Metal to insulator transitions in clusters

The strict criterion for metallicity, a finite density of states (DOS) at the Fermi energy (E_F), cannot be applied to clusters because energy levels are always discrete in a system of finite size. We propose an alternative definition whereby clusters can be considered metallic when the gap between occupied and unoccupied states at E_F is consistently smaller than or equal to the Kubo band gap S. We use the experimental findings of photoelectron spectroscopy of anionic clusters to analyze band gaps of various cluster families. Monovalent clusters (alkali and noble metals) grossly follow the shell structure pattern, producing band gaps smaller than δ for most cluster sizes, with some exceptional sizes exhibiting electronic shell closure or symmetry-induced band gaps. Among the bivalent metals, only mercury shows consistent band gap closure with increasing cluster size, that is a simple insulator-metal transition. Other bivalent elements such as Zn and Mg exhibit a much more complicated behavior. We also briefly discuss complex cluster families such as aluminum and transition metals.