Pseudopotential calculation of the total energy of small sodium clusters: Crossover from electronic closed shells to geometrical-structure stability

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Abstract
A pseudopotential calculation of the total energy of small sodium clusters is presented. It is based on a local-pseudopotential scheme and local-density correlation and exchange. It includes a spherical distribution of electronic charge and minimizes the energy with respect to the position of the ions. It is found that the most stable clusters are (1) those that correspond to closed electronic shells for clusters with fewer than approximately 100 atoms, and (2) those that correspond to geometrical polyhedral clusters for numbers larger than that. A crossover between electronic-level dominance and geometrical-structure stability, found experimentally for high temperatures at larger numbers, is thus theoretically established.