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I am doing band structure calculations of 2 by 2 by 1 MoS2/MoSe2 van der Waals heterostructure in Quantum Espresso. I have noticed that adding Grimme DFT-D3 correction to PBE functional has very negligible effect on the obtained band gap from PBE functional alone.

It is an established fact that van der Waals interactions are significant in such structures. So my question is why band gap is not improved?

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    $\begingroup$ How much underestimation are we talking about? You are still using PBE functional, adding DFT-D3 will affect the total energy (and hence the geometry, phonons, etc) but shouldn't improve the band gap or any excitonic properties by much, right? You need HSE or other functionals if you solely looking to improve the band gap. See this where they used both PBE and HSE functionals with DFT-D3 corrections and only in HSE, the band gap seems to be close to the experimental value. $\endgroup$
    – Abdul Muhaymin -Free Palestine
    Commented 2 days ago
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    $\begingroup$ If you look at the expression for the Grimme D3 correction here, this would not change the electronic structure if you just run an SCF with D3 on top of PBE (in fact, it doesn't even affect the SCF, just the energy, forces and stresses computed from the self-consistent solutions of the SCF). However, if you relax the structure with PBE-D3 and recompute the band structure, then you'd likely see a tangible difference. $\endgroup$
    – CW Tan
    Commented 2 days ago

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This is an easy question to probe. Any changes to the total energy, forces, and stress in the post-SCF stage will not change the band gap. Because the D3 correction amounts to such a correction, it does not have a direct influence on the band gap; in fact, you can determine the D3 correction without even running a DFT calculation.

The influence will come in by the change in geometry. If you compress or decompress the structure, do you see changes in band gap? If so, the stress contribution from D3 may play a role in the band gap of your material. Similarly, D3 may change the stable positions of less rigid parts of a crystal structure which will also affect band gap.

I should also stress this will happen when using D2, D3, D4 or any other vdW approach which is simply an emperical energy, force, stress correction ontop of a DFT calculation.

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    $\begingroup$ One should specify that D3 is an empirical dispersion correction: it is evaluated in a way that is unrelated to the electronic structure calculation. Non-local correlation functionals would, however, affect orbital energies; however, even there the differences would likely be unnoticeable. $\endgroup$
    – Susi Lehtola
    Commented 2 days ago
  • $\begingroup$ @SusiLehtola This is what i meant by a energy, force, stress correction, but I did add the word empirical to stress this. If you see any other wording you don't like, feel free to fix it, I think this topic of empirical vdW in general confuses a lot of newer DFT people. $\endgroup$
    – Tristan Maxson
    Commented 2 days ago
  • $\begingroup$ I'm doing DFT calculations with ab initio non local VdW-DF3 opt1. Also to compare results, Empirical approach of Grimme D3 is being implemented. After reading your comments and answers, I guess that I should first relax the structure and then proceed with band structure calculations in case of both ab initio and empirical approaches. $\endgroup$
    – Rafi Ullah
    Commented 2 days ago
  • $\begingroup$ A little confusion! After using vdw_corr parameter in relax calculation. Should I use same parameter in scf calculation also? $\endgroup$
    – Rafi Ullah
    Commented 2 days ago
  • $\begingroup$ @RafiUllah please ask that follow-up question in the appropriate place (a brand new post), since your original question was answered and accepted. $\endgroup$
    – Nike Dattani - No Free Time
    Commented yesterday

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