Structural evolution of the sodium cluster anions Na20--Na57-

Sodium clusters anions Na-n(-) (n=20-57) have been studied by low-temperature photoelectron spectroscopy (PES) and density-functional theory calculations. The geometrical structures of the clusters were determined by a genetic algorithm search and the optimization of a large number of candidate structures. For most of the sizes the calculated density of states of the lowest-energy structures and the measured photoelectron spectra are in excellent agreement, indicating that the correct ground-state structures were found. In the studied size range the sodium clusters follow a simple growth pattern. From Na-20(-) to Na-34(-) a 19 atom double-icosahedral core is stepwise decorated by a 15 atom equatorial belt. The resulting D-5h Na-34(-) is then capped by an anti-Mackay overlayer in the size range Na-34(-) to Na-44(-). From Na-52(-) to Na-55(-) a Mackay overlayer on a 13 atom icosahedron core is completed. Na-56(-) and Na-57(-) result from the 55 atom icosahedron by incorporation of additional adatoms into the outer Mackay layer. Comparison of the ab initio derived structures with results from jellium or Nilsson models reveal that for sizes below Na-40(-) the overall cluster shapes are rather accurately predicted by these simple free-electron models. For larger sizes the agreement is less good, as here optimum atomic packing plays a stronger role. This is most obvious close to size 55, where the icosahedral shell closing leads to a spherical shape of the cluster, whereas the free-electron models predict significant distortions.