Hybridization Defects

In addition to the absolutely small size of the 2p-shell, the relative similarity of its radial extent to that of the 2s-orbital (see earlier text) is crucial for understanding the differences between the 2p-elements and their heavier congeners. Covalent bonding is often discussed using the tools of valence-bond (VB) theory (see Chapter 5 in Volume 1), and hybridization is a main requirement of VB models. Kutzelnigg, in 

The Inert-Pair Effect and its Dependence on Partial Charge of the Central Atom 

These observations provide a modem framework for rationalizing the inert-pair effect, that is, the fact that the highest oxidation state becomes increasingly 

As already discussed, electronegative substituents destabilize the heavy p-block elements in their maximum oxidation state. Computationally, this may be seen clearly for calculated energies for 1,1-ehmination reactions. For example, along the series PbR, PbRjF PbRjF, PbRFj, PbF4 (R=H, CHj), ehmination of Rj, 

RF or F2 becomes less endothermic or more exothermic [24]. However, at the same time, it is found, that the Pb-R and Pb-F bonds become shorter along the same series. That is, increasing hybridization defects due to electronegative substituents destabiHze the Pb(IV) compounds thermochemically yet they contract the bonds, essentially due to the smaller size of the more positively charged central atom [24]. Indeed, as the 6s-character of the bonds increases on average with increasing fluorine substitution, they become shorter, consistent with the smaller size of 6s- compared to 6p-orbitals. Yet the large difference in the sizes of 6s- and 

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Figure 3.8 Scheme showing the more common covalent reactions at the CNT edge/defects and at the CNT sidewalls. The figure also shows the typical defects in a SWNT (a) five- or seven-membered rings in the C network, instead ofthe normal six-membered ring, leads to a bend in the tube, (b) sp -hybridized defects... 

Influence of Hybridization Defects on Magnetic-Resonance Parameters... 

Other properties in magnetic resonance may be mentioned here, for example, hyperfine couplings. As the isotropic hyperfine coupling also depends crucially on the spherical spin-density distribution around the nucleus in question, s-character in bonding and, thus, hybridization defects will be important. Obviously, for open-shell radicals the s-character of the singly occupied MO(s) is the most cmcial aspect, but spin polarization of doubly occupied MOs with core or valence s-character may also be relevant (e.g., when the singly occupied molecular orbital is of pure p-character at the given atom). 

Of course, the octet is usually not actually violated. Multicenter bonding models require some MOs that are essentially nonbonding and concentrated only on the substituents, and thus, the number of electrons in the valence shell of the central atom rarely exceeds the octet. However, here we should distinguish, between what Musher [61] more than 40 years ago termed hypervalent compounds of first and second kind, respectively. In the first class, the central atom is not in its maximum oxidation state, and thus, the central-atom s-character concentrates in a Ip. Then, as we have discussed in detail above, the bonds are made mainly from np-orbitals of the central atom, and thus, the assumptions of the usual three-center-four-electron bonding models are nicely fulfilled. In contrast, hypervalent compounds of the second kind exhibit the maximum oxidation state and, thus, necessarily involve the ns-orbitals fuUy in bonding. One thus sees (i) extensive hybridization defects... 

In this chapter, we have tried to emphasize general aspects of main-group chemical bonding, with particular emphasis on periodic trends. The periodic table remains the most important classification tool in chemistry, and it is crucial to understand even subtle secondary periodicities if one is to make efficient use of the various elements for different chemical applications. The radial nodal structure of the valence orbitals has been pointed out to account for more of the known trends than most practitioners of chemistry are aware of. For example, the inversion barriers of phosphines or silyl anions, the dependence of the inert-pair effect on the electronegativity of the substituents, the stability of carbene- or carbyne-type species or of multiple bonds between heavy main-group elements are aU intricately linked to hybridization defects of s- and p-valence orbitals of disparate sizes. Even the question of hypervalency is closely connected to the effects of primogenic repulsion . 

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