The radial moments of the electron density, < r(n)>, have been calculated for N-2 and H2O at the quadratic configuration interaction (with singles and doubles) levels of theory by use of a variety of basis sets. An optimal basis set was chosen from the first set of calculations and then used with several conventional ab initio and density functional methods to compute the moments for a representative set of molecules: N-2, CO, CH4, NH3, H2O, HF, SiH4, PH3, H2S, HCl, CH3OH, and CH3SH. The effects of solvation on the radial moments were also studied using the Onsager model and an extension of the Tomasi polarized continuum model.