Diabatic free energy curves and coordination fluctuations for the aqueous $Ag+∕Ag2+$ redox couple: A biased Born-Oppenheimer molecular dynamics investigation Available to Purchase

Biased Born-Oppenheimer molecular dynamics simulations are performed to compute redox potential and free energy curves for the redox half reaction $Ag+→Ag2++e−$ in aqueous solution. The potential energy surfaces of reactant and product state are linearly coupled and the system transferred from the reduced state to the oxidized state by variation of the coupling parameter from 0 to 1. The redox potential is obtained by thermodynamic integration of the average ionization energy of $Ag+$⁠. Diabatic free energy curves of reduced $(R)$ and oxidized $(O)$ states are obtained to good statistical accuracy by reweighting and combining the set of biased distributions of the ionization energy. The diabatic free energy curves of $Ag+$ and $Ag2+$ are parabolic over a wide range of the reaction coordinate in agreement with the linear response assumption that underlies Marcus theory. However, we observe deviations from parabolic behavior in the equilibrium region of $Ag+$ and find different values for the reorganization free energy of $R$ (1.4 eV) and $O$ (0.9 eV). The computed reorganization free energy of $Ag2+$ is in good agreement with the experimental estimate of 0.9–1.2 eV obtained from photoelectron spectroscopy. As suggested by our calculations, the moderate deviation from linear response behavior found for $Ag+$ is likely related to the highly fluxional solvation shell of this ion, which exhibits water exchange reactions on the picosecond time scale of the present molecular dynamics simulation.