Molecular orbital electron counting rule

The location of electrons linking more than three atoms cannot be illustrated as easily. The simple, descriptive models must give way to the theoretical treatment by molecular orbital theory. With its aid, however, certain electron counting rules have been deduced for cluster compounds that set up relations between the structure and the number of valence electrons. A bridge between molecular-orbital theory and vividness is offered by the electron-localization function (cf p. 89). 

In Part II, besides adding Chapter 11,1 have considerably changed Chapter 8 to place more emphasis on LCAO molecular orbitals and somewhat less on hybridization. A section on the basis for electron counting rules for clusters has also been added. 

There is a connection between an orbital description of electronic structure and the more elementary bonding discussions such as those reviewed in the Appendix. In this section we describe the connection of the 8- and 18-electron rules in order to provide a basis for understanding how the cluster electron-counting rules emerge from and are connected to molecular orbital descriptions of cluster bonding. 

A series of alkali metal and alkaline earth metal-arsenic clusters formulated as M[c-Ass] (M = Li, Na, K, Rb, Cs) andM [c-Ass]+(M = Be, Mg, Ca, Sr, Ba) were investigated by Xu and Jin [173] using DFT methods. All M[c-Assj andM [c-Ass]" clusters adopt a pentagonal pyramidal structure with Csv symmetry, its basal plane involving the planar pentagonal [c-Ass] anion. From molecular orbital and NICS analysis, it was established that each of these species had three delocalized n MOs that satisfied the 4h - - 2 electron counting rule and therefore exhibit n-aromatic character. 

Even more. Figure 16.7 puts forward one more interesting feature. Namely we observe that it is not only the n valence molecular orbital set of AI4" (see Figure 16.7) which possesses two delocalized (see Figure 16.6) electrons, but also the a, set aud the Cy sets do have two delocalized electrons each. Consequently, the three sets satisfy the Hiickel s electron counting rule for aromaticity (4n + 2), with n = 0. This constitutes one neat example of multiple-fold aromaticity the simultaneous occurrence of more than one set of valence molecular orbital, each of them conforming to the (4n + 2), n e N, Hiickel s electron counting rule. 

In particular, we have reviewed here how aromaticity can account for the electronic structure of ring-like molecules made of both main group metals and metalloids and transition metals. Of the many ways and indexes to characterize aromaticity, a loosely defined concept in itself, we have demonstrated that the very first of them, namely the analysis of the valence molecular orbitals complanented with the Aufbau principle and the Hund s rule for their occupation, and the Hiickel electron counting rules, yields a very appealing, albeit approximate, picture to assess the aromaticity of any particular ring-like molecule. 

A symmetry-based molecular orbital description of the unusual four-coordinate C3v W(RC=CR)3(CO) series of molecules was presented by King in 1968 (32). The tt orbitals of the three alkynes yield linear combinations of A2 and E symmetry. Since there is no metal orbital of A2 symmetry only the degenerate E combination of n orbitals finds metal orbital mates for bonding and antibonding combinations. The three alkyne 7T orbitals serve as er donors [(Ax + E) symmetry] as does the fourth ligand (Al symmetry). Thus the total metal electron count adheres to the effective atomic number rule [W(0)(6) + 37T j(6) + 2ir (4) + lo-(2) = 18 electrons]. 

The TEC model developed by Teo also has been successfully applied to rationalize the geometries of a large number of cluster compounds. The TEC model combines Lauher s rule with Euler s theorem and adds an adjustable parameter This parameter X is equal to the number of electron pairs present in excess of that predicted by the 18-electron rule. " X has also been interpreted in terms of the number of missing antibonding orbitals. Given a value for X, determined by the shape of the cluster, an equation predicts the electron count for a cluster. Theoretical justification of the parameter X is based largely upon the classical molecular orbital calculations performed by Hoffmann and Lipscomb via the extended Hiickel method on the corresponding polyhedral boron hydride clusters The values... 

Thus the rule is irrelevant (even when, as in Fe(H20)e, accidentally obeyed) for all high-spin complexes, but is useful for carbonyls and other complexes in which back-bonding is important. It shows that a certain number of metal orbitals are used, but does not show whether the resultant molecular orbital is concentrated mainly on the ligands or on the metal. For example, co-ordinated hydrogen increases the electron count by one, whether described as M - H+ (one for charge, none for bond), M—H (one for bond), or M+ H ( — 1 for charge, 2 for bond). The usefulness of the rule is thus, fortunately, independent of detailed assumptions concerning the actual electron distribution in the complex. 

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