Quadrupole coupling constants, chi(Q), for the deuteron and the oxygen nuclei in I;eat, liquid water were determined by both theoretical and experimental methods. The : theoretical values of chi(D)=264 kHz and chi(O) 8.4 MHz obtained from ab initio calculations at the MP2/6-31+G* level in combination with a quantum cluster equilibrium model for liquids are in good agreement with results from NMR relaxation time experiments. Both theory and experiment show no observable temperature dependence of the quadrupole coupling constants. The theoretical values reported here for the oxygen quadrupole coupling constant and both the oxygen and deuterium asymmetry parameters are different from values obtained from ab initio calculations of clusters using molecular dynamics methods. This may be due to the use of pairwise additive potentials in the molecular dynamics simulations which do not take into account many-body or polarizability effects.