Energy resonance, in benzene

Pauling L, Wheland GW (1933) Nature of the chemical bond V. The quantum mechanical calculation of the resonance energies in benzene and naphthalene and the hydrocarbon free radicals. J Chem Phys 1 362-374... 

Fig. 1.9. Resonance energy in benzene molecule. Comparison of resonance energies by considering only Kekule structures 1- 3 (REi) and Kekule plus Dewar structures i- 5(RE2)...

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 precise value of the resonance energy of benzene depends, as comparisons with 1,3,5-cyclohexatriene and (Z)-l,3,5-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 in a separate category that we call aromatic. 

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. 

For symmetrical and unsymmetrical diphenyl-urea we expect some extra resonance energy in addition to that for two benzene rings and urea because of conjugation of these groups the values found are 0.55 v.e. and 0.50 v.e., respectively. 

V. The Quantum-Mechanical Calculation of the Resonance Energy of Benzene and Naphthalene and the Hydrocarbon Free Radicals," J.Chem.Physics 1 (1933) 362374 Linus Pauling and J. Sherman, "The Nature of the Chemical Bond. VI. Calculation from Thermochemical Data of the Energy of Resonance of Molecules Among Several Electronic Structures," J.Chem.Physics 1 (1933) 606617 and Pauling and Sherman, "The Nature of the Chemical Bond. VH. The Calculation of Resonance Energy in Conjugated Systems," J.Chem.Physics 1 (1933) 679686. 

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. 

On the other hand, we should perhaps not be too surprised if values of fi derived from different kinds of measurements do not agree exactly, and indeed this is the case. We have seen above that/ obtained from the vertical resonance energy of benzene is about 37 kcal/mol, whereas Platt first showed that the best overall fit to the spectra of benzene and other unsaturated hydrocarbons was obtained in the framework of the Huckel approximation by taking / to be 55-60 kcal/mol. This high value, which has subsequently been widely adopted to estimate actual differences in energies between MOs, is generally known as the spectroscopic value of / . 

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