Electron-counting and isolobal relationships

At first glance, the structures and stoichiometries of polynuclear carbonyls and their derivatives are of baffling complexity. As we shall see in the next section, some very simple electron book-keeping devices help to bring some order from the apparent chaos. 

The octet rule (discussed in Section 6.1) is nearly always followed by C, N, O and F atoms it is very often followed by other Main Group atoms. This eight-electron rule - of inestimable value to organic chemists - arises from the fact that these atoms have four valence orbitals (one ns, three np). If all of these are being used in bonding, or for the accommodation of lone pairs, the atom will necessarily have an octet configuration. Does an analogous rule apply to compounds of the d block elements  

Other geometries than octahedral will also obey the rule - given n acceptor ligands - if nine bonding MOs can be constructed, although VB theory is often adequate. For example, in a tetrahedral complex we 

Mn2(CO)w Each Mn atom is bonded to 5 CO groups (see Fig. 8.8). Thus it has a share in 7 + (5 x 2) = 17 electrons, one short of the required 18. This is remedied by forming a single Mn-Mn bond, just as the 7-electron CH3 radical will tend to dimerise to give C2H6 in which the C atoms obey the octet rule. 

Like most rules in bonding theory and structural chemistry, the 18-electron rule is often violated, even among the nonclassical complexes containing n acceptor ligands where, we have suggested, it should apply. Square planar complexes follow a 16-electron rule examples include Wilkinson s catalyst Rh(PPh3)3Cl (see also Section 9.8) and the vast number of square Pt(II) complexes. 

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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. 

In Section 13.11, we introduced Wade s rules to rationalize the structures of borane and related clusters. This method of counting electrons can be extended to simple organome-tallic clusters by making use of the isolobal relationship between cluster fragments. 

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