1. Carbon Nanotube with Square Cross-section: An Ab Initio Investigation
P.A.S. Autreto, S.B. Legoas, M.Z.S. Flores, and D.S.Galvão
Supplementary Material

2. INTRODUCTION

3. Smallest metal nanotube with square cross-section
Frontal view
Lagos, M. et al. Observation of the smallest metal nanotube with a square cross-section. Nature Nanotechnology, 4, (2008)

4. Smallest carbon nanotube experimentally observed
SWNT(2,2)
Frontal View
D. Stojkovic, P. Zhang, and V. H. Crespi, Phys. Rev. Lett. 87, (2001).
X. Zhao, Y. Liu, S. Inoue, T. Suzuki, R. O. Jones, and Y. Ando, Phys. Rev. Lett. 92, (2004).

5. Cubane Cubane (C8H8) Molecule
P. E. Eaton and T. H. Cole Jr., J. Amer. Chem. Soc. 86, 962 (1964).

6. Objective: investigation of the properties of Carbon Nanotube with Square Cross-section (CNTSC)
Frontal View

7. Polymeric Approach to produce Carbon Nanotube
B. Esser et al., Synthesis of [6.8]3Cyclacene: Conjugated Belt and Model for an Unusual Type of Carbon Nanotube. JACS 130, 6716 (2008)

8. Cubane-like oligomers

9. METHODOLOGY

10. Method (Ab initio method)
Dmol3*
Exchange and correlation terms were treat within generalized gradient (GGA) functional by Perdew, Burke and Ernzerholf
Core electrons were treated in non-relativistic implementation
Double numerical quality basis set with polarization function (DNP) were considered.
The tolerances of energy, gradient, and displacement convergence were eV, eV/˚A and ˚A, respectively.
Ab initio total energy calculation in the framework of the density fuctional theory. Implemented in
Dmol3
*B.Delley, J.Chem. Phys. 92, 508 (1990)

11. Procedures Dmol3 Dmol3 SWNT(2,2) to CNTSC
Finite and infinite structures
Dmol3
Geometry optimization
SWNT(2,2) to CNTSC
Dmol3
Geometry optimization (decreasing radii of SWNT(2,2))

12. RESULTS

13. Infinite Structures Structure Energy per atom (Ha) CNTSC -38.0027
TABLE I: DMol3 results for crystalline carbon allotropic structures: Graphite, Cubic diamond, SWNT(2,2), and CNTSC.
Structure
Energy per atom (Ha)
CNTSC
SWNT (2,2)
Diamond
Graphite

14. Infinite Structures
Binding energy per unit cell as a function of axial c lattice parameter for SWNT(2,2) and CNTSC nanotubes.

15. Bands Metallic character
Band structure and total density of states (in electrons/Ha) results for the (a) SWNT(2,2) and (b) carbon square-cross-section CNTSC. Energy is relative to Fermi level (dashed horizontal lines). Primitive unit cells have eight and four carbon atoms for SWNT(2,2) and CNTSC, respectively.

16. Oligomers
Energy per carbon atom of the n-cubane oligomers, calculated with DMol3. Index n refers to the number of squares in the oligomer cross section. The horizontal dashed line indicate the carbon square-cross-section nanotube (CNTSC) energy ( Ha).

17. Oligomers
Distance between carbon atoms as a function of the number of square cross-sections. The number labeling follows the presented in slide #8.

18. SWNT(2,2) to CNTSC (see video1)

19. CONCLUSIONS

20. Summary and Conclusions
In summary, based on a recent discovery of the smallest possible silver nanotube with a square cross-section , we have investigated whether a similar carbon-based structure could exist. We have used ab initio methodology to investigate the structural, stability and electronic properties of carbon nanotubes with square cross-section (CNTSC). Our results show that stable (or at least metastable) CNTSC (finite and infinite) structures can exist. They also show that it is possible to convert SWNT(2,2) to CNTSC.

21. Acknowledgments