Any thoughts on Dr. Sanchez\'s new article

Alloy Theoretic Automated Toolkit (ATAT)
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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.

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I agree that in some system composition-dependent CE may be more rapidly converging.
In my experience, however, the main problem we face when doing cluster expansions is the problem of mechanical stability. That is, structure that relax to another completely different lattice. That really slows down convergence and sometimes makes it impossible to get the right ground state.
To that more important problem, I have two solutions:

  1. constrain the composition range so that the code does not try to reproduce the ground state at all compositions (i.e. exclude those composition where the lattice is unstable).
  2. The inflection-detection method: https://dx.doi.org/10.1038/ncomms8559 which prevents structure from relaxing too far from the intended lattice. This solution is simple and rigorous.
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Dear Dr. Axel,

Many thanks for your replying! I appreciate the chance to talk with you in this forum.

Yes, your inflection-detection paper is the first which came into my mind. I knew I should learn much more from it, but I did not know where to start. The robus relax prevents too much relaxation, that had been hiden in plain sight for me!

I still have some quick questions, hoping it will not cost too more of your time.

  1. Thanks to the quantity as defined in the checkcell, we can monitor the distorion of lattice. But what about internal displacements. Do you think they should be monitored too? In some of my cases, the displacements may reach 0.05 1NN distance or more, especially in SQS structures. I think, the displacements, just like lattice distortion, will break the symmetry of clusters, thus introduce system errors into ECIs.
  2. And on the structures, do you think it is worthy to increase the order of complexity of maps?(the -c option, large number would force maps to seek more low symmetrical structures with small cell size, do I understand its function correctly?) This question originates from my doubt on the connection between Dr. Sanchez’s VBCE and GPM. In practice, the smaller cell has the advantage on time cost, even with the low symmetry. But I am not sure whether those structures are actually helpful on providing a valid ECI set, because those structure are ordered in strange ways, hence are unlikely to happen in real life.
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  1. Yes, it would be better to account for the internal degrees of freedom as well. It’s just not a situation I’ve encountered very often. It’s on my todo list.
  2. The order of complexity parameter in maps does something very simple : it tells the code how quickly ab initio calc become expensive as cell size increases. If you increase it, maps will tend to generate more small-cell structure.
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Okay, I think I got your ideas.
Thank you very much.