# Cluster expansion for molecular crystals?

Hi! I’m looking for good ways to model conformational disorder in molecular crystals and someone has suggested I check out icet.

Has anyone had experience using cluster expansion methods on molecular crystals to describe such disorder (e.g. a molecule within a crystal being in one of a discrete set of possible orientations)?

Thanks,
Kane

Hi Kane,
I have no experience with molecular crystals, but if your molecules are more or less static on a lattice and the only difference between them being their orientation, then I think you could attempt to do this with a cluster expansion.

First things that come to mind is to map each molecule with an orientation to atom-type, so in the case of three different orientations you would end up with a ternary system (A, B, C).
So e.g. a linear chain of these molecules would be mapped to A, B, B, A, C, C, A, C, B, … and modeling the energy of such system should work fine with cluster expansion.

Yes, the molecules should be statically disordered and so such a mapping could work in principle, I think. One thing that I’m concerned about is the symmetry analysis being a bit overzealous if it’s treating the molecule orientations as point-atoms — e.g. a mirror might be a valid symmetry operation for a structure with atoms but not for one with molecules at the same sites. Does that make sense? Is it a valid concern?

Yes I can definitely see how symmetries would be a problem since your molecules have an orientation.
If you have two lattice sites p1 & p2 at (0,0,0) and (1,0,0) then I guess it is not necessary that energy between two molecules A and B is the same if A is at p1 and B at p2 or if A is at p2 and B at p1?

That sounds right to me. Could you put it this way perhaps:

There are fewer symmetry operations that map p1 onto p2 in the case of molecules compared to the case of atoms (like you say, because of their orientation). As a consequence, if p1 and p2 are related according to the symmetry of the atom-structure but not according to the symmetry of the molecular structure, then exchanging A and B could indeed result in a different energy.

Yes I think that’s a correct take.
So maybe it is not as easy to do this with a regular cluster expansion approach as I initially thought.

OK, thanks for your help in any case!

I’ll look into other approaches for now, but I’d be interested in coming back to this at some point — perhaps there is a simple extension/modification that would cover the molecular crystal cases (e.g. forcing the code to use the lower symmetry of molecular crystal?).

Best,
Kane