A Fermi Golden Rule, Liouville-space approach to the study of intramolecular electron transfer rate in solution

Abstract

We consider the problem of the calculation of the intramolecular electron transfer (ET) rate for molecules in solution and focus on the case of rapid, almost activationless processes. We assume that the weak-coupling, nonadiabatic limit holds and utilize the Fermi golden rule expression for the ET rate, avoiding the introduction of phenomenological data. The Fermi Golden Rule is elaborated in the Liouville space formalism taking into account at second order the coupling to the bath of instantaneous normal modes (INM) of the solvent as well as to the intramolecular bath responsible for relaxation in the isolated molecule. The couplings among the principal modes (the ones more directly involved in the ET process), mainly intramolecular, are taken into account exactly. The main inputs are weighted densities of states which can be, at least in principle, calculated. For those concerning the solvent we take advantage from the recent progresses in the INM approach to the description of the short time dynamics. We compute the ET line shape (i.e., the ET rate as a function of the electronic energy gap E) for some model cases, with one, two or more principal modes, investigating the influence of the solvent and of the temperature. The ET rates show a complex, but not dramatic, dependence on the solvent and are quite sensitive to the energy gap E. The temperature dependence is generally weak. The results seem to be in general agreement with recent experimental data on molecular systems exhibiting rapid ET.