text: In Chapter 12 of The Conservation of Orbital Symmetry, entitled "Violations," Woodward and Hoffmann famously stated:This pronouncement notwithstanding, it is important to recognize that the Woodward–Hoffmann rules are used to predict relative barrier heights, and thus likely reaction mechanisms, and that they only take into account barriers due to conservation of orbital symmetry.  Thus it is not guaranteed that a WH symmetry-allowed reaction actually takes place in a facile manner.  Conversely, it is possible, upon enough energetic input, to achieve an anti-Woodward-Hoffmann product.  This is especially prevalent in sterically constrained systems, where the WH-product has an added steric barrier to overcome.  For example, in the electrocyclic ring-opening of the dimethylbicyclo[0.2.3]heptene derivative (1), a conrotatory mechanism is not possible due to resulting angle strain and the reaction proceeds slowly through a disrotatory mechanism at 400 C to give a cycloheptadiene product.  Violations may also be observed in cases with very strong thermodynamic driving forces.  The decomposition of dioxetane-1,2-dione to two molecules of carbon dioxide, famous for its role in the luminescence of glowsticks, has been scrutinized computationally.  In the absence of fluorescers, the reaction is now believed to proceed in a concerted (though asynchronous) fashion, via a retro-[2+2]-cycloaddition that formally violates the Woodward–Hoffmann rules.
  Similarly, a recent paper describes how mechanical stress can be used to reshape chemical reaction pathways to lead to products that apparently violate Woodward–Hoffman rules.  In this paper, they use ultrasound irradiation to induce a mechanical stress on link-functionalized polymers attached syn or anti on the cyclobutene ring.  Computational studies predict that the mechanical force, resulting from friction of the polymers, induces bond lengthening along the reaction coordinate of the conrotatory mechanism in the anti-bisubstituted-cyclobutene, and along the reaction coordinate of the disrotatory mechanism in the syn-bisubstituted-cyclobutene.  Thus in the syn-bisubstituted-cyclobutene, the anti-WH product is predicted to be formed.
  This computational prediction was backed up by experiment on the system below.  Link-functionalized polymers were conjugated to cis benzocyclobutene in both syn- and anti- conformations.  As predicted, both products gave the same (Z,Z) product as determined by quenching by a stereospecific Diels-Alder reaction with the substituted maleimide.  In particular, the syn-substituted product gave the anti-WH product, presumably as the mechanical stretching along the coordinate of the disrotatory pathway lowered the barrier of the reaction under the disrotatory pathway enough to bias that mechanism.