Variational transition state theory evaluation of the rate constant for proton transfer in a polar solvent

Variational transition state theory (VTST) is used to calculate rate consta nts for a model proton transfer reaction in a polar solvent. We start from an explicit description of the reacting solute in a solvent, and we model t he effects of solvation on the reaction dynamics by a generalized Langevin equation (GLE) for the solute. In this description, the effects of solvatio n on the reaction energetics are included in the potential of mean force, a nd dynamical, or nonequilibrium, solvation is included by solvent friction. The GLE solvation dynamics are approximated by a collection of harmonic os cillators that are linearly coupled to the coordinates of the reacting syst em. This approach is applied to a model developed by Azzouz and Borgis [J. Chem. Phys. 98, 7361 (1993)] to represent proton transfer in a phenol-amine complex in liquid methyl chloride. In particular, semiclassical VTST, incl uding multidimensional tunneling contributions, is applied to this model wi th three explicit solute coordinates and a multioscillator GLE description of solvation to calculate rate constants. We compare our computed rate cons tants and H/D kinetic isotope effects to previous calculations using other approximate dynamical theories, including approaches based on one-dimension al models, molecular dynamics with quantum transitions, and path integrals. By examining a systematic sequence of 18 different sets of approximations, we clarify some of the factors (such as classical vibrations, harmonic app roximations, quantum character of reaction-coordinate motion, and nonequili brium solvation) that contribute to the different predictions of various ap proximation schemes in the literature. (C) 2001 American Institute of Physi cs.