In a previous paper [J. Chem. Phys. 111, 3357 (1999)] we showed that the electric field gradient at the copper nucleus in CuCl is incorrectly described by most of the density functionals currently in use, including gradient corrected and hybrid versions of DFT. Here we analyze whether this error is systematic or not by comparing DFT electric field gradients for a number of diatomic compounds MX. The molecules chosen include representatives from early transition metal compounds, ScX, from late transition metal compounds, CuX, and from main group compounds, GaX, where X=F, Cl, Br, I, H and Li. From experimental nuclear quadrupole coupling data and electric field gradient calculations for each of the three sets (ScX, CuX and GaX) the nuclear quadrupole moment at the metal can be deduced at a specific DFT level. It is demonstrated that density functionals work well for main group compounds (GaX), but contain large systematic errors for transition metals such as copper. This leads to unreasonable copper nuclear quadrupole moments obtained for the CuX set. The error mainly originates from the incorrect description of the Cu(3d) core being polarized by electronegative ligands such as fluorine. For copper this can be remedied in an ad-hoc way by adjusting the Hartree-Fock contribution in the exchange part of the hybrid functional (modified B3LYP). Using this modified B3LYP functional we obtain reasonable results for the copper electric field gradient in CuF3, a case where the Cu(3d) core is strongly polarized by the fluorine ligands. (C) 2003 American Institute of Physics.