New expression for the effective transfer matrix element in long-range electron transfer reactions

Abstract

A new expression for the effective transfer matrix element, TDA, in long-range electron transfer is derived. This expression corrects the second-order perturbation theory estimate by accounting for an infinite number of terms in the perturbation expansion. The correction factors measure the extent of delocalization of the diabatic donor and acceptor states. A simple procedure is devised to adjust the molecule to its transition state, which is the point of avoided crossing of the energies of the adiabatic states. The new expression is used to compute the half-splitting in these eigenenergies, which equals TDA, without recourse to diagonalization. When checked against direct diagonalization for a truncated model of a ruthenium-modified azurin protein, this method located the point of avoided crossing and produced an estimate of the energy half-splitting which agreed with the result of diagonalization with exceptional accuracy.