Quantum theory of activated rate processes: A maximum free energy approach

Abstract

A quantum theory of activated rate processes applicable to nonlinear potentials of interaction is developed. The central premise is that the rate is determined by the point of maximal quantum free energy separating reactants and products. The quantum free energy is defined in terms of a quantum centroid potential. The resulting rate expressions reduce to known limits for generalized Langevin equations and their Hamiltonian representation. They also reduce in the classical limit to previous results derived using an optimal planar dividing surface classical variational transition-state theory. A saddle-point estimate of the quantum rate leads to a generalization of Wolynes’ high temperature rate expression valid for nonlinear system bath interactions and anharmonic baths. Maximizing the free energy leads to a quantum friction function. Application to realistic systems demands the computation only of centroid densities.