Analytic Quantum Theory of Electron Transfer with a Reaction Mode Strongly Coupled to the Electron and Weakly Coupled to the Bath

We develop an effective analytic framework built around our own extension of standard small polaron theory. We assume a Hamiltonian in which the electron operators are strongly coupled to a single linear oscillator, the reaction mode, which is in turn weakly coupled to the heat bath. The Hamiltonian is transformed so that the previously bare electron is dressed in the quanta of the reaction mode but not in the quanta of the rest of the bath modes. The dressed electron, or [open quotes]reaction[close quotes], has no residual interaction with the transformed reaction mode; its remaining interactions with the bath can be treated perturbatively. Although our formalism describes the full kinetics, we present in detail here only the results of a Golden Rule calculation of the electron-transfer rate constant. We find that in the strict high-temperature limit the rate constant is of the Marcus form but with a reorganization energy that is simply the product of the reaction mode quantum energy and the dimensionless (strong) coupling constant squared, independent of the details of the phonon spectrum. This contrasts with earlier findings based on the standard polaron model that the reorganization energy is a weighted sum over the bath mode frequencies. 13 refs., 1 fig.