Bridge-mediated two-electron transfer via delocalized bridge orbitals

Bridge mediated two-electron transfer (TET) in a donor-acceptor (D-A) complex is studied theoretically. A type of bridge is considered where the intersite coupling in the bridge becomes so large that the TET proceeds along delocalized bridge states but against the background of fast vibrational transitions within and between these states. The assumption of fast vibrational relaxations allows us to follow our earlier approach (Petrov; et al. J. Phys. Chem. B 2002, 106, 3092) and to derive kinetic equations governing the populations of the states involved in the TET reaction. The conditions are explained in detail at which a reduction to distant D-A TET can be carried out. Moreover, an analytic expression for the overall D-A TET rate is given for the case of a regular bridge as well as for a bridge perturbed by an intersite energetic bias. The stepwise and the concerted route of the D-A TET is analyzed in dependence on the bridge length. It is shown that the stepwise route follows from a thermal activation of a specific intermediate state. Its contribution to the overall transfer rate is determined by two single-electron transfer steps each of them related to two single-electron pathways through the bridge. The first pathway requires a population of the extended bridge state by thermal activation and thus can be termed the thermally activated pathway. The second pathway utilizes the bridging states as virtual intermediate states and thus is termed the single-electron superexchange pathway. The concerted D-A TET mechanism uses the extended bridge states as well as the mentioned intermediate state as virtual states. Therefore, it can be understood as a two-electron unistep superexchange transition between the D and the A. This transition can take place even at zero temperature. The perturbation of a regular arrangement of bridge levels by an energetic bias favors the stepwise route because it includes thermal activation of the intermediate state. This fact also explains that the efficiency of the concerted twoelectron superexchange route is larger than that of the thermally activated stepwise route if low temperatures and short bridges (one or two units) are considered.