We determined the ionic and electronic structures of sodium clusters with e
ven electron numbers and 2 to 59 atoms in axially averaged and three-dimens
ional density functional calculations. A local, phenomenological pseudopote
ntial that reproduces important bulk and atomic properties and facilitates
structure calculations has been developed. Photoabsorption spectra have bee
n calculated for Na-2, Na-8, and Na-9(+) to Na-59(+). The consistent inclus
ion of ionic structure considerably improves agreement with experiment. An
icosahedral growth pattern is observed for Na-19(+) to Na-59(+). This findi
ng is supported by photoabsorption data.