Deltahedron

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) ... 

Solving the simultaneous equations (2a) and (2b) leads to y = 3 and t = n — 2, implying the presence of three B-B bonds and n — 2 B-B-B bonds in the boron skeleton. Since a deltahedron with n vertices has In — 4 faces, the n — 2 B-B-B bonds cover exactly half of the faces. In this sense a Kekule-type structure for the deltahedral boranes B H 2- has exactly half of the faces covered by B-B-B bonds just as a Kekule structure for benzene has half of its edges covered by C=C double bonds. In 1977 Lipscomb and co-workers [29] reported a variety of such Kekule-type localized bonding structures with the lowest energies for deltahedral boranes. These structures were computed using wave functions in the differential overlap approximation. 

Balakrishnarajan and Jemmis [32, 33] have very recently extended the Wade-Mingos rules from isolated borane deltahedra to fused borane ("conjuncto ) delta -hedra. They arrive at the requirement of n I m skeletal electron pairs corresponding to 2n + 2m skeletal electrons for such fused deltahedra having n total vertices and m individual deltahedra. Note that for a single deltahedron (i.e., m = 1) the Jemmis 2n + 2m rule reduces to the Wade-Mingos 2n I 2 rule. 

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]. 

Cap each of the non-triangular faces of the core polyhedron with one or more additional gallium atoms. This leads to a supraicosahedral deltahedron since the capping process removes all of the non-triangular faces. 

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-... 

Wade electron counting rules borane-like cluster nomenclature. On initially studying compounds such as boranes (boron hydrides) and carboranes (or carbaboranes boron—carbon hydrides), Wade (1976) proposed a number of rules which have then been extended to several compounds and which relate the number of skeletal electrons with the structure of deltahedral clusters. A polyhedron which has only A-shaped, that is triangular, faces is also called a deltahedron. 

Series Parent Formula Skeletal Electrons Cluster Geometry (deltahedron = closed triangulated polyhedron)... 

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. 

The following sections expand on the deltahedron-deltahedral fragment hypothesis (structural rule 1), and in the order of decreasing importance add three additional rules, one involving the placement of BE hydrogens (rule 2), next the placement of the various heteroelements (with emphasis on carbon) (rule 3) 172), and finally the structural accommodations of boron, including the influences of endohydrogens (rule 4). All are shown to have their roots firmly and simply embedded in CNPB, considerations. 

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. 

The rules in overall decreasing order of importance essentially state that the ideal structures for carboranes will be based on most spherical deltahedra (rule 1) the BE hydrogens will tend to be placed in the lowest possible coordination environments (rule 2) when elements to the right of boron in the periodic table are incorporated into the deltahedron or deltahedral fragment, they will tend to preempt low-coordination sites (e.g., carbon) or, if electron-deficient, high coordination sites (rule 3) and, lastly, boron will eschew seven-coordinate BH or six-coordinate... 

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... 

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