Redox potentials of small inorganic radicals and hexa-aquo complexes of first-row transition metals in water: a dft study based on the grand canonical ensemble

The potentials of redox systems involving nitrogen, oxygen, and metal ions of the first-row transition series have been computed according to the general approach of the grand canonical ensemble, which leads to the equilibrium value of the reduction potential via a (complete) sampling of configuration space at a given temperature. The approach is a single configuration approach in the sense that identical molecular structures are sampled for both the oxidized and reduced species considered in water solution. In this study, the solute and a cluster of 11-12 water molecules are treated explicitly at the same level of theory and embedded in a continuum solvent. The molecular energies are computed in the framework of the density functional theory. Our approach is basically different from the approach based on the ThermoDynamic Cycle involving gas-phase calculations of the electron affinity of the oxidized species, corrected by the differential hydration energy (obtained from continuum solvent models only) between oxidized and reduced forms. The calculated redox potentials are in agreement with the available experimental data much closer than other results so far presented in the literature. Our results are very satisfactory also in the case of the 3+/2+ redox states of the first-row transition metals, i.e., systems with a high positive charge for which enhanced effects of the solvent are expected.