Free energy of oxidation of metal aqua ions by an enforced change of coordination

A new thermodynamic integration method is introduced to calculate the free-energy difference between the reactant (reduced species) and product (oxidized species) of an electrochemical half reaction. The redox reaction is enforced by a controlled change of a suitable structural characteristic (order parameter) of the solvent coordination. The potential energy surface (PES) of the redox system is constructed from the PESs of the reduced and oxidized states shifted relative to each other by a constant energy mu. As shown in a previous publication (Tavernelli, I.; Vuilleumier, R.; Sprik, M. Phys. Rev. Lett. 2002, 88, 213002), this potential can be interpreted as the effective potential experienced by the nuclear degrees of freedom in an open system exchanging electrons with a reservoir at fixed electronic chemical potential mu. The method is applied to the half reaction Ag-aq(+) --> Ag-aq(2+) + e(-) using constrained Car-Parrinello molecular dynamics simulation. The order parameter (constraint variable) is chosen to be the oxygen coordination number of the first solvation shell, which is 4 for Ag-aq(+) and 5 for Ag-aq(2+). We show that if the external chemical potentialu is set to the reaction free energy obtained for the same model system using an alternative grand canonical scheme then the reduced species can be oxidized at zero cost in reversible work, confirming the consistency of our grand canonical method.