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Hybrid density functionals with screened Hartree-Fock exchange at long range have become popular for modeling solids. I'm curious as to what the reasoning is behind this functional form. I understand that exchange interactions are expensive to compute and so eliminating long range ones can help to maintain low scaling for larger systems. My initial intuition would say that screening these interactions would reduce the accuracy, but I have heard that full exchange at long range is actually unphysical. What makes long range exchange incorrect for solids?

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    $\begingroup$ @NikeDattani that's a different issue, in a similar vein to dispersions corrections to fix DFTs treatment of noncovalent interactions. The issues with the exchange functional are a bit different. The functionals I had seen that do this sort of screening are M06-SX and the HSE06, among others. $\endgroup$
    – Tyberius
    May 15 '20 at 4:10
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    $\begingroup$ I see. Shows how little I knew about DFT! I'm learning though, thanks to this site :) $\endgroup$ May 15 '20 at 4:13
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I think the rationale is pretty well explained in the paper by Heyd, Scuseria and Ernzerhof, i.e. Journal of Chemical Physics 118, 8207 (2003)

For insulators there is a large gap, and the density matrix and the exchange interactions decay exponentially when you go farther and farther from the cell at the origin. (This means that in this case, you can easily also apply further screening to the exchange.)

For metals there is no gap, which leads to a divergence in Hartree-Fock. (This problem is just an issue of Hartree-Fock, as it neglects correlation which should become significant for metals!) However, if you switch to short-range only exchange, you kill the divergence, thus making the functional better behaved.

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  • $\begingroup$ +1. This question was unanswered for a long time! How did you come across it? Was it the "Answering these particular questions will earn you extra badges!" advertisement we put in the side-bar on the right-side of the page? $\endgroup$ Jul 10 '20 at 16:02
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    $\begingroup$ @NikeDattani yeah, although I saw it on the meta page that I almost never look at. $\endgroup$ Jul 10 '20 at 16:44
  • $\begingroup$ It's good to know what strategies are working and what strategies are not! Thanks to you seeing this on Meta, we are now at 92% answered, and that much closer to "graduation", which is when SE finally removes the "beta" label and the design team gives us a proper logo: area51.stackexchange.com/proposals/122958/matter-modeling $\endgroup$ Jul 10 '20 at 16:47

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