Two-electron transfer reactions involving three paraboloidal potential surfaces in solvents with multiple solvation time scales

The effect of solvent nuclear relaxation dynamics on the rate of two-electron transfer reaction is investigated. We present here a generalized treatment of the Zusman and Beratan model of two-electron transfer reaction using a theoretical scheme that starts from the Liouville equation of motion for the electronic population wave packets to obtain the transfer rates following projection operator formalism. This generalization enables us to treat the three free energy surfaces (three surfaces for D–A, D+–A−, and D+2–A−2 donor–acceptor pairs) involved in such reactions on an equal footing such that the rates for each one- and two-electron transfer step can be obtained when all three diabatic surfaces are present in the system with nonzero electronic coupling elements between them. The reaction takes place on a two-dimensional potential energy surface with two coordinates representing the solvent polarization. The dynamics are governed by overdamped diffusion along these polarization coordinates with differen...