A self-consistent treatment of electron transfer in the limit of strong friction via the mixed quantum classical Liouville method

Electron transfer is investigated at the limit of strong friction. The analysis is based on the generic model of a two-state system bilinearly coupled to a harmonic bath. The dynamics is described within the framework of the mixed quantum classical Liouville (MQCL) equation, which is known to be exact for this model. In the case of zero electronic coupling, it is shown that while the dynamics of the electronic populations can be described by a Markovian quantum Smoluchowski equation, that of the electronic coherences are inherently non-Markovian. A non-Markovian modified Zusman equation is derived in the presence of electronic coupling and shown to be self-consistent in cases where the standard Zusman equation is not.