Molecular three-centre electron transfer (ET) systems contain an intermediate electronic bridge group state in addition to the donor and acceptor states. This feature is encountered in long-range ET patterns of metalloproteins, in bacterial photosynthetic reaction centres, in electrochemical processes at modified metal electrodes and in hypothetical or real molecular shift register and photodiode device-like systems. Overall ET is by superexchange when the intermediate group energy is high. When the energy is low enough that the state is temporarily populated, a range of vibrational features arise depending on the vibrational coupling and relaxation time of the intermediate state. In external fields these properties induce characteristic ‘switch’ effects reflected in rapid changes in the current derivatives and other features in the current–voltage relations. We provide a quantum mechanical frame for three-centre ET in such molecular systems. The theory rests on second-order perturbation theory. In contrast to most applications of superexchange concepts, the theory includes explicitly nuclear coupling in the intermediate state and is valid both for high energy superexchange and for low-energy populated intermediate states. Moreover, mild, finite resonances arise in the transition regions between the various energy ranges represented by analytical rate constants. The theory is appropriate to the molecular electronic behaviour of several biological and synthetic three-level ‘switch’ ET systems.
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