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Pericyclic Reactions: Aromaticity of Transition States

Aromaticity of Transition States: Hückel and Möbius Aromatic Systems

Pericyclic transition states show additional special features as there are Möbius as well as Hückel aromatic systems. In the former the cyclic conjugated system is twisted by 180° around its axis. A Möbius system can be thought of being constructed from a Hückel system by cleaving the latter, twisting the generated linear system by 180° and fastening the ends together to form a cycle.

Formal transformation of a Hückel system into a Möbius system
Orbital representationStrip representation
1. Cyclic Hückel system
2. "Normal" linear system
3. System twisted by 180°
4. Cyclic Möbius system

Möbius systems exhibit interesting topological properties which were investigated by the German mathematician and astronomer A. F. Möbius. In 1964 Edgar Heilbronner postulated that such hypothetical Möbius systems are aromatic if they contain 4n electrons and are antiaromatic with 4n+2 electrons.

Hückel system

  • 4n+2 Electrons: aromatic
  • 4n Electrons: antiaromatic

Möbius system

  • 4n Electrons: aromatic
  • 4n+2 Electrons: antiaromatic

After numerous unsuccessful attempts, the first stable Möbius aromatic compound was synthesized in 2003 (D. Ajami, O. Oeckler, A. Simon, R. Herges, Nature 2003, 426, 819-821):

3D model of the first stable Möbius aromatic compound

However, Möbius aromatic transition states occur relatively frequently. To define a transition state as aromatic (favorable)) or antiaromatic (unfavorable) it is important to first find out whether the transition state exists in Hückel or Möbius topology. To simplify the determination Dewar and Zimmerman proposed in 1966 the following simple rule: The basis set of orbitals in Hückel systems always has to show zero or an even number of sign inversions (antibonding overlap).

Examples representing Hückel systems
0 Sign inversion2 Sign inversions4 Sign inversions

No matter how the inversion signs are drawn in the orbital basis set the number of inversions remains even. If one orbital is "turned around", i.e. the signs are changed, overlap with its two neighbors also changes and the change of sign inversions remains even. For the purpose of clarity it is always better to draw the orbitals in such a way that the fewest number of inversions are generated. Generally, the signs in Hückel systems can be chosen such that no sign inversion is included. It should be noted that the diagrams do not represent molecular orbitals but basis sets of p orbitals with signs arbitrarily selected.

Contrary to Hückel systems Möbius systems must have at least one sign inversion caused by the twisting. Similar to Hückel systems the number of sign inversions remains zero or changes by two if one of the participating orbitals is turned around. In these systems the number of sign inversions is always odd.

Examples representing Möbius systems
1 Sign inversion3 Sign inversions

Passing the line through the orbital origin does not count as sign inversion, since it does not represent antibonding overlap of two neighboring orbitals.

No sign inversion
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