Quantifying Allowedness Cubane - Cyclooctatetraene

The fact that the benzvalene-benzene interconversion is allowed in global symmetry led Mulder [31] to conclude that the Woodward-Hoffmann Rules that were designed to deduce stereochemistry, should be distinguished from the use of orbital correlation diagrams, and that correlation of the occupied orbitals of the reactant and product is no guarantee that the reaction will not have a high activation energy. 

The reliability of stereochemical criteria of allowedness will be looked into more carefully in the following chapters. Let us here consider the validity of the equations  

There is a logical difficulty here If the fact that certain reactions proceed more readily than others is explained by the fact that the former are symmetry-allowed and the latter are not, it is not very enlightening to define symmetry-allowed reactions as those that proceed readily and symmetry-forbidden as those that do not. Needless to say, the distinction between symmetry-allowed and symmetry-forbidden reactions is useful only if it can be shown to have energetic consequences, but the criteria that distinguish between them surely have to be based on symmetry rather than on energy. 

A particularly instructive case in point is the reluctance of cyclooctatetraene (COT) to isomerize to cubane in one step [1, pp. 32-33]. Cubane is substantially 

Since the energetic criterion of allowedness is logically questionable and its application to the Cubane-COT interconversion is so uncertain in practice, it had best be abandoned in favor of a distinction that is based firmly on symmetry properties the relative utility of local symmetry vs. global symmetry for this purpose arises once more. 

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