Correspondence diagram for interconversion of butadiene and bicyclobutane

In bicyclobutane, the CH bonds to Ci and C4 all lie in the xz plane and are not interconvertible. Accordingly, two of the four CH-bonding combinations are totally symmetric (ai) and the remaining two are labelled 61. In contrast, the CC bonds that form the four-membered ring are inter con verted by the sym-ops of C2VJ and their combinations span its four irreps. For completeness, we add the fifth CC-bonding orbital. In zeroth order, it is localized in the central bond between C2 and C3, but it interacts - favorably and unfavorably - with the totally symmetric acc combination to produce two ai orbitals, Ci and (T5. Since the analysis of the reaction is being formulated as an 18-electron problem, butadiene too has to be represented by nine doubly-occupied orbitals To the six in Fig. 5.5 we add three (Tcc orbitals to house the three electron pairs in the 

As in Fig. 5.5, the two totally symmetric CH-bonding orbitals correlate across the diagram, but the other two, both of them bi on one side and 62 on the other, can only be induced to correspond by displacement along an U2 coordinate, viz, a conrotation. The five CC-bonding orbitals correlate across the diagram without requiring any non-totally symmetric displacement at all. Evidently, the reaction has to be characterized formally as allowed in the subgroup C2, the kernel of fl2- This conclusion not only differs from that of the Rules but stands in apparent contradiction to experiment Bicyclobutene is thermodynamically much less stable than butadiene if its conversion to the latter can take place with conservation of orbital symmetry, why is it so difficult  

Every group has the trivial subgroup Ci, which only contains the identity element. 

The question posed in the preceding paragraphs as to the need for a reevaluation of the concept of allowedness , can be dismissed as a non-problem as long as it is taken as axiomatic that, for an orbital symmetry analysis to be of any use, the symmetry elements [retained along the pathway] must bisect bonds made or broken in the process . In contrast to the allowed conrotatory cyclization of butadiene to cyclobutene, in which the C2 axis bisects a newly formed cr bond, the only bond bisected by the axis in its conversion to bicyclobutane is the one between C2 and C3, which is essentially single in both the reactant and the product. 

It has already been pointed out that the bond-bisection requirement is imprecise.Moreover, even if this restriction is accepted provisionally, the problem reappears as soon as we get to the higher homologs of bicyclobutane benzvalene, in which the bicyclobutane moiety is fused onto ethylene, and naphth-valene, in which it is fused to a benzene ring. Both of these molecules are much less stable thermodynamically than their respective aromatic valence isomers, benzene and naphthalene, but - like cyclobutadiene - are remarkably resistant to thermal isomerization. Naphthvalene will be discussed at some length in a subsequent chapter, in connection with its unusual photochemical properties. We will here restrict our attention to the reluctance of benzvalene to undergo thermal isomerization to benzene. 

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Figure 5.8. Correspondence diagram for interconversion of butadiene and bicyclobutane...

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