Deltahedron closo

Nido Clusters 2n + 4 Systems). Many closo boranes and heteroboranes add two electrons and undergo a concomitant stmctural transformation from a deltahedron to a deltahedral fragment. For instance, closo-2 ()-(Z, [17764-89-OJ, (2n + 2 = 24e ), is readily reduced to... 

Consider the closo-BnHn2 (6 < n < 12) boranes (Figure 1-2). Such deltahedral boranes cannot have any terminal BH2 groups or three-center two-electron B-H-B bonds but acquire two extra electrons from the —2 charge on the ion. Therefore s = x = 0 in the equations of balance (la) and (lb) these reduce to (2a) and (2b) in which n is the number of boron atoms in the deltahedron corresponding to p in (la) and (lb) ... 

Wade expanded the 1971 hypothesis to incorporate metal hydrocarbon 7T complexes, electron-rich aromatic ring systems, and aspects of transition metal cluster compounds [a parallel that had previously been noted by Corbett 19) for cationic bismuth clusters]. Rudolph and Pretzer chose to emphasize the redox nature of the closo, nido, and arachno interconversions within a given size framework, and based the attendant opening of the deltahedron after reduction (diagonally downward from left to right in Fig. 1) on first- and second-order Jahn-Teller distortions 115, 123). Rudolph and Pretzer have also successfully utilized the author s approach to predict the most stable configuration of SB9H9 (1-25) 115) and other thiaboranes. 

If one vertex and its attendant bonds are removed from a ball-and-stick model of the closo twelve-vertex icosahedron and two bonds are subsequently inserted into the open face, the eleven-vertex deltahedron results. If from each resulting smaller deltahedron any one of the lowest-coordination vertices, and its attendant bonds, are monotonically removed and one bond is inserted, the next smaller deltahedron results in all cases, from the icosahedron to the trigonal bip3U amid. It was the exact reverse of this primitive ball-and-stick degradation concept (process L) which allowed the correct bisdisphenoid 154) structure for C2BeHg (VI-02) to be anticipated 172) prior to its production. 

Boranes of the general formula B Hn2 and isoelectronic carboranes such as CB iHk- and C2B 2H have closo structures, in which n skeletal B and C atoms are located at the vertices of a polyhedron bounded by trianglular faces (deltahedron). For the BMH 2 cfo.vo-boranes... 

Incomplete spherical clusters that require the addition of two fragments to be closed are called arachno-clusters (spider web-like). As the shape is based on a deltahedron of order n but with only n —2 vertices occupied, the number of cluster bonding electrons per cluster fragment is larger than that for closo- and mdo-clusters. It follows that a continuation of the closo-, nido-, arachno- progression eventually leads to electron precise rings or chains. 

The Os7(CO)2i cluster provides a simple illustration. The TEC is given by (7x8) + (21 x 2), namely, 98. Subtracting 7 x 12 = 84 and dividing by 2, we obtain S = 7, which implicates a six-vertex central polyhedron. This is consistent with there being a closo six-atom deltahedron (namely, an octahedron) capped on one face—which is, indeed, the actual structure of Os7(CO)2i. Correct results are similarly obtained for [Os8(CO)22]2-, which is a bicapped octahedron (16-XX) and [Osi0C(CO)24]2-, which is a tetracapped octahedron. For the latter, a capsule summary of the analysis is as follows ... 

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 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. 

Number of Skeletal Electron Pairs" Parent Deltahedron (Symmetry) Closo Species CjB,H,+2 (H ) Nido Species C,B,H,44 (H"), Arachno Species C3,H + (H ),... 

There are (n+ 1) pairs of electrons for n vertices, and so C2B4H6 is a closo-cage, a six-vertex deltahedron, i.e. the octahedron is adopted (see Figure 12.24). 

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