ENUMERATION OF THE ISOMERS OF THE GALLIUM ARSENIDE CLUSTERS (Ga,,,As,,)

Possible isomers of the gallium arsenide clusters of the formula Ga,,As, containing up to ten atoms and icosahedral clusters are enumerated. The possible parent polyhedrons up to ten vertices are constructed and then Pdlya’s theorem is applied to each polyhedron to calculate the generating functions for the enumeration of the isomers of gallium arsenide clusters of the formula Ga,,,As,. The distributions of clusters of Ga,,As, clusters observed by Smalley and co-workers using the laser vaporization method is explained. Specifically, generating functions obtained here together with the criteria of bond strengths explain the observed deviations from binomial distributions for smaller clusters.