Kinetics and thermodynamics of electron transfer in Debye solvents: An analytical and nonperturbative reduced density matrix theory

A nonperturbative electron transfer rate theory is developed based on the reduced density matrix dynamics, which can be evaluated readily for the Debye solvent model without further approximation. Not only does it recover for reaction rates the celebrated Marcus' inversion and Kramers' turnover behaviors, the present theory also predicts for reaction thermodynamics, such as equilibrium Gibbs free-energy and entropy, some interesting solvent-dependent features that are calling for experimental verification. Moreover, a continued fraction Green's function formalism is also constructed, which can be used together with Dyson equation technique, for efficient evaluation of nonperturbative reduced density matrix dynamics.