From http://www.lsbu.ac.uk/water/models.html, I see that are many models of water that can "explain" one or some properties of water but no model is accurate enough to explain all the properties of water. From what I understand, all models assume classical mechanics interactions (positive-negative charges as for the protons and electrons) with the Coulombian potential and other potentials. It seems that no model takes into account quantum mechanics "effects" like let's say electron tunneling. I know that water molecule has 2 hydrogen atoms and one would expect the quantum effects to be relevant if one had to build a model that can explain the behaviour of water molecules. I wonder why no model (correct me if I'm wrong) deal with quantum effects? Why are all the models "so bad" at describing water in general? They're only "good" or "so so" in very restricted ranges of parameters like temperature, pressure, etc. Would the models be much more accurate if quantum effects would be taken into account? Hmm I had lots of other questions but I forgot them . Thanks for any input.
"Properties of water" may include properties of a large number of water molecules, which usually requires to simulate a large number of water molecules, which by mere constraints of reality requires a certain degree of computational simplicity for the description and treatment of the individual molecules. The simulation of quantum mechanical effects in Chemistry usually involves a certain amount of computational effort that does not suit well to the computational simplicity demanded by the requirement to simulate many molecules. It is not true that there are no models that try to take into account QM effects. Using Google scholar for "water model quantum mechanics simulation" gives me 50,000 hits of which at least some of them seem to be exactly that: the description of a simulation of water that takes into account quantum mechanical effects. Note that usually QM simulations are also approximations, and will certainly not take into account all in principle possible degrees of freedom.
In addition to what Timo described, you will be surprised to know that the classical water models (SPC, TIP5P,...) do a much better job compared to quantum mechanical models (DFT, Hybrid DFT+HF,..) in terms of describing bulk liquid state water properties. Of course this is not because water is well-described by classical mechanics, it seems that there is significant error cancellation that makes these models work fine. Understanding why quatum mechanical models fail to describe liquid state water is an active research area. On the other hand, gas phase water or let's say the single water molecule properties are more or less well-described by quantum mechanical models. This indicates that the problem is indeed in describing water-water interaction.
Ok thank you guys. Finding a good -in that it gives several if not most properities of water quite accurately- liquid water numerically applicable model looks a really nice and interesting challenge.