The zeroth-order regular approximation (ZORA) is used for the evaluation of the electric field gradient, and hence nuclear quadrupole coupling constants, in some closed shell molecules. It is shown that for valence orbitals the ZORA-4 electron density, which includes a small component density ("picture-change correction"), very accurately agrees with the Dirac electron density. For hydrogen-like atoms exact relations between the ZORA-4 and Dirac formalism are given for the calculation of the electric field gradient. Density functional (DFT) calculations of the electric field gradients for a number of diatomic halides at the halogen nuclei Cl, Br, and I and at the metallic nuclei Al, Ga, In, Th, Cu, and Ag are presented. Scalar relativistic effects, spin-orbit effects, and the effects of picture-change correction, which introduces the small component density, are discussed. The results for the thallium halides show a large effect of spin-orbit coupling. Our ZORA-4 DFT calculations suggest adjustment of some of the nuclear quadrupole moments to Q(Br-79)=0.30(1) barn, Q(I-127)=-0.69(3) barn, and Q(In-115)=0.74(3) barn, which should be checked by future highly correlated ab initio relativistic calculations. In the copper and silver halides the results with the used gradient corrected density functional are not in good agreement with experiment.