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We are all aware of the fact that negative charge densities in the atomic cores are an artefact of Density Functional theory Calculations using Projector Augmented Wave (PAW) method. But what is the justification for these negative charges? They certainly did not appear out of nowhere. I request an explanation and a convincing proof if available.

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    $\begingroup$ I'm not sure what you mean by "proof", they arise directly from the augmentation charges in the PAW (or ultrasoft) method. The way these methods work is they rearrange the charge density inside the core region, but this charge rearrangement is computed for a reference system which is usually an isolated neutral atom. When used in a material, it's entirely possible that they "remove" more charge density than there actually is, which leads to negative charge densities there. This can also arise from aliasing, if you have too low a plane-wave cut-off energy. Is that what you meant? $\endgroup$ Oct 9 at 22:36

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