It turns out that the amount of deuterium in liquid water depends on the temperature at which the water was condensed. This can be measured very accurately and has proven to be a sensitive probe in climate change studies (see for example, figure 1 in this Nature paper).
For most temperatures there is a preference for HOD to reside in the liquid rather than the vapour phase. This is a purely quantum effect! According to the Born-Oppenheimer approximation the intermolecular and intramolecular interaction potentials for H2O and HOD are identical. However, different isotopic masses lead to different vibrational frequencies, zero point energies, and free energies.
Calculating the free energy of the liquid phase where one treats the H and D atoms fully quantum mechanically is a highly non-trivial exercise. Markland has done this using a path integral method based on mapping quantum dynamics to fictitious polymer beads.
A few notes:
- Different models for the water interactions give quite different results. It seems including the anharmonic part of the OH stretch potential is important.
- This is an extremely small effect. The differences in free energies are less than k_B T/10 ~ 3 meV at T=300 K. Hence, it is impressive that one can calculate it successfully (provided one has the "right" potential).
- The effect gets smaller with increasing temperature because the density of the liquid phase (along the liquid-vapour co-existence line) decreases with increasing temperature and vanishes at the critical temperature (around 650 K). For example, between 300 and 600 K the density of the liquid decreases by a factor of 1.5. This corresponds to an increase of the average oxygen atom separation from 3.0 to 3.4 Angstroms. I would estimate this corresponds to an eight-fold decrease in the hydrogen bonding energy. There will be an associated significant change in the intermolecular potential, it becoming much more like that in the vapour phase.