One year following the Woodward–Hoffmann and Longuet-Higgins–Abrahmson publications, it was noted by Zimmerman that both transition states and stable molecules sometimes involved a Möbius array of basis orbitals. 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. In contrast, the Möbius–Hückel concept considers systems with an equal twist for Hückel and Möbius systems.