SOLVENT DYNAMICAL EFFECTS ON ELECTRON-TRANSFER REACTIONS

An integral equation [Rasaiah and Zhu, J. Chem. Phys. 98, 1213 (1993)] for the survival probabilities of electron transfer (ET) between thermally equilibrated reactants in solution is extended to include quantum effects on the ligand vibration and ET from a nonequilibrium initial state. We derive the kernel of the integral equation using a Green's function technique and demonstrate that it is determined by the solvent dynamics, the relative contributions of ligand and solvent reorganization energies, and the barrier heights for electron transfer. The extension of the theory to ET from a nonequilibrium initial state modifies the integral equation to provide the survival probabilities for the reactants that are not necessarily kinetically of first order, but can be directly compared with experiment. The long time rate, however, shows a simple exponential time dependence that is analyzed in terms of a rate constant with a diffusive solvent controlled component and a remainder. The effect of solvent dynamics on the diffusive part is governed by the same factors that determine the kernel. We find that the fast diffusive mode (small relaxation time) affects the rate of ET reactions with high barriers, while the slow diffusive part (large relaxation times) influences the rate when the barriers are low. Quantum corrections to these effects are calculated using the semiclassical approximation. The theory is used to analyze the ET kinetics of betaine-30 in glycerol triacetate (GTA) over a 100° temperature range and the influence of the details of solvent dynamics on the rates of electron transfer is elucidated. An appendix discusses improved saddle point approximations for the rates of electron transfer reactions calculated using the golden rule. © 1994 American Institute of Physics.