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Electron transfer processes in Debye solvents are studied using a spectral analysis method recently proposed. Spectral structure of a nonadiabatic two-state diffusion equation is investigated to reveal various kinetic regimes characterized by a broad range of physical parameters; electronic coupling, energy bias, reorganization energy, and solvent relaxation rate. Within this unified framework, several kinetic behaviors of the electron transfer kinetics, including adiabatic Rabi oscillation, crossover from the nonadiabatic to adiabatic limits, transition from the incoherent to coherent kinetic limits, and dynamic bath effect, are demonstrated and compared with results from previous theoretical models. Dynamics of the electron transfer system is also calculated with the spectral analysis method. It is pointed out that in the large reorganization energy case the nonadiabatic diffusion equation exhibits a nonphysical behavior, yielding a negative eigenvalue. [ABSTRACT FROM AUTHOR]

A spectral analysis method is proposed to characterize multiple time scales in electron transfer processes, including vibrational relaxation, electronic coherence, activated curve crossing, or barrier crossing. Within this unified framework, observed rate behavior, biexponential and multiexponential decay, and population recurrences and oscillations are different components of the same kinetic spectrum; thus, several existing theoretical models, developed for limiting cases of electron transfer, can be analyzed, tested, and extended. In particular, the rate constant extracted from the analysis does not saturate as the electronic coupling increases but shows a crossover from the nonadiabatic to adiabatic limits, and the kinetic spectrum in the large coupling regime reveals the nature of the localization-delocalization transition as the consequence of two competing mechanisms. Though the analysis is presented in the context of electron transfer, this approach provides a different perspective for understanding dissipative dynamics and hence can be applied to study condensed-phase laser spectroscopy, quantum coherence control, energy transfer, and other charge transfer processes. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]