Nido polyhedra

Nido polyhedra can be classified into two fundamental types the pyramids with only one interior vertex (the apex) and the nonpyramids with more than one interior vertex. If n is the total number of vertices and v is the number of interior vertices in a nonpyramidal nido polyhedron, the interactions between the internal orbitals which generate bonding orbitals are of the following three different types ... 

In sandwich compounds and metallocarboranes an alternative distortion mode is observed which converts an antibonding orbital into a non bonding orbital. This distortion has been described as a slip distortion [42-43] and involves the mutual displacement of the rings or nido polyhedra shown in (9). The manner in which the antibonding... 

The total numbers of skeletal bonding orbitals in pyramidal nido systems generated by these three interactions are n — 1,1, and 2, respectively, leading to a total of 77 -I- 2 bonding orbitals holding 2n +4 skeletal electrons. Thus, the graph-theoretical treatment of nonpyramidal and pyramidal nido polyhedra with n vertices leads to the prediction of the same numbers of skeletal bonding orbitals, namely, n + 2, in accord with experimental observations. However,... 

Polymetallic anions, prepared by dissolution of alloys of the alkali and post-transition metals in amine solvents (often with a complexand for the alkali metal cation), have been characterized in crystalline and solution phases. Clusters TlSng3, Ge92 (with 20 skeletal bonding electrons), Sn93- (21 skeletal e) and Bi95+ (22 skeletal e) possess a tricapped trigonal prismatic structure, symmetry D3A, with variations of dimensional detail which correlate with the electron population.291 292 This structure is a ctoso-deltahedron, and with 20 (2h + 2) skeletal electrons can be construed to be three-dimensionally aromatic.292 The 22e clusters M94 (M = Ge, Sn, Pb) occur as the C4v monocapped square antiprism, a nido polyhedron. 

Figure 16-13 Two osmium clusters whose structures illustrate the capping of incomplete polyhedra (a) capping of a nido polyhedron (b) capping of an arachno polyhedron.

A theory which shows greater applicability to bonding in cluster compounds is the Polyhedral Skeletal Electron Pair Theory (PSEPT) which allows the probable structure to be deduced from the total number of skeletal bond pairs (400). Molecular orbital calculations show that a closed polyhedron with n vertex atoms is held together by a total of (n + 1) skeletal bond pairs. A nido polyhedron, with one vertex vacant, is held together by (n + 2) skeletal bond pairs, and an arachno polyhedron, with two vacant vertices, by (n + 3) skeletal bond pairs. Further, more open structures are obtainable by adding additional pairs of electrons. This discussion of these polyhedral shapes is normally confined to metal atoms, but it is possible to consider an alkyne, RC=CR, either as an external ligand or as a source of two skeletal CR units. So that, for example, the cluster skeleton in the complex Co4(CO)10(RCCR), shown in Fig. 16, may be considered as a nido trigonal bipyramid (a butterfly cluster) with a coordinated alkyne or as a closo octahedron with two carbon atoms in the core. 

Capped square antiprism. Geq , Snq", and Pbg" with (9)(2) -h 4 - 22 = 2n -h 4 skeletal electrons required for an n = 9 vertex C4, nido polyhedron having 12 triangular faces and one square face. 

The mathematical aspects developed above can be summarised as follows. Whenever a nido polyhedron with C y (n > 3) symmetry is generated from a closo deltahedron it will have a non-bonding e set of molecular orbitals. This e set is localised predominately on the open face of the polyhedron and the n and components conform to the vector diagrams shown in Figs. 19 and 22. If this e set is filled, then the nido polyhedron is characterised by n -I- 2 skeletal electron pairs. 

Nido Polyhedron one vertex short of closo configuration (nest like). 

T. Baker, DuPont Central Research In reference to your so-called iso-closo iridaborane complex, H(PPh3)2IrB9H9, we have recently published two papers (1,2) dealing with isoelec-tronic, isostructural ten-vertex ruthenacarborane complexes and have demonstrated that these structures are related to the common closo bicapped square antiprismatic structure by the removal of two electrons (i.e. 2N skeletal electrons for an N vertex polyhedron). Such complexes have been referred to as hyper-closo to imply that the electronic unsaturation is not primarily metal-based (as in, for example, nido-(PPh3)2RhC2B8-Hx 2 (3) or closo-(PPh3)ClRh(1,7-C,BQH,) (4), but is delocal-... 

One particularly interesting category of metallocarborane is that in which a single metal atom is shared between two polyhedra that have a vertex in eommon. In effect, the metal is sandwiched between two nido-carborane residues. Examples are shown in Fig. 17. For such commo compounds, the metal can be assumed to contribute three AO s to the skeletal bonding of each polyhedron, when the (n + 1) rule for closo clusters is found to be obeyed. For example, the isoelectronic... 

Fundamental polyhedron h Closo species (0 = 6-1) Nido species (0 = 6-2) Arachno species (0 = 6-3)... 

Yet other factors influence the interatomic distances in nido- and orocAwo-boranes, for example whether the polyhedron edges border the open face of the polyhedral fragment, and if so whether they are sewn... 

Reduction of cZoso-dicarbaboranes, CaBn-zHn, to the dianionic nido species, CaB 2Hn , which are more susceptible to rearrangement reactions, also provides a route to isomers of the starting materials in which the carbon atoms have moved to different polyhedron vertices, e.g. 185,186),... 

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