DOI: 10.1002/cphc.201402266 The Nature of One-Dimensional Carbon: Polyynic versus Cumulenic Christian Neiss,* Egor Trushin, and Andreas Gçrling [a] 1. Introduction Besides fullerenes, carbon nanotubes, and graphene (and graphynes), one-dimensional carbon, that is, long linear chains of carbon atoms called “linear carbon” or carbyne, constitutes another promising carbon-based material. Linear carbon is ex- pected to possess intriguing physical properties such an extra- ordinarily high tensile strength and modulus, [1] making them interesting candidates for mechanical applications. Most im- portant, perhaps, is their potential use in molecular electronics, for example in novel field-effect transistors or molecular wires. [1, 2] Carbyne can be viewed as both a (virtually) infinitely long polyyne chain ( C  C ) 1 with alternating long and short bonds, and an infinite cumulene chain ( =C =C =) 1 with equal bond lengths (cf. Figure 1), thus, the fundamental question arises, which picture is more appropriate, i.e. whether an infin- ite linear carbon chain exhibits bond-length alternation (BLA) or not. The question is not only of academic interest but is also of practical importance because the band structure, most notably the band gap, strongly depends on the BLA and there- fore the electronic properties will be different in both cases. In the last decades several theoretical studies on both finite- sized linear carbon chains [3–11] and rings, [4, 12–15] and infinite linear carbon [13, 16–24] have been conducted. In the simple ex- tended Hückel and (closed-shell) Hartree–Fock approximations, the end groups of a finite chain determine whether the mole- cule is a polyyne or a cumulene up to quite large chain lengths. [3] With the chain length going to infinity, however, end group effects must be negligible and properties of both com- pounds must coincide. In complete analogy to a polyacetylene chain, linear carbon can be expected to undergo a Peierls dis- tortion, that is, the cumulenic geometry with all bonds being equal should not be stable and should turn into a polyynic structure with alternating longer and shorter C C bonds. This has been found in virtually all calculations on infinite linear carbon chains. The extent of the distortion, that is, the size of the BLA, depends quite strongly on the method used. Whereas the Hartree–Fock (HF) method predicts strong BLA of about 20 pm, [19, 20] local density (LDA) and generalized gradient (GGA) approximations within the framework of density-functional theory (DFT) calculations result in structures with small BLA values about 2–4 pm, [13, 24] illustrating the tendency of HF to lo- calize bonds, whereas LDA/GGA density functionals tend to generate more delocalized electronic structures. Hybrid density functionals yield results between those of HF and LDA/GGA methods and, for linear and cyclic carbon molecules up to 18 carbon atoms, are in good agreement with high level coupled- cluster CCSD(T) and MCSCF/quantum Monte Carlo (QMC) cal- culations. [4, 14, 15] A question of both fundamental as well as practical impor- tance is the nature of one-dimensional carbon, in particular whether a one-dimensional carbon allotrope is polyynic or cu- mulenic, that is, whether bond-length alternation occurs or not. By combining the concept of aromaticity and antiaroma- ticity 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 cru- cially 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. Figure 1. Lewis formulas for carbon chains and rings (here: C 14 ). Left: polyyn- ic structure with alternating bonds. Right: cumulenic structure with equal bond lengths. [a] Dr. C. Neiss, E. Trushin, Prof. Dr. A. Gçrling Lehrstuhl für Theoretische Chemie Universität Erlangen-Nürnberg and Interdisciplinary Center of Molecular Materials (ICMM) Egerlandstr. 3, D-91058 Erlangen (Germany) E-mail : christian.neiss@fau.de Supporting Information for this article is available on the WWW under http://dx.doi.org/10.1002/cphc.201402266. # 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim ChemPhysChem 0000, 00,1–7 &1& These are not the final page numbers! ÞÞ CHEMPHYSCHEM ARTICLES