The widely used near-Hartree-Fock functions of Clementi and Roetti [At
. Data Nucl. Data Tables 14, 177 (1974)] are compared with the newer f
unctions of Bunge et al. [At. Data Nucl. Data Tables 53, 113 (1993)] b
y means of different measures of functional distance on the charge den
sity rho for the atoms He to Xe. The results are correlated with the e
nergy improvement, and an empirical relation between the linear deviat
ion in the first derivative of rho and the total energy is reported.