Three-center bond networks

Figure 1.15. Two- and three-center bond networks in some boron hydrides and their hydrocarbon counterparts.

In anhydrous a, a-trehalose [DEKYEXJ (Fig. 13.47), the structure consists of a long eight-link finite chain weakly bound to form a network structure by the minor components of three-center bonds. Both ring oxygens are included, but the linkage oxygen is not. These crystals have been studied by solid-state C13 NMR spectroscopy [293],... 

Figure 3.7. Skeletal two- and three-center bond arrangements possible for CH units of skeletal connectivity k = 3,4,5, or 6 (exo-hydrogens not shown). Bond orders h refer to the mean number of electron pairs per B-C hnk for the bond network in question.

This concept of Kekule structures can be extended to the 3D deltahedral borane anionsB H " (6Kekule structures make use of three-center B-B-B bonds instead of the carbon-carbon double bonds in benzenoid Kekule structures. Lipscomb s semitopological method"" " for studying the electron and orbital balance in boron networks containing mixtures of B-B two-center and B-B-B three-center bonds is essential for extending the concept of Kekule structures from 2D benzenoid hydrocarbons to 3D deltahedral boranes. 

In Chapter 2 (Section 2.9) we see how the cluster bonding requirements for the icosahedron, plus two-center and three-center inter-cluster bonds perfectly uses the three available valence electrons and four available valence orbitals in a covalently bonded cluster network. Once one has these advanced bonding models in hand, then the explanation of the B network structure is no more difficult than that of the C diamond structure. One purpose of this text is to provide these advanced models, but for now the solution to the problem remains hidden. Hey, a little suspense always helps the story line. At this empirical stage of the presentation you have learned that the nature of bonding (distribution of electrons) is expressed in geometry. The tricky bit is to interpret the empirical nuclear position in terms of a useful (simplest one that answers the question asked) model for the distribution of valence electrons. 

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