Benzene resonance model

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 model in figure 4.14 results from a 2 1 bend-stretch Fermi resonance model for IVR from benzene overtone states (Sibert et al., 1984a). The first tier is a group of states for which one quantum of CH stretch, Wch. has been transferred to two quanta of CH bend, n. In the second tier an additional cn quantum has been transferred to two more quanta. Though this model is based on strong physical arguments, it is still not known whether this Fermi resonance and tier model is the complete picture for IVR in benzene. 

This is the most widely quoted benzene resonance energy, but one must recognize that resonance energy is an unusually artificial concept in that it represents the difference in energy of formation expected for some purely hypothetical molecule and an actual molecule. The choice of hypothetical model is arbitrary to the point of exasperation. Estimates of the "true" resonance energy of benzene range from 10 to 70 kcal./mole. ... 

PROBLEM 4.4 How does the resonance model for benzene explain the fact that there are only three isomers of dibromobenzene ... 

A representation that reflects both resonance structures has the six tt electrons spread out aroimd the entire ring, as shown in Figure 9.28(c). This figure corresponds to the "circle in a hexagon" drawing that we often use to represent benzene. This model leads to the description of each carbon-carbon bond as having identical... 

Although his proposal was consistent with many experimental observations, it did not totally solve the problem and was contested for years. The major objection was that it did not account for the unusual chemical behavior of benzene. If benzene contains three double bonds, Kekule s critics argued, why doesn t it show reactions typical of alkenes Why, for example, doesn t benzene add three moles of bromine to form 1,2,3,4,5,6-hexabromocyclohexane We now understand the surprising unreactivity of benzene on the basis of two complementary descriptions, the molecular orbital model and the resonance model. 

Figure 15.2 A calculated structure for the arenium ion intermediate formed by electrophilic addition of bromine to benzene (Section 15.3). The electrostatic potential map for the principal location of bonding electrons (indicated by the solid surface) shows that positive charge (blue) resides primarily at the ortho and para carbons relative to the carbon where the electrophile has bonded. This distribution of charge is consistent with the resonance model for an arenium ion. (The van der Waals surface is indicated by the wire mesh.)...

The electron delocalization associated with the resonance model is also invoked to account for aromatic stabilization. Accordingly, the benzene carbon atom should be more stable than the corresponding atom in butadiene and the theory of atoms in molecules shows this to be the case with the difference in their energies equaling —10.0 kcal mol . The... 

The results of the derivation (which is reproduced in Appendix A) are summarized in Figure 7. This figure applies to both reactive and resonance stabilized (such as benzene) systems. The compounds A and B are the reactant and product in a pericyclic reaction, or the two equivalent Kekule structures in an aromatic system. The parameter t, is the reaction coordinate in a pericyclic reaction or the coordinate interchanging two Kekule structures in aromatic (and antiaromatic) systems. The avoided crossing model [26-28] predicts that the two eigenfunctions of the two-state system may be fomred by in-phase and out-of-phase combinations of the noninteracting basic states A) and B). State A) differs from B) by the spin-pairing scheme. 

As pointed out in Chapter 7, the atomic orbital (valence bond) model regards benzene as a resonance hybrid of the two structures... 

Here the operator af creates (and the operator a, removes) an electron at site i the nn denotes near-neighbors only, and /i,y = J drr/),/l(j)j denotes a Coulomb integral if i = j and a resonance integral otherwise. The second quantization form of this equation clearly requires a basis set. It is a model for the behavior of benzene - not a terribly accurate one, but one that helps us understand many things about its spectroscopy, its stability, its binding patterns, and other physical and chemical properties. 

Regardless of how we wish to define the resonance stabilization of the n = 6 case of benzene, it is unequivocal that this substance enjoys considerable stabilization relative to classical expectations related to acyclic and/or less unsaturated precedent. Rather than discussing the plethora of models and even greater experimental evidence that documents this aromaticity , we consider benzene itself as the paradigm. We will return to olefinic paradigms later in this section. 

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