Outer sphere electron transfer in polar solvents. Activationless and inverted regimes

In this paper we apply the stochastic Liouville equation for the study of outer sphere electron transfer (ET) in a polar solvent, which is characterized by a Debye dielectric relaxation. Explicit expressions, which bridge between the nonadiabatic and solvent-controlled adiabatic limits, are derived for the ET rates spanning a broad range of the energetic parameters, which include normal ET, activationless ET, and ET in the inverted region. The many-body result for the ET rate, which is accurate for symmetric ET, constitutes a useful approximate interpolation formula, which accounts well for the ET dynamics over a broad range of the energetic parameters.