ADDGRID: Difference between revisions

Revision as of 07:02, 18 August 2020

<ADDGRID = .TRUE. | .FALSE.
Default: ADDGRID = .FALSE.

Description: ADDGRID determines whether an additional support grid is used for the evaluation of the augmentation charges.

When ADDGRID=.TRUE. VASP uses an additional support grid for the evaluation of the augmentation charges. This grid contains 8 times more points than the standard "fine" grid (NGXF×NGYF×NGZF). Whenever terms involving augmentation charges are evaluated, this additional grid is used. For instance: The augmentation charge is evaluated first in real space on this additional grid, FFT-transformed to reciprocal space and then added to the total charge density on the standard "fine" grid (NGXF×NGYF×NGZF). The additional grid often helps to reduce the noise in the forces. In some cases, it even allows to perform calculations with NGXF=NGX.

Caveat: If there is any contribution in the density or potential at the highest Fourier component $G$ 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 $G_{cut}$ i.e. $e^{(i G_{cut} r)}$ . 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 $e^{i G_{cut} r}$ in the interpolated potential (where $G_{cut}$ 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!

Examples that use this tag

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@@ Line 10: / Line 10: @@
 oscillations in real space. These oscillations correspond to the largest wave vector <math> G_{cut} </math> i.e. <math>e^{(i G_{cut} r)}</math>.
 In real space, the charge density or potential will therefore alternate between positive and negative
-values, in particular, in regions where the density or potential is small.
+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 in the interpolated charge density or potential  <math>e^{i G_{cut} r}</math> (where <math> G_{cut}</math> corresponds to
+The upshot is that Fourier-interpolation can lead to termination wiggles with oscillations <math>e^{i G_{cut} r}</math> in the interpolated potential   (where <math> G_{cut}</math> corresponds to
-the largest Fourier components on the fine grid). Therefore, we recommend to perform careful tests, whether {{TAG|ADDGRID}} works as desired; please do not use
+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.
-this tag as default in all your calculations!
+Therefore, we recommend to perform careful tests, whether {{TAG|ADDGRID}} works as desired; please do not use this tag as default in all your calculations!
 {{sc|ADDGRID|Examples|Examples that use this tag}}