Electron transfer rates from time-dependent correlation functions. Wavepacket dynamics, solvent effects, and applications

The golden-rule expression for the non-adiabatic electron-transfer rate constant in donor/acceptor system is analyzed using a Fourier (time-dependent) representation. The rate constant is written in terms on an evolving overlap of wavepackets on initial and final state potential-energy surfaces. By the following the explicit time-dependence of these functions, we can obtained both standard results of electron-transfer theory for the specific case of a standard polaron-type model (including inverted-region behavior, temperature dependence, nuclear tunneling effects, energy sharing) and some important generalizations, including situations of breakdown of the Condon approximation, analysis of the effects of the frequency changes, and simplifications of the relevant vibrational modes due to solvent, to intra-molecular vibrations, or to both. The correlation-function method is briefly described, and results of a number of calculations are discussed. Analysis includes the effect of inhomogeneous broadening and energy flow into solvent and vibrational degrees of freedom. Analysis of two particular cases, subjects of recent elegant experimental investigation, are included to show the applicability of the technique.