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.

The numerical grid implementations should be in https://sunqm.github.io/pyscf/_modules/pyscf/dft/numint.html for molecules and https://sunqm.github.io/pyscf/_modules/pyscf/pbc/dft/numint.html for periodic systems. 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
    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. $\endgroup$ Apr 15, 2021 at 0:16

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