Unified expression for the rate constant of the bridged electron transfer derived by renormalization

Electron transfer (ET) from a donor to an acceptor through an energetically close intermediary state on a midway molecule is a process found often in natural and artificial solar-energy capturing systems such as photosynthesis. This process has often been thought of in terms of opposing "superexchange" and "sequential or hopping" mechanisms, and the recent theory of Sumi and Kakitani (SK) [J. Phys. Chem. B 105, 9603 (2001)] has shown an interpolation between these mechanisms. In their theory, however, dynamics governing the most interesting intermediary region between them has artificially been introduced by phenomenologies. The dynamics is played by decoherence among electronic states, their decay, and thermalization of phonons in the medium. The present work clarifies the dynamics on a microscopic basis by means of renormalization in electronic coupling among the states, and gives a complete unified expression of the rate constant of the ET. It merges to that given by the SK theory in the semiclassical approximation for phonons interacting with an electron transferred.