Orbital hybridization in benzene

Benzene s relative lack of reactivity is a consequence of its electronic structure. As shown by the orbital picture in Figure 23.3b, each of the six carbons in benzene is sp2-hybridized and has a p orbital perpendicular to the ring. When these p orbitals overlap to form pi bonds, there are two possibilities, shown in Figure 23.3c. 

Figure 9.47 (a) The tt molecular orbital system in benzene is formed by combining the six p orbitals from the six sp hybridized carbon atoms, (b) The electrons in the resulting TT molecular orbitals are delocalized over the entire ring of carbon atoms, giving six equivalent bonds. A composite of these orbitals is represented here. 

Because all six carbon atoms and all six p orbitals in benzene are equivalent, it s impossible lo define three localized tt bonds in which a given p orbital overlaps only one neighboring p orbital. Rather, each p orbital overlaps equally well with both neighboring p orbitals, leading to a picture of benzene in which the six -tt electrons are completely delocalized around the ring. In resonance terms (Sections 2.4 and 2.5), benzene is a hybrid of two equivalent forms. Neither form 

FIGURE 3.20 The framework of a-bonds in benzene each carbon atom is sp2 hybridized, and the array of hybrid orbitals matches the bond angles (of 120°) in the hexagonal molecule. The bonds around only one carbon atom are labeled all the others are the same. 

FIGURE 17. Schematic representation of the symmetry-unique spin-coupling patterns in cyclopropane (above) and benzene (below). In the case of cyclopropane, carbon hybrid orbitals and, in the case of benzene, carbon p n orbitals are shown. For each structure, Gallup-Norbeck occupation numbers as determined by spin-coupled valence bond theory are given. All data from Reference 51 

A common example of the Peieds distortion is the linear polyene, polyacetylene. A simple molecular orbital approach would predict sp hybridization at each carbon and metallic behavior as a result of a half-filled delocalized 7t-orbital along the chain. Uniform bond lengths would be expected (as in benzene) as a result of the delocalization. However, a Peieds distortion leads to alternating single and double bonds (Fig. 3) and the opening up of a band gap. As a result, undoped polyacetylene is a semiconductor. 

With the advent of the computer era, it is now possible to reexamine and rethink the resonance theory at the ab initio level. For example, throughout Pauling and Wheland s books, benzene is supposed to be a hybrid of two Kekule structures, by noting that Dewar and other ionic structures make little contribution to the resonance in benzene. However, classical ab initio VB calculations with all possible 175 resonance structures by Norbeck et al. [51] and Tantardini et al. [3], where strictly atomic orbitals are used to construct VB functions, manifested that the five covalent Kekule and Dewar structures make even less contribution to the ground state of benzene than the other 170 ionic structures. This prompts us to reconsider the mathematical formulations for resonance structures [52]. 

A special class of cyclic unsaturated hydrocarbons is known as the aromatic hydrocarbons. The simplest of these is benzene (C6H6), which has a planar ring structure, as shown in Fig. 22.11(a). In the localized electron model of the bonding in benzene, resonance structures of the type shown in Fig. 22.11(b) are used to account for the known equivalence of all the carbon-carbon bonds. But as we discussed in Section 14.5, the best description of the benzene molecule assumes that sp2 hybrid orbitals on each carbon are used to form the C—C and C—H a bonds, while the remaining 2p orbital on each carbon is used to form 77 molecular orbitals. The delocalization of these 1r electrons is usually indicated by a circle inside the ring [Fig. 22.11(c)]. 

The method that commonly is used is to draw a set of structures, each of which represents a reasonable way in which the electrons (usually in p orbitals) could be paired. If more than one such structure can be written, the actual molecule, ion, or radical will have properties corresponding to some hybrid of these structures. A double-headed arrow <—> is written between the structures that we consider to contribute to the hybrid. For example, the two Kekule forms are two possible electron-pairing schemes or valence-bond structures that could contribute to the resonance hybrid of benzene  

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