Neutral and negatively chargedAl12X(X=Si, Ge, Sn, Pb) clusters studied from first principles
Physical Review B
First-principles calculations have been performed to study the ground states of both neutral and anionic Al 12 X ͑X = Si, Ge, Sn, Pb͒ clusters. We find that both neutral and charged Al 12 Si cluster prefer icosahedral structure, in agreement with previous calculations. However, each of Al 12 X ͑X = Ge, Sn, Pb͒, either neutral or anionic clusters, shows symmetry of C 5v with atom X located on the cluster surface, contrary to the conclusion from the previous experimental work ͓Phys. Rev. B 65,
... Phys. Rev. B 65, 153404 ͑2002͔͒. The structure and stability of atomic clusters have been extensively studied in past decades. One of the reasons is that the physical and chemical properties of small clusters are very different from that of their bulk phases, so it is expected that cluster-assembled materials may show unique properties. Fullerenes 1 and their subsequent bulk synthesis 2 are typical examples in this area. Extensive theoretical studies have been carried out to examine electronically stable metal clusters in this field. 3-18 One typical example is Al cluster, 6,12,17,18 which has been the subject of many theoretical and experimental studies. Since the valence electrons of Al are free-electron-like, the stability of small Al n clusters has been explained by the jellium model. 14,15 The anion of the Al 13 cluster, having 40 valence electrons, is characterized by a closed electronic shell with a significant gap between the highest-occupied and the lowestunoccupied molecular orbitals ͑HOMO-LUMO͒, 4,16-20 which was confirmed by experiments. 17, 18, 13 Calculations based on density functional theory ͑DFT͒ show that the structure of the Al 13 − cluster is icosahedral-like, while the structure of the neutral Al 13 cluster looks like a distorted icosahedron, due to Jahn-Teller effects. However, because of the Coulomb repulsion, the charged cluster Al 13 − cannot be used to assemble new materials despite high symmetry and high stability. Some effort has been made to study neutral icosahedral clusters by substituting a tetravalent atom, such as C, Si, Ge, or Sn for one Al atom in Al 13 , 3-10 such doped Al 12 X ͑X =C, Si, Ge, Sn͒ clusters would have 40 valence electrons forming a closed electronic shell without any net charge. Previous DFT calculations 4, 9, 20 have indicated that the structures of Al 12 X ͑X = C, Si, Ge͒ clusters are icosahedral-like with large HOMO-LUMO gaps, whereas Al 12 Sn cluster has been predicated to have a structure, in which the Sn atom replaces a surface atom instead of the central atom of Al 13 . 9 To our knowledge, no theoretical calculations for Al 12 Pb have been reported yet so far. Recently, Li and Wang 12 predicated that Al 12 C − cluster should have low symmetry rather than I h high symmetry, which has been confirmed by our latest DFT calculations. 20 Meanwhile, based on the comparison between the photoelectron spectra ͑PES͒ of Al 12 X − and Al 13 − , Li and Wang 12 argued that the anionic Al 12 X − ͑X = Ge, Sn, Pb͒ clusters would have I h symmetry with X located at the center of the clusters.