The relative energies of H and D bonds are due to differences in zero-point vibrational energy (ZPVE). Ab initio calculations are used to assess the changes in this quantity that accompany all possible substitutions of protium by deuterium in a number of complexes. The ZPVE of the D bond is lower than that of the I-I bond in the neutral dimer and trimer of water. This difference can be traced to one particular vibrational mode, the one which displaces the bridging atom away from the O...O axis. The heavier mass of D lowers the frequency, and hence the ZPVE associated with it. The situation reverses itself in ionic H bonds. The total ZPVE of the (H2O..H..OH2)(+) complex is higher when a D occupies the bridging position, as compared to a terminal site. This difference is attributed to the intramolecular modes. Although replacement of the central H by D reduces the intermolecular ZPVE, the reduction of the intramolecular ZPVE is even larger when the substitution is made at a peripheral atom, so a D would tend to migrate away from a bridging location. This effect is noted also in the larger complex in which two methanol molecules are bound by a proton. The lower energy of a H bond as compared to a D bond is observed as well in the anionic (HOH..OH)(-) system, although the magnitude of the preference is smaller here. In all cases, raising the temperature, and thus invoking thermal vibrational and entropic effects, tends to preferentially stabilize H over D bonds.