A molecule with half-Möbius topology.

Stereoisomers of C13Cl2 exhibiting helical orbitals around a ring of carbon atoms were synthesized by atom manipulation on NaCl surfaces. We resolved the enantiomeric geometries of the singlet states by atomic force microscopy and mapped their helical orbital densities by scanning tunneling microscopy. A π-orbital basis of the helical, nonplanar 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. A quasiparticle on a ring with this boundary condition could be interpreted as carrying a Berry phase of π/2. We demonstrate reversible switching of the topology between the two singlets of oppositely threaded half-Möbius topology and the planar, topologically trivial triplet state. Multireference calculations, including large-scale, sample-based ab initio calculations executed on quantum hardware, revealed that the switching is associated with a helical pseudo–Jahn-Teller effect. Editor's summary: C13Cl2 forms a strained ring of carbon atoms with a curious electronic structure. The nonplanar singlet state is periodic only after four circulations of the ring system and is consistent with a half-Möbius topology. Rončević et al. synthesized this molecule on a sodium chloride surface by dechlorinating a larger precursor and mapped the helical orbital densities using scanning tunneling microscopy. They could reversibly switch the topology between two singlets of oppositely threaded half-Möbius topology and the planar, topologically trivial triplet state. —Phil Szuromi INTRODUCTION: Topologically nontrivial molecules are rare but highly appealing because of their unusual electronic structure, with profound implications on stability, coherent transport, and aromaticity. To realize such systems, chemists have long theorized about molecules with geometries resembling a Möbius strip where the p-orbitals form a helical basis, potentially giving rise to a Möbius topology and helical orbitals. The properties of topologically nontrivial molecules are challenging to predict and remain largely unexplored, rendering them excellent systems to benchmark theoretical approaches. RATIONALE: An sp-hybridized carbon atom has two mutually orthogonal p-orbitals without a fixed orientation, allowing different orbital bases for a given geometry. In systems with both sp and sp2 carbons, such as the studied C13Cl2 (compound 2 in the figure: carbons connected to Cl atoms are sp2-hybridized, whereas all other carbons are sp-hybridized), both helical and nonhelical π-bases are allowed by geometry, and the realization of a trivial or nontrivial topology is determined by electronic structure. A Möbius topology implies a helical twist by 180° in one circulation and periodicity upon two circumnavigations. However, in 2, the two orthogonal p-orbitals of the sp-carbons allow a twist of the π-basis by 90° in one circumnavigation and periodicity upon four circumnavigations, characterizing a nontrivial topology that we refer to as half-Möbius. RESULTS: From the precursor molecule C13Cl101, we synthesized stereoisomers of C13Cl22 by atom manipulation on NaCl surfaces at cryogenic temperatures. We resolved the enantiomeric geometries of the singlet states 12-P and 12-M by atomic force microscopy and mapped their helical orbital densities by scanning tunneling microscopy. These observables are rationalized by a π-orbital basis that twists by 90° in one circulation, consistent with the half-Möbius topology. We demonstrated tip-induced reversible switching of the topology by interconverting between the two singlet enantiomer ground states with oppositely threaded half-Möbius topology and the planar, topologically trivial, metastable triplet state 32. Ab initio multireference calculations, including large-scale sample-based calculations executed on quantum hardware, revealed that the switching is associated with a helical pseudo–Jahn-Teller effect. CONCLUSION: The half-Möbius topology has intriguing and not yet explored consequences; for example, the aromaticity rules for Hückel and Möbius molecules do not apply. Moreover, the half-Möbius topology corresponds to a boundary condition differing from that of both Hückel (Berry phase of 0) and Möbius (Berry phase of π) systems. The demonstrated on-demand switching between trivial and nontrivial topologies and chiralities offers the possibility of exploring quasiparticle properties rooted in topology. Building on the half-Möbius topology, more complex molecules and molecular networks with braiding of connectivity and topology that might even be switchable can be envisioned. Future experiments on molecules with nontrivial topology and/or complex electronic structures could serve for the validation of quantum hardware calculations beyond the reach of their classical counterparts. Switching molecular topology.: From precursor 1, isomers of 2 were synthesized using tip-induced chemistry. Compound 2 was reversibly switched between the nonplanar singlets 12-P and 12-M and the planar triplet 32. Stereoisomers 12-P and 12-M differ by the threading of their orbitals (see calculated Dyson orbitals in this figure) and π-orbital bases, which are of half-Möbius topology. These orbital bases change sign with respect to two circumnavigations and are periodic with respect to four circumnavigations. [ABSTRACT FROM AUTHOR]