I am writing my own DFT code using Gaussian basis and now I am writing the periodic boundary conditions (PBC). What integration grid people usually use for Gaussian basis PBC (+ reference please)? For isolated molecules, I used the SG3 integration grid with Becke's scheme to combine multi-atomic grids.


1 Answer 1


Exactly the same grids as for molecules, i.e. Becke grids. You just need to take the periodic boundary conditions into account when building the grid weights.

edit: e.g. PySCF has both molecules and periodic boundary conditions with Gaussian basis sets, and is in my experience a pretty fast code that is also easy to install.

See the pyscf documentation for info. Note: as usual for LCAO programs, PySCF implements PBC in 0, 1, 2, and 3 dimensions.

  • $\begingroup$ Thanks! Is there any paper reference on how to adjust the grid weights for periodic boundary conditions? $\endgroup$
    – Firman
    Commented Apr 6, 2021 at 19:31
  • $\begingroup$ I'm not sure; I think the algorithm is pretty obvious, i.e. you just need to include the periodic copies of your cell in all the necessary dimensions. Then, these weights are the same in every cell. $\endgroup$ Commented Apr 15, 2021 at 0:16
  • $\begingroup$ @SusiLehtola The links in your answer aare broken. Could you update the links, please? $\endgroup$ Commented Sep 5, 2023 at 7:58
  • $\begingroup$ I'm seeing the same issue with the links, I'm getting a 404 error "There isn't a GitHub Pages site here." for both. Are they set to be private? $\endgroup$
    – Tyberius
    Commented Sep 7, 2023 at 20:09
  • 1
    $\begingroup$ Next time just go ahead and fix the broken links. I would rather spend my time answering new questions than doing busywork with maintaining solved questions. $\endgroup$ Commented Sep 9, 2023 at 13:03

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