Steepest Descent Path Study of Electron-Transfer Reactions†

A nonadiabatic steepest descent path method is developed as a qualitative tool to analyze and characterize three different kinetic regimes of electron transfer. In this approach, Miller’s semiclassical instanton solution and Pechukas’ self-consistent treatment of nonadiabatic coupling are applied to the path integral representation of the two-state diffusion equation. The resulting steepest descent solution defines the diffusive solvent trajectory that has the highest probability to induce electron transfer. Numerical examples demonstrate curve crossing in the nonadiabatic regime, barrier crossing in the adiabatic regime, and delocalized effects in the coherent regime, thus providing a revealing picture for the crossover from the nonadiabatic to adiabatic regime and the transition from incoherent to coherent electron transfer.