An algorithm searching for point subsets with applications to the analysis of the atomic structure of modelled clusters

This article presents the results of efforts to develop a method for analyzing the atomic structure of clusters obtained in computer simulations. The method is based on looking for coordination polyhedra in the clusters and constructing a graph to describe their relative positions. It requires us to calculate topological invariants of this graph in order to compare them with the physical and chemical properties of the corresponding clusters. To find coordination polyhedra, we propose an algorithm searching for point subsets using a template. We apply the method to clusters of various form, structure, and composition. We suggest several simple graph invariants reflecting the structure of clusters. The algorithm is implemented in a program which enables us to find coordination polyhedra, construct the corresponding graph, and calculate the invariants.