The Hückel model for small metal clusters. I. Geometry, stability, and relationship to graph theory

Abstract

The relative stabilities of alkali-like metal clusters, Mn and M+n with 2≤n≤9, are calculated within the framework of the simple Hückel model. With the aid of graph theory, the binding energies for all possible Hückel structures are determined. With the exception of M+5 and M+6 , the Hückel model gives minimum energy structures which are the same as those predicted by recent local-spin-density and configuration interaction calculations. Since the Hückel method is independent of the mechanical details of the bonding, a close connection is inferred between a cluster’s stability and its topology. In the paper following this one, the Hückel results are extended to include absolute atomization energies and ionization potentials. In addition, it is shown that cluster energies may be quantitatively extrapolated to the bulk phase.