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I am trying to understand Quantum ESPRESSO input file, line by line. So far everything seems pretty easy to understand. However, I do not know what occupations='tetrahedra' means?

I saw that it should be used when calculating the density of states, but I do not know why.

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  • $\begingroup$ Somewhat relevant: mattermodeling.stackexchange.com/q/2414/671 Not proposing it as a duplicate, since a) the answer to that question doesn't address 'tetrahedra', and b) it might be beneficial to separate 'tetrahedra' into its own question (this one). $\endgroup$
    – Anyon
    Commented Jul 12, 2021 at 17:32
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    $\begingroup$ Seems to be addressed partially here: quantum-espresso.org/Doc/INPUT_DOS.html $\endgroup$
    – Anyon
    Commented Jul 12, 2021 at 17:33
  • $\begingroup$ +1. Welcome to our new community and thank you for contributing your question here! We hope to see much more of you in the future! I agree with Anyon's comment, and I've made some minor edits to match the format we have for most of our questions here. $\endgroup$
    – Nike Dattani - No Free Time
    Commented Jul 12, 2021 at 17:33

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For the "why" you should use the tetrahedron method when computing the density of states, check out this paper on exactly that topic! In short, other approaches (e.g. Gaussian smearing) will occasionally obscure (and artificially introduce) some features of the density of states.

As for how the method works, quoting from the paper directly about the tetrahedron method:

"The tetrahedron method... divides the Brillouin zone into tetrahedra, calculates the eigenenergies at the corners of each tetrahedron, and linearly interpolates the eigenenergies inside of each tetrahedron to perform the integration. The tetrahedron method is reminiscent of the trapezoidal rule for approximating the integral of single-variable functions."

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