Hartree-Fock (HF) and density functional theory calculations indicate that a (4,0) carbon nanotube (CNT) of sub-0.4-nm diameter is stable and its heat of formation is close to that of the stable ${\mathrm{C}}_{36}$ $\left({\mathrm{D}}_{6h}\right).\mathrm{}$ Semiempirical molecular-orbital calculation shows that such narrow tubular structure is more stable than the corresponding opened fragment in the innermost zone of a large CNT. Simulated TEM images show that an extra-narrow CNT does not show the typical CNT image regardless of the microscopic resolution. In order to aid experimental identification, the Raman spectrum of the (4,0) CNT obtained from HF calculation shows $A_{1g}$ breathing modes in $489–725\hspace{0.5em}{\mathrm{cm}}^{-1}.$

• Received 1 July 2002

DOI:https://doi.org/10.1103/PhysRevB.66.113403