Numbering polyhedral borane clusters

Rules for counting the number of skeletal electrons provided by each vertex atom need to be established in order to determine the number of skeletal electrons in polygonal and polyhedral clusters of the post-transition elements. The rules discussed above for polyhedral boranes can be adapted to bare post-transition metal vertices as follows ... 

Another very useful rule for classifying the structures of polyboranes and hetero-boranes as well as many metal boron cluster compounds and their derivatives has been developed by Rudolph, Williams, Mingos and Wade (see Chapter 1.1.2) [4]. Today these are generally termed the Wade rules. They can be derived from the structures and electronic requirements of closed polyhedral boranes, such as an octahedron or an icosahedron, which are present in the anions B6H62 and B,2 H, 22. Since there are only exopolyhedral B-H bonds the number of electron... 

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. 

Exo-polyhedral interactions (Figure 5.19) do not affect the skeletal bonding in individual monomeric units and hence Wade s rales can stiU be applied. These macro-polyhedral boranes where Wade s rule is apphcable can be called connected polyhedral boranes, in contrast to condensed polyhedral boranes in which the monomeric units share one or more boron vertices and do not obey Wade s rale. In order to be applicable to condensed polyhedral boranes as well, Wade s rule can be extended by incorporating a new variable, m, corresponding to the number of polyhedra. In Wade s n-i-l-i-p rale, 1 is added to include the core BMO. If m closo clusters condense to form a condensed polyhedral borane, there will be m core BMOs. Thus, the n-El-Ep rale can be modified to where m is the... 

In the area of synthesis, the structural and theoretical framework contributed by Lipscomb provided a foundation for the monumental synthetic work of M. F. Hawthorne and his students, who transformed boron cluster chemistry first by their synthesis of the polyhedral borane anions BioHio and Bi2Hi2 (30) and later by the synthesis of metallacarboranes (31). In our own laboratory, considerations of charge distribution in borane anions (14) prompted us to explore reactions of transition metal ions with small borane and carborane anions (32). This, in turn, led to a number of advances including the first closed polyhedral metallaboranes (33), the discovery of metal-induced oxidative cage fusion (34), and the synthesis of B12H16, the only neutral Bi2 hydride, via metal-promoted fusion of BeHQ (35)... 

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