Dielectric friction and the transition from adiabatic to nonadiabatic electron transfer. I. Solvation dynamics in Liouville space

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Abstract
A microscopic theory for electron transfer rates in a polar medium, which interpolates continuously from the adiabatic to the nonadiabatic limits, is developed. Both static (polarity) interactions, which affect the reaction energetics and dynamic (friction) effects, are incorporated using a macroscopic solvation coordinate, whose dynamics and statistical properties are related to the entire frequency and wave vector dependent dielectric function of the solvent ε(k,ω). The present approach is based on using an expansion of the density matrix in Liouville space and utilizing the analogy with the calculation of nonlinear optical line shapes. A new criterion for adiabaticity is derived, and the role of the solvent longitudinal dielectric relaxation in inducing the crossover from the nonadiabatic to the adiabatic regimes is clarified. The applicability of a Landau–Zener‐type resumation for the rate is critically analyzed. The origin of the fractional power dependence of the rate on the solvent time scale, observed in several electron transfer and isomerization reactions, is discussed.