  We report a computational study, using the "moments method" [Y. Gao and M.
Daw, Modelling Simul. Mater. Sci. Eng. 23 045002 (2015)], of the anharmonicity
of the vibrational modes of single-walled carbon nanotubes. We find that modes
with displacements largely within the wall are more anharmonic than modes with
dominantly radial character, except for a set of modes that are related to the
radial breathing mode which are the most anharmonic of all. We also find that
periodicity of the calculation along the tube length does not strongly affect
the anharmonicity of the modes, but that the tubes with larger diameter show
more anharmonicity. Comparison is made with available experiments and other
calculations.
