Hueckel Model for Small Metal Clusters. 1. Geometry, Stability, and Relationship to Graph Theory

摘要

The relative stabilities of alkali-like metal clusters, Mn and Mn (+) with 2 < or = n < or = 9, are calculated within the framework of the simple Huckel model. With the aid of graph theory, the binding energies for all possible Huckel structures are determined. With the exception of M5 and M6, (+) the Huckel model gives minimum energy structures which are the same as those predicted by recent Local-Spin-Density and Configuration Interaction calculations. Since the Huckel 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 Huckel 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. Keywords: METAL CLUSTERS, HUCKEL MODELS, GEOMETRY, STABILITY, GRAPH THEORY, BULK, LIMITS.