Deltahedron 11-vertex

Fig. 1-4. Generation of the 13-vertex polyhedron found in 1,2-,2-C2Bii Hio-3Ph by breaking a single edge (hashed line) in a 13-vertex deltahedron.

Bicapped Square Antiprism. TlSn93 has the (1)(1) + (9)(2) + 3 = 22 = 2n + 2 skeletal electrons required for an n = 10 vertex globally delocalized D4( deltahedron (cf. the bicapped square antiprism in Figure 1-7) analogous to that found in the BioHio2- anion [84]. 

The [Ga19 C(SiMe3)3 6 anion (Figure 1-12) This anion has a structure based on a centered Ga Ga18 deltahedron [104]. The structure of this 18-vertex del-... 

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. 

That the initially suggested structure for TEG-C2B10H12 (IV-24) (33) has been shown to be incorrect augurs well for the CNPR approach, since IV-24 was based on an illogical thirteen-vertex deltahedron... 

This consideration also applies to 8-vertex clusters with interstitial atoms. The most spherical 8-vertex deltahedron, namely the bisdisphenoid (Eig. 1), appears to have too small a cavity for an interstitial transition metal. Plowever, the square antiprism has two fewer edges and can be partially flattened to make a puckered eight-membered ring, which can accommodate a transition metal in the center (Pig. 8). Known clusters of this type include M E8" (M = Cr [98], Mo [98], Nb [99] E = As, Sb n = 2,3 for Cr and Mo = 3 for Nb). The transition metal in such structures can be considered to be eight-coordinate with flattened square antiprismatic coordination. The Eg ring (E = As, Sb) can be considered formally to be an octaanion, isoelectronic with the common form of elemental sulfur, Sg. Thus in M Eg (M = Cr, Mo E = As, Sb), the central transition metal has the formal oxidation state of +6. Similarly in Nb Eg , the central niobium atom has its d formal oxidation state of +5. 

The deltahedron for n = 10, a bicapped square antiprism, exhibits two four-connect and eight five-connect vertices. Hence, for one heteroatom in a ten vertex c/oso-cluster we have 1 - and 2-isomers and two heteroatoms in 1,10-, 1,6-1,2-, 2,3-, 2,4-, 2,6- 2,8-isomers. Different placements generate different cluster stabilities. A rule of thumb is that the more electronegative element prefers the lower-connectivity vertex. Multiple heteroatoms more electronegative than B prefer non-adjacent positions as far apart as possible. Rearrangement to the most stable isomeric form need not be fast. In the case of icosahedral clusters, for example, the barrier to rearrangement is large and isomers can be isolated. 

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. 

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