Effects of the Duschinsky mode-mixing mechanism on temperature dependence of electron transfer processes

Electron transfer processes involving a multimode mixing mechanism (the Duschinsky rotation) are systematically examined. Such processes can be analyzed with a very general “spin–boson” model with N displaced and quadratically coupled harmonic potentials. The very general Franck–Condon factor obtained here is applicable to the studies of electron transfer as well as energy transfer processes, where frequency shifts and the Duschinsky rotation are involved. Although there are several numerical studies of such a mechanism, the derivation of an analytical expression for the rate constant is presented here and the temperature dependence is examined. As, in general, at very low temperatures where the thermal energy is smaller, the electron transfer rate becomes temperature independent due to nuclear quantum tunneling. However, in the presence of Duschinsky rotation, the pre-exponential factor in the rate constant can deviate from the characteristic 1/√T dependence of the Marcus theory. For processes with no or a small activation energy, the rate can be dominated by the pre-exponential factor and becomes 1/T dependence in the high-temperature regime.