Geometries, stabilities, and electronic properties of different-sized ZrSin (n=1–16) clusters: A density-functional investigation

Abstract

The ZrSi(n) (n=1-16) clusters with different spin configurations have been systematically investigated by using the density-functional approach. The total energies, equilibrium geometries, growth-pattern mechanisms, natural population analysis, etc., are discussed. The equilibrium structures of different-sized ZrSi(n) clusters can be determined by two evolution patterns. Theoretical results indicate that the most stable ZrSi(n) (n=1-7) geometries, except ZrSi3, keep the analogous frameworks as the lowest-energy or the second lowest-energy Si(n+1) clusters. However, for large ZrSi(n) (n=8-16) clusters, Zr atom obviously disturbs the framework of silicon clusters, and the localized position of the transition-metal (TM) Zr atom gradually varies from the surface insertion site to the concave site of the open silicon cage and to the encapsulated site of the sealed silicon cage. It should be mentioned that the lowest-energy sandwich-like ZrSi12 geometry is not a sealed structure and appears irregular as compared with other TM@Si12 (TM = Re,Ni). The growth patterns of ZrSi(n) (n=1-16) clusters are concerned showing the Zr-encapsulated structures as the favorable geometries. In addition, the calculated fragmentation energies of the ZrSi(n) (n=1-16) clusters manifest that the magic numbers of stabilities are 6, 8, 10, 14, and 16, and that the fullerene-like ZrSi16 is the most stable structure, which is in good agreement with the calculated atomic binding energies of ZrSi(n) (n=8-16) and with available experimental and theoretical results. Natural population analysis shows that the natural charge population of Zr atom in the most stable ZrSi(n) (n=1-16) structures exactly varies from positive to negative at the critical-sized ZrSi8 cluster; furthermore, the charge distribution around the Zr atom appears clearly covalent in character for the small- or middle-sized clusters and metallic in character for the large-sized clusters. Finally, the properties of frontier orbitals and polarizabilities of ZrSi(n) are also discussed.