Static electric polarizabilities as evidence for cluster geometries

We present self-consistent local-spin-density calculations of the static electric dipole polarizability tensor for several isomers of sodium clusters with up to nine atoms. We show how the comparison of the calculated polarizabilities with the experimental data can be used to identify which isomer is observed in the experiments. Our results indicate that sodium clusters with six atoms or less are planar and that the drop in the polarizability of ${\mathrm{Na}}_7$ is related to the change from two-dimensional to three-dimensional geometries. We also present an analysis of recent measurements of photoabsorption resonance frequencies.