Hydration numbers of biologically relevant divalent metal cations from ab initio molecular dynamics and continuum solvation methods

Hydration and, in particular, the coordination number of a metal ion is of paramount importance as it defines many of its (bio)physicochemical properties. It is not only essential for understanding its behavior in aqueous solutions but also determines the metal ion reference state and its binding energy to (bio)molecules. In this paper, for divalent metal cations Ca2+, Cd2+, Cu2+, Fe2+, Hg2+, Mg2+, Ni2+, Pb2+, and Zn2+, we compare two approaches for predicting hydration numbers: (1) a mixed explicit/continuum DFT-D3//COSMO-RS solvation model and (2) density functional theory based ab initio molecular dynamics. The former approach is employed to calculate the Gibbs free energy change for the sequential hydration reactions, starting from [M(H2O)2]2+ aqua complexes to [M(H2O)9]2+, allowing explicit water molecules to bind in the first or second coordination sphere and determining the most stable [M(H2O)n]2+ structure. In the latter approach, the hydration number is obtained by integrating the ion-water radial distribution function. With a couple of exceptions, the metal ion hydration numbers predicted by the two approaches are in mutual agreement, as well as in agreement with the experimental data.