Computational electrochemistry: The aqueous Ru³⁺|Ru²⁺ reduction potential

We present results of density functional calculations for the standard reduction potential of the Ru³⁺|Ru²⁺ couple in aqueous solution. The metal cations are modeled as [Ru(H₂O)_n] ^q+ surrounded by continuum solvent (q = 2, 3; n = 6, 18). The continuum model includes bulk electrostatic polarization as well as atomic surface tensions accounting for the deviation of the second or third hydration shell from the bulk. After consideration of 37 density functionals with 5 different basis sets, it has been found that hybrid and hybrid meta functionals provide the most accurate predictions for the [Ru(H₂O) _n]^q+ geometries and for the corresponding reduction potential in comparison with available experimental data. The gas-phase ionization potentials of [Ru(H₂O)_n]²⁺ calculated by density functional theory are also compared to results of ab initio computations using second-order Møller-Plesset perturbation theory. The difference in solvation free energies of Ru³⁺ and Ru ²⁺ varies from -10.56 to -10.99 eV for n = 6 and from -6.83 to -7.45 eV for n = 18 depending on the density functional and basis set quality. The aqueous standard reduction potential is overestimated when only the first solvation shell is treated explicitly and is underestimated when the first and second solvation shells are treated explicitly.