Clusters polyhedra

Edge-sharing and face-sharing poly-condensed clusters. Polyhedra... 

One way to describe the structure of a coordination compound, or any molecule, AB , wherein a central atom A is linked to n peripheral atoms, B, is to state the polyhedron whose vertices correspond to the positions of the B atoms. Thus, we describe TiCl4 as tetrahedral and PF5 as trigonal bipyramidal. For cluster compounds, with or without a central atom, it is obvious that the polyhedron defined is a useful description of the structure. In this section the major coordination and cluster polyhedra will be reviewed. 

Metallacarbaboranes (or metallacarboranes) are compounds that contain cluster polyhedra comprising carbon, boron, and metal atoms in various combinations. The first metallacarbaborane clusters were prepared by Hawthorne in 1965, and were derived from the icosahedral closo-carbaborane l,2-C2BioHi2 see Boron Polyhedral Carbo-ranes) by the replacement of one BH vertex with a metal center. Compounds such as [Fe(C2B9Hn)2]" (n = 1 or 2) can be represented as the commo-metallacarbaborane (1) or as... 

Another classification is based on the presence or absence of translation in a symmetry element or operation. Symmetry elements containing a translational component, such as a simple translation, screw axis or glide plane, produce infinite numbers of symmetrically equivalent objects, and therefore, these are called infinite symmetry elements. For example, the lattice is infinite because of the presence of translations. All other symmetry elements that do not contain translations always produce a finite number of objects and they are called finite symmetry elements. Center of inversion, mirror plane, rotation and roto-inversion axes are all finite symmetry elements. Finite symmetry elements and operations are used to describe the symmetry of finite objects, e.g. molecules, clusters, polyhedra, crystal forms, unit cell shape, and any non-crystallographic finite objects, for example, the human body. Both finite and infinite symmetry elements are necessary to describe the symmetry of infinite or continuous structures, such as a crystal structure, two-dimensional wall patterns, and others. We will begin the detailed analysis of crystallographic symmetry from simpler finite symmetry elements, followed by the consideration of more complex infinite symmetry elements. 

Equations (38) and (39) are not, however, valid for cluster polyhedra possessing vertices (i.e. atoms) which lie on the principal rotation axis, where pz and dz2 have purely... 

Cluster polyhedra as found in boranes, metal carbonyl clusters, coinage metal clusters, and post-transition element clusters... 

Stereochemical non-rigid behavior of metal cluster polyhedra... 

There are five regular (Platonic) polyhedra with equivalent faces and equivalent vertices. Of these, the tetrahedron, octahedron, cube (hexahedron) and icosahedron are widely represented in cluster polyhedra. The structure descriptions in Table 1 illustrate the occurrence of regular polyhedra in cages and demonstrate the descriptive notation based on expanding concentric... 

Polyhedra are very useful for describing diverse chemical structures. In coordination chemistry polyhedra can appear as coordination polyhedra in which the vertices represent ligands surrounding a central atom which is often, but not always, a metal and cluster polyhedra in which the vertices represent multivalent atoms and the edges represent bonding distances. Deltahedra, in which all faces are triangles, are a special type of polyhedra that appear often in chemical structures. 

In accord with and in addition to Plato s view of convex polyhedra, there is only a limited number of polyhedra, regular or irregular, mostly more or less distorted, that are observed as cluster polyhedra, mostly deltahedra. 

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