Distance Dependence of Electron-Transfer Reactions in Organized Systems: The Role of Superexchange and Non-Condon Effects in Photosynthetic Reaction Centers

Extremely long distance electron transfer is observed in some photosynthetic reaction centers. For several charge recombination reactions, the rate appears to fall off much more slowly with distance than expected from simple models. A general model is proposed for sequential electron-transfer reactions, which often occur in biological systems, in which each ion pair in the forward direction acts as the mediating state for recombination of the next ion-pair in the sequence. Inclusion of these mediating states in a conventional superexchange formalism improves the agreement between theory and experiment, but the results are far from satisfactory. Because the energy gap between the reactant and mediating state is small for some of these reactions, the next level of analysis is to explicitly consider non-Condon effects by using a two-state model. This gives a substantial improvement in the agreement between theory and experiment. We conclude that (1) superexchange coupling is likely quite significant for the long-distance charge recombination reactions in bacterial RCs at cryogenic temperature, (2) the coupling provided by low-lying intermediates states is often accompanied by significant non-Condon effects within a two-state model, and (3) both of these effects can significantly alter the dependence of the rate on distance. Implications of these results for the initial ultrafast charge separation step are discussed.