Curvature effects on the structural, electronic and optical properties of isolated single-walled carbon nanotubes within a symmetry-adapted non-orthogonal tight-binding model

The effects of curvature on the structure, electronic and optical properties of isolated single-walled carbon nanotubes are studied within a symmetry-adapted non-orthogonal tight-binding model using 2s and 2p electrons of carbon. The symmetry-adapted scheme allows reducing the matrix eigenvalue problem for the electrons to diagonalization of 8 x 8 matrices for any nanotube type. Due to this simplification, the electronic band structure of nanotubes with a very large number of atoms in the unit cell can be calculated. Using this model, the structure of 187 small- and moderate-radius nanotubes is optimized. It is found that the deviations of the optimized structure from the non-optimized one are large for tube radii smaller than 5Angstrom. The band structure and the dielectric function of 101 small- and moderate-radius nanotubes are calculated. The optical transition energies for these nanotubes are derived from the dielectric function and plotted versus tube radius. It is shown that the structural optimization introduces small changes to the transition energies obtained within the non-orthogonal tight-binding model. The transition energies for the optimized structure within this model agree well with the available ab initio data for a few nanotube types. On the other hand, the results for the former deviate widely from those used for nanotube characterization in pi-band tight-binding model especially for small-radius tubes. The derived transition energies can be used for the assignment of nanotube absorption spectra and for the selection of nanotube types for which the Raman scattering is resonant.