Iconography of icosahedra. Calculations of metallic energies and relative stabilities of stereoisomers of binary icosahedral clusters

The first part of this paper provides a complete iconography of all possible stereoisomers of a binary icosahedron (a total of 96 for a noncentered A(n)B(12-n) (n = 0-12) and 192 for a centered A(n)B(13-n) (n = 0-13) icosahedron) by utilizing a simple symmetry-based algorithm. The second part of this paper deals with the relative stabilities of these stereoisomers for a given combination of A and B atoms. A simple theory, based on the Lennard-Jones potential and cohesive energies of transition metals, has been developed in order to model metallic bonding in a metal cluster. This provides a relative measure of the strengths of metal-metal bonds in a; mixed-metal cluster and hence the relative energetic stabilities of various stereoisomers. The utility of this simple theory is illustrated by applying it to all possible stereoisomers of binary icosahedral clusters A(n)B(13-n) (n = 0-13) containing the Au-Ag, Au-Ni, and Au-Pt combinations. Considerable insight into metal-metal interactions in mixed-metal systems can be gained by detailed analysis of the contributions-covalent vs ionic-to the metallic bonding energy. Indeed, on the basis of the calculated energies, two simple rules-the Strong-Bond rule and the Hetero-Bond rule-were formulated. These rules are useful in predicting the relative stabilities of these stereoisomers, thereby furthering the understanding of site preference in multimetallic systems: including mixed-metal clusters, metal alloy systems, multimetallic catalysts, etc.