  The electron transfer kinetics of mixed-valence systems is studied via
solving the eigen-structure of the two-state non-adiabatic diffusion operator
for a wide range of electronic coupling constants and energy bias constants.
The calculated spectral structure consists of three branches in the
eigen-diagram, a real branch corresponding to exponential or multi-exponential
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 eigen-solution to the
non-equilibrium 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.
