Electronic and structural properties of sodium clusters

We present an investigation of the structural and electronic properties of the sodium clusters Na_n and Na_n ⁺ with n≤8 and n=13, based on self-consistent pseudopotential local-spin-density calculations. In order to obtain the equilibrium geometries without imposing any symmetry constraint, we start from 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. We find that the clusters with up to five atoms have planar equilibrium geometries, the six-atom cluster is quasiplanar, and real three-dimensional structures only begin to occur when the number of atoms is greater than or equal to seven. We compare our results with recently obtained experimental data and find good agreement with the measured photoionization appearance potentials and the electron-spin-resonance spectra. Metallic bonding is the dominant feature of our calculated electronic structures and we show that the equilibrium geometries can be explained with a simple model having the delocalized nature of the metallic electrons and the Jahn-Teller effect as basic ingredients.