Electron Transfer Using Non-Orthogonal Basis Functions

We reconsider standard models of electron transfer in molecular solids formulated with non-orthogonal wavefunctions characterized by weak coupling matrix element $V$ and small wavefunction overlap $S$. Using the method of Weisskopf and Wigner, we derive a new expression for the phonon-assisted electron hopping rate (Marcus rate) between non-degenerate sites separated by energy difference $\Delta$. We show that electron localization occurs for a particular value of the ratio $S\Delta/V$, and we discuss the implication this has for the Marcus inverted regime.