Geometrical Characteristics of Regular Polyhedra: Application to EXAFS Studies of Nanoclusters

EXAFS data modeling of nanoparticles can be done at a very high level of detail if regular polyhedral geometries are considered as possible structural models. Such geometries can be characterized by unique sequence of indices (coordination numbers) of the first few coordination shells that serve as a signature of a shape, size, morphology and packing model of atoms in the cluster. We wrote a suite of programs for cluster geometry generation and its pair radial distribution function analysis. The programs generate x,y,z coordinates and calculate the coordination numbers of the corresponding clusters for any order of a large number of regular polyhedra. We present the results for the first few nearest neighboring shells in the icosahedral, cuboctahedral, hcp structures for the small, 10–1000 atom clusters.