Vacant vertices

In related reactions, units, such as Cr(CO)3, Mn(CO)3", Fe(CO)8 , Co(C5H5) +, Mc3N, Be +, or T1+, that can supply 1 skeletal atom and three vacant AO s (no skeletal electrons) for cluster bonding can be used to fill in the vacant vertices of nido or arachno species, thereby converting them into closo or nido species, e.g. 184,194),... 

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. 

Answer. With two C-H fragments, nine B-H fragments and a charge of —2, the cluster has (2x3 + 9x2 + 2)12 =13 sep. Thus, the structure must be derived from an icosahedron (12-vertex deltahedron) but there are only 11 fragments. One vertex (all are equivalent in an icosahedron) is left vacant (a ra do-structure). Show for yourself that the eve count of 48 gives the same result. 

The eve count, which includes the external ligands, hides the similarity in cluster bonding counts that exists for capped and uncapped clusters. The simple octahedral cluster has 14n + 2 = 86 eve whereas the capped octahedral cluster possesses 98 eve, i.e., 14 x 6 + 2 + 12. The correction is numerically the same but in the opposite sense to that necessary when a single vertex of a closed cluster is left vacant, i.e., in the case of capping one adds the non-bonding and ligand electrons associated with the added vertex. It follows that one adds 12 electrons to the eve count of the primary cluster for each cap present. 

With the structure of 54 in mind, the related structure of the [Sb2F7] anion should be considered, two forms of which have been observed. In Cs[Sb2F7] (55) (71) this anion is present as a discrete dimer, with a structure as shown in O. A reasonable description is of two equatorially vacant, trigonal bipyramids that share an axial vertex. The terminal Sb-F bonds average about 1.95 A, whereas the bridging Sb-F distance is 2.24 A (a C2 axis passes through the p-F atom) the Sb-F-Sb angle is 125.3°. 

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... 

A nido cluster possesses a cage based on an n vertex deltahedron with one vertex vacant and has (n+ ) pairs of cluster-bonding electrons. 

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. 

The parent deltahedron is an octahedron and the B5-core of [BsHg] will be derived from an octahedron with one vertex left vacant ... 

This means that there are n + 2) pairs of electrons for n vertices, and so [Sng]" is a nido-cage, based on a 10-vertex deltahedron (see Figure 12.24) with one vertex vacant. This corresponds to the observed structure of a monocapped square-antiprism. 

Each BH -unit occupies one vertex in the parent deltahedron, and from the number of vertices left vacant, the class of cluster can be determined if vertices are nonequivalent, the first to be left vacant tends to be either one of highest connectivity or a cap in capped structures (e.g. H = 9 and 10 in Figure 13.27). 

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