Icosahedral cluster

Rare-gas clusters can be produced easily using supersonic expansion. They are attractive to study theoretically because the interaction potentials are relatively simple and dominated by the van der Waals interactions. The Lennard-Jones pair potential describes the stmctures of the rare-gas clusters well and predicts magic clusters with icosahedral stmctures [139, 140]. The first five icosahedral clusters occur at 13, 55, 147, 309 and 561 atoms and are observed in experiments of Ar, Kr and Xe clusters [1411. Small helium clusters are difficult to produce because of the extremely weak interactions between helium atoms. Due to the large zero-point energy, bulk helium is a quantum fluid and does not solidify under standard pressure. Large helium clusters, which are liquid-like, have been produced and studied by Toennies and coworkers [142]. Recent experiments have provided evidence of... 

Miehle W, Kandler O, Leisner T and Echt O 1989 Mass spectrometric evidence for icosahedral structure in large rare gas clusters Ar, Kr, Xe J. Chem. Phys. 91 5940... 

Rhodacarborane catalysts have been immobilized by attachment to polystyrene beads with appreciable retention of catalytic activity (227). A 13-vertex /oj iJ-hydridorhodacarborane has also been synthesized and demonstrated to possess catalytic activity similar to that of the icosahedral species (228). Ak-oxidation of closo- >(2- P((Z [) 2 - i- > l[l-Bih(Z, results in a brilliant purple dimer. This compound contains two formal Rh " centers linked by a sigma bond and a pak of Rh—H—B bridge bonds. A number of similar dimer complexes have been characterized and the mechanism of dimer formation in these rhodacarborane clusters have been studied in detail (229). 

In the T = 4 structure there are 240 subunits (4 x 60) in four different environments, A, B, C, and D, in the asymmetric unit. The A subunits interact around the fivefold axes, and the D subunits around the threefold axes (Figure 16.7). The B and C subunits are arranged so that two copies of each interact around the twofold axes in addition to two D subunits. For a T = 4 structure the twofold axes thus form pseudosixfold axes. The A, B, and C subunits interact around pseudothreefold axes clustered around the fivefold axes. There are 60 such pseudothreefold axes. The T = 4 structure therefore has a total of 80 threefold axes 20 with strict icosahedral symmetry and 60 with pseudosymmetry. 

Key Words —Fullerenes, mass spectrometry, clusters, eieclroiiic shells, icosahedral layers. 

The structure of the bimetallic 10-vertex cluster was shown by X-ray diffraction to be (84). When the icosahedral carborane l,2-C2BioHi2 was used, the reaction led to the first supraicosahedral metallocarboranes with 13- and 14-vertex polyhedral structures (85)-(89). Facile isomerism of the 13-vertex monometallodicarbaboranes was observed as indicated in the scheme above (in which = CH and O = BH). 

Our optimized cluster geometries agree well with other reported results for most part. One noticeable exception, however, is the case of Niia for which we find a capped distorted trigonal anti-prism structure with a central atom to be the most stable geometry, while the previously proposed distorted icosahedral structure was found to be unstable. We note that no full geometry unrestricted Optimization was done in obtaining the structure of Ref. 13. 

M. PeUarin, B. Baguenard, J. L. Vialle, J. Lerme, M. Broyer, J. Miller and A. Perez, Evidence for icosahedral atomic shell structure in nickel and cobalt clusters. Comparison with iron clusters , Chem. Phys. Lett. 217 349 (1994). 

The first complex intermetallic compound found to have large clusters of atoms with local icosahedral symmetry was Mg32Al4, which has 162 atoms in a body-centred cubic unit17. The unit cube contains 98 icosahedra, 20 Friauf polyhedra and 44 others. 

The structure factor for the 104-atom complex with almost perfect icosahedral symmetry determines the intensities of the diffraction maxima, in correspondence with the inverse relationship between intensity in reciprocal space and the atom-pair vectors in real space that was discovered fifty years ago by Patterson.27 The icosahedral nature of the clusters in the cubic crystal explains the appearance of the Fibonacci numbers and the golden ratio. 

Lithium has been alloyed with gaUium and small amounts of valence-electron poorer elements Cu, Ag, Zn and Cd. like the early p-block elements (especially group 13), these elements are icosogen, a term which was coined by King for elements that can form icosahedron-based clusters [24]. In these combinations, the valence electron concentrations are reduced to such a degree that low-coordinated Ga atoms are no longer present, and icosahedral clustering prevails [25]. Periodic 3-D networks are formed from an icosahedron kernel and the icosahedral symmetry is extended within the boundary of a few shells. 

Hybrid density functional calculations have been carried out for AU-O2, Au-CO, Aui3, AU13-O2, Au -CO, AU13-H2, and AU55 clusters to discuss the catalytic behavior of Au clusters with different sizes and structures for CO oxidation [179]. From these calculations, it was found that O2 and CO could adsorb onto several Au model systems. Especially, icosahedral Aun cluster has a relatively weak interaction with O2 while both icosahedral and cubooctahedral Aui3 clusters have interactions with CO. These findings suggest that the surfaces of the Au clusters are the active sites for the catalytic reactions on the supported and unsupported Au catalysts. 

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