Ionic and electronic structure of sodium clusters up toN=59

We determined the ionic and electronic structures of sodium clusters with even electron numbers and 2 to 59 atoms in axially averaged and three-dimensional density functional calculations. A local, phenomenological pseudopotential that reproduces important bulk and atomic properties and facilitates structure calculations has been developed. Photoabsorption spectra have been calculated for ${\mathrm{Na}}_2,$ ${\mathrm{Na}}_8,$ and ${\mathrm{Na}}_9^{+}$ to ${\mathrm{Na}}_{59}^{+}.$ The consistent inclusion of ionic structure considerably improves agreement with experiment. An icosahedral growth pattern is observed for ${\mathrm{Na}}_{19}^{+}$ to ${\mathrm{Na}}_{59}^{+}.$ This finding is supported by photoabsorption data.