SOLVENT RELAXATION DYNAMICS AND ELECTRON-TRANSFER

In this paper we explore the effects of medium dynamics on activationl ess and inverted-region electron transfer (ET), when medium-induced dy namics is slow on the time scale of the electronic processes. ET dynam ics, with electron-nuclear coupling to the medium modes, was character ized in terms of incoherent population decay of vibronic states in the initial donor-acceptor manifold, which is characterized by nonadiabat ic, energy (E)-dependent, microscopic ET rates, k(E). These k(E)'s are determined by average Franck-Condon densities (AFDs), which were eval uated by quantum and classical formalisms, with model calculations bei ng performed for multimode harmonic systems with displaced potential s urfaces. In spite of the intrinsic limitations of the classical AFDs, which do not account for mode specificity and nuclear tunneling effect s, the classical Franck-Condon factors provide a good description of t he E dependence of the microscopic ET rates. For activationless ET we show that k(E) is-proportional-to (E+nepsilon)-1/2, where ne is the ze ro point energy, implying a weak energy dependence of k(E). Accordingl y, the averaged experimental activationless ET rates exhibit a weak va riation 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-freq uency intramolecular vibrational modes, providing a unified descriptio n 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 characteristic s of medium relaxation dynamics, and can be appreciably higher than th e solvent-controlled values (i.e., the reciprocal values of the medium relaxation time induced by a constant charge distribution). Our analy sis provides an adequate explanation for recent experimental observati ons of ultrafast (k = (1 ps)-1-(100 fs)-1) activationless and inverted -region ET, which apparently violate the predictions of solvent-contro lled ET theory.