A question of both fundamental as well as practical importance is the nature of one-dimensional carbon, in particular whether a one-dimensional carbon allotrope is polyynic or cumulenic, that is, whether bond-length alternation occurs or not. By combining the concept of aromaticity and antiaromaticity with the rule of Peierls distortion, the occurrence and magnitude of bond-length alternation in carbon chains with periodic boundary conditions and corresponding carbon rings as a function of the chain or ring length can be explained. The electronic properties of one-dimensional carbon depend crucially on the bond-length alternation. Whereas it is generally accepted that carbon chains in the limit of infinite length have a polyynic structure at the minimum of the potential energy surface with bond-length alternation, we show here that zero-point vibrations lead to an effective equalization of all carbon–carbon bond lengths and thus to a cumulenic structure.
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