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There are various questions on this SE that discuss DFT in terms of band gaps - here, here, here, and elsewhere - but they touch upon different aspects.

Cautionary note: I'm asking this from the mind-frame of someone who doesn't know much more than how to put tags together in some DFT code's input file and get a shining, all-hail-lords-Kohn-and-Sham energy per atom value as the output.

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    $\begingroup$ This can end up excessively broad. Id suggest narrowing it to one or the other. Dft often can only handle a band gap or Fermi level at the same time. The fermi level of semiconductors is ill defined for dft. $\endgroup$ – Tristan Maxson Oct 14 at 13:20
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    $\begingroup$ Good decision. The fermi level is a different topic potentially, but I fear there may not be a ton to say about it. $\endgroup$ – Tristan Maxson Oct 14 at 13:41
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    $\begingroup$ "Summarise/discuss everything about band gap in terms of DFT (all flavours) calculations." still seems excessively broad to me. $\endgroup$ – Anyon Oct 14 at 18:42
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    $\begingroup$ You are asking too general equation for the StackExchange Q&A format. This is not a forum in the conventional meaning. $\endgroup$ – freude Oct 15 at 5:29
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    $\begingroup$ @HitanshuSachania. We already have 2 close votes for the question. The question is lacking clarity (not a specific question. summarize everything type question). It might be better to edit the question $\endgroup$ – Thomas Oct 15 at 15:05
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The important thing to keep in mind is that the Kohn-Sham (KS) band gap is not the fundamental/quasiparticle gap. Even theoretically. This is not an 'underestimation' of the band gap. They are not the same gap.

The fundamental quasiparticle (QP) gap is calculated as the difference between valence band maxima and conduction band minima, but for different hamiltonians.

A part of the exchange-correlation potential called the response potential has changed in a discontinuous manner as you've added the new electron to see where your conduction band minima is. That added electron has changed the hamiltonian.

I think this little bit is really a dominant pitfall (I'm sure there are many others). It helps to keep in mind that the KS gap is not the QP gap. Even with the 'exact' KS functional, you wouldn't get the bandgap that compares favourably with experimental QP gaps.

Almost the entirety of the above rant has been taken from:

  1. https://pubs.rsc.org/en/content/articlelanding/2017/cp/c7cp02123b#!divAbstract
  2. https://pubs.rsc.org/en/content/articlelanding/2013/cp/c3cp52547c#!divAbstract

As above, I'm sure there are many other pitfalls, but this is the one I like to keep in mind the most.

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  • $\begingroup$ This is a good, succinct answer. If you are interested in calculating band gaps, it's essential to understand exactly what you're calculating! Reading up on the K-S gap literature is a must. $\endgroup$ – Kevin J. M. Oct 15 at 21:07
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DFT is not applicable for computing the bandgap. If it gives it close to the experimental results, it is more or less accidentally. Usually, DFT is used as a basis set generator for subsequent computations based on GW theory or TDDFT.

DFT is by definition the ground-state theory - all Kohn-Sham theorems constituting the basis of DFT have been derived regarding the ground state properties. Also, there is no proof (at least I have not seen any) that Kohn-Sham orbitals can be somehow related to the excited states. The bandgap is a property related to the excited states though.

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  • $\begingroup$ Thank you for your reply. Can you elaborate on why DFT is not applicable for computing the band gap? $\endgroup$ – Hitanshu Sachania Oct 15 at 10:50
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    $\begingroup$ This answer dismisses what can be calculated. I strongly agree that DFT is not applicable for computing the band gap in terms of absolute value (although some improvements exist to allow for this). However trends and band structures still tend to be useful. This is not really an answer to the question. $\endgroup$ – Tristan Maxson Oct 15 at 14:08
  • $\begingroup$ As suggested by @TristanMaxson, the answer can have much more details. Please elaborate your answer $\endgroup$ – Thomas Oct 15 at 14:57
  • $\begingroup$ @TristanMaxson, I am very glad that you strongly agree with my statement. Can you specify in more detail what do you mean by "absolute value", is this something like |Eg|? $\endgroup$ – freude Oct 15 at 22:35
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    $\begingroup$ Good to see healthy conversation guys, just be careful not to click the "let's continue this conversation in chat" button, as I explained here: meta.stackexchange.com/q/353643/391772 $\endgroup$ – Nike Dattani Oct 17 at 3:02

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