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Möbius–Hückel concept
The Möbius–Hückel treatment is one of two predicting reaction allowedness versus forbiddenness. The concept is the counterpart of the Woodward–Hoffmann approach. The methodology in this treatment utilizes the plus-minus sign parity in proceeding around a cycle of orbitals in a molecule or reaction while the Woodward–Hoffmann methodology uses a large number of rules with the same consequences.
==Introduction==
The Möbius–Hückel (M–H) Concept for reaction allowedness and forbiddeness. One year following the Woodward Hoffmann〔“Stereochemistry of electrocyclic reactions”, Woodward, R. B.; Hoffmann, Roald. J. Amer. Chem. Soc. 1965, 87, 395-397.〕 and Longuet-Higgins〔 "The Electronic Mechanism of Electrocyclic Reactions" Longuet-Higgins, H. C.; Abrahamson, E. W. J. Am. Chem. Soc., 1965, 87, 2045-2046.〕 publications, it was noted by Zimmerman that both transition states and stable molecules sometimes involved a Möbius array of basis orbitals〔"On Molecular Orbital Correlation Diagrams, the Occurrence of Möbius Systems in Cyclization Reactions, and Factors Controlling Ground and Excited State Reactions. I," Zimmerman, H. E. J. Am. Chem. Soc., 1966, 88, 1564-1565.〕〔"On Molecular Orbital Correlation Diagrams, Möbius Systems, and Factors Controlling Ground and Excited State Reactions. II," Zimmerman, H. E. J. Am. Chem. Soc., 1966, 88, 1566-1567.〕 The Möbius–Hückel treatment provides an alternative to the Woodward–Hoffmann one. In contrast to the Woodward–Hoffmann approach the Möbius–Hückel treatment is not dependent on symmetry and only requires counting the number of plus-minus sign inversions in proceeding around the cyclic array of orbitals. Where one has zero or an even number of sign inversions there is a Hückel array. Where an odd-number of sign inversions is found a Möbius array is determined to be present. Thus the approach goes beyond the geometric consideration of Edgar Heilbronner. In any case, symmetry may be present or may not.
Edgar Heilbronner had described twisted annulenes which had Möbius topology, but in including the twist of these systems, he concluded that Möbius systems could never be lower in energy than the Hückel counterparts.〔"Hueckel molecular orbitals of Moebius-type conformations of annulenes," Heilbronner, E. Tetrahedron Letts 1964, 1923-1928.〕 In contrast, the Möbius–Hückel (M–H) Concept considers systems with an equal twist for Hückel and Möbius Systems.
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