Quantum-chemical simulations of the hydration of Pb(II) ion: structure, hydration energies, and pK 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(HO) 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(HO) complexes with six to nine water molecules have comparable thermodynamic stabilities, such complexes are likely to coexist in aqueous solutions. The deprotonation of Pb(HO) complexes was shown to result in the formation of the mono-hydroxo complex [Pb(HO)OH]. The pK value determined for this reaction (7.58 for Pb(HO)) 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. Graphical abstract Structures of Pb(II) ions with varying numbers of water molecules in the inner hydration shell.