Hybrid-bond theory

As predicted by elementary hybrid bonding theory, the multiple bonds of the chemist s Lewis-structure diagram are usually found to correspond to two distinct types of NBOs (1) sigma-type, having exact or approximate cylindrical symmetry about the bond axis (as discussed in Sections 3.2.5-3.2.7), and (2) pi-type, having a nodal mirror plane passing through the nuclei 44... 

In terms of hybrid-bond theory it appears reasonable that the deformation density could be negative in some bonds. When a p-block atom with n valence electrons forms a bond, the valence shell is polarized into a tetrahedral distribution with n/4 electrons concentrated around each potential... 

Section 2 6 Bonding m methane is most often described by an orbital hybridization model which is a modified form of valence bond theory Four equiva lent sp hybrid orbitals of carbon are generated by mixing the 2s 2p 2py and 2p orbitals Overlap of each half filled sp hybrid orbital with a half filled hydrogen Is orbital gives a ct bond... 

Valence bond theory (Section 2 3) Theory of chemical bond mg based on overlap of half filled atomic orbitals between two atoms Orbital hybridization is an important element of valence bond theory... 

The concepts of directed valence and orbital hybridization were developed by Linus Pauling soon after the description of the hydrogen molecule by the valence bond theory. These concepts were applied to an issue of specific concern to organic chemistry, the tetrahedral orientation of the bonds to tetracoordinate carbon. Pauling reasoned that because covalent bonds require mutual overlap of orbitals, stronger bonds would result from better overlap. Orbitals that possess directional properties, such as p orbitals, should therefore be more effective than spherically symmetric 5 orbitals. 

It is not possible to write down a single, satisfactory, classical bonding diagram for S4N4 and, in valence-bond theory, numerous resonance hybrids must be considered of which the following are typical ... 

In his valence bond theory (VB), L. Pauling extended the idea of electron-pair donation by considering the orbitals of the metal which would be needed to accommodate them, and the stereochemical consequences of their hybridization (1931-3). He was thereby able to account for much that was known in the 1930s about the stereochemistry and kinetic behaviour of complexes, and demonstrated the diagnostic value of measuring their magnetic properties. Unfortunately the theory offers no satisfactory explanation of spectroscopic properties and so was... 

We said in Section 1.5 that chemists use two models for describing covalent bonds valence bond theory and molecular orbital theory. Having now seen the valence bond approach, which uses hybrid atomic orbitals to account for geometry and assumes the overlap of atomic orbitals to account for electron sharing, let s look briefly at the molecular orbital approach to bonding. We ll return to the topic in Chapters 14 and 15 for a more in-depth discussion. 

What accounts for the stability of conjugated dienes According to valence bond theory (Sections 1.5 and 1.8), the stability is due to orbital hybridization. Typical C—C bonds like those in alkanes result from a overlap of 5p3 orbitals on both carbons. In a conjugated diene, however, the central C—C bond results from conjugated diene results in part from the greater amount of s character in the orbitals forming the C-C bond. 

Benzene is described by valence-bond theory as a resonance hybrid of two equivalent structures. 

To explain these and other discrepancies, simple valence bond theory must be modified. It is necessary to invoke a new kind of orbital, called a hybrid orbital. 

In Chapter 7, we used valence bond theory to explain bonding in molecules. It accounts, at least qualitatively, for the stability of the covalent bond in terms of the overlap of atomic orbitals. By invoking hybridization, valence bond theory can account for the molecular geometries predicted by electron-pair repulsion. Where Lewis structures are inadequate, as in S02, the concept of resonance allows us to explain the observed properties. 

Valence bond theory (Chapter 7) explains the fact that the three N—O bonds are identical by invoking the idea of resonance, with three contributing structures. MO theory, on the other hand, considers that the skeleton of the nitrate ion is established by the three sigma bonds while the electron pair in the pi orbital is delocalized, shared by all of the atoms in the molecule. According to MO theory, a similar interpretation applies with all of the resonance hybrids described in Chapter 7, including SO S03, and C032-. 

FIGURE 3.14 Each C H bond in methane is formed by the pairing of an electron in a hydrogen U-orbital and an electron in one of the four sp hybrid orbitals of carbon. Therefore, valence-bond theory predicts four equivalent cr-bonds in a tetrahedral arrangement, which is consistent with experimental results. 

The VB and MO theories are both procedures for constructing approximations to the wavefunctions of electrons, but they construct these approximations in different ways. The language of valence-bond theory, in which the focus is on bonds between pairs of atoms, pervades the whole of organic chemistry, where chemists speak of o- and TT-bonds between particular pairs of atoms, hybridization, and resonance. However, molecular orbital theory, in which the focus is on electrons that spread throughout the nuclear framework and bind the entire collection of atoms together, has been developed far more extensively than valence-bond... 

A note on good practice The concepts of promotion, hybridization, and resonance belong to valence bond theory, not molecular orbital theory. Instead, molecular orbitals are built from all the available atomic orbitals by noting whether or not they have the right shape to overlap with one another. 

Bond angles in transition-metal tricarbonyl compounds A test of the theory of hybrid bond orbitals ... 

Some 50 years have now passed since the publication of a series of papers bearing the title The Nature of the Chemical Bond. 1 7 These papers have provided chemists, physicists, biologists, and mineralogists with the conceptual framework, based on simple valence bond theory and the theory of hybrid bond orbitals, required to investigate a myriad of problems involving the nature of the bonding exhibited in molecules and solids. The ideas contained in these papers were subsequently elaborated on in The Nature of the Chemical Bond which is probably the most often-cited book in the scientific literature.9... 

Second, the theory of hybrid bond orbitals was utilized recently to discover a new type of chemical bond involving the resonating unshared electron pair.30 31 For example, bis(bistrimethylsilylmethyl) tin(II), (CH3)3 Si 2HCSnCH Si(CH3)3 2, forms dimers in the solid state having a tin-tin bond characterized by resonance of an unshared electron pair or... 

Pauling, L. Bond Angles in Transition-Metal Tricarbonyl Compounds A Test of the Theory of Hybrid Bond Orbitals Proc. Natl. Acad. Sci. (USA) 1978, 75, 12-15. 

Herman, Z.S. Recent Advances in Simple Valence-Bond Theory and the Theory of Hybrid Bond Orbitals Int. J. Quantum Chem. 1983, 23, 921-943. 

The general qualitative agreement with experiment provides support for the theory that the potential barriers to internal rotation result from the interaction of adjacent hybrid bond orbitals with a small amount of / character. The magnitude of the potential barriers, about 4 per cent of the energy of the axial bond in case that there are three interacting bonds on each of the two atoms and proportionately less for a smaller number of bonds, is also reasonable. A detailed quantum-mechanical treatment of restricted rotation carried out along the lines sketched here should yield results that would permit a detailed test of the theory to be made in the meantime I believe that the above simple treatment and the extensive empirical support of the theory provide justification for it. 

In the spirit of elementary bonding theories, we expect that the dominant contributions to h,(A) come only from the first summation, consisting (for an s/p-block atom) simply of the four contributions (s, px, pv, p-) from the valence shell. At this level, the hybrid can be written simply as (dropping the atom label throughout)... 

This graduate-level text presents the first comprehensive overview of modern chemical valency and bonding theory, written by internationally recognized experts in the held. The authors build on the foundation of Lewis- and Pauling-like localized structural and hybridization concepts to present a book that is directly based on current ab initio computational technology. 

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