Cage structures electron counting, 364

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. 

A generalization of the electron counting rules for clusters to accommodate various types of fused cluster structures with common cluster vertices has appeared. The wide variety of examples aheady known illustrates a richness of cluster structure greatly exceeding that of the single cluster (see Electronic Structure of Clusters). Indeed, these ideas provide new insight into the structures of elemental boron in which complex fused cages are observed, and one can see that cluster versions of, for example, metal chains (31), are possible. ... 

---