On the alternating structure of cyclo[18]carbon

Abstract

Cyclo[18]carbon, has been recently characterized by high-resolution atomic force microscopy which revealed a polyynic structure with alternating single and triple bonds. It is natural to ask why it does not exhibit bond equalization and adopt a cumulenic structure. This paper, on the other hand, begins with the opposite question: why we expect it to exhibit bond equalization in the first place. We then reexamine whether these intuitive arguments are theoretically sound. Hückel model, which was often attributed as the underlying reason for the famous 4N+2 electron-counting rule for aromatics, was reviewed with minimal structural flexibility introduced, which surprisingly revealed that even benzene would undergo bond alternation under the Hückel framework. This analysis is confirmed by extended Hückel calculations. DFT and semi-empirical calculations revealed that internuclear repulsion would be necessary for a model to correctly predict the D6h structure of benzene. Similar scenario was observed for C18, except that a greater fraction of exact exchange may result in a small energy gain when molecule distorts from D18h to D9h geometry. HOMO energy lowering and LUMO energy rising were found in the symmetry-lowering distortion of both benzene and C18, thus disqualifying the usual explanation of the bond alternating structure of C18 based on second-order Jahn-Teller effect. Finally, a hydrogen-ring model was presented as a toy model to investigate the origin of bond equalization of so-called aromatic systems, which clearly revealed the role of nuclear repulsion in favoring high-symmetry structure while electronic energy monotonically decreases in symmetry-lowering process.

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