Functional Mode Electron-Transfer Theory

A solid approach has been developed to ascertain the correlation of electron transfer with molecular vibration in a quantitative manner. Specifically, the reaction coordinate is identified by maximizing the linear Pearson's correlation coefficient between atomic displacement and the diabatic energy gap. In the limit of fast molecular vibration, the rates of electron transfer driven by multiple vibrational modes have been derived respectively under the strong and weak vibronic coupling conditions. Our functional mode electron-transfer theory is then justified by investigating the electron transfer of a betaine-30 molecule from its first excited state to its ground state when being solvated in glycerol triacetate. Among the 210 available vibrational modes of betaine-30, only seven are essential to the electron transfer by cumulatively accounting for more than 60% of the total reorganization energy. Because all essential vibrational modes are significantly faster than thermal fluctuation, the electron transfer is primarily driven by intramolecular quantum tunneling. Interestingly, the calculated reaction driving force of 1.95 eV is substantially greater than the reorganization energy of 0.58 eV, placing the reaction in the inverted Marcus region. Nevertheless, a sizable Franck-Condon factor of 1.58 × 10(-3) eV(-1) is still achieved due to the large vibronically weighted zero-point energy of the essential vibrational modes. After determining the electronic coupling strength as 0.14 eV by the constrained density functional theory, the overall electron-transfer rate at 300 K is found to be 0.30 ps(-1), which agrees nearly perfectly with experimental values.