On the classical reaction rate and the first-time problems of Brownian motion

Abstract

We have developed efficient techniques to solve the first-time problems of Brownian motion. Based on a time-scale separation of recrossings, we show that Eyring's transmission coefficient (kappa) equals to the one (kappa V) corresponding to an absorbing boundary consistent with the transition state theory, which is greater than the one (kappa K) derived by Kramers. We also propose methods for reaction rate determination by analyzing shorttime trajectories from the barrier maximum, and discuss the relation to the reactive flux method and the significance of reaction coordinates. (c) 2023 Elsevier B.V. All rights reserved.