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The one-sided Möbius strip with its characteristic 180° twist in the loop has inspired philosophers, artists and scientists since hundreds of years and continues to do so. On the molecular level, only in the last 15 years have some groups succeeded in synthesizing new expanded porphyrin compounds large enough to adopt Möbius-strip topology and Möbius aromaticity, the first being Lechosław Latos-Grażyński and collaborators in Wroclaw (2007) and Atsuhiro Osuka and collaborators in Kyoto (2008). We report on new studies of expanded porphyrins with either Möbius topology or Hückel topology that were synthesized in these laboratories. In this minireview, we focus on recent continuous-wave and time-resolved EPR, ENDOR and DFT MO studies on open-shell states of di-p-benzi[28]hexaphyrin(1.1.1.1.1.1), specifically, on the ground-state radical cation doublet state (total electron spin S = 1/2) and the first excited triplet state (S = 1). The review is largely based on the results and discussions of two previous publications: Möbius et al. (Appl Magn Reson 47:757–780, 2016) and Ema et al. (J Phys Chem Lett 9:2685–2690, 2018). In the open-shell systems, besides the electron-nuclear hyperfine couplings also the zero-field interaction tensor turned out to be a viable sensor for electronic structure changes between Möbius and Hückel topologies. In the Outlook section, we address the cyclotides, a new class of natural circular mini-proteins, usually less than 100 amino acids long. They are distinguished by exceptional chemical and biological stability. This is due to topological constraints imposed by threefoil knot and Möbius-strip formation. As a result, their physical qualities are “topologically protected”. This makes them highly interesting for medical or agricultural applications, for example as novel active ingredients against autoimmune diseases, viral infections, or as agents against insect damage to crops.

Klaus Möbius gives a selection of his biographical experiences which have shaped his academic and personal life.