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I have found only one reason, this being polarisation isn't accounted for. See for example this PDF - it is in the middle of the second paragraph, first page.

What other reasons lead to the failure of Lennard-Jones potential in simple molecules?

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  • $\begingroup$ Could you be more concrete on what you mean with "failure" of the potential? Or what you mean by "accurate"? (For example physicists' and (theoretical) chemists' notions of accuracy are often quite different). $\endgroup$ – LLang May 19 '16 at 6:17
  • $\begingroup$ Basically what I mean to ask is why the Leonard-Jones potential would not be a good model for the interaction between two molecules of ammonia. Failure and accurate are perhaps bad choices of wording, I will edit. $\endgroup$ – Maitiu May 19 '16 at 6:36
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The Lennard-Jones potential arises from the mutual polarisation of the two molecules. It is present for all molecules however it is a weak interaction and easily overwhelmed by electromagnetic forces. For example two ions would interact via their electric fields much more strongly than via the LJ mechanism and we'd get a $1/r^2$ force ($1/r$ potential).

Ammonia is neutral, but it has a large electric dipole moment and this dominates the interaction. Dipolar forces fall off as rough $1/r^3$, but they are also strongly dependent on the mutual orientation of the two molecules so the potential is not isotropic. The LJ potential will still be present and make a contribution to the total potential, but it will be very small compared to the dipole-dipole interaction.

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