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 o f kinetic equations which simultaneously account for the sequential (hoppin g) as well as the superexchange mechanism. The analysis is based on the int roduction 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 con stants for the transition from the bridge to the donor as well as to the ac ceptor exceed those for the reverse transitions the ET reduces to a single- exponential process with an effective forward and backward transfer rate. T hese effective rates contain a contribution from the sequential and a contr ibution from the superexchange mechanisms. A detailed analysis of both mech anisms is given showing their temperature dependence, their dependence on t he number of bridge units, and the influence of the energy gap and the driv ing force. It is demonstrated that for integral bridge populations less tha n 10(-3) the complicated bridge-mediated ET reduces to a donor-acceptor ET with an effective overall transfer rate. This transfer rate contains contri butions from the sequential as well as the superexchange mechanisms, and th us can be used for a quantitative analysis of the efficiency of different e lectron pathways. For room-temperature conditions and even at a very small bridge population of 10(-4)-10(-10) the superexchange mechanism is superimp osed by the sequential one if the number of bridge units exceeds 4 or 5. (C ) 2001 American Institute of Physics.