VTST). Before continuing it should be pointed out that it is customary in publications in this area to use an assortment of alphabetical symbols (e.g. TST and VTST) as a short hand tool of notation for various theoretical methodologies. 

Table 6.3 Tests of variational transition state theory by comparing with exact quantum calculations isotope effects at 300 K. The numbers in the table are ratios of rate constants for the two selected reactions...

Truhlar, D. G. Variational transition state theory and multidimensional tunneling for simple and complex reactions in the gas phase, solids, liquids, and enzymes, in Kohen, A. and Limbach, H. H., Eds. Isotope Effects in Chemistry and Biology. CRC Press/Taylor Francis, Boca Raton, FL (2006), pp. 579-619. 

To calculate the mixed solvent isotope effect on rate constants one applies simple ideas from transition state theory to evaluate the isotope effect on the... 

As is implied by the name, a unimolecular reaction is one in which a single molecule of reactant decomposes or rearranges to give rise to product molecules. Ordinary thermal reactions can be modeled by a process which considers the reactant to be in thermal equilibrium with a transition state which then decomposes (rearranges) to give products. One can theoretically describe the process and its isotope effects using transition state theory. For unimolecular reactions, on the other hand, while there is still a transition state, it is not in thermal equilibrium with the reactant except for systems at high pressure. Consequently, a more elaborate theoretical framework is required to understand unimolecular reactions and their isotope effects. 

The ratios in Equation 14.34 can be calculated using either conventional (Chapter 4) or variational (Chapter 6) transition state theory. In either case one expects a small normal secondary isotope effect (refer to the discussion in Chapter 10) and this is... 

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