Digression on Entropy of Activation

Correspondence between the mismatched ai and 62 orbitals is induced by incorporating in the reaction coordinate a 62 displacement that lengthens one of the a bonds more than the other. As a result, the reaction takes a stepwise course, in which the bonds are ruptured one by one and the increased enthalpy of activation is compensated by a large positive activation entropy. 

It follows from the analysis that the syn dimer is the isomer that is more likely to break both bonds of the four-membered ring at once, for precisely the 

No reduction of symmetry below Cg is formally called for, so the transition state is less sterically strained than that of the yn-o,o -dimer. Accordingly the activation entalpy, AH = 14.3 kcal/mol, is appreciably lower and the entropy of activation, AS = -6. cal/mol°K, is less negative, but both sets of activation parameters are consistent with simultaneous rupture of both bonds. 

The anti isomer cannot conveniently break both bonds as once, but it has an alternative stepwise pathway at its disposal  

The first step is a disrotatory cyclohexadiene-hexatriene isomerization. Its product, cf5-dihydrobenzocyclooctatetraene, is less stable than the trans dimer and is known to isomerize to it, [27] the isomerization presumably taking place via an a displacement that reduces symmetry to Ci, in which no reaction is forbidden. At the higher temperatures at which fragmentation occurs, the first product should be in equilibrium with the reactant, and its eight-membered ring is sufficiently flexible that a similar desymmetrization would allow it to serve as an unstable intermediate. The activation parameters cited above, which - for the postulated mechanism - measure the enthalpy and entropy differences between the reactant and the transition state of the second step, are not inconsistent with concerted electrocyclic rupture of both bonds via a relatively unconstrained transition state. 

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