Solvent relaxation dynamics and electron transfer

In this paper we explore the effects of medium dynamics on activationless and inverted-region electron transfer (ET), when medium-induced dynamics is slow on the time scale of the electronic processes. ET dynamics, with electron-nuclear coupling to the medium modes, was characterized in terms of incoherent population decay of vibronic states in the initial donor-acceptor manifold, which is characterized by nonadiabatic, energy (E)-dependent, microscopic ET rates, k(E). These k(E)'s are determined by average Franck-Condon densities (AFDs), which were evaluated by quantum and classical formalisms, with model calculations being performed for multimode harmonic systems with displaced potential surfaces. In spite of the intrinsic limitations of the classical AFDs, which do not account for mode specificity and nuclear tunneling effects, the classical Franck-Condon factors provide a good description of the E dependence of the microscopic ET rates. For activationless ET we show that k(E)∝(E+nε{lunate})^{- 1 2}, where nε{lunate} is the zero point energy, implying a weak energy dependence of k(E). Accordingly, the averaged experimental activationless ET rates exhibit a weak variation between the limits of slow medium-induced relaxation and that of fast medium-induced dynamics. Subsequently, the theory of k(E) was extended to include the effects of ET-induced excitations of high-frequency intramolecular vibrational modes, providing a unified description of the weak E dependence of k(E) in the activationless and inverted regions. We predict that for activationless and inverted-region ET the experimental ET rates are only weakly dependent on the characteristics of medium relaxation dynamics, and can be appreciably higher than the solvent-controlled values (i.e., the reciprocal values of the medium relaxation time induced by a constant charge distribution). Our analysis provides an adequate explanation for recent experimental observations of ultrafast (k=(1 ps)^-1-(100 fs)^-1) activationless and inverted-region ET, which apparently violate the predictions of solvent-controlled ET theory.