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Effects of anharmonicity on diffusive-controlled symmetric electron transfer rates: From the weak to the strong electronic coupling regions.

The approach for the diffusive-controlled electron transfer rates [W. Zhu and Y. Zhao, J. Chem. Phys. 126, 184105 (2007)], which is modeled after the Sumi-Marcus theory, is applied to symmetric electron-transfer reactions in a solvent environment with anharmonic potential functions. The electron-transfer rates are evaluated using the quantum R-matrix theory for dealing with the intramolecular vibrational motions and imaginary-time split operator technique for solving the diffusive equations, thereby taking explicit account of the weak-to-strong electronic couplings. The effect of anharmonicity for both the solvent and intramolecular vibrational degrees of freedom are investigated. It is found that the anharmonicity of the intramolecular modes always enhances the rate while the solvent anharmonicity decreases the rate, compared with the harmonic modes. The possible mechanisms have been clarified.