Throwing jellium at gallium--a systematic superatom analysis of metalloid gallium clusters

Motivated by recent developments in the field of so-called "superatom complexes", as well as by the challenge posed to theory in understanding the many polymorphs of gallium, we analyse the electronic structure of several previously synthesised ligand-protected gallium clusters and their model derivatives using density functional theory. The calculated electron charge densities within the respective gallium cores are shown to be consistent with the jellium superatom model, exhibiting well-defined global spherical shells and wide HOMO-LUMO gaps--indicating enhanced chemical stability. It is demonstrated that the HOMO-LUMO gaps are widened due to the presence of covalent gallium-ligand bonds and a closed electron shell (i.e. electron "magic" number). The tendency of retaining a filled electron shell is shown to be particularly apparent in two closely-related clusters, with one derived from the other simply via substituting a doubly negative charge by a single protective moiety containing a lone electron pair. This analysis verifies that spherical electron shells can influence the chemical stability of ligand-protected gallium clusters, and also demonstrates the significant stabilising effects of metal-ligand interactions-something that is poorly accounted for in the current superatom model.