Electron Tunneling Barriers in Marcus Theory of Electron Transfer: Incorporating Bridge State Thermal Fluctuations

The semi-classical and quantum theories of electron transfer (ET) are extensively used to understand and predict tunnelling ET reaction rates in condensed phase and build on the two-state Donor-Acceptor thermodynamic framework of Marcus theory. Previously, 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 examine the previously proposed three-state extended Marcus model (EMM) and generalize it 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 tunnelling barrier is derived. The EMM model predicts that relative thermodynamics of the D-A states and B state reorganization energies can both 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.