The electron transfer kinetics of mixed-valence systems is studied via solving the eigenstructure of the two-state nonadiabatic diffusion operator for a wide range of electronic coupling constants and energy bias constants. The calculated spectral structure consists of three branches in the eigendiagram: a real branch corresponding to exponential or multiexponential decay, and two symmetric branches corresponding to population oscillations between donor and acceptor states. The observed electronic coherence is shown as a result of underdamped Rabi oscillations in an overdamped solvent environment. The time evolution of electron population is calculated by applying the propagator constructed from the eigensolution to the nonequilibrium initial preparation, and it agrees perfectly with the result of a direct numerical propagation of the density matrix. The resulting population dynamics confirms that increasing the energy bias destroys electronic coherence.
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