Tunneling barriers in an extended Marcus theory of electron transfer: Incorporating effects of the bridging medium

The Marcus semi-classical and quantum theories of electron transfer (ET) have been extensively used to understand and predict tunneling ET reaction rates in the condensed phase. Previously, the traditional Marcus two-state model has been extended to a three-state model, which assumes a harmonic dependence of donor (D), bridge (B), and acceptor (A) free energies on the reaction (e.g., solvent polarization) coordinate. Here, we generalize the previously proposed three-state extended Marcus model (EMM) to an (N + 2)-state model for N bridge sites separating the D from the A. Using the EMM, an analytic expression for the electron tunneling barrier is derived. The EMM model predicts that both the relative thermodynamics of the D-A states and B state reorganization energies can influence the D-A electronic coupling. We discuss signatures of bridge state thermal fluctuations using the EMM on the driving force and distance dependence of ET rates, which can be tested experimentally.