Van der Waals vs. Hydrogen bonds

[silly_sheep]

I know that the two are different thing, that vdW appears in inert gas crystals and alike while hydrogen bond bonds molecules of water. My question is, how does the potential look for hydrogen bond?

For vdWaals we have the two terms proportional to 1/R^6 that describes attraction and 1/R^12 that describes repulsion. Can we say that hydrogen bond has similar dependence? I am curiou cause in nuclear matter systems we say that nuclear matter has forces between nucleons similar as forces between water molecules, but then we use the vdW like potential. So I am not sure, can we compare it with water bonds or not?

 

[TeethWhitener]

To a very rough approximation, the answer is yes (edit: that is, hydrogen bonds can be approximated with an LJ potential). I'm assuming that for the nuclear interaction, you're referring to the liquid drop model, which is a semi-empirical model of nuclear structure. Your 6-12 potential is known as a Lennard-Jones potential, and it's also semi-empirical. The 1/r⁶ term comes from dispersion, but the 1/r¹² term is merely a "big repulsive wall" for computational convenience. Molecular dynamics water models use Lennard-Jones potentials with varying degrees of sophistication, and these usually do a decent job of replicating several facets of liquid water behavior. However, a full reckoning of the hydrogen bond requires quantum chemistry and the interaction is not a simple function of distance.