On the transition from electronically nonadiabatic to solvent-controlled electron transfer

Path integral techniques are used to study a simple model of barrierless electron transfer where the energy gap between two electronic states is subject to Gaussian random noise induced by solvent fluctuations. The kinetics of electron transfer are related to the statistics of zero-crossings of the noise. We argue that these statistics are different in the cases of Markovian and non-Markovian Gaussian-correlated noise, leading to qualitatively different types of transition from electronically nonadiabatic to solvent-controlled electron transfer. We also demonstrate that for the typical situation where solvent relaxation consists of a fast inertial Gaussian-correlated and a slow exponentially relaxing component, the rate of electron transfer is primarily controlled by the fast component.