Möbius aromaticity

[1][2] In terms of molecular orbital theory these compounds have in common a monocyclic array of molecular orbitals in which there is an odd number of out-of-phase overlaps, the opposite pattern compared to the aromatic character in Hückel systems.

The nodal plane of the orbitals, viewed as a ribbon, is a Möbius strip, rather than a cylinder, hence the name.

Möbius molecular systems were considered in 1964 by Edgar Heilbronner by application of the Hückel method,[3] but the first such isolable compound was not synthesized until 2003 by the group of Rainer Herges.

[4] However, the fleeting trans-C9H9+ cation, one conformation of which is shown on the right, was proposed to be a Möbius aromatic reactive intermediate in 1998 based on computational and experimental evidence.

The Herges compound (6 in the image below) was synthesized in several photochemical cycloaddition reactions from tetradehydrodianthracene 1 and the ladderane syn-tricyclooctadiene 2 as a substitute for cyclooctatetraene.

With bond lengths deduced from X-ray crystallography a HOMA value was obtained of 0.50 (for the polyene part alone) and 0.35 for the whole compound which qualifies it as a moderate aromat.

Henry Rzepa pointed out that the conversion of intermediate 5 to 6 can proceed by either a Hückel or a Möbius transition state.

The Hückel TS (left) involves 6 electrons (arrow pushing in red) with Cs molecular symmetry conserved throughout the reaction.

Another interesting system is the cyclononatetraenyl cation explored for over 30 years by Paul v. R. Schleyer et al.

This observation is explained by invoking a twisted 8-electron cyclononatetraenyl cation 2 for which a NICS value of -13.4 (outsmarting benzene) is calculated.

[8] A more recent study, however, suggests that the stability of trans-C9H9+ is not much different in energy compared to a Hückel topology isomer.

The same study suggested that for [13]annulenyl cation, the Möbius topology penta-trans-C13H13+ is a global energy minimum and predicts that it may be directly observable.

[9] In 2005 the same P. v. R. Schleyer [10] questioned the 2003 Herges claim: he analyzed the same crystallographic data and concluded that there was indeed a large degree of bond length alternation resulting in a HOMA value of -0.02, a computed NICS value of -3.4 ppm also did not point towards aromaticity and (also inferred from a computer model) steric strain would prevent effective pi-orbital overlap.

A Hückel-Möbius aromaticity switch (2007) has been described based on a 28 pi-electron porphyrin system:[11][note 2] The phenylene rings in this molecule are free to rotate forming a set of conformers: one with a Möbius half-twist and another with a Hückel double-twist (a figure-eight configuration) of roughly equal energy.

In 2014, Zhu and Xia (with the help of Schleyer) synthesized a planar Möbius system that consisted of two pentene rings connected with an osmium atom.

is the angle of twisting between consecutive orbitals, compared to the usual Hückel system.

Defining the variable we have: To find nontrivial solutions to this equation, we set the determinant of this matrix to zero to obtain Hence, we find the energy levels for a cyclic system with Möbius topology, In contrast, recall the energy levels for a cyclic system with Hückel topology,

Möbius versus Hückel
Möbius versus Hückel
The computed lowest energy conformation of trans -C 9 H 9 + . This conformation is believed to be Möbius aromatic based on computational and experimental data.
Computed structure of trans -C 9 H 9 + , 2 , illustrating the twisted nature of the ring, allowing incremental rotation of the orientation of p atomic orbitals around the ring: tracing the p orbitals all the way around the ring results in a phase inversion relative to the starting p orbital. The plane of the carbon skeleton (i.e., the nodal plane of the p orbitals) forms a Möbius strip.