Reactive dynamics for diffusive barrier crossing

Abstract

A theory is presented for intramolecular reactions A?B regarded as potential barrier crossing between two stable states A and B in the large friction limit. This limit, in which dynamics are governed by spatial diffusion in the potential, is an important example of extreme deviation from transition state theory predictions. Our theory expresses the full reaction rate constants in terms of simpler contributions: (a) the barrier rate constants and (b) the internal rate constants. The former depend solely on dynamics near the barrier top and govern the rate when stable state internal equilibrium is maintained. The latter depend solely on internal equilibration dynamics in the stable states A and B (defined away from the barrier top). The internal rate constants correct the barrier rate constants for stable state internal nonequilibrium effects. These two contributions are discussed in dynamical terms in some detail. Our theoretical rate constants are evaluated and compared with the rate constants observed by monitoring population decays obtained by direct numerical integration of the Smoluchowski equation. A simple minimum principle predicts the reaction rate constants with high accuracy at any value of the barrier height. For high barriers, our predictions approach (but are more accurate than) those of the classic approximate analysis of Kramers. For very low barriers (e.g., 1.6k_BT), internal nonequilibrium effects neglected by Kramers are found by our theory to account for approximately 33% of the rate constant.