Anisotropic dynamical effects on two-dimensional potential energy surface reactions: Bond breaking electron transfer reactions

The effect of solvent and intramolecular dynamics on the rate of a bond breaking electron transfer reaction is investigated. The reaction takes place on a two-dimensional potential energy surface with one coordinate the solvent's polarization and the other the breaking bond's displacement. The dynamics are governed by overdamped spatial diffusion along the polarization coordinate and by energy diffusion along the bond coordinate. A scheme is presented that treats the transition from rate control by the equilibrium rate constant k(r) (as evaluated by, e.g., a Golden Rule calculation) to dynamical control, where the rate is controlled by diffusion on the surface, with rate constant kd, that accounts for the different character of the dynamics in the two directions. The overall rate constant has the form appropriate to a consecutive reaction mechanism: k(-1)=k(d)(-1)+k(r)(-1). The k(d) rate constant is analyzed numerically and the results compared with a number of approximation schemes. A method of analysis is developed for situations where one dynamics is fast/slow compared with the other. Which time controls k(d) depends strongly on the relation between the fast diffusion rate and k(r). (C) 1996 American Institute of Physics.