Electronic structure of small sodium clusters

We have calculated the electronic structure of three small clusters of sodium consisting of 9, 15 and 27 atoms. These clusters have the cubic symmetry of the first three shells of atoms in body-centered cubic metallic sodium and were not allowed to relax. The total energy per atom was found to decrease as one goes from Na9 to Na27, with the difference between Na15 and Na27 being smaller than the difference between Na9, and Na15. The charge density and density of states (DOS) of these clusters was also examined. The charge density of the interior atoms was found to become more spherical as more shells are added to the cluster. The cluster densities of states do not resemble closely the free electron like DOS of bulk metallic sodium.