Dynamical corrections to transition state theory for multistate systems: Surface self-diffusion in the rare-event regime

TLDR

In the rare‑event regime where dynamical recrossings outpace reactive state changes, defining a rate between nonadjacent states becomes meaningful. The authors derive a general expression for the classical rate constant between any two states of a multistate system. They express the rate as the transition‑state‑theory escape rate multiplied by a dynamical correction factor computed from a time‑correlation function via molecular dynamics, enabling study of infrequent events. The method is applied to surface diffusion of Rh on Rh(100) at temperatures used in field‑ion‑microscope experiments.

Abstract

We derive an expression for the classical rate constant between any two states of a multistate system. The rate is given as the transition state theory rate of escape from the originating state, multiplied by a dynamical correction factor in the form of a time-correlation function which is evaluated using molecular dynamics techniques. This method is desiged to treat cases in which reactive state-change events are so infrequent (e.g., at low temperature) that direct molecular dynamics calculations are unfeasible. In this regime where dynamical recrossings occur much more quickly than the average time between reactive state changes, the concept of a rate between two nonadjacent states becomes meaningful. We apply the method to the surface diffusion of Rh on Rh(100) at the temperatures employed in field ion microscope experiments.