Quantum Mechanical Effects in VTST

Calculations of reaction rates with variationally determined dynamical bottlenecks and realistic treatments of tunneling require knowledge of an appreciable, but still manageably localized, region of the potential energy surface [33[. In this chapter we assume that such potentials are available or can be modeled or calculated by direct dynamics, and we focus attention on the dynamical methods. 

In this chapter we provide a review of variational transition state theory with a focus on how quantum mechanical effects are incorporated. We use illustrative examples of H-transfer reactions to assist in the presentation of the concepts and to highlight special considerations or procedures required in different cases. The examples span the range from simple gas-phase hydrogen atom transfer reactions (triatomic to polyatomic systems), to solid-state and liquid-phase reactions, including complex reactions in biomolecular enzyme systems. 

With this choice of dividing surfaces, a generalized expression for the transition state theory rate constant for a bimolecular reaction is given by  

Canonical variational theory (CVT) is obtained by minimizing the generalized transition state rate expression s) with respect to the location s of the divid- 

Although we have described the theory in terms of taking the reaction path as the MEP in isoinertial coordinates, this can be generalized to arbitrary paths by methods discussed elsewhere [41], The treatment of the reaction coordinate at geometries off the reaction path also has a significant effect on the results one can use either rectilinear [34, 37-39] or curvilinear [40, 42] coordinates for this pur- 

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