Molecular orbitals isolobal fragments

The axially symmetric metal carbonyl fragments M(CO)n (n = 1, 3, 4) have three outpointing hybrid orbitals with a high proportion of s and p orbital character, which are suitable for forming cluster skeletal molecular orbitals (77, 78, 238). The number and radial characteristics of these frontier molecular orbitals, which are illustrated schematically in Fig. 26a, are reminiscent of the frontier orbitals of a main group diatomic hydride fragment E—H, where E = C or B (Fig. 26b). To describe this similarity the term isolobal has been introduced (77). Molecular orbital... 

It is often found that a transition metal fragment containing ten electrons more than a corresponding main group fragment has similar properties. This has been attributed to the 18 VE rule. However, a simple electron count is not enough to establish an isolobal relationship. For an isolobal relationship to be established, the molecular orbitals used to bind to other fragments (known as frontier orbitals) need to display a close similarity. 

The analogy between the electronic structures of two isolobal fragments is, of course, still present if we consider their molecular orbitals. 

Three-dimensional polyhedral molecules such as the borane anions, B Hn , are characterised by a total of n -I- 1 skeletal electron pairs or 4 n -I- 2 valence electrons in total [33]. The isolobal analogy between the BH and ML3 fragments has provided a theoretical relationship between the borane and the transition metal cluster compounds [34]. A detailed analysis of the molecular orbitals of deltahedral transition metal clusters showed that they also have a total of n -h 1 bonding skeletal molecular orbitals, which is the same as that in the borane clusters, and 6 n orbitals that are either non-bonding or involved in the metal-ligand bonding. Therefore, such clusters are characterised by 14 n -I- 2 valence electrons in total. 

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