Symmetry properties of hexatriene molecular orbitals

During the disrotatory opening of cyclobutene to butadiene, a plane of S3mi-metry is maintained at every stage of the reaction  

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FIGURE 1.11 Symmetry properties of the molecular orbitals of butadiene and hexatriene systems. 

However, for systems containing (4n + 2) rr-electrons, theoretical predictions are entirely different and are in conformity with the actual observations. A typical system of this type is the interconversion of cyclohexadiene and hexatriene. In this transformation, six molecular orbitals (Wj to We) of hexatriene and six molecular orbitals (four tt and two ct) of cyclohexadiene are actually involved and, therefore, need to be considered. Symmetry properties of the six molecular orbitals of hexatriene and cyclohexadiene are shown in Figure 2.6. 

FIGURE 2.6 Symmetry properties of molecular orbitals of cyclohexadiene and hexatriene. 

Fig. 1.4 Molecular orbitals of 1,3,5-hexatriene and their wave functions and symmetry properties...

Table 7 summarizes several predictions of mid-sized aromatic molecules from the study of Matsuzawa and Dixon. The p value for a molecule with the inversion symmetry operation (benzene) is zero from symmetry arguments. Note that there are sizeable deviations among the experimental observations of p and Y values, as they are also properties difficult to measure. Agreement in Table 7 should be considered reasonably good. Matsuzawa and Dixon have also compared their calculated y values of ethylene, frans-butadiene, and trans-hexatriene with those obtained from ab initio molecular orbital methods the results from their study show that B-LYP calculations are more accurate than those at the Hartree-Fock level and are of comparable accuracy to MP2 results. 

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