Skeletal bonding MOs

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. 

That the number of skeletal bonding MO s associated with a particular polyhedral arrangement of BH units need not change if 1 or 2 BH units are removed from the closo species is illustrated in Fig. 9 for species based on an octahedron, namely, the closo anion BgHg and the hypo-... 

The tetrahedron constitutes a special case in that the number of skeletal bonding MOs is usually 6, accommodating 6 electron pairs since this is also the number of edges, most tetrahedral clusters can also be viewed as classical species having one electron pair for each bonding interaction. 

The removal of one or more vertices from a closo polyhedral system leaves the number of skeletal bonding MOs unchanged thus, a 6-vertex closo cluster (octahedral, as in Fig. 5-5), a 5-vertex nido cluster (square pyramidal), and a 4-vertex arachno cluster (butterfly or square planar, depending on whether adjacent or nonadjacent vertices are removed from the octahedron) all have 6 bonding MOs and hence require 7 bonding electron pairs. Expressed in terms of the number of vertices n, this equals n+1, n+2, n+3, and n+4 pairs for closo, nido, arachno, and hypho clusters, respectively. 

H. C. Longuet-Higgins and M. de V. Roberts, who predicted thereby that the icosahedron of 12 boron atoms familiar from elemental boron, boron carbide, and some borides should be stabilized in molecular hydride form, not as the neutral entity B Hu (which if icosahedral would be a diradical) but as the dianion [B12H12] , which contained the 25 valence shell electron pairs needed for the 12 exo B-H bonds and 13 skeletal bonding MOs. Subsequent MO treatments of the closo deltahedral anions B I 1 and carboranes (AB, 2H, in Figure 3.1 have shown that these are the shapes that make best bonding use of their (n + 1) pairs of electrons available for skeletal bonding. ... 

Figure 3.9. Orbitals that a CH or BH unit can use for cluster bonding and the skeletal bonding MOs they generate in 1,6-C2B4H6- (a) CH unit s AOs (b) skeleton of 1,6-C2B4H6 (c) the A,g bonding MO (d) the B> bonding MO (e) the Eg bonding MOs (f) the Aj, bonding MO (g) the Ii, bonding MOs.

Figure 4.15. Schematic representation of the types of skeletal bonding MOs of [Rhe(CO)e(n -CO)9C] that can be stabilized by the core carbon AOs. " (Metal AOs are shown monolobal for simplicity).

Wade s rules provide an electronic rationalization of the regularities, based on the MO prediction that an n atom deltahedron, with 5 andp valence orbitals, should have +1 skeletal bonding MOs. For example, in [B6H6] there are seven such MOs, and electrons may be counted as follows there... 

LUMO gaps >14 eV for BeHe . The shapes and locations of the nodes of the skeletal bonding MOs were consistent with the S , P , and D designations of spherical harmonics predicted by tensor surface harmonic theory (section II.E). 

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