Reaction dynamics on a fluctuating potential

Abstract

The steady state rate constant for passage over a fluctuating potential barrier is derived from the Fokker–Planck equation using the stable states picture. The time scale of fluctuations in barrier height and position do not influence the reactive frequency; however, the reactive frequency does depend upon the time scale of fluctuations in the barrier curvature. If these are fast relative to [ω2m+(ξ/2)2]1/2, where ωm is the mean barrier frequency and ξ is the friction for motion along the reaction coordinate, then the crossing takes place on the potential of mean force. If the barrier fluctuations are slow on the same time scale, then the rate is an average over that for the distribution of barriers. In both of these limits the form of the Kramers solutions is recovered, whereas in the intermediate case, the rate also depends explicitly on the relaxation time scale of the fluctuations. A physically reasonable model for the decay of fluctuations in the potential is proposed and used to obtain an analytic expression for the rate that covers the range between these two limits.