Can structure relaxation be included in cluster expansion?

Alloy Theoretic Automated Toolkit (ATAT)
1

Dear Axel,

As far as I’m concerned, the energy calculated by first-principle code includes the effect of structure relaxation, while we have to map the relaxed structure to ideal occupied lattice in order to calculate the effective cluster interactions. Does it mean that the cluster expansion will converge slowly if the sizes of component atoms are quite different? Is there any method to consider the effect of structure relaxation in the frame of cluster expansion?

2

There is the constituent "strain formalism" that does that, which is implemented in ATAT in the csfit command (and, afterwards, via the option -ks=cs in maps and emc2) There is also the "second order expansion" in both configurations and displacements, which is not implemented in ATAT because it is complex and limited to linear regime elasticity.
But overall, most users seem to get good results with just a plain cluster expansion.