Effects of a fluctuating electronic coupling matrix element on electron transfer rate

The effects of a fluctuating electronic coupling matrix element on an electron transfer process are examined theoretically. An analytical expression for the electron transfer rate constant was derived using the spin-boson model. In the limit of long correlation time (τv) for the fluctuation, our results are identical to the Marcus expression for the static coupling. The electron transfer rate in the intermediate range of τv, however, can be either enhanced or reduced, depending on the free energy gap and the reorganization energy. In the limit of very short τv, the electron transfer rate decreases with τv, and depends only on τv and the coupling matrix element.