Nonadiabatic donor–acceptor electron transfer mediated by a molecular bridge: A unified theoretical description of the superexchange and hopping mechanism

Nonadiabatic bridge-assisted electron transfer (ET) is described by a set of kinetic equations which simultaneously account for the sequential (hopping) as well as the superexchange mechanism. The analysis is based on the introduction of a certain reduced density operator describing a particular set of electron-vibrational levels of the molecular units (sites) involved in the transfer act. For the limiting case of intrasite relaxations proceeding fast compared to intersite transitions a set of rate equations is obtained. This set describes the time evolution of the electronic site populations and is valid for bridges with an arbitrary number of units. If the rate constants for the transition from the bridge to the donor as well as to the acceptor exceed those for the reverse transitions the ET reduces to a single-exponential process with an effective forward and backward transfer rate. These effective rates contain a contribution from the sequential and a contribution from the superexchange mechanisms. A ...