Cuboctahedron structure

FIGURE 8.2 Calculated -projected density of states (DOS) for a number of platinum clusters in the cuboctahedron structure. The figure clearly shows the transition between a continuous band structure of highly delocalized electrons for large clusters (>2nm) and the more discrete energy levels for smaller clusters. For comparison, the ealculated s-projeeted DOS for Pt( 111) is shown as well. We note the resemblance between the DOS for the Pt and the Pt(lll) slab, suggesting that already at sizes above 2nm, the band structure is close to converge to the metallic state. 

Figure 4.9 Clusters in the fluorite structure (a, b) transformation of a cube into a square antiprism (c, d) transformation of a cube into a cuboctahedron (e) a single square antiprism formed by tbe creation of < 110> interstitial defects (/) an M6F36 cluster in a fluorite structure matrix. Cations in the plane of tbe section are represented by smaller spheres anions above and below the plane are represented by larger spheres.

A formulation of structures by layers, such as that represented by the sequence (1) or (2), allows one to derive in a simple way the coordination of the atoms. In the case of perovskite, for example, the atom A of a layer (AX)C is surrounded by twelve atoms X, four located at the corners of the same mesh, and eight at the midpoints of the edges of the (BX2)0 layers above and below (AX)C. The coordination polyhedron is a cuboctahedron. In the case of the rock salt structure, the atom A of a layer (AX)C has coordination six, being surrounded by four atoms X at the corners of the same mesh, and by two atoms X at the center of the meshes (AX)0 above and below (AX)C. In this case the coordination polyhedron is an octahedron. 

In Zeolite A. An extensive series of papers concerned with the sorption location and isotherms of Xe in zeolite A have been published (118-122). The locations of sorbates and their structures were investigated by using Metropolis Monte Carlo simulations of zeolite A models (118, 119). Initially, an idealized truncated cuboctahedron was used, with Si and Al atoms occupying vertices and O atoms occupying the midpoints of line segments (118). Subsequent calculations were based on the positions of atoms in... 

This derivative of the [OMo6Ojg]z structure (Section 4.6.8.1), by addition of an ML3 cap on a triangular (ji-0)3 face of the (fi-0)i2 cuboctahedron, is proposed269 for [(C0)3ReNb2W4019]3 (prepared by [Nb2W4Oi9]4 + [(CO)3Re(MeCN)3]+ in MeCN), which belongs to a class of mixed mode clusters amalgamating polyoxometallates and metal carbonyls. 

Many of the magic number combinations observed in the CMS of inert gas atoms have been identified with stable structures having an icosahedral symmetry (Echt et al. 1981). The Mackay icosahedra series (Hoare 1979 Mackay 1962) exhibits completion of the first three solvation shells as = 13, 55, and 147, respectively, such that the completion of solvation shells at n = 13, 55, etc., can arise from structures with a cuboctahedron symmetry (Hoare 1979). However, theoretical studies indicate that the icosahedral structures are more stable than those with cuboctahedral symmetry (Hoare 1979). The theoretical studies of Farges et al. (1986) and Northby (1987) provide insight into the growth of icosahedral structures. 

In body-centred cubic coordination, the eight ligands surrounding a transition metal ion lie at the vertices of a cube (cf. fig. 2.6a.). In one type of dodecahedral coordination site found in the ideal perovskite structure (cf. fig. 9.3), the 12 nearest-neighbour anions lie at the vertices of a cuboctahedron illustrated in fig. 2.6b. The relative energies of the eg and t2g orbital groups in these two cen-trosymmetric coordinations are identical to those of the e and t2 orbital groups... 

Icosahedral capsid viruses and clathrins are examples of coat proteins of which there are many. Another example that has been extensively studied is coat protein II, or COPII, which is composed of an inner cage and outer coat [5], The inner cage is a cuboctahedron approximately 60 nm across. It has square and triangular faces which can only be constructed if four protein strands emanate from the structure s hub, rather than the three seen in clathrins. It also transpires that the proteins interact with each other at the vertices without any of the extensive interdigitation seen in clathrin cages. 

Similar surface structures should exist in large clusters, beginning with a two-layer 55 atom cuboctahedron. The question arises, whether or not the best coverage of a metal surface can be realized by many small ligands or by fewer bulky ligands, such as phosphines. In contrast to CO, phosphines and related ligands can easily be dosed, in order to prevent formation of smaller clusters. 

Figure 7 0-D truncated cuboctahedron (MOP-1), 2-D square grid framework (MOF-1) and 3-D network structure (MOF-2). (Reproduced fromN.L. Rosi, M. Eddaoudi, J. Kim, M. O Keeffe, O.M. Yaghi, CrystEngComm., 2002, 4, 401 by permission of Royal Society for Chemistry)...

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