THE MATHEMATICAL-MODELING OF CLUSTER GEOMETRY

Calculations of minimum energy configurations for aggregates of up to forty atoms, commonly referred to as clusters, are presented. In contrast to previous studies, random initial configurations have been optimised to find the lowest energy structure for a given number of atoms. Three different two-body, bireciprocal potential functions were used in these calculations and in the case of the Lennard-Jones potential, previously calculated results have been confirmed. New structures obtained using softer potentials are also presented. Minimum energy structures of small clusters containing two different types of atoms have also been calculated, and the relationship between the geometry of a cluster and the relative sizes of its constituent atoms examined.