Deltahedra closo

Fig. 2. Idealized deltahedra and deltahedral fragments for closo, nido and arachno boranes and heteroboranes. From left to right the vertical columns give generic closo, nido, and arachno frameworks bridge hydrogens and BH2 groups are not shown, but when appropriate they are placed around the open...

The shapes of the deltahedra in the apparently hypoelectronic clusters of the heavier group 13 metals bear an interesting relationship to their electron counts. All such hypoelectronic deltahedra can be derived formally from the standard closo-borane structures (Figure 1-2) by flattening one or more vertices towards... 

Closo, nido, arachno, hypho deltahedral clusters based on n main group vertex atoms are characterized by An + 2, An + 4, An + 6 and An + 8 total valence electrons respectively. The corresponding optimum VEC for closo and nido deltahedra... 

Figure 4.26. Optimum values, in accordance with Wade s rules and as summarized by Miller et al. (2002), of the valence electron concentration VEC (total number of electrons divided by the cluster atom number) as a function of the number of cluster atoms for closo and nido deltahedra. On the left the values computed for the main group elements and on the right those relevant to the transition metals.

A simplified model may be used to rationalize the bonding in the heteroatomic species [Zn ZnsBi4 Bi7]5. According to the electron counting theory proposed by Wade, the formation of a closo deltahedra of 12 vertices is stabilized by 13 skeletal electron pairs. The total of 26 electrons required for skeletal bonding may be considered to be provided as follows 2 from the interstitial Zn atom, (8x0 + 4x3 = 12) from the ZngBi4 icosahedral unit (each vertex atom carries an exo lone pair or bond pair), 7 from the capping Bi atoms, and 5 from... 

Most of the structures of metallacarbaborane clusters derive from triangular-faced polyhedra. Figure 1 shows regular deltahedra up to the icosahedron with the corresponding lUPAC vertex numbering schemes. General cluster classes are closo (a complete deltahedral structure), nido (a deltahedron with one vertex vacant), arachno (a deltahedron with two... 

Group 13 clusters with electron counts less than the 2n - - 2 electrons corresponding to closo deltahedra have also been described. The classic examples of these are the boron subhalides, B C1 where n = 4, 8 -12 (and a more limited set of bromides and iodides), which have an electron count of 2n and are known as hypercloso clusters. These are based on the same closo structures expected for the 2n - - 2 electron clusters, namely, tetrahedral, dodecahedral, and tricapped trigonal prismatic for n = 4, 8, and 9. The 2n - - 2 dianions B C1 also show the expected deltahedral structures. The stability of the B C1 clusters has been attributed to a combination of the r-donor properties of the halides and steric effects. ... 

Other carboranes have the more open, nido (nest-like) and arachno (cobweblike) structures that are illustrated in columns 2,3, and 4 in Figure 3.1. Their structures can be regarded as fragments of the closo deltahedra. One vertex... 

We showed above that metal atoms have been incorporated in the whole range of closo borane/carborane deltahedra, and also in many nido and some arachno systems. Indeed, metallacarborane chemistry has become far too large a branch of organometalhc chemistry to discuss in detail here. Excellent surveys of the area are available in specialist texts. There is, however, one particular category of metallacarborane worthy of brief consideration to illustrate how the presence of boron atoms in otherwise familiar organometalhc sandwich compounds can enrich their chemistry. The compounds in question are metal... 

Table 2. Closo, nido and arachno transition metal clusters (based on deltahedra with more than 6 skeletal atoms) possessing interstitial main group atoms...

The development of metallaborane chemistry in recent years has led to the discovery of some metallaborane structures containing the so-called isocloso deltahedra, which have a transition metal atom (e.g., Ru, Rh, Ir) located at a degree 6 vertex. Such isocloso metalla-borane dehahedra, except for the 11-vertex structures, are topologically different from the closo borane deltahedra foimd in the simple boranes and the... 

There are boron hydrides in which one or more of the polyhedral sites is truly removed. Figure 3-26b shows the systematics of borane polyhedral fragments as obtained from closo boranes, after Williams [3-27] and Rudolph [3-24]. All the faces of the polyhedral skeletons are triangular, and thus the polyhedra may be termed deltahedra and the derived fragments deltahedral. The starting deltahedra are the tetrahedron, the trigonal bipyramid, the octa-... 

Capped closo deltahedra Closed (n — 1) cornered polyhedron, one triangular face capped 4n... 

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