Deltahedral boranes

Fig. 2. Idealized deltahedra and deltahedral fragments for closo, nido and arachno boranes and heteroboranes. From left to right the vertical columns give generic closo, nido, and arachno frameworks bridge hydrogens and BH2 groups are not shown, but when appropriate they are placed around the open...

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... 

A comprehensive summary of the theoretical contributions over the past 40 years towards the understanding of the relationship between two-dimensional aromaticity (hydrocarbons) and the electronic structure of three-dimensional deltahedral boranes. Note in particular that rearrangement processes and the isocloso problem in metallaboranes have also been discussed.11... 

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. 

Interstitial Polygonal Aromatic-Deltahedral Borane Relationships... 

Mingos rules. This hypoelectronicity or electron poverty (fewer than the Wade-Mingos 2n + 2 skeletal electrons) in the bare metal cluster anions Enz (z < n + 2) leads to deltahedra not only different from those in the deltahedral boranes but also different from those in hypoelectronic metal carbonyl clusters of metals such as osmium. 

An unusual type of deltahedral cluster found in organoindium chemistry but not in deltahedral borane chemistry is the eight-vertex In8[Si(CMe3)3]6 (see Chapter 2.3.4.2) its structure is based on a bicapped octahedron with idealized D34 sym-... 

In contrast to the polyhedral boranes B H +m there exist a number of neutral boron duster molecules B X (X = Cl, Br, I, NR2, R) all of them having closed deltahedral structures in spite of the fact that the number of bonding electron pairs is only n. For this reason these homonudear cluster compounds of boron are called hypercloso polyboranes. However, there also exist anions of type B X 2 which fit Wade s rules. 

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. 

Five main series of boranes (neutral, anionic, corresponding to deltahedral, triangular-faced polyhedra) can be considered ... 

The structures, relative stabilities, and relative Lowry-Bronsted acidities of carboranes and boranes as well as related anions, Lewis base adducts, and heteroelement analogs are rationalized primarily on the basis of rudimentary coordination numbers. The principal factors, in decreasing order of importance, are (a) the various deltahedra and deltahedral fragments, (b) the placement of bridge and endohydrogens, (c) the placement of carbon and other heteroelements, and d) the resulting coordination number of boron. 

An alternative approach to aromaticity in some deltahedral boranes is based on the Jemmis and Schleyer [41] interstitial electron rule, originally introduced for nido half-sandwich species. This also relates aromaticity in deltahedral boranes to the 4A + 2 Hiickel mle, but for deltahedral boranes k is typically 0. 

One of the most interesting bare Group 13 metal clusters is the first one to be discovered [66], namely the 11-atom cluster frin in the intermetallic Kglnn-Analogous 11-vertex clusters were subsequently synthesized containing gallium [67] and thallium [68]. The frin cluster has 11+7=18 skeletal electrons = 2 n - 4 for n = 11. It is thus a highly hypoelectronic system relative to the 2n + 2 skeletal electron deltahedral boranes B H . The polyhedron found in Inn is... 

Molecular Orbital Descriptions. In addition to the localized bond descriptions, molecular orbital (MO) descriptions of bonding in boranes and carboranes have been developed (4). Early work on boranes helped develop one of the most widely applicable approximate MO methods, the extended Htckel method. Molecular orbital descriptions are particulady useful for c/oso molecules where localized bond descriptions become cumbersome because of the large number of resonance structures that do not accurately reflect molecular symmetry. Such descriptions show that the highest occupied MO (HOMO) is degenerate for most deltahedral B H molecules, but that a closed shell is obtained for the corresponding [B H l2 anions. After... 

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