Geometries, electronic structures and energetics of small-diameter single-walled carbon nanotubes

We study the detailed geometries, electronic structures and energetics of small-diameter single-walled carbon nanotubes in the framework of the density functional theory with the local density approximation. In the present work, we study 41 kinds of nanotubes including 16 chiral nanotubes. It is found that electronic properties of optimized nanotubes as well as their geometrical properties depend strongly on not only diameter but also chiral angle. The largest difference from graphene values for both bond lengths and bond angles is found in zigzag nanotubes among all the nanotubes with similar diameters. Interestingly, the bond length decreases relative to that of graphene when the angle between the bond direction and tube axis is less than about 22°. As for the electronic structures, because of significant curvature effect, the band gap values of small-diameter nanotubes are show significant deviation from the classification from the tight-binding study. Interestingly, we also find that so-called "near-armchair" nanotubes have large band gaps even in the small-diameter region.