Hi, dear Dr. Axel , other developers and users,
7 years after Dr. Sanchez proposed the name of "variable basis CE" (PRB, 81, 224202 ^A2010^B), he published another article on this topic, Foundations and Practical Implementations of the Cluster Expansion(https://link.springer.com/article/10.10 … 017-0521-3, it is open access).
In this article he calls (again) for the distinction between common CW fitting and the "CE".
Part of problems he had mentioned before, such as the convergence, i.e. the Ising like CW fitting will not systematically converge. He also brought new ideas that whether we should do relaxation during CE fitting.
From a starter and practicer’s opinion, we might easily "feel" the convergece problem. For example, as some article discussed, there appears to be a tendency of the need of large multi-site clusters during CE fitting. In some way, I think, those large clusters actually plays a role of "concentration dependent" functions. I have done CE in several bcc alloys systems, indeed, while pair ECIs appear to converge to small values with the increament of training set, the multi-site ECIs are difficult to be so; and the more points, the more difficult.
The relaxation issue is a problem puzzled me a long time. Dr. Sanchez emphasized on the importance of unrelaxed structures. Frankly, not even partly comprehended, I think he means though the volume can be relaxed(or rather "should"), the internal forces should not be relaxed, for the symmetry problem.
For my understanding, currently, our dear developers do leave some options that we can try the VBCE or other possibilities, such as user re-writable subroutine on the basis, and independent fitting program lsfit etc… But generally the CE within ATAT is the one what would be called as empirical CW fitting in Dr. Sanchez’s article. So there are questions, 1 exactly how important is the convergence problem 2 the relaxation and the symmetry issue, how do you understand it, and how important it is?
(VBCE also appears to be much more difficult for multicomponent system, it is very not so straightforward [for me at least] as Dr. Sanchez says)
Also, to me, Dr. Sanchez’s concepts now have more similar arguments with Dr. Ruban’s generalized
perturbation method(Rep. Prog. Phys. 71 (2008) 046501 (30pp) ). Since relaxation breaks the "symmetry" of ECIs, would it be possible in future, CE is more practically reasonable within the generalized perturbation method, but not with ordered structures and supercell approach? I mean, what kind of information exactly is the ordered structures good at giving us?
I also feel I should read again and again on the "robust relaxation" article, I feel now it contains much more important things I should have learn from.