Binary icosahedral clusters: Atom and electron counting rules

Abstract

The first part of this paper deals with the enumeration of all possible stereoisomers (or polytypes) of a binary (two-colored) icosahedron (either noncentered or centered) via Polya’s theorem. The numbers of achiral and chiral structures for each combination of the two types of atoms (or colors) A and B are determined. In cluster chemistry, A and B may represent two different kinds of atoms (e.g., main-group elements vs transition metals) in a heteronuclear cluster, two different ligand environments in a homonuclear cluster, or atoms and holes (vacant sites) in an icosahedral cluster with missing vertices. The second part deals with the electronic requirements of binary icosahedral clusters where A and B may represent main-group elements and transition metals, or, atoms and holes. Significantly different electron counts are observed for centered vs noncentered icosahedral clusters, depending upon the nature of the interstitial atom. Thus, icosahedral clusters can be classified into four broad categories according to their electron counts: Type I: the majority are those with 13 electron pairs as represented by noncentered icosahedral clusters, or those centered with main-group elements or early transition metals as the interstitial atom; Type II: those with more than 13 electron pairs as exemplified by centered icosahedral clusters with late transition metals as the interstitial atom; and Types III and IV: those with less than 13 electron pairs as observed for centered Au icosahedral clusters. The atom and electron counting rules developed are rationalized in terms of molecular orbital theory. The utilities of the atom and electron counting rules in systematizing structural and spectroscopic data of icosahedral clusters (in both solid-state and gas-phase) as well as in rationalizing the variations of the electron counts in different icosahedral cluster systems are discussed.