  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.
