Rate-Constant Expressions for Nonadiabatic Electron-Transfer Reactions

Abstract
Expressions for the rate constants for nonadiabatic electron-transfer reactions are presented. These expressions are valid when the electronic coupling between the two redox sites is small and the energy surfaces for the initial and final states are harmonic with identical force constants. High- and low-temperature limiting forms of the rate equations are presented and closed-form expressions which are good approximations to the Franck-Condon sums appearing in these equations are described. Systems in which the electron transfer causes a displacement in one or more vibrational modes are considered. When several vibrational modes are “active,” the higher frequency modes have different effects on the rate constants in the normal and inverted free-energy regions. In the inverted region nuclear tunneling effects are large when hwf > 2kT. Under these conditions the rate has only a weak dependence on temperature and the rate constants can exhibit “quantum beats.” Nuclear tunneling effects are smaller in the normal region: the rate has a stronger dependence on temperature and quantum beats are not observed.

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