Structural, electronic and optical properties of smallest (2,2) carbon nanotube: A plane-wave pseudopotential total energy calculation

Based on plane-wave pseudopotential total energy calculations, we investigate the structural, electronic and optical properties of the smallest (2,2) carbon nanotube. Our calculated results indicate that severe structural changes take place due to the large curvature in the smallest (2,2) carbon nanotube. The energy gap obtained from ultrasoft pseduopotential and norm-conserving pseudopotential is 0.132 eV and 0.166 eV, respectively. Distributions of charge density indicate that the electron localization in the bonds perpendicular to the axis of (2,2) carbon nanotube optimized by using norm-conserving pseudopotential has a more distinct trend than that optimized by using ultrasoft pseudopotential, which leads to a relative smaller energy gap in the latter. For the electric field parallel to the nanotube axis, the ε″ spectrum of the dielectric function in the low-energy region is dominated by a single peak, which can be compared with the recent Raman spectra measures. In high-energy region, the optical anisotropy is found to be remarkable.