Violations of the noncrossing rule due to special symmetry and alternance

This paper reports a study on which behavior of the Hamiltonian gives rise to violation of the noncrossing rule. In principle, the noncrossing rule may be violated when a special symmetry other than spatial and spin symmetries is present or there exists the so‐called alternance, which corresponds to a Hamiltonian in a real vector space anticommuting with a Hermitian operator. In the HMO models for pericyclic reactions, violations due to special symmetry or alternance have been found. The [ m , n ] supra – antara cycloadditions have no symmetry in the traditional sense, but have special symmetry leading to the existence of crossings in the correlation diagram. Alternance results in one crossing in the middle of the correlation diagram of a forbidden pericyclic reaction with intermediate states in the form of even alternant hydrocarbon. For the reactions with intermediate states in the form of odd alternant hydrocarbon such as [2,4]‐cycloaddition of an allyl cation or an allyl anion to butadiene, there should be no crossing in the correlation diagrams, and both the supra – supra and the supra – antara processes are predicted to be allowed. Such a prediction is beyond the Woodward–Hoffmann rule.