I recently answered the question of whether twisted polyene chains were known by pointing towards Möbius aromatic system. While in conventional Hückel aromatic systems the lowest-lying π-orbital obviously has a nodal plane containing all the nuclei, this is not possible in a Möbius aromat since topologically these only have one side.
A number of Möbius aromatic systems have been both synthesised[1] and calculated;[2] for an X-ray determined structure of one, see the second structure in the figure below.[3]
One can easily see that the π chain would have green and white or plus phase and minus phase overlapping. This got me thinking and wondering: what would this system’s molecular orbitals look like? Specifically: is there a set of MOs that would correspond approximately to the π system of such a Möbius aromat? If not, how are the π bonds seen in an MO analysis? The only calculations I could find searching the literature were both very old and without nice pictures.
References:
[1]: M. Stępień, N. Sprutta, L. Latos-Grażyński, Angew. Chem. Int. Ed. 2011, 50, 4288–4340. DOI: 10.1002/anie.201003353.
[2]: H. S. Rzepa, Chem. Rev. 2005, 105, 3697−3715. DOI: 10.1021/cr030092l.
[3]: Y. Tanaka, S. Saito, S. Mori, N. Aratani, H. Shinokubo, N. Shibata, Y. Higuchi, Z. S. Yoon, K. S. Kim, S. B. Noh, J. K. Park, D. Kim, A. Osuka, Angew. Chem. Int. Ed. 2008, 47, 681–684. DOI: 10.1002/anie.200704407.