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# PRECFOCK

PRECFOCK = Normal | Accurate | Fast | Medium | Single | Low

Default: **PRECFOCK** = Normal

Description: PRECFOCK controls the FFT grids used in the exact exchange routines (Hartree-Fock and hybrid functionals).

The FFT grid used for the exact exchange contributions can be chose to be different from the one used for the Hartree and DFT potentials. Information on the FFT grid that is used in the exact Fock exchange routines is written to the OUTCAR file after the lines

FFT grid for exact exchange (Hartree Fock)

We recommend to set PRECFOCK=Normal for routine calculations. If speed is an issue, you can also use PRECFOCK=Fast (e.g. use this to pre-converge the orbitals). For very high precision, in particular for phonon calculations, PRECFOCK=Accurate is recommended. The two setting, PRECFOCK=Medium and PRECFOCK=Low are not recommended, but have been kept to maintain compatibility with older VASP versions.

Generally, as opposed to gradient corrected density functionals, the exact exchange energy is rather insensitive to the FFT grids, and in many cases a rather coarse grid can be used to calculate the overlap densities and the exact exchange (Fock) potential. Exact exchange requires one to evaluation the overlap density

between two orbitals. Strictly speaking, 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|G_{cut}|. As usual, |G_{cut}| is determined by the plane wave cutoff (ENCUT).
A grid avoiding aliasing errors is chosen by setting PRECFOCK=Accurate. In this case, the FFT grid for the exact exchange is identical to the FFT grid used for the orbitals for PREC=Accurate in the DFT part. PRECFOCK=Accurate is the recommended setting for very accurate calculations.

For PRECFOCK=Low and Fast, the smallest possible FFT grid that just encloses the cutoff sphere (G_{cut}|) is used. This accelerates the calculations by roughly a factor two to three, but causes slight errors in the total energies and some noise in the calculated forces. To reduce the noise, the augmentation charges
are made very soft for PRECFOCK=Fast (whereas PRECFOCK=Low uses the standard augmentation charges also used for DFT).

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. In this case, the grid density is between the ones for PRECFOCK=Accurate and PRECFOCK=Fast. This is often a very reasonable comprise and hence recommended for most routine calculations.

For PRECFOCK=Fast, Normal and Accurate, the augmentation charges (required to restore the norm and dipoles of the overlap density on the plane wave grid) are softened, 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

Since VASP always uses one-center terms to correct for the difference between all-electron and pseudo orbitals, the precise shape of the augmentation charges matters little for exchange energies. Still it is recommended to keep PRECFOCK and PREC the same if relative energies are calculated (for instance adsorption energies, energies differences between different phases, etc.).

The following table summarizes the possible setting:

PRECFOCK FFT-grid Augmentation charge Quality Comment Normal 3/2×G _{cut}identical to std. FFT for PREC=Normalsoft augmentation charge ^{a}accurate forces and energy good compromise Accurate 2×G _{cut}identical to std. FFT for PREC=Accuratesoft augmentation charge ^{a}very accurate forces and energy for phonons Fast G _{cut}dvery soft augmentation charge ^{b}some noise in forces/good energy need for speed Medium strictly identical to std. FFT identical to standard DFT identical to standard DFT outdated Single ^{c}strictly identical to std. FFT identical to standard DFT identical to standard DFT if compatibility between Hartree and exchange is desired Low G _{cut}identical to standard DFT large noise in forces/energy errors outdated ^{a}radius for augmentation sphere is increased by factor 1.25 compared to default.^{b}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.^{c}available in development version only, if user selects PREC = Single, the default for PRECFOCK also becomes Single.

Medium and Single are synonyms. They are useful the select the same treatment for the Hartree and exchange term. This can be advantageously for correlated wave function calculations to obtain a numerically exact balance and compensation between Hartree and exchange (for instance for the upcoming auxiliary field Monte-Carlo module in VASP). For conventional Hartree-Fock or hybrid functional calculations, Normal or Accurate should be used.

In this table, G_{cut} is determined by the relation

with E_{cut}=ENCUT.

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.

Any combination of PREC and PRECFOCK is allowed by the code. Useful settings of increasing precision are however:

PREC = Normal ; PRECFOCK = Fast ! if your are in need for speed PREC = Normal ; PRECFOCK = Normal ! the default PREC = Accurate ; PRECFOCK = Normal ! increase the precision for DFT part; since exchange dominates the compute time, only slightly slower PREC = Accurate ; PRECFOCK = Accurate ! highest accuracy, suggested for phonons

## Related Tags and Sections

PREC, ENCUT, hybrid functionals, settings for specific hybrid functionals