Memory and temperature induced suppression of activated rate processes

Abstract

A detailed study of memory and temperature induced suppression of activated rate processes is presented. Numerical computations demonstrate that long memory in the presence of moderate barriers can induce noticeable deviation of the reaction rate constant from the predictions of the Kramers–Grote–Hynes theory. A canonical variational transition state theory, based on finding the optimized planar dividing surface, is shown to account quantitatively for the observed suppression of the rate. The suppression is associated with an almost perpendicular rotation of the optimal dividing surface away from the usual one. A further generalization of the Pollak–Grabert–Hänggi theory for the Kramers turnover is presented and shown to account for the computed rate constants for the whole range of damping at a fixed bath memory time.

Qualitative dynamics of generalized Langevin equations and the theory of chemical reaction rates

“…38,39 In addition, augmented dynamical systems similar to the ones presented here have been used as the basis of formal analysis 40 and numerical algorithms for solving the GLE by computer simulation. 41,42 Our emphasis here is different: We interpret the GLE as a dynamical system and analyze its qualitative character in detail. The geometrical approach of qualitative dynamics yields useful additional physical insights into this general mathematical approach to non-Markovian systems.…”

“…͑40͒ ͑when augmented by a random force͒ are commonly employed as the basis of a numerical method for solving the non-Markovian GLE with exponential memory. 41,42 FIG. 5.…”

Variational transition state theory for electron transfer reactions in solution

“…The details of solution of the variational problem can be found elsewhere. [55][56][57] Some specific details are given in Appendix A. The result for the coefficients ͕a j ͖ is…”

Phase-space geometry of the generalized Langevin equation

“…Martens [33], following earlier approaches [30,31,32], suggested a construction of the dynamical phase space under the assumption that the friction kernel γ(t) satisfies a linear differential equation with constant coefficients of the form…”

“…Several constructions of appropriate phase spaces have been suggested in the literature, e.g. in [30,31,32,33]. It will here be shown that the phase space depends critically on the way in which the system is prepared.…”