Benzene vs. Cyclobutadiene

In the framework of ab initio classical VB method, totally there are 175 and 20 VB structures for benzene and cyclobutadiene, respectively. On the other hand, for the hypothetically localized 1,3,5-cyclohexatriene and 1,3-cyclobutadiene, 27 and 9 classical VB structures are needed to run the VB-CI calculations. For all calculations, a STO-6G basis set is employed. 

At first we define two types of resonance energies, namely vertical resonance energy (VRE) and theoretical resonance energy (TRE). The former is the energy difference between the optimal delocalized molecule such as benzene and the localized reference molecule such as 1,3,5-cyclohexatriene whose geometries are kept the same. The latter is the energy difference between the delocalized molecule and the optimal localized reference molecule, whose geometries are not kept the same. Fig.l shows the relationship between VRE and TRE. The computed results are listed in Table 1. 

Optimized bond lengths and (7 cc) resonance energies (RE) in benzene and cyclobutadiene 

Experimentally, the estimation of resonance energy is based on the heat of hydrogenation or combustion, and the value for benzene is -36 kcal/mol, which is comparable to the TRE of -44.5 kcal/mol. The small discrepancy between the experimental resonance energy and TRE is due mainly to the hyperconjugation 

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