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I'd like to know how to treat VdW interactions among layers. Specifically I'm using Quantum Espresso and I'd like to know how VdW forces are implemented in the Kohn-Sham equation. Does it insert a $V \propto \frac{1}{r^6}$ in the effective potential?

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    $\begingroup$ This discussion should be relevant (mattermodeling.stackexchange.com/questions/1119/…) $\endgroup$
    – CW Tan
    Commented Sep 17, 2023 at 4:06
  • $\begingroup$ Yes, VdW effects are implemented in QE as a corrective factor in the total energy, $E_{DFT-D}=E_{DFT}+E_{VdW}$. The exact form of $E_{VdW}$ depends on which type of correction you choose but almost all of them have the $1/r^6$ dependence. You can find the exact form in the references given in the input description of vdw_corr. $\endgroup$ Commented Oct 10, 2023 at 7:03

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The documentation for pw.x, version 7.2, lists several different ways to compute van der Waals corrections:

  • Grimme's semiempirical DFT-D2 and DFT-D3;
  • Tkatchenko–Scheffler ab initio vdW;
  • many-body dispersion (MBD); and
  • the exchange-hole dipole-moment model (XDM).

Each of these will compute the forces differently, but the references in the documentation will detail each one.

In addition, various nonlocal van der Waals functionals have been implemented, with names mostly of the form vdw-DF* (this is in the file Modules/funct.f90). Again, references to the papers are included in the comments of that file.

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