The deuterium quadrupole coupling constant and asymmetry parameter in heavy water were determined using ab initio SCF calculations. Snapshots from a molecular dynamics simulation were used to give liquid water cluster configurations and the influence of simulation parameters on the quadrupole coupling constant was investigated. The electronic potential model and the number of molecules in the molecular dynamics simulation and the pressure of the system were found to have only a small influence on the quadrupole coupling constant. The average value of the quadrupole coupling constant at room temperature, corrected for the known deficiency of the ab initio calculation in the gas phase, yields a quadrupole coupling constant of 253 kHz, in perfect agreement with the most recent experiments. The oxygen-deuterium bond lengths in ice Ih, ice 11, and ice IX were determined using experimental quadrupole coupling constants and a model equation. An averaged bond length of 98.9 pm was obtained for the Ih form, which is approximately 2 pm shorter than that determined by neutron diffraction studies, whereas the bond lengths for the four deuterium sites in ice I1 and the three sites in ice IX are in fair agreement with experiment.