On the role of nuclear motions in electron and excitation transfer rates: Importance of transfer-integral dependence upon nuclear coordinate

The role of nuclear degrees of freedom in modifying the electron or exciton transfer rates between molecules is investigated. In addition to the usual Franck-Condon overlap factors which arise from the overlaps of initial and final vibrational states, we discuss a dependence of the transfer integral upon nuclear motions, a dependence which has been often cited, but nearly always ignored, in the usual dynamical theories of transfer processes. We show, within a Bom-Oppenheimer treatment, that the transfer integral dependence upon librational, rotational and vibrational modes can profoundly change both the rate itself and its functional dependences (upon temperature, upon orientation, etc.). Using a simple cosine form for the dependence of the transfer integral upon the modifying nuclear mode and a simple displaced-oscillator transformation, we obtain a closed-form solution for the transfer rate, which includes a new overlap factor arising from the dependence of the transfer integral upon nuclear coordinates. Some general remarks about the role of this dependence are made, and applications to particular transfer systems are briefly discussed.