Coordination of lead(ii) in solvated clusters with water [Pb(H2O)1–8]2+: insights from relativistic effects, energy analysis, molecular orbitals, and electron density

Abstract

Understanding the nature of the interaction between the lead(II) ion, Pb²⁺, and water molecules is crucial to describe the stability and chemical behaviour of structures formed during solvation, as well as the conditions that favour the coordination or hydrolysis of Pb²⁺. In this work, we studied relativistic effects in the solvation process of Pb²⁺ using the zeroth-order regular approximation (ZORA) Hamiltonian at both scalar (SR-ZORA) and spin–orbit (SO-ZORA) levels. We analysed the potential energy surface of the lead ion coordinated with up to eight water molecules in order to identify the motifs that can be characterized as true minima. We applied several methodologies for studying the energies and interactions of the clusters, such as energy decomposition analysis (EDA), molecular orbital analysis, quantum theory of atoms in molecules (QTAIM) analysis, and natural bond orbital (NBO) analysis. The inclusion of relativity at a higher level (spin–orbit) is mandatory for solvation and binding energy calculations, changing the energetic ordering of the [Pb(H₂O)_n]²⁺ clusters. We found that at least two water molecules are needed to initiate deprotonation and form the OH⁻ and H₃O⁺ pair, thereby starting the hydrolysis by Pb²⁺. In addition, we examined the influence of the 6s² inert pair in the formation of holodirected and hemidirected clusters. According to the geometric parameters, the stereochemistry of the [Pb(H₂O)_2–8]²⁺ clusters is mainly influenced by the relativistic effects stabilising the 6s² lone pair of the lead ion, removing it from the HOMO, which reduces its stereochemical activity.