Polyhedral structures with an odd number of vertices: nine-atom clusters and supramolecular architectures†
Abstract
The geometries of metal clusters and supramolecular architectures that contain nine metal atoms are analyzed within the framework of continuous shape measures (CShM). The most common polyhedra in nine coordinate complexes, the capped square antiprism and the tricapped trigonal prism, are also found among these families of compounds, even if much more scarcely. In addition, a variety of new shapes, not found among coordination polyhedra, can be identified and their proximity to the ideal geometries quantified. These include a linear chain, two types of trigonal columns, the planar regular enneagon, two-dimensional hexagonal and square grids, fragments of a close-packed structure, the triangular cupola, the tridiminished icosahedron or different fragments of the icosahedron. Among the nine-atom