Electronic shell structure in simple metal clusters

The total energies of simple metal clusters (sodium, magnesium, and aluminium) containing up to 100 valence electrons are calculated in the spherical jellium approximation using the local-density-functional scheme. Because of the existence of electronic shell structure, there are abrupt changes in the total energy at certain cluster sizes. This behavior accounts for the peaks or steps found in the mass spectrum of sodium clusters. Predictions for the sizes of magnesium and aluminium clusters which should be abundant in the mass spectra are also discussed.