Electron transfer (ET) reactions are one of the most important processes in chemistry and biology. Because of the quantum nature of the processes and the complicated roles of the solvent, theoretical study of ET processes is challenging. To simulate ET processes at the electronic level, we have developed an efficient DFT QM/MM approach that uses the fractional number of electrons as the order parameter to calculate the redox free energy of ET reactions in solution. We applied this method to study the ET reactions of the aqueous metal complexes and . The calculated oxidation potentials, 5.82 eV for Fe(II/III) and 5.14 eV for Ru(II/III), agree well with the experimental data, 5.50 eV and 4.96 eV, for iron and ruthenium, respectively. Furthermore, we have constructed the diabatic free energy surfaces from histogram analysis based on the molecular dynamics trajectories. The resulting reorganization energy and the diabatic activation energy also show good agreement with experimental data. Our calculations show that using the fractional number of electrons (FNE) as the order parameter in the thermodynamic integration process leads to efficient sampling and validate the ab initio QM/MM approach in the calculation of redox free energies.
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