Electron transfer via superexchange: A time-dependent approach

The superexchange model for the facilitation of electron transfer between donors and acceptors by means of intermediate bridges is recast in a time-dependent framework. We develop a model in which three electronic states (donor, bridge, and acceptor) are considered and vibronic levels are included on the donor and acceptor. An explicitly time-dependent formulation, in which the golden rule is rewritten in the form of an integral over a time-dependent correlation function, is used to calculate the rate. Simple example calculations for model three-site systems are given; inverted region behavior and reasonable values are obtained. The model is a general one and should be useful for interpretation of superexchange-assisted transfer based on experimental observations of frequencies and displacements (such as the information that can be obtained with Raman spectroscopy). The model can be generalized to include effects such as dephasing, relaxation, solvent dynamics, and anharmonicities, as well as breakdown of the Condon approximation.