Correspondence diagram for cyclization of butadiene

The four CH bonds of cyclobutene interconvert under the four sym-ops of C2v and their linear combinations span its four irreps. In butadiene, all four bonds are in the molecular plane and come in two distinct pairs, an inner and an outer as a result, only those irreps appear that are symmetric to reflection in cr(i/z), i.e. Ui and 62 each one twice. 

Few organic chemists would contest the proposition that the CH-bonding electrons remain localized in the CH bonds as the methylene groups rotate.  

The CH-bonding orbitals would therfore be expected to correlate across the diagram. This can be accomplished either by a conrotation, which induces 

In the preceding subsection we have merely reproduced the familiar prediction once more, but the viewpoint adopted above may perhaps have provided additional insight into its origin. When it is recognized that a reaction that is forbidden by orbital symmetry conservation to take place in a group of high symmetry can be made allowed by an suitable desymmetrizing perturbation, it becomes appropriate to ask whether substitutional desymmetrization, such as that discussed in Section 2.3.2, may not be as effective for that purpose as distortional desymmetrization. 

The experimental enthalpy of activation for disrotatory thermal isomerization of cis-l,3,5-hexatriene to 1,3-cyclohexadiene in the gas phase at 100 C is 29.2 kcal/mol [13]. The reaction is exothermic by 14.5 kcal/mol [14, p. 127], so of the reverse reaction is 43.7 kcal/mol, but - in spite of its high activation energy - it is characterized as allowed by all of the common orbital symmetry criteria. In norcaradiene ([4.1.0]hepta-2,4-diene), the cyclopropane ring bridging Cl and Ce of cyclohexadiene has built the disrotation into the molecule, desymmetrizing it - and its monocyclic isomer, cycloheptatriene - to C, in which the 61 and ai orbitals correlate directly (Fig. 5.3). The rate of isomerization is so much faster that it had to be measured at low temperature (ca. 100 K) in a hydrocarbon glass [15] is only 6.3 kcal/mol  

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Figure 5.1. Rudimentary correspondence diagram for cyclization of Butadiene. (The orbitals are labeled as in Fig. 19 of ref. [1] their irreps in are given in parenthesis)...

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