A Molecule with Half-Möbius Topology

Stereoisomers of $C_{13}$ $Cl_2$ exhibiting helical orbitals around a ring of carbon atoms were synthesized by atom manipulation on bilayer NaCl on Au(111). We resolved the enantiomeric geometries of the closed-shell singlet states by atomic force microscopy and mapped their helical orbital densities by scanning tunnelling microscopy. A 𝜋 -orbital basis of the helical, non-planar singlets that twists by 90 ∘ in one circulation is consistent with a half-Möbius topology. In such a topology, the 𝜋 -orbital basis changes sign with respect to two circumnavigations and is periodic with respect to four circumnavigations. This is in contrast to a topologically trivial Hückel basis, which shows no twist, and a Möbius basis, which twist by 180 ∘ in one circulation. We demonstrate reversible switching of the topology, between the two singlets of oppositely threaded half-Möbius topology, and the planar, topologically trivial, triplet state.