Topological indices for nanoclusters

Nanoclusters create the possibility of designing novel properties and devices based on finite structures, with small dimensions. Clusters are of interest for catalytic, optical, biochemical, and structural characteristics. We examine clusters of icosahedral, cuboctahedral, and decahedral symmetry. Examples of these types of structures are shown from gold and platinum nanoclusters. Starting with only the atomic coordinates, we create an adjacency and distance matrix that facilitates the calculation of topological indices, including the Wiener, hyper-Wiener, reverse Wiener, Szeged, Balaban, and Kirchhoff indices. Some of these indices correlate to properties of the cluster. We find these indices exhibit polynomial and inverse behavior as a function of an increasing number of shells. Additionally, all the indices can be modeled with power law curves, as a function of N, the number of atoms. The magnitude of the exponent in the power law is associated with an index. The asymptotic limits of the topological indices are determined as a function of N. A conjecture previously published on the asymptotic behavior of the Wiener index is experimentally confirmed. (C) 2014 Elsevier B.V. All rights reserved.