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

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.