Electron count, polyhedral

Williams [1] has given an excellent review on Early Carboranes and Their Structural Legacy and he defines carboranes as follows Carboranes are mixed hydrides of carbon and boron in which atoms of both elements feature in the electron-deficient polyhedral molecular skeleton . According to the electron counting rules [2] for closo- (2n + 2 SE), nido- (2n + 4 SE) and arachno-clusters (2n + 6 SE SE = skeletal electrons, n = number of framework atoms) and the An + 2 n electron Hiickel rule, small compounds with skeletal carbon and boron atoms may have an electron count for carboranes and for aromatics (see Chapters 1.1.2 and 1.1.3). 

Use ihe polyhedral skeletal electron-counting rules and show that they are consistent with the nido I l-vencx structure shown below.1 1... 

A generalized electron-counting scheme, known as the mno rule, is applicable to a wide range of polycondensed polyhedral boranes and heteroboranes, metal -laboranes, metallocenes, and any of their combinations. According to this mno rule, the number of electron pairs N necessary for a macropolyhedral system to be stable is... 

Table 13 4 4. Application of the mno rule for electron counting in some condensed polyhedral boranes and related compounds ...

For polyhedral clusters (sometimes called deltahedral, because the faces are all triangles resembling the Greek letter delta) the ancestor of all electron counting schemes is the correlation proposed by Wade between borane (or carborane) cages and metal carbonyl cages. Wade first drew attention to the similarity of a M(CO)3 unit and a BH (or CH) unit, a relationship that we would now call isolobality (Section 1-6). He then proposed that the 2n + 2 rule for closo boranes (Chapter 5) would also apply to closo metal cluster species such as [Os CO) ]2, and that 2n + 4 and 2n + 6 electron counts would, similarly, be appropriate for stable M clusters with nido and arachno structures. Hydrogen atoms are assumed to contribute one electron each, an interstitial carbon atom four electrons, and so on. 

Let us now ask how we could predict the correct total electron count, as just defined, for a stable cluster of known structure (i.e., closo, nido, or arachno). To do this for metal carbonyl clusters, it is postulated that in addition to the electrons necessary for skeletal bonding each metal atom will also have 12 nonskeletal electrons. The basis for this assumption is that in the pyramidal M(CO)3 unit each M—CO bond will comprise two formally carbon tr electrons that are donated to the metal atom and two formally metal it electrons that backbond, at least partially, to the CO ligand. Thus, in predicting the total electron count for a closo polyhedral cluster of n vertices, the result would be 12n + 2 n + 1). Similarly, for nido and arachno clusters that are derived from an n-vertex polyhedron (their parent polyhedron) by removal of one or two vertices, respectively, there will be 12 and 24 fewer total electrons, respectively. 

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