Accurate density functional calculations for the phonon dispersion relations of carbon nanotubes

Accurate calculations for the phonon dispersion relations of single wall armchair and zigzag nanotubes are presented. The calculations are performed using a plane wave basis set and density functional theory (DFT). The dependency of Raman active and infrared active modes on the radius is investigated in detail. To access the accuracy of the present calculations, the phonon dispersion relations of an isolated graphene sheet is calculated and the results are compared to experiment. As expected errors are small, but some notable discrepancies between experiment and theory are observed and discussed.