How icosahedral are icosahedral clusters?

Abstract

Icosahedral symmetry, not contemplated within the crystallographic space groups, is nevertheless present to a high degree of perfection in a variety of clusters, in molecular, ionic, covalent or metallic structures. The application of continuous shape measures to those structures allows for a quantification of the degree of icosahedral symmetry present in each case, a first necessary step for a deeper discussion of the factors that favor the adoption of the icosahedron as a stable structural motif. Examples analyzed include boranes and carbaboranes, main group, rare earth or transition metal clusters, ligand-bridged polynuclear complexes and sets of donor atoms in mono- or polynuclear complexes. Specific examples are found of structures that appear along the minimal distortion pathways from the icosahedron to the cuboctahedron or the anticuboctahedron.