Calculation of redox potentials and pK(a) values of hydrated transition metal cations by a combined density functional and continuum dielectric theory

Density functional and continuum dielectric theories have been combined to calculate molecular properties such as hydration enthalpies, redox potentials, and absolute pK(a) values of transition metal cations in solution. The discrete cluster model, which is treated explicitly by density functional theory, includes six waters in the first hydration shell and another twelve waters in the second shell. The solvent reaction field is obtained from a finite-difference solution to the Poisson-Boltzmann equation and is coupled to the nonlocal density functional calculation in a self-consistent way. The calculated hydration enthalpies are 409, 1073, 431, and 1046 kcal/mol for Mn2+, Mn3+, Fe2+, and Fe3+, respectively, comparing fairly well to the experimental measurements of 440, 1087, 465, and 1060 kcal/mol. The calculated redox potentials for the Mn2+/Mn3+ and Fe2+/Fe3+ pairs are 1.59 and 1.06 V, respectively, in good agreement with the experimental values of 1.56 and 0.77 V. The computed absolute pK(a) values, 14.0, -6.5, 9.0, and -4.0 for Mn2+, Mn3+, Fe2+, and Fe3+, respectively, deviate significantly from the experimental results of 10.6, 0.1, 9.5, and 2.2 but show the proper behavior with changes in oxidation state and metal type. The calculated redox potentials and pK(a) values appear to converge toward the experimental data with increasing size of the cluster models. For such highly charged cations, the second hydration shell in the cluster model is indispensable, since this buffer shell retains strong hydrogen bonds and electron transfer between the inner and outer shells as well as the solute-solvent dispersion interaction.