Transition from Metallic to Covalent Structures in Silicon Clusters

The structural properties of silicon clusters are examined to determine at what size clusters with covalentlike open structures become energetically more stable than those with metalliclike close-packed structures. By calculation of the total energy of diamond and face-centered cubic fragments as a function of the number of atoms, an estimate of the "critical" cluster size is made. The estimate is that for clusters of less than about 50 atoms, metallic structures are favored over covalent structures, with the inequality reversed for more than 50 atoms. This result agrees well with recent observations on the relative stability of $\mathrm{Si}_n^{}{}_{}{}^{+}$.