The geometries, stabilities, and electronic properties of Au12M (M=Na, Mg, Al, Si, P, S, Cl) clusters were systematically investigated by using first-principles calculations based on density functional theory (DFT). For each cluster, the average binding energy, the embedding energy, the vertical ionization potential, the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), the natural charge population analysis, and the natural bond orbital analysis (NBO) were calculated. The lowest-energy structures of Au12M (M=Na, Mg, Al) clusters are cages with M encapsulated in the center, while structures of Au12M (M=Si, P, S, Cl) clusters are pyramidal with M at the apex. The Au12S cluster, having the full closed-shells, is the most stable. Furthermore, from the natural population analysis, it follows that charges transfer from Au to M in all the clusters. The NBO and HOMO analyses reveal that hybridization occurs between the Au s-d orbitals and the M p orbitals.
The geometric structures and stabilities of small ZrmOn (1≤m≤5, 1≤n≤2m) clusters were studied using density functional theory (DFT) calculations with the Perdew-Wang exchange correlation functional and the generalized gradient approximation (GGA). The lowest energy structures of all these clusters were obtained by the sequential oxidation of the small"core"zirconium clusters. In general, the O atoms prefer the bridge sites along the Zrm skeleton. The ground-state structures of the (ZrO2)3 and (ZrO2)5 clusters are consistent with coordination number rules and bonding regularity. The fragmentation channels and fragmentation energies of the small zirconium oxide clusters were discussed. We found that the ZrmO2m-1 clusters (not including Zr4O7) had the largest fragmentation energy among the clusters with the same number of zirconium atoms.
The geometries, stability, and electronic and magnetic properties of TbSin (n=2-13) clusters were systematically investigated using relativistic density functional theory (DFT) within the generalized gradient approximation. The average binding energies, dissociation energies, charge transfer, the highest occupied molecular orbital and the lowest unoccupied molecular orbital (HOMO-LUMO) gaps, Mulliken populations (MP), and magnetic properties were calculated and were discussed. The TbSin (n=2-13) clusters do not form encapsulated structures at n=10. We conclude that the stability of TbSin is consistent with the encapsulated geometric structure and also with the inherent electronic stabilization. Furthermore, results of the calculated Mulliken populations show that the charge always transfers from Tb to Si. The magnetic moment is largely located on Tb and is mainly populated by f-block electrons. The f electrons are very localized and to a large extent not responsible for chemical bonding. The partial density of states (PDOS) of TbSi10 shows that there is strong sp hybridization between Tb and Si.
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