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VASP provides two sets of pseudopotentials(PP) for LDA and GGA respectively, but as I understand the PP is dependent on the exchange-correlation functional I use, so if I am using meta-GGA, could I use the PP designed for GGA?

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In practice, you're likely to be okay. Borlido and coworkers (the article is open access) stuied just this for band gaps in 2020, concluding that the error based on the choice of functional is generally larger than the pseudopotential error.

Still, if you want to be careful, it might be worth checking the pseudopotential of interest against a converged all-electron calculation for some representative subset of your systems.

Update (May 2023): A new paper by Rosomme et al. (ACS paper, I can't find a preprint version) just appeared, detailing the effect of pseudopoential inconsistencies for molecules. Its conclusions:

  • Nonbonded interactions and reaction barrier heights are okay!
  • Dimerization and reaction energies for transition metals induce larger errors than chemical accuracy.
  • Bond breaking for main-group elements is often quite bad if the pseudopotential is inconsistent.

So a fuller answer is that it depends on the application at which you're looking. Depending on what that is, the advice to double-check your results could become quite important.

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In the case of an hybrid functional this is exactly what we do by using the GGA pseudopotentials, besides hybrid functionals are not often used for generating pseudopotentials from an all-electron calculation.

If it works fine for hybrid GGA functionals very different compared to GGA, it should work for meta-GGA as a simple correction of GGA.

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