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- TL;DR Summary
- Would it be possible to create a molecule that interacts with other identical molecules with an interaction potential that has more than one local minimum value?

Pair interactions between atoms and molecules (in gas kinetic theory simulations or other applications) are described by empirical potential energy functions such as the Lennard-Jones potential:

##V_{LJ} (r) = 4\epsilon \left[ \left(\frac{\sigma}{r} \right)^{12} - \left(\frac{\sigma}{r}\right)^6 \right]##

these always seem to be functions where the energy reaches minumum value at some distance and then the interaction becomes repulsive at too short distance.

Is there known to be any molecular species where the pair interaction has more than one local minima? I believe that at least this doesn't happen in practice unless you specifically design a molecule that is easily deformed by the "tidal" effect of the intermolecular interactions. If that kind of molecule can't exist, I guess it would be really difficult to prove that impossibility mathematically from the Schrödinger equation.

If there exist that kind of molecules, my first guess would be that those compounds are more likely than usual to exist in more than one liquid or solid phase.

##V_{LJ} (r) = 4\epsilon \left[ \left(\frac{\sigma}{r} \right)^{12} - \left(\frac{\sigma}{r}\right)^6 \right]##

these always seem to be functions where the energy reaches minumum value at some distance and then the interaction becomes repulsive at too short distance.

Is there known to be any molecular species where the pair interaction has more than one local minima? I believe that at least this doesn't happen in practice unless you specifically design a molecule that is easily deformed by the "tidal" effect of the intermolecular interactions. If that kind of molecule can't exist, I guess it would be really difficult to prove that impossibility mathematically from the Schrödinger equation.

If there exist that kind of molecules, my first guess would be that those compounds are more likely than usual to exist in more than one liquid or solid phase.

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