Electronic and structural properties of sodium clusters

The structural and electronic properties of Na_n and Na⁺_n clusters (n ≤ 8 and n = 13) are studied using the pseudopotential and the local-spin-density approximations. In order to obtain the equilibrium geometries, we start with randomly generated cluster geometries and let them relax under the action of the forces on the atoms, which are derived from the Hellmann-Feynman theory. The clusters with five atoms or less have planar equilibrium geometries built from triangles, whereas the larger clusters are three dimensional with interatomic distances in a given cluster almost equal. The bonding in the sodium aggregates is metallic and there is no sign of dimerization, as previously reported. The influence of the electronic structure and the Jahn-Teller effect on the equilibrium geometries are discussed in detail. The calculated adiabatic ionization potentials agree well with the experimental values and the equilibrium geometries are consistent with the known ESR measurements.