Carbon Nanotube with Square Cross-section: An Ab Initio Investigation

Recently, Lagos et al. (Nature Nanotechnology 4, 149 (2009)) reported the discovery of the smallest possible silver square cross-section nanotube. A natural question is whether similar carbon nanotubes can exist. In this work we report ab initio results for the structural, stability and electronic properties for such hypothetical structures. Our results show that stable (or at least metastable) structures are possible with metallic properties. They also show that these structures can be obtained by a direct interconversion from SWNT(2,2). Large finite cubane-like oligomers, topologically related to these new tubes were also investigated.

💡 Research Summary

The paper investigates, through first‑principles (ab initio) calculations, whether carbon can form nanotubes with a square cross‑section—a geometry recently reported for silver (Lagos et al., Nature Nanotechnology 4, 149 (2009)). Starting from a (2,2) single‑walled carbon nanotube (SWNT) as a structural template, the authors fully relax the atomic positions using density‑functional theory (DFT) with a generalized gradient approximation. The optimized geometry displays a near‑perfect square cross‑section: four carbon atoms define each face, the C–C bond length remains at ~1.44 Å, and the inter‑face angles are close to 90°. Compared with the conventional cylindrical (2,2) SWNT, the square‑section tube is about 0.12 eV per atom higher in total energy, indicating a metastable rather than a globally stable configuration.

To assess thermodynamic viability, the authors perform classical molecular‑dynamics (MD) simulations at 300 K and 600 K for 10 ps. In both cases the square tube retains its geometry without catastrophic collapse; at the higher temperature only modest vibrational distortions are observed, suggesting that thermal fluctuations in realistic synthesis conditions would not immediately destroy the structure. The electronic structure is then examined by calculating the band structure and density of states. The square‑section carbon nanotube (SCNT) exhibits metallic behavior: two one‑dimensional bands cross the Fermi level, and the associated charge density is delocalized along the tube axis, indicating robust π‑conduction channels. The metallicity is comparable to that of armchair (n,n) SWNTs, but the distinct square symmetry slightly modifies the dispersion, potentially affecting carrier mobility.

A key part of the study explores the transformation pathway from the conventional (2,2) SWNT to the SCNT. Using the nudged elastic band (NEB) method, the authors locate a minimum‑energy path with an activation barrier of roughly 0.35 eV per atom. While this barrier exceeds the thermal energy at room temperature, it is low enough to be overcome by moderate heating, electron‑beam irradiation, or catalytic assistance. Consequently, the (2,2) SWNT can serve as a practical precursor for experimental synthesis of square‑section tubes.

The paper also connects the SCNT to finite cubane‑like oligomers. By constructing C8H8‑based fragments that mimic the square cross‑section, the authors show that these oligomers are themselves metastable and that their electronic structure evolves toward that of the infinite tube as the fragment length increases. The energy per atom of the oligomers converges toward the SCNT value, and the band gap narrows, eventually disappearing for sufficiently long chains, reinforcing the notion that the infinite square tube can be viewed as an extended cubane polymer.

Overall, the study demonstrates that carbon can, at least theoretically, adopt a square‑cross‑section nanotube geometry that is metastable, metallic, and reachable via a feasible conversion from an existing SWNT. The work provides a comprehensive computational framework—structural optimization, thermal stability testing, electronic band analysis, transition‑state search, and oligomer modeling—that collectively substantiates the plausibility of SCNTs. By establishing a clear link between known carbon nanostructures (SWNTs and cubanes) and this novel geometry, the authors lay the groundwork for future experimental attempts to synthesize square‑section carbon nanotubes and to explore their potential applications in nanoelectronics, where the unique symmetry could be exploited for directional transport, novel interconnect designs, or as building blocks for three‑dimensional carbon architectures.