Solvent dynamical effects in electron transfer: The solvent inertial limit and the predicted influence of quantum effects

Analytical continuum formulations for the solvent inertial frequency, constituting the anticipated zero-friction limit for adiabatic barrier crossing in solvent-controlled electron-transfer processes, are derived and discussed. The role of the solvent inertia in solvent dynamical effects is discussed with emphasis on the likely modifications brought about by nuclear tunneling. Approximate formulations suitable for assessing the latter correction in the presence as well as absence of solvent friction are outlined and compared. Numerical calculations are provided that illustrate the partly compensatory influence on the rate-solvent friction dependence resulting from nuclear tunneling together with reaction nonadiabaticity. Such combined quantum effects are anticipated typically to mask the clearcut emergence of solvent inertial effects on electron-transfer reaction dynamics in common low-friction media.