Resonance in benzene

Benzene is commonly represented by omitting the hydrogen atoms and showing only the carbon-carbon framework with the vertices unlabeled. In this convention, the resonance in the molecule is represented either by two structures separated by a double-headed arrow or by a shorthand notation in which we draw a hexagon with a circle inside  

The shorthand notation reminds us that benzene is a blend of two resonance structures— it emphasizes that the C = C double bonds caimot be assigned to specific edges of the hexagon. Chemists use both representations of benzene interchangeably. 

The bonding arrangement in benzene confers special stabihty to the molecule. As a result, millions of organic compounds contain the six-membered ring characteristic of benzene. Many of these compounds are important in biochemistry, in pharmaceuticals, and in the production of modern materials. 

Each Lewis structure of benzene has three C=C double bonds. Another hydrocarbon containing three C = C double bonds is hexatriene, CeHs. A Lewis structure of hexatriene is 

Do you expect hexatriene to have multiple resonance structures If not, why is this molecule different from benzene with respect to resonance  

What is the significance of the dashed bonds in this ball-and-stick model  

Note that the double bonds are in different places in the two structures. Each of these resonance structures shows three carbon-carbon single bonds and three carbon-carbon double bonds. However, experimental data show that all six C — C bonds are of equal length, 1.40 A, intermediate between the typical bond lengths for a C — C single bond (1.54 A) and a C = C double bond (1.34 A). Each of the C—C bonds in benzene can be thought of as a blend of a single bond and a double bond ( FIGURE 8.14). 

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The values of and can be estimated from their internal consistency to be accurate to about 0.1 v.e., the value of 1.71 v.e. for the resonance energy being accurate to about 0.15 v.e. The quantum mechanical discussion of resonance in benzene and naphthalene is given in the preceding paper.1... 

The Number of Aromatic Resonances in Benzenes with Different Substitution Patterns... 

These three structures, the most stable valence-bond structures that can be formulated for naphthalene, are seen to have about the same energy and to correspond to about the same molecular configuration. It is to be expected then that they will be combined to represent the normal state of the naphthalene molecule, to which they should contribute about equally. Resonance among these three stable structures should stabilize the molecule to a greater extent than does the Kekul resonance in benzene, involving two equivalent structures it is seen from Table 6-2 that the resonance energy of naphthalene, 75 kcal/mole, is indeed much greater than that of benzene. 

In this they somewhat resemble the curly arrows used to show resonance. in benzene, where the arrows show where to draw the new bonds, and which ones not to draw in the canonical structure but in this case there is neither a sense of direction nor even an actual movement. The analogy between the resonance of benzene and the electron shift in the Diels-Alder reaction is not far fetched, but it is as well to be clear that one is a reaction, with starting materials and a product, and the other is not. 

Fig. 3. (a) The singlet states originating from Kekule and Dewar resonances in benzene. The marked points show the CASSCF computed values, the continuous and dashed lines corresponding to the fit with Hamiltonian of equation (14) (left side) (b) the geometry dependence of spin Hamiltonian parameters (right side). 

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]. 

The curly arrows are drawn clockwise, but they could equally well have been drawn anticlockwise. Thus, there is no absolute sense in which the hydrogen atom that moves from one carbon atom to the other in the ene reaction is a hydride shift, as seems to be implied by the clockwise curly arrow, or a proton shift, as it would seem to be if the arrows were to have been drawn in the opposite direction. In other words, neither component can be associated with the supply of electrons to any of the new bonds. The curly arrows therefore have a somewhat different meaning from those used in ionic reactions. They share with all curly arrows the function of showing where to draw the new bonds and which ones not to draw in the resulting structure. They are related to the arrows used to illustrate resonance in benzene, in having no sense of direction, but the Diels-Alder reaction has starting materials and a product, and aromatic resonance in benzene does not. 

Molecules or species with resonance structures are generally considered to be more stable than those without them. The delocalization of the electrons lowers the orbital energies, imparting this stability. The resonance in benzene gives rise to the property of w aromaticity. The gain in stability is called the resonance energy. 

In the remainder of this section we consider the higher lying resonances in benzene. In general, the simple classification of resonances involving valence orbitals as either "shape" or "core-excited" appears to break down as the anion energy Increases (38). 

Instead of employing the above notation, a convenient way of expressing the resonance in benzene is by writing the molecule as... 

Figure 30. Construction of the 1 2 CH stretch/CC bend anharmonic resonance in benzene.

The diamagnetic tetrameric ethoxide Mo4(OEt)i2 obtained by the reaction of Mo2(NMe2)e with ethanol (>6 equiv.) shows a very complex NMR spectrum due to overlapping of several ethyl resonances. In benzene-dg the C H spectrum at 40°C shows eight methylene carbon signals in the intensity ratio 1 1 1 1 2 2 2 2, consistent with the tetrameric, Mo4(OEt)i2 structure. 

Pauling could not disagree more. For him, the double bond in ethylene was as "man-made" as resonance in benzene. Pauling summarized their divergent viewpoints by saying that for Wheland, there was a "quantitative difference" in the man-made character of resonance theory compared with ordinary structure theory—a difference he could not find anywhere. He further asserted that his former student made a disservice to resonance theory by overemphasizing its "man-made character." Wheland conceded that resonance theory and classical structural theory were qualitatively alike, but he still defended, contrary to Pauling, that there was a "quantitative difference" between the two. 

The delocalization of tt bonds represented by resonance in benzene results in a gain in stability according to the principle stated above. It should be noticed, however, that by this description benzene owes its special position as the most stable of the cyclic hydrocarbons, G H , particularly to the fact that its six-membered ring exactly accommodates the 120 angle, resulting in maximum overlap in the a bonds. In any carbon ring other than the six-membered this is not the case23. ... 

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