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

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Abstract
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 detailed analysis of both mechanisms is given showing their temperature dependence, their dependence on the number of bridge units, and the influence of the energy gap and the driving force. It is demonstrated that for integral bridge populations less than 10−3 the complicated bridge-mediated ET reduces to a donor–acceptor ET with an effective overall transfer rate. This transfer rate contains contributions from the sequential as well as the superexchange mechanisms, and thus can be used for a quantitative analysis of the efficiency of different electron pathways. For room-temperature conditions and even at a very small bridge population of 10−4–10−10 the superexchange mechanism is superimposed by the sequential one if the number of bridge units exceeds 4 or 5.