Oscillations and non-exponential decays in electron-transfer reactions

Mechanisms for oscillations and non-exponential population decays in electron-transfer reactions are discussed. A non-Markovian equation with time-retarded rate kernels is derived using the spin-boson model. Three kinds of spectral distributions for the heat bath are considered: the Debye model with an optical phonon mode centered at zero frequency, the low frequency classical modes, and the high frequency quantum modes. Results of numerical simulation are illustrated to demonstrate the usual exponential decays as well as the non-exponential decays and the rare behavior with damped sinusoidal oscillations in electron-transfer reactions.