Quantum-chemical simulations of the hydration of Pb(II) ion: structure, hydration energies, and p K a 1 value

Thermodynamic and structural aspects of the hydration of Pb(II) ions were explored based on DFT calculations combined with the supermolecular/continuum solvent model. Hydration of Pb(II) was considered as the formation of Pb(H2O)n2+ aqua complexes (n=6−9) from the gas phase Pb(II) ion. Hexa- and hepta-aqua Pb(II) complexes were shown to exhibit the hemidirected symmetry, while those containing eight and nine water molecules are characterized by the holodirected symmetry. The calculations showed that because Pb(H2O)n2+ complexes with six to nine water molecules have comparable thermodynamic stabilities, such complexes are likely to coexist in aqueous solutions. The deprotonation of Pb(H2O)n2+ complexes was shown to result in the formation of the mono-hydroxo complex [Pb(H2O)4OH]+. The pKa1 value determined for this reaction (7.58 for Pb(H2O)62+) was close to the experimental value of 7.61 used in recent models of aquatic equilibria. The density functional method ω-B97X(PCM-UAO) in combination with the atomic basis set 6-311++G(d,p) for O and H and the small-core electron effective pseudopotential (ECP) with the aug-cc-pvdz-PP basis set for Pb can be recommended for such calculations.