Electronic structure of gold, aluminum, and gallium superatom complexes

Using ab initio computational techniques on crystal determined clusters, we report on the similarities and differences of Al(50)(C(5)(CH(3))(5))(12), Ga(23)(N(Si(CH3)(3))(2))(11), and Au(102)(SC(7)O(2)H(5))(44) ligand-protected clusters. Each of the ligand-protected clusters in this study shows a similar stable character which can be described via an electronic shell model. We show here that the same type of analysis leads consistently to derivation of a superatomic electronic counting rule, independently of the metal and ligand compositions. One can define the cluster core as the set of atoms where delocalized single-angular-momentum-character orbitals have high weights using a combination of Bader analysis and evaluation of Khon-Sham orbitals. Subsequently, one can derive the nature of the ligand-core interaction. These results yield further insight into the superatom analogy for the class of ligand-protected metal clusters.