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# PRECFOCK

PRECFOCK = Low | Medium | Fast | Normal | Accurate
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 may differ from the one used for the local Hartree and DFT potentials. In fact, the exact exchange 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 potentials. Since the exact exchange requires the evaluation of an overlap density:

${\displaystyle \psi _{{{\mathbf {k}}n}}^{{*}}({\mathbf {r}})\psi _{{{\mathbf {q}}m}}({\mathbf {r}})}$

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|Gcut|.

For PRECFOCK=Low and Fast, however, the smallest possible FFT grid, which just encloses the cutoff sphere (|Gcut|) 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 (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


The following table summarizes the possible setting:

 PRECFOCK FFT-grid Augmentation charge Quality Low Gcut 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 Fast Gcut very soft augmentation chargea some noise in forces/good energy Normal 3/2×Gcut soft augmentation chargeb accurate forces and energy Accurate 2×Gcut soft augmentation chargeb very accurate forces and energy 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.

where

${\displaystyle E_{\rm {cut}}={\frac {\hbar ^{2}}{2m_{e}}}G_{\rm {cut}}^{2}}$

with Ecut=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.