How to Identify Lone Pairs, Van der Waals Gaps, and Metavalent Bonding Using Charge and Pair Density Methods: From Elemental Chalcogens to Lead Chalcogenides and Phase-Change Materials

Lone pairs explain the structure of many molecular solids, as well as the chain-like or layered structures encountered in many chalcogenide crystals. Such chalcogenides have enabled a plethora of applications, including phase-change memories, thermoelectrics, topological insulators or photoconductors. In many of these, lone pairs also are invoked to explain the unconventional material properties. The presence of so-called van der Waals gaps in layered chalcogenides and their low thermal conductivity have also been linked to lone pairs. However, for some of these systems, a second view of bonding has been proposed, where atoms are held together across the interlayer spacing by shared electrons. To clarify this situation, herein, several systems for which lone pairs have been frequently emphasized are reinvestigated theoretically. By comparing the charge and electron localization analysis in terms of a Hartree-Fock-like pair density obtained from Kohn-Sham density functional theory (KS-DFT), it is verified that the structure of several chalcogenides is governed by the presence of lone pairs, whereas others are not. As an example, crystalline Se is demonstrated to form a structure with two covalent bonds and a lone pair, whereas metavalenty bonds are the essential characteristics of crystalline Sb, crystalline Te being an intermediate case.