Despite the fact that in theory it is entirely reducible to quantum mechanics, chemists do not have a mathematical model of water molecules that completely explains its behavior.
Update. Sigfpe has more thoughts at his blog.
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“Despite the fact that…”
A water molecule is two hydrogen atoms and one oxygen atom. Let’s treat the nuclei as single particles. So a water molecule has 2+8=10 electrons and 3 nuceli. So we’re looking at a 13 body system. Let’s drop the two electrons from the inner shell of the oxygen atom so we’re down to 11 bodies. This means we’re looking at a system with 33 degrees of freedom with a highly non-trivial Hamiltonian. To investigate water in ‘bulk’ we need at least 2 molecules. So that’s a 66 dimensional system. We need to solve the Schrodinger equation on a 66-dimensional space. If we discretise this space with just 8 points along each axis we still need 2^198 samples to represent the wavefunction.
So I think you mean “Because of the fact that…” rather than “Despite the fact that…”
But water molecules are so little. How complicated can they be?
For a classical system, I don’t think 33 degrees of freedom would be overwhelming, especially since you could probably make some simplifying assumptions. So I think you’re right that the reason it’s so complicated is strictly a quantum phenomenon. It’s still kinda depressing, though.