Hybridization theory formats

There are six valence atomic orbitals on the metal which contribute to the formation of the six metal-ligand bonds the s orbital, the three p orbitals, and two of the d orbitals. This result may be compared with that given by hybridization theory, where one forms six equivalent hybrids, directed towards the six vertices of an octahedron. One does indeed talk of d sp hybridisation, each hybrid orbital being a suitable linear combination of two d orbitals, the s orbital, and the three p orbitals. 

Molecular orbital (MO) theory describes covalent bond formation as arising from a mathematical combination of atomic orbitals (wave functions) on different atoms to form molecular orbitals, so called because they belong to the entire molecule rather than to an individual atom. Just as an atomic orbital, whether un hybridized or hybridized, describes a region of space around an atom where an electron is likely to be found, so a molecular orbital describes a region of space in a molecule where electrons are most likely to be found. 

Frequently, directionality is a property attributed to the covalent bond which supposedly is taken to be the cause of the resulting structures. However, as the success of the valence electron pair repulsion theory shows, there exists no need to assume any orbitals directed a priori. The concept of directed orbitals is based on calculations in which hybridization is used as a mathematical aid. The popular use of hybridization models occasionally has created the false impression that hybridization is some kind of process occurring prior to bond formation and committing stereochemistry. 

For Li—F, the quantal ionic interaction can be qualitatively pictured in terms of the donor-acceptor interaction between a filled 2pf. orbital of the anion and the vacant 2su orbital of the cation. However, ionic-bond formation is accompanied by continuous changes in orbital hybridization and atomic charges whose magnitude can be estimated by the perturbation theory of donor-acceptor interactions. These changes affect not only the attractive interactions between filled and unfilled orbitals, but also the opposing filled—filled orbital interactions (steric repulsions) as the ionic valence shells begin to overlap. 

Because of the presence of two azide groups in positions adjacent to the ring nitrogen atoms in compound 13a, valence bond isomerization can result in formation of 6-azido-7-methyltetrazolo[l,5-A pyridazine 14a, 6-azido-8-methyltetrazolo[l,5-A pyridazine 15a, and the bis-tetrazole compound 16a. Calculations have been carried out by using hybrid density functional theory (B3LYP/6-311+G(d,p)) and complete basis set treatments (CBS-4M). All calculations revealed that the 8-methyl derivative 15a is the most stable isomer. Similar studies on the triazide derivative 13b, however, indicated that in this case the equilibrium is shifted to the 7-methyl form 14b. All these conclusions proved to be in entire agreement with the experimental findings (see Section 11.18.3.2.). 

Density functional theory methods using the hybrid B3LYP functionals have been performed to study geometries and energetics of several intramolecular [2+3] dipolar cycloadditions of azides to nitriles (Section 11.06.6.1) toward fused tetrazole formation, including tetrazoles 14 and 15 <2003JOC9076>. 

In the valence bond theory, hybridization of orbitals is an integral part of bond formation. As we shall see, the concept need not be explicitly considered in molecular orbital theory but may be helpful in visualizing the process of bond formation. 

Dewar and coworkers offered an alternative view.79 In their model the d and d)Z orbitals are hybridized to give two orbitals which are directed toward the adjacent nitrogen atoms (Fig. 16.25). This allows for formation of three-center bonds about each nitrogen. 9 This scheme, sometimes called the island model, results in delocalization over selected three-atom segments of the ring, but nodes are present at each phosphorus atom since the two hybrid orbitals of phosphorus are orthogonal to each other. Evidence has been offered in support of both models, but neither theory has been confirmed to the exclusion of the other. A third viewpoint holds that rf orbital participation is relatively unimportant in the bonding in these molecules. 1... 

FIGURE 10.14 Hybrid model of the TS for hydrogenation of acetophenone by Ru(BINAP) (cyclohexanediamine)H2 (see Section 10.4.3). The central Ru(PH3)2(NH3)2H2 + CH20 system (shown in ball-and-stick format) is treated at a high level of theory, with the phenyl, naphthyl, methyl, and cyclohexyl groups (stick format) treated at a lower level. 

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