Electrostriction effects on electron transfer reactions in solution. I. Adiabatic regime

Abstract

The outer-sphere unimolecular electron transfer reactions, DA⇌D+A−, in polar solvents are studied theoretically. By employing a recent theory of fluctuating cavities [H. J. Kim, J. Chem. Phys. 105, 6818, 6833 (1996)], we construct a nonequilibrium free energy formulation that accounts for both the solvation and electrostriction aspects of the changing solute dipole moment during the reaction. With a two-state diabatic description for the solute electronic structure, we obtain a two-dimensional free energy surface in terms of the cavity radius a and a solvent coordinate that gauges the nonequilibrium solvent orientational polarization Por. The equilibrium a values for the reactant and product states are found to differ significantly, indicating that the cavity reorganization plays an important role in the reaction free energetics and dynamics. The reaction mechanism and rate constant are analyzed via the solution-phase reaction path, which is found to vary markedly with the relative time scales of the Por and a motions. To be specific, the charge transfer proceeds in a concerted fashion with active participation of both Por and a when their characteristic times are comparable. By contrast, a stepwise mechanism results when there is a large mismatch between the Por and a time scales. In the slow cavity limit where a is much slower than Por, the reorganization through the cavity size adjustment precedes the barrier crossing that occurs exclusively along the Por coordinate. In the opposite fast cavity regime where Por is mainly responsible for activation and deactivation, it is found that the saddle point on the free energy surface is no longer rate-determining due to the nonlinear residual entropic effects. A brief comparison with other reaction systems involving charge shift in solution is also made.