Electronic structure of gold, aluminum, and gallium superatom complexes

Abstract

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(CH${}_{3}{)}_{3}$)${}_{2}$)${}_{11}$, 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.