Relative molecular stability. Carbyne rings have been proposed as a transitional form of carbon during the synthesis of fullerenes [60–63]. Other intermediate forms occurring with chain self-adhesion may form (e.g., so-called bow tie structures). To assess the stability of the rings during folding/three-loop configuration, the atomistic energy of cumulene rings and example intermediate’ structures was assessed with n = 20 (top, blue) and n = 36 (bottom, red) carbon atoms. We see that, aside from the fullerenes, the closed-loop ring polyyne carbyne structures are more energetically favorable (lower energy) than the intermediates depicted, suggesting a relative stability for the equilibrium simulations undertaken.