The resonance energy of benzene

The symbol Ph is sometimes used as an abbreviation for the phenyl group. The use of these group names is illustrated in the following examples  

We have asserted that a resonance hybrid is always more stable than any of its contributing structures. Fortunately, in the case of benzene, this assertion can be proved experimentally, and we can even measure how much more stable benzene is than the hypothetical molecule 1,3,5-cyclohexatriene (the lUPAC name for one Kekule structure). 

Hydrogenation of a carbon-carbon double bond is an exothermic reaction. The amount of energy (heat) released is about 26 to 30 kcal/mol for each double bond (eq. 4.5). (The exact value depends on the substituents attached to the double bond.) When two double bonds in a molecule are hydrogenated, twice as much heat is evolved, and so on. 

Comparison of heat released by the hydrogenation of cyclohexene, 1,3-cyclohexadiene, and benzene to produce cyclohexane. 

The stabilization energy, or resonance energy, of a substance is the difference between the energy of the real molecule and the calculated energy of the most stable contributing structure. 

Once Kekule had deduced the correct structure of benzene, chemists soon realized that the double bonds in it were considerably more stable than isolated double 

It is possible to make a successful comparison of theory with experiment for the resonance energy modified according to the Mulliken and Parr prescription[60], but there are still many assumptions that must be made that have uncertain consequences. A better approach is to attempt calculations that match more closely what experiment gives directly. This still requires making calculations on what is a nonexistent molecule, but the unreality pertains only to geometry, not to restricted wave functions. 

Following these ideas, Table 15.10 shows results of 6-3IG calculations of the TV system of normal benzene and benzene distorted to have alternating bond lengths matching standard double and single bonds, which we will call cyclohexatriene. 

The cyclohexatriene molecule has a wave function considerably modified from that of benzene. The first few terms are shown in Table 15.11, where the two 

This is the standard Kekule structure with the n bonds principally at the short distance. 

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The precise value of the resonance energy of benzene depends as comparisons with 13 5 cyclohexatriene and (Z) 13 5 hexatriene illustrate on the compound chosen as the reference What is important is that the resonance energy of benzene is quite large SIX to ten times that of a conjugated triene It is this very large increment of resonance energy that places benzene and related compounds m a separate category that we call aromatic... 

The most impressive example of resonance stabilization is benzene, in which the delocalization is responsible for a stabilization of 30-36 kcal/mol, the resonance energy of benzene. 

The Nature of the Chemical Bond. V. The Quantum-Mechanical Calculation of the Resonance Energy of Benzene and Naphthalene and the Hydrocarbon... 

In the following paper of this series6 a value of about 1.7 v.e. has been found from thermochemical data for the resonance energy of benzene. Equating the negative of this quantity to 1.1055a, we calculate the value of a to be about —1.5 v.e. This value may not be very reliable, however, since it is based on the assumption that values of bond energies obtained from aliphatic compounds can be applied directly to aromatic compounds. 

Pauling, L. Wheland, G.W. The Nature of the Chemical Bond. V. The Quantum-Mechanical Calculation of the Resonance Energy of Benzene and Naphthalene and the Hydrocarbon Free Radicals J. Chem. Phys. 1933, 1, 362-374 Errata, ibid, 1934, 2, 482. 

Those familiar with the long history of the attacks on the question of the resonance energy of benzene may be somewhat surprised at the small numbers in Table 15.3. The energy differences that are given there are for just the sort of process that might be expected to yield a theoretical value for the resonance energy, but experimental determinations deld numbers in the range 1.7-2.3 eV. This is an important question, which we will take up in Section 15.3, where it will turn out that some subtleties must be dealt with. 

There is still interest in the resonance energy of benzene. Beckhaus et al. [65] have synthesized a molecule with a strained benzene ring in it and measured heats of hychogenation. This is an ejq)erimental attempt to assay what we did theoretically. They found similar results. 

Since a calculation of the resonance energy of benzene by the valence bond method shows that the greater part of it is a result of the resonance between the two Kekule structures shown, we might suppose that its homologs would also have significant resonance stabilization energies. Such conclusions are at variance with experimental fact, however, since cyclobutadiene appears to be too unstable to have any permanent existence, and cyclooctatetraene exists as a nonplanar tetraolefin, having no resonance stabilization of the sort considered. 

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