Geometries, electronic properties, and energetics of isolated single walled carbon nanotubes

Using the density-functional electronic-structure calculations, we study so-called zig-zag carbon nanotubes. From the complete geometry optimization, it is found that two kinds of bond lengths are considerably different from each other. They possess strong tube-diameter dependence. We determine the bond lengths up to the order of 10(-2) Angstrom and the bond angles to 10(-2) degree. In addition, changes of the electronic band structure upon the geometry relaxation from the uniform bond-length tube are found to be sizable. Also the electronic properties and energetics obtained for optimized geometries are discussed.