Electronic coherence in mixed-valence systems: Spectral analysis

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.