Electron Transfer Transitions among Many Electronic States Coupled to Multidimensional Diffusive Nuclear Modes: A Supramolecular Triad System

A theory for the electron transfer (ET) transition rates among many electronic states taking into account multidimensional solvation dynamics is developed. An expression for the frequency-dependent ET rate is derived. The detailed balance principle for the frequency-dependent ET rate is proved for the first time. The theory is applied to ET which involves more than two electronic states, including the supramolecular triad system. The ET rate which depends on solvation timescale in a nonmonotonic way is found in the case where the transfer of an electron occurs from a donor to an acceptor states through an intermediate states, which is not fully equilibrated during the transfer. We explored the physical condition under which such a mechanism prevails. For this purpose useful approximations for the Green's function of the Smoluchowski equation in the frequency domain are developed.