Phase-change rule, pericyclic reactions

Diels-Alder reaction, phase-change rule, pericyclic reactions, 447-450... 

Longuet-Higgins phase-based treatment, three-particle reactive system, 157-168 theoretical background, 43-44 observability, 208 quantum theory, 200 Phase-inverting reactions molecular model, 496-499 phase-change rule, pericyclic reactions, 449-450... 

Antisymmetric matrix, non-adiabatic coupling, vector potential, Yang-Mills field, 94-95 Aromaticity, phase-change rule, chemical reaction, 446-453 pericyclic reactions, 447-450 pi-bond reactions, 452-453 sigma bond reactions, 452 Aromatic transition state (ATS), phase-change rule, permutational mechanism, 451-453... 

Sigmatropic shifts represent another important class of pericyclic reactions to which the Woodward-Hoffmann rules apply. The selection rules for these reactions are best discussed by means of the Dewar-Evans-Zimmerman rules. It is then easy to see that a suprafacial [1,3]-hydrogen shift is forbidden in the ground state but allowed in the excited state, since the transition state is isoelectronic with an antiaromatic 4N-HQckel system (with n = 1), in which the signs of the 4N AOs can be chosen such that all overlaps are positive. The antarafacial reaction, on the other hand, is thermally allowed, inasmuch as the transition state may be considered as a Mobius system with just one change in phase. 

Therefore, if we derive or remember one rule for a pericyclic reaction, then any time an MO phase change is added the rule will reverse. Two reversals cancel each other. For example, 4n face to face (supra-supra) cycloadditions are not thermally allowed. If we add two electrons, we fill the next highest MO, which has a phase reversal. This means An+2 cycloadditions are thermally favored. Thermal electrocyclic reactions of 4n species go conrotatory, whereas thermal 4n+2 electrocyclic reactions go disrotatory. Thermal sigmatropic reactions of 4n species go supra-inversion or antara-retention. Count arrows to tell whether the pericyclic reaction is 4n or 4n + 2. Phase reversals occur between retention/inversion at the migrating center, between antarafacial/suprafacial migration, with 4n vs. 4n+2 electrons, and between thermal and photochemically excited species. 

The concepts of frontier orbital HOMO LUMO interactions, the idea of an aromatic transition state, and the alternative concept of conservation of orbital symmetry (not developed in this chapter) all lead to the same result for pericyclic reactions which involve a cyclic overlap of orbitals in the transition slate, thermal reactions are allowed for reactions involving 4n + 2 electrons in Hiickel systems (no change in phase between overlapped orbitals in the cyclic transition state) or for 4/j electrons in Mobius systems (phase between overlapped orbitals in the cyclic transition state changes once on going round the ring). For photochemical systems, these rules are reversed. 

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