Kinetic isotope effects transition-state variation

It was concluded that while kinetic isotope effects are much more sensitive than Bronsted exponents to variations in pKa, the use of either quantity as an index of transition state symmetry may be doubtful. 

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. 

Alhambra and co-workers adopted a QM/MM strategy to better understand quantum mechanical effects, and particularly the influence of tunneling, on the observed primary kinetic isotope effect of 3.3 in this system (that is, the reaction proceeds 3.3 times more slowly when the hydrogen isotope at C-2 is deuterium instead of protium). In order to carry out their analysis they combined fully classical MD trajectories with QM/MM modeling and analysis using variational transition-state theory. Kinetic isotope effects (KIEs), tunneling, and variational transition state theory are discussed in detail in Chapter 15 - we will not explore these topics in any particular depth in this case study, but will focus primarily on the QM/MM protocol. 

Kinetic isotope effects (KIE) of silylene insertion reactions were determined in solution as well as in the gas phase. Steele and Weber39 found KIEs between 1.8 and 2.3 for the insertion of silylene 13 into various alcohols no significant variation of these values was observed with a change of solvent from cyclohexane to THF. These results are consistent with two mechanisms (Scheme 8), both of them proceeding via a nonlinear or triangular transition state. Mechanism B, which is favored over mechanism A by the authors, is in agreement with theoretical results, which, in general,... 

Theoretical studies of the microsolvation effect on SN2 reactions have also been reported by our coworkers and ourselves (Gonzalez-Lafont et al. 1991 Truhlar et al. 1992 Tucker and Truhlar 1990 Zhao et al. 1991b, 1992). Two approaches were used for interfacing electronic structure calculations with variational transitional state theory (VST) and tunneling calculations. We analyzed both the detailed dynamics of microsolvation and also its macroscopic consequences (rate coefficient values and kinetic isotope effects and their temperature... 

Experimental data on primary and secondary kinetic isotope effects in the hydride-transfer step in liver alcohol dehydrogenase, LADH, were analyzed using canonical variational transition theory (CVT) for overbarrier dynamics and the optimized multidimentional path (OMT) for the nuclear tunneling (Alhambra et al., 2000 and references therein). This work demonstrates somewhat better agreement of theoretical values of primary and secondary Schaad- Swein exponents calculated by combining CVT/OMT methods with the experimental values instead of CVT and classical transition states (TST). 

The variationally optimized transition state geometries were found to be different for transfer of a proton or a deuteron, the first indication of such a difference for an enzyme reaction [67]. Quantum treatment of vibrations was found to be important for the calculation of the rate constant, and variational transition state theory was important for calculating kinetic isotope effects. The... 

Various quantum-mechanical theories have been proposed which allow one to calculate isotopic Arrhenius curves from first principles, where tunneling is included. These theories generally start with an ab initio calculation of the reaction surface and use either quantum or statistical rate theories in order to calculate rate constants and kinetic isotope effects. Among these are the variational transition state theory of Truhlar [15], the instanton approach of Smedarchina et al. 

Joseph, T.R., Steckler, R. and Truhlar, D.G. (1987) A new potential energy surface for the CH3 + H2 CH + H reaction Calibration and calculation of rate constants and kinetic isotope effects by variational transition state theory and semi-classical tunneling calculations, J. Chem. Phys. 87, 7036-7049. 

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