Relying on the molecular quadrupole moment functions of the HF and N-2 molecules in their electronic ground state, as obtained by the ab initio calculations at various levels of approximation of the coupled cluster method, as well as on the corresponding theoretical and experimental potential energy functions, the effective rovibrational averages and transition moments were evaluated over a wide range of values for the vibrational and rotational quantum numbers. The reliability of the ab initio data was also checked by evaluating the theoretical vibrational energies and comparing them with the experimental ones. The predicted quadrupole moments were found to be in close agreement with the available (rather scarce) experimental data, indicating the reliability of the calculated effective quadrupole moments for the broad range of rovibrational levels where no experimental data are available.