Microscopic examination of free-energy relationships for electron transfer in polar solvents

Abstract

A recently developed semiclassical trajectory (ST) approach is used to explore the microscopic free-energy relationship for electron-transfer reactions in polar solvents. The free-energy functional is evaluated by an adiabatic charging process based on the umbrella sampling method. The relevant energy fluctuations are generated by molecular dynamics simulation, representing the solvent molecules by the surface constrained all atom solvent (SCAAS) model. The specific model considered is composed of two benzene-like molecules with variable redox potentials. The simulation gives stable results with a relatively small convergence error. The results are compared to the free-energy profile predicted by the macroscopic Marcus' model. It is found that the solvent contribution to the activation barrier follows Marcus' relationship, provided that the reorganization energy parameter is evaluated from the microscopic simulation. The experimentally observed deviations from Marcus' relationship are shown, by realistic microscopic calculations, to be due to the solute vibronic channels. It is pointed out that the approximately quadratic behavior of the free-energy functional might reflect an inherent property of solvents with high dielectric constant.