Arachno polyhedra

Removal of two vertices from a deltahedron leads to arachno polyhedra having 2n + 6 skeletal electrons according to the Wade-Mingos rules [13-16]. Among the many theoretical possibilities for arachno polyhedra, the pentagonal antiprism, generated by removal of a pair of antipodal vertices from an icosahedron, is the most significant in bare post-transition metal cluster chemistry. 

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. 

Arachno Polyhedron two vertices short of close configuration (weblike). 

For a B Hm borane based on an anion B H 6-, an arachno-structure is preferred with B at n vertices of an (n + 2) vertices polyhedron (n + 3) pairs of framework bonding electrons are required. 

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

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

The structures of boranes can be grouped into several classifications. If the structure contains a complete polyhedron of boron atoms, it is referred to as a closo borane (closo comes from a Greek word meaning closed ). If the structure has one boron atom missing from a comer of the polyhedron, the structure is referred to as a nido borane (nido comes from a Latin word for nest ). In this type of structure, a polyhedron having n comers has (n - 1) comers that are occupied by boron atoms. A borane in which two comers are unoccupied is referred to as an arachno structure (arachno comes from a Greek word for web ). Other types of boranes have structures that are classified in different ways, but they are less numerous and will not be described. 

Let us now ask how we could predict the correct total electron count, as just defined, for a stable cluster of known structure (i.e., closo, nido, or arachno). To do this for metal carbonyl clusters, it is postulated that in addition to the electrons necessary for skeletal bonding each metal atom will also have 12 nonskeletal electrons. The basis for this assumption is that in the pyramidal M(CO)3 unit each M—CO bond will comprise two formally carbon tr electrons that are donated to the metal atom and two formally metal it electrons that backbond, at least partially, to the CO ligand. Thus, in predicting the total electron count for a closo polyhedral cluster of n vertices, the result would be 12n + 2 n + 1). Similarly, for nido and arachno clusters that are derived from an n-vertex polyhedron (their parent polyhedron) by removal of one or two vertices, respectively, there will be 12 and 24 fewer total electrons, respectively. 

The predictions for TEC can therefore be stated in the following equations (where n is the number of vertices in the parent polyhedron for the nido and arachno cases—not the actual number of metal atoms in the cluster itself) ... 

The next two examples in Table 16-2, Os5C(CO)15 and [Fe4C(CO)12]2 show how nido and arachno structures are predicted. The nido structure already shown in Fig. 16-12(a) for the iron analogue, Fe5C(CO)i5, is derived by removal of one vertex from the parent polyhedron, which is an octahedron. The [Fe4C(CO)i2]2 cluster should be isostructural with the Fe4C(CO)13 cluster, whose structure has been shown in Fig. 1642(d). It is derived from a parent octahedron by removal of two vertices. 

A deltahedron is a polyhedron whose faces are all triangular. Fora given number of vertices, a closo polyhedron is the most highly symmetric deltahedron. For example, an icosahedron, rather than a tetiacapped cuneane, is the closo polyhedron for 12 Vertex polyhedra. A nido (netlike) polyhedron is a closo polyhedron with one vertex removed, while an arachno (web-like) polyhedron is a closo polyhedron with two vertices, not necessarily adjacent, removed. 

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