The effect of electron statistics on the ionization potential of small metal clusters

The ionization potential of a small metal cluster, as a function of N, the number of atoms in the cluster, shows an even-odd or sawtooth variation. We show that this effect, due to electron statistics, can be described using simple bulk-metal models. We analyze it both with the electron gas model and the electron spin-density functional model in the spherical jellium approximation. Both models predict that the even-odd part of the ionization potential varies as 1/N.