Water

The water molecule H₂O contains 10 electrons, so solving its Schr¨odinger equation is highly nontrivial, even in the Born–Oppenheimer approximation. There are many sophisticated calculations, which demonstrate that the B–O shape of the molecule lies in a plane, with a bond angle between 110 and 100 degrees, in good agreement with experimental data. The rough scale of rotational energy levels of water is m_e/mH₂O × 10 eV, or about 10⁻⁴ eV, which is in the microwave range. Water vapor indeed accounts for much of the atmospheric absorption of electromagnetic radiation in this range. Absorption of microwaves by water is also the basic physical principle behind the microwave oven. Most of our foods contain a lot of water and the ovens excite the rotational levels of those water molecules, uniformly in the food sample. The dissipation of that rotational energy is what cooks the food. Many of the most important properties of water, such as the fact that its solid form is less dense than the liquid, near the freezing point, or its solvent properties, have to do with the interactions between water molecules and are not understood on a quantitative level. However, it is clear that the relatively weak binding of hydrogen to oxygen in individual molecules is crucial.We know this because heavy water, where hydrogen nuclei are replaced by deuterium behaves very differently. The larger mass of the deuterium atoms means that their nuclei are more tightly bound to the oxygen atom. Indeed, there is experimental evidence that the bond lengths in heavy water molecules are shorter than those in ordinary water. Note that in the Born–Oppenheimer approximation, the bond lengths are independent of nuclear masses, as long as they are large. It is possible that the correct explanation of these observations will involve a study of the effect of rotational levels of water on the scattering experiments, rather than a breakdown of the Born–Oppenheimer approximation. The size of the effect looks like something of order These experiments also show that the properties of the liquid state of heavy water are different than those of light water. Clearly, even for molecules as simple as water there is much to be done. Indeed, replacing 25%–50% of a multicelled animals water content with heavy water leads to a variety of toxic effects, from sterility to breakdown of numerous important reactions essential to life. The effects are undoubtedly a result of the tighter binding, but detailed mechanisms have not yet been worked out. Remarkably, single celled organisms like bacteria seem to tolerate up to 90% replacement of their water supply by heavy water.