Electronic shell structure in Ga12 icosahedra and the relation to the bulk forms of gallium

The electronic structure of known cluster compounds with a cage-like icosahedral Ga(12) centre is studied by first-principles theoretical methods, based on density functional theory. We consider these hollow metalloid nanostructures in the context of the polymorphism of the bulk, and identify a close relation to the α phase of gallium. This previously unrecognised connection is established using the electron localisation function, which reveals the ubiquitous presence of radially-pointing covalent bonds around the Ga(12) centre--analogous to the covalent bonds between buckled deltahedral planes in α-Ga. Furthermore, we find prominent superatom shell structure in these clusters, despite their hollow icosahedral motif and the presence of covalent bonds. The exact nature of the electronic shell structure is contrasted with simple electron shell models based on jellium, and we demonstrate how the interplay between gallium dimerisation, ligand- and crystal-field effects can alter the splitting of the partially filled 1F shell. Finally, in the unique compound where the Ga(12) centre is bridged by six phosphorus ligands, the electronic structure most closely resembles that of δ-Ga and there are no well-defined superatom orbitals. The results of this comprehensive study bring new insights into the nature of chemical bonding in metalloid gallium compounds and the relation to bulk gallium metal, and they may also guide the development of more general models for ligand-protected clusters.