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Caveat: If there is any contribution in the density or potential at the highest Fourier component ${\displaystyle G}$ of the conventional fine grid (given by NGXF×NGYF×NGZF), then Fourier interpolation to twice the grid density leads to oscillations in real space. These oscillations correspond to the largest wave vector ${\displaystyle G_{cut}}$ i.e. ${\displaystyle e^{iG_{cut}r}}$. In real space, the charge density or potential will therefore alternate between positive and negative values on the ultra-fine grid, in particular, in regions where the density or potential are small. The terminus techniques is "termination wiggles". Although this is a somewhat over-simplified presentation, it is fairly straightforward to derive more rigorous results in 1D. The upshot is that Fourier-interpolation can lead to termination wiggles with oscillations ${\displaystyle e^{iG_{cut}r}}$ in the interpolated potential (where ${\displaystyle G_{cut}}$ corresponds to the largest Fourier components on the fine grid). Fourier smoothing, which is in essence used for the augmentation densities, is generally less problematic, but it can also result in negative density in real space. Therefore, we recommend to perform careful tests, whether ADDGRID works as desired; please do not use this tag as default in all your calculations!