Huckel-Mobius Concept

Kei-wei Shen, Huckel-MObius Concept in Concerted Reactions," J. Chem. Educ. 50, 238 (1973). 

While the initial formulation of homoaromaticity pre-dated the introduction of orbital symmetry by some eight years the two concepts are inextricably linkedThis is most evident when pericyclic reactions are considered from the perspective of aromatic or antiaromatic transitions states and the Huckel/Mobius concept. The inter-relationship can be demonstrated by the electrocyclic reaction shown in Scheme 1. ... 

H. E. Zimmerman, The Mobius-Huckel Concept in Organic Chemistry. Application to Organic Molecules and Reactions, Accounts Chem. Res. 4, 272 (1971). 

We start with some biographical notes on Erich Huckel, in the context of which we also mention the merits of Otto Schmidt, the inventor of the free-electron model. The basic assumptions behind the HMO (Huckel Molecular Orbital) model are discussed, and those aspects of this model are reviewed that make it still a powerful tool in Theoretical Chemistry. We ask whether HMO should be regarded as semiempirical or parameter-free. We present closed solutions for special classes of molecules, review the important concept of alternant hydrocarbons and point out how useful perturbation theory within the HMO model is. We then come to bond alternation and the question whether the pi or the sigma bonds are responsible for bond delocalization in benzene and related molecules. Mobius hydrocarbons and diamagnetic ring currents are other topics. We come to optimistic conclusions as to the further role of the HMO model, not as an approximation for the solution of the Schrodinger equation, but as a way towards the understanding of some aspects of the Chemical Bond. 

The Mobius-Huckel concept was introduced by Zimmerman in 1966 35). It was suggested that each cyclic array of orbitals in a reacting system may be categorized as a Hiickel type or a Mobius type , depending on the number of plus-minus overlaps between adjacent orbitals. With zero or an even number of such sign inversions, the system is a Hiickel variety array while with one or some other odd number the system is a Mobius system. 

Zimmerman, H. Mobius-Huckel concept in organic chemistry. Application of organic molecules and reactions, Acc. Chem. Res. 1971,4, 272-280. 

The [nlannulenes may be defined as cyclic polyaUcenes possessing a closed circuit of n Ti-conjugated pz-orbitals. The first three small annulenes are shown in Fig. 1 and include [4]annulene (cyclobutadiene), [6]annulene (benzene), and [8]annulene (cyclooctatetraene). The bracketed number, n, can be classified as either a 4n+2 (Hiickel aromatic/Mobous antiasomatic) or 4n (Huckel antiaromatic/ Mobius aromatic) delocalized n-electron species. That said, it is not surprising that the concept of aromaticity is closely associated with the annulenes. Indeed, the first three annulenes listed cover the concepts of Hiickel aromatic, antiaromatic, and nonaromatic properties (see Fig. 1). 

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