We performed density-functional theory calculations in the local-density approximation of the structural, electronic, and optical properties of 4-Å-diameter single-walled carbon nanotubes. The calculated relaxed geometries show significant deviations from the ideal rolled graphene sheet configuration. We study the effect of the geometry on the electronic band structure finding the metallic character of the (5,0) nanotube to be a consequence of the high curvature of the nanotube wall. Calculations of the dielectric function and optical absorption of the isolated nanotubes were performed under light polarized parallel and perpendicular to the tube axis. We compare our results to measurements of the optical absorption of zeolite-grown nanotubes and are able to assign the observed maxima to the nanotube chiralities.