Quantum activated rates—an evolution operator approach

This article presents a derivation of the rate of reaction in the quantum activated rate problem. In this problem, one studies the rate of a chemical reaction when the reaction is placed in a dissipative bath. Our derivation defines the rate in terms of the flux autocorrelation function and proceeds via the recently developed interaction representation for nonadiabatic corrections to adiabatic evolution operators. This methodology is an infinite order resummation of nonadiabatic corrections to evolution operators. The approach produces an analytic expression which yields accurate results over a range of temperatures, viscosities and system parameters through the Kramers turnover region.