Skeletal bond pairs

The problems outlined in the previous section can be avoided if, instead of allocating the skeletal bonding electron pairs to localized bonds, one simply compares their number with the number of skeletal bonding MO s (199). The closo, nido, and arachno structures of boranes and carboranes can then be seen to reflect the numbers of skeletal bond pairs that are available to hold their skeletal atoms together. 

The polyhedra in Fig. 1 thus represent suitable shapes for cluster species with n skeletal atoms (each of which can furnish three AO s for use in skeletal bonding) and with (n + 1) skeletal bond pairs. Since it is the cluster symmetry that determines the number of bonding MO s, the same polyhedra can serve as the basis for the structures of a whole range of isoelectronic species, including neutral carboranes of formula C2B 2Hn, bismuth clusters, such as the trigonal-bipyramidal Bis " ",... 

Compounds with a skeletal atoms and b skeletal bond pairs adopt closo structures if 6 = (o + 1), nido structures if 6 = (a + 2), and arachno structures if 6 = (o + 3). 

The relationship between boranes and metal-carbonyl clusters can be extended by considering the compound Fe5(CO)i5C, which has the square-based pyramidal structure shown in Fig. 13, with the carbide carbon atom just below the center of the Fe square, clearly contributing all its valence shell electrons to the cluster 24). The metal-carbonyl residue FeB(CO)i4 formally left by removal of this carbon as has the nido structure appropriate for a cluster with 5 skeletal atoms and seven skeletal bond pairs. 

In addition to the close- and nido-metal-carbonyl clusters already mentioned, with structures based on the octahedron, another interesting category of structure that is found among metal-carbonyl clusters is one in which n skeletal atoms are held together formally by n skeletal bond pairs. These adopt structures based on polyhedra with ( — 1) vertices, as might be expected. The extra metal atom caps one of the triangular faces of the closo residue, where the three vacant orbitals that it can formally furnish for cluster bonding enable it to bond to the 3 metal... 

FlO. 21. Skeletons of some mixed clusters with 8 skeletal bond pairs. 

Fig. 22. Some mixed clusters with 7 skeletal bond pairs.

The mixed cluster Co4(CO)io(C2Et2) (50) has already been quoted (Fig. 15) as an example of a closo cluster with 6 skeletal atoms and 7 skeletal bond pairs. Nido clusters also formally based on an octahed-... 

The average edge bond order for a particular closo species can be calculated by dividing the total number of skeletal bond pairs ( 4- 1) by the number of edges, which, for exclusively triangular-faced poly-hedra with n vertices, is (3 — 6). This leads directly to the formal boron-boron bond order for those borane anions (ITU) and... 

Different bismuth clusters are apparently formed in reactions between bismuth and bismuth trichloride-aluminum trichloride mixtures, from which the salts (Big) " (AICl4 )3, and (Bi8) + (AICl4 )2 have been isolated 43). A trigonal-bipyramidal structure was predicted for Big (a closo 6 skeletal bond pair system cf. C2B3Hg), and a square anti-prismatic structure for Bi8 , as appropriate for an arachno 8-atom, 11 skeletal bond pair cluster. Similar polyhedral shapes appear likely for other clusters not only of bismuth but also of other heavy main group metals (the anion Pbg ", for example, is isoelectronic with Bi9 " ). 

No. of Skeletal Bonding Pairs Basic Polyhedron closo- Borane nido- Borane arachno- Borane hypho- Borane... 

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. 

FIGURE 15-20 Metal Cores for Clusters Containing Seven Skeletal Bond Pairs. 

The neutral chloride B4CLt, with four skeletal bond pairs, and tetrahedrane C4H4 or tetraphosphorus P4 and related molecules, with six skeletal bond pairs, are systems with regular tetrahedral structures. Tetrahedral molecules held together by six skeletal bond pairs can of course be accommodated in the carborane cluster systematics as nido clusters with n atoms and n -1- 2 skeletal bond pairs, if a low connectivity (axial) vertex of the parent trigonal bipyramid is left vacant, instead of the expected high-connectivity (equatorial) vertex. 

Interestingly, these regular tetrahedral systems are readily accommodated by localized bond schemes Four 3c-2e bonds in the tetrahedral faces when there are four skeletal bond pairs, as in B4CI4 and six 2c-2e bonds along the edges of the tetrahedra when there are six skeletal bond pairs, as in P4. 

If the compounds shown in Figures 4.1 and 4.2 are regarded as mixed metal-carbon clusters, the pyramidal shapes of their MC skeletons will be seen to be those appropriate for nido systems in which (n -1-1) skeletal atoms are formally held together by (n -1- 3) skeletal bond pairs. This number includes the n pairs of electrons in the ring carbon-carbon o bonds as well as the three pairs of electrons in their K-systems. For example, in the cyclobutadiene complex (r " -C4H4)Fe(CO)3, 5 each CH unit can contribute three electrons, and the Fe(CO)3 unit can contribute two electrons for skeletal bonding, making... 

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