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PRECFOCK: FFT grid in the Hartree-Fock and GW related routines

PRECFOCK= Low | Medium | Fast | Normal | Accurate

Default: PRECFOCK=Normal

The PRECFOCK parameter controls the FFT grid for the exact exchange (Hartree-Fock) routines, i.e. it is possible to chose a different grid for the exact exchange part, and for the local Hartree and DFT potentials. In fact, the exchange is rather insensitive to the FFT grids, and in many cases a rather coarse grid can be used to calculate the overlap density and the potentials. Since the exact exchange requires the evaluation of an overlap density (compare 6.57)

$\displaystyle \phi_{{\bf k}n}^{*}({\bf r})\phi_{{\bf q}m}^{*}({\bf r})

errors in the convolution (aliasing errors) are only avoided, if the FFT grid contains all Fourier components up to twice the plane wave with the largest wave vector ( $ 2 \vert G_{\rm cut}\vert$).

For Low and Fast, however, the smallest possible FFT grid, which just encloses the cutoff sphere ( $ \vert G_{\rm cut}\vert$) determined by the plane wave cutoff (ENCUT), is used. This accelerates the calculations by roughly a factor two to three, but causes slight changes in the total energies and some noise in the calculated forces. The corresponding FFT grid that is used in the Hartree Fock routines is written to the OUTCAR file after the lines

 FFT grid for exact exchange (Hartree Fock)
For PRECFOCK=Normal, the FFT grid for the exact exchange is identical to the FFT grid used for the orbitals for PREC=Normal in the DFT part. For PRECFOCK=Accurate, the FFT grid for the exact exchange is identical to the FFT grid used for the orbitals for PREC=Accurate in the DFT part (any combination of PREC and PRECFOCK is allowed).

For PRECFOCK=Fast, Normal and Accurate, the augmentation charges--which are required to restore the norm and dipoles of the overlap density on the plane wave grid --are made soft, such that an accurate presentation on the plane wave grid is possible even for relatively coarse FFT grids. The sphere size is printed out after

 Radii for the augmentation spheres in the non-local exchange
The following table summarises the possible setting:

PRECFOCK FFT grid augmentation charge advantage/disatvantage
VASP.5.2.2 compatible, not recommended
Low $ G_{\rm cut}^a$ identical to standard DFT large noise in forces/energy errors
Medium identical to std. FFT identical to standard DFT some noise in forces/good energy
VASP.5.2.4 and newer, recommended
Fast $ G_{\rm cut}^a$ very soft augmentation charge$ ^c$ some noise in forces/good energy
Normal 3/2 $ G_{\rm cut}^a$ soft augmentation charge$ ^b$ accurate forces and energy
Accurate 2 $ G_{\rm cut}^a$ soft augmentation charge$ ^b$ very accurate forces and energy

$ ^a \quad \frac{ \hbar^2}{2 m_e} \vert G_{\rm cut}\vert^2 = {\tt ENCUT} $
$ ^b$ soft augmentation charge: radius for augmentation sphere is increased by factor 1.25 compared to default
$ ^c$ very soft augmentation charge: radius is increased by factor 1.35 compared to default except for $ s$ like charge, for the $ s$ channel the radius of the augmentation sphere is increased by a factor 1.25

Even PRECFOCK=Fast yields fairly low noise in the forces and virtually no egg-box effects (aliasing errors). In the forces, the noise is usually below 0.01 eV/Å. For PRECFOCK=N and PRECFOCK=A, noise is usually not an issue, and the accuracy is sufficient even for phonon calculations in large supercells.

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