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I'm afraid this question might be too basic or too naive or both, but here goes!

For optical diffraction by periodic nano-structures (gratings, semiconductor manufacturing metrology) the rigorous coupled wave equation or RCWA (also) was sort-of a gold standard until Finite Difference Time Domain or FDTD methods were computationally achievable.

Analogous to the optical diffraction situation, the dynamical diffraction of electrons and X-rays has been traditionally calculated with static solutions.

Question: Have FDTD methods had inroads into simulation of scattering of electrons and X-rays by crystals for the purposes of comparing to measured patterns and/or spectra?

One reason that I'm asking is that LEED calculations are somewhat of a black box in that much of the code is from the 1980's and '90's and reimplementing them in a modern computational environment in a friendly way (e.g. Python wrapper, calls to standard libraries instead of all those DIY methods) will be hard. While computationally intense, FDTD methods might be somewhat easier to implement using modern techniques; but I'd like to see if this has been tried, and if so with what degree of success.

For more on traditional low energy electron diffraction (LEED) simulation see:

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    $\begingroup$ +1. I do worry that we don't have so many experts from the FDTD and diffraction communities here. I did use FDTD once in 2008 but I work a lot more in electronic structure theory now. I've been able to bring a lot of expert electronic structure theorists to this site, but I don't know a lot of people in the diffraction community, so unfortunately they are less represented here. At some point we ought to think about how to fill in the gaps by reaching out to all the communities/experts that are under-represented here. $\endgroup$
    – Nike Dattani - No Free Time
    Sep 27, 2020 at 21:42
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    $\begingroup$ @NikeDattani I really, really appreciate this site putting community development front and center. I'd once imagined An “Escalate to an Astronomer (in related field)” button? and it seems you are an AI version of that button in that it is self-pushing (button detects a need for escalation without needing the user to push it first). Perhaps the analogy is a bit oblique, but thanks nonetheless! $\endgroup$
    – uhoh
    Sep 27, 2020 at 23:21
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    $\begingroup$ Maybe related! mattermodeling.stackexchange.com/q/3585/5. This has caused me to create the finite-difference-time-domain tag. $\endgroup$
    – Nike Dattani - No Free Time
    Oct 22, 2020 at 21:49
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    $\begingroup$ @NikeDattani thank you for your persistence, I need to slide over and spend more time here and less time in space obviously. :-) $\endgroup$
    – uhoh
    Oct 22, 2020 at 22:04
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    $\begingroup$ Well, I want to help get all the unanswered questions answered, because the longer that list grows, the easier it is for such questions to get "lost" in a huge list that's not very searchable or manageable. I posted something on Meta about trying to get our community to help each other get unanswered questions solved: mattermodeling.meta.stackexchange.com/q/200/5 $\endgroup$
    – Nike Dattani - No Free Time
    Oct 22, 2020 at 22:21

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