Analytic expression for the transmission coefficient in quantum mechanical transition state theory

Abstract

An analytic expression for the transmission coefficient in a recently formulated quantum mechanical transition state theory is derived. This formula is developed for a reaction coordinate having a general nonlinear potential energy barrier coupled to a linearly responding environment or “bath”. The final result has the same compact form as the classical Grote-Hynes transmission coefficient, but it also reflects important properties of the quantum mechanical tunneling. The present quantum transmission coefficient may be evaluated from a classical molecular dynamics simulation in conjunction with a quantum statistical mechanical variational principle.