Tight-binding model for calcium nanoclusters: Structural, electronic, and dynamical properties

Abstract

The tight-binding (TB) Hamiltonian is parametrized for Ca nanoclusters by fitting to the energy surfaces of small clusters and to the total energy and band structure of bulk fcc and bcc calcium calculated within an all-electron density-functional formalism. Clusters of $32\phantom{\rule{0.5em}{0ex}}\text{to}\phantom{\rule{0.5em}{0ex}}84\phantom{\rule{0.3em}{0ex}}\text{atoms}$ are optimized using the TB model and a combination of molecular dynamics--simulated annealing and genetic algorithms. At zero temperature, magic numbers are predicted for 34-, 37-, 39-, 45-, 53-, 57- 61-, and $82\text{\penalty1000-\hskip0pt}\text{atoms}$ clusters, which range from $1\phantom{\rule{0.5em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}2\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ in size. The nanoclusters' positive ions keep the same geometrical structure as their neutral counterparts. Novel structures are obtained for 35-, 38-, 43-, 50-, 58-, 59-, 62-, 63-, and $76--84\text{\penalty1000-\hskip0pt}\text{atoms}$ nanoclusters. There is an enhanced ratio of surface to bulk atoms in these nanoclusters that favors an expansion of the surface bond lengths. Furthermore, based on TB molecular-dynamics results of the mean-square displacement as a function of temperature, a premelting of the surface occurs around $600\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The energy gap between occupied and empty states in the valence band is cluster-size-dependent. Large fluctuations of this energy gap indicate that nanoclusters with more than $50\phantom{\rule{0.3em}{0ex}}\text{atoms}$ have metallic characteristics. A normal mode vibrational analysis predicts that the structure of the magic number clusters is maintained even at temperatures around $600\phantom{\rule{0.3em}{0ex}}\mathrm{K}$.