I have a question regarding the Qeq implementation in LAMMPS. How do you deal with the PBC case? According to my knowledge, different matrix elements should be considered in this case (i.e. reciprocal and real space terms, self-interaction, neutralization term, etc.) if Ewald summation is used. However, I did not find any mention of those terms in the function compute_H of fix_qeq_point.

They almost certainly donâ€™t. QEq charges are evaluated using conjugate gradients (CG) to solve a sparse matrix equation. If you include the KSpace component, the matrix becomes dense, and every CG now includes an FFT with the required all-to-all communication.

Avoiding long-range communication also makes sense because charge isnâ€™t transferred long-range in real life (unphysical long-range charge transfer is a well-known theoretical weakness of QEq).

The ELECTRODE package (and its predecessors) have always included long-range effects in what is essentially QEq with Gaussian charges, first for Ewald summation and recently for PPPM. You can try it out and look at the source code to see what complexities come with that.

Thank you very much, I will have a look at the ELECTRODE package.
Would you suggest the Wolf summation method or the damped shifted force model (C. J. Fennell, J. D. Gezelter, J Chem Phys, 124, 234104 (2006)) as a valid alternative to Ewald ?
I saw that in fix_qeq_slater of the QEQ package matrix elements coming from Wolf summation method are used.

With apologies to George Box â€“ all molecular dynamics models are wrong, but some are at least useful. After all, PPPM is technically more wrong than Ewald (for the same number of k-vectors), but it can be made accurate enough and fast enough that we can accept the discretization error.

In your position, I would advise you to make sure you have really solid benchmarks â€“ that is, when you have run your QEq calculation and it has told you what all the partial charges are, how will you know how right or wrong its answers are? That way, you can determine for yourself whether the slower-but-more-accurate methods are worth it.

For what itâ€™s worth, I personally have no physical or mathematical intuition for how the â€śshort-range correctionâ€ť family of electrostatic methods actually work, so I personally donâ€™t go near them. But if you understand how they work then thereâ€™s nothing stopping you from giving it a shot.