Duodectet rule

It must be emphasized that the duodectet rule (4.6) initially has no structural connotation, but is based on composition only. Indeed, the compositional regularity expressed by (4.6) encompasses both molecular species (such as the metal alkyls) and extended lattices (such as the oxides and halides) and therefore appears to transcend important structural classifications. Nevertheless, we expect (following Lewis) that such a rule of 12 may be associated with specific electronic configurations, bond connectivities, and geometrical propensities (perhaps quite different from those of octet-rule-conforming main-group atoms) that provide a useful qualitative model of the chemical and structural properties of transition metals. 

Following the obvious parallels with p-block hybridization and bonding, the formation of a duodectet-rule-conforming Lewis-like structural formula for an idealized ML transition-metal complex5 can be pictured as occurring in several steps. 

The distribution of six electron pairs around a duodectet-rule-conforming transition-metal atom M can be represented with a hexagonally shaped dot diagram ... 

Furthermore, according to (4.9a) the total number of covalent M—L bonds (n + m, both oml and 7TMl) is 10 — k. Because main-group ligands generally are more electronegative than the central transition-metal atom, each such covalent M—L bond can be termed a formal one-electron oxidation of M. The duodectet-rule-conforming oxidation number ( ox) of M is therefore... 

Let us now specialize to the case of pure sd hybridization, which underlies the duodectet-rule-conforming Lewis-like structures described in Sections 4.2.2 and 4.2.3. Lor equivalent sdM hybrids, Eq. (4.27) becomes... 

Let us begin by considering the duodectet-rule-conforming metal hydrides of the third transition series (W-Au), which have the Lewis-like diagrams... 

The Lewis-like picture suggests20 that saturated metal alkylidenes (carbenes) H M=CH2 of special stability should correspond to duodectet-rule-conforming... 

A corresponding Lewis-like picture can be developed for triply bonded metal alkylidynes (H MCH), such as the duodectet-rule-conforming examples... 

Finally, one can readily visualize various duodectet-rule-conforming alkyli-dene/alkylidyne complexes with more extensive multiple bonding, such as... 

Let us first consider metal-metal bonding26 in simple dinuclear hydrides H MMH . For M = Re, for example, the four possible duodectet-rule-conforming Lewis-like structures are... 

Figure 4.23 Variations of metal-metal bond length with nominal formal bond order (the number of bonds in the natural Lewis structure) in duodectet-rule-conforming dinuclear hydrides H MMH (see Table 4.15).

In summary, the Lewis-like model seems to predict the composition, qualitative molecular shape, and general forms of hybrids and bond functions accurately for a wide variety of main-group derivatives of transition metals. The sd-hybridization and duodectet-rule concepts for d-block elements therefore appear to offer an extended zeroth-order Lewis-like model of covalent bonding that spans main-group and transition-metal chemistry in a satisfactorily unified manner. 

To illustrate the dependence of hypervalency on steric and electrostatic factors, let us consider cu-additions of neutral or ionic ligands to [PtF4]2+, a duodectet-rule-conforming Pt(VI) species with Lewis-like formula... 

However, significant stabilization is also contributed by nN—>-szn donor-acceptor interactions, each with estimated second-order interaction energy 49.4 kcal mol-1, as depicted in Fig. 4.52. Each ammine ligand thereby donates about 0.061 e to the zinc cation, primarily to the vacant 4s orbital which acquires about 0.371 e total occupancy. As before, the high formal hypervalency at the metal center is achieved within the limits of the duodectet rule, i.e., without significant involvement of extravalent metal p orbitals. 

As previously recognized (e.g., Table 4.52), this corresponds to the ideal pattern of three cu bonds, three lone pairs, and sd2 (90°) hybridization, locking in a rigid octahedral structure. On the basis of the formally duodectet-rule-consistent parent species FeH3, the overall co-bonding is compactly described by the two resonance structures... 

The remarkable Lewis-like bonding of transition metals (see V B, pp. 365-387) is based on the primacy of sd hybridization and the associated 12-electron ( duodectet rule ) modification of Lewis structure diagrams. The idealized bond angles cDy between sd hybrid h, and sd - hybrid h, are found to satisfy an equation analogous to the Coulson orthogonality theorem (4.9) for the geometric mean hybridization parameter jx = namely,... 

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