NMAXFOCKAE

NMAXFOCKAE = 1|2
Default: NMAXFOCKAE = 1 

LMAXFOCKAE = [integer] 

Default: LAXMFOCKAE	= -1	for DFT, Hartree-Fock
	= 4	for post DFT methods

Description: NMAXFOCKAE and LMAXFOCKAE determine whether the overlap densities in the Fock exchange and correlated wave function methods are accurately reconstructed on the plane wave grid.

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In the PAW method, the difference between the charge density of the all-electron partial waves and the pseudo partial waves $Q_{\alpha\beta}(r)= \phi^*_\alpha(r)\phi_\beta(r) - \tilde \phi^*_\alpha(r)\tilde \phi_\beta(r)$ is usually restored on spherical grids centered at each atom (one-center terms inside the PAW spheres). To describe long range electrostatic terms, the the moments of the differences of the all-electron and pseudo charge density are usually also added on the plane wave grid up to a certain l quantum number (see LMAXFOCK). These augmentation charges restore the moments of the all-electron density on the plane wave grid.

For the RPA, GW, and most post DFT methods, the one-center terms are presently, however, not implemented. Depending on the material, this can cause sizable errors in particular for 3d and (to a lesser extent) 2p, 4d and 5d elements. To correct for this error, an alternative treatment is implemented on the plane wave grid. This allows to restore the all-electron charge density accurately on the plane wave grid, using the flags LMAXFOCKAE and NMAXFOCKAE.

To achieve this, $Q_{\alpha\beta}(r)$ is Fourier transformed to reciprocal space $Q_{\alpha\beta}(q)$ and then expanded in a set of orthogonal functions localized at each atomic site.

If the LMAXFOCKAE=-1 (the default for DFT and Hartree-Fock calculations), only the moments of the all-electron charge density is restored on the plane wave grid. This setting is exact for density functional theory, Hartree-Fock as well as hybrid functionals, since the one-center terms are implemented.

If NMAXFOCKAE=1 and LMAXFOCKAE is set, the moments of the all-electron charge density are restored on the plane wave grid. Furthermore, the all-electron charge density is restored up to a typical plane wave energy of 140 eV. This setting yields very accurate results for post DFT methods (MP2, RPA, GW, etc.) for most sp bonded materials. LMAXFOCKAE is used to specify the maximum spherical (l) quantum number up to which this more accurate treatment is used. The default is LMAXFOCKAE=4, for post DFT methods. If no accurate augmentation is desired by the user, simply set LMAXFOCKAE=-1 in the INCAR file.

If NMAXFOCKAE=2 and LMAXFOCKAE is set, the charge density is restored accurately on the plane wave grid up to a typical plane wave energies of 380 eV. As before, LMAXFOCKAE can be used to specify the maximum spherical (l) quantum number up to which this more accurate treatment is used. NMAXFOCKAE=2 yields very accurate results for post DFT methods (MP2, RPA, GW) even for difficult 3d elements. For RPA and MP2 total energy calculations, differences between NMAXFOCKAE=1 and NMAXFOCKAE=2 are usually tiny for total energy differences. Since the absolute correlation energies might change, it is vital to use the same setting for NMAXFOCKAE and LMAXFOCKAE, if energy differences are calculated. For GW calculations, increasing NMAXFOCKAE from 1 to 2 might change QP energies by 100-200 meV for 3d and late 4d and 5d elements.

If NMAXFOCKAE is used, the setting for LMAXFOCKAE should be also considered carefully. Generally, it suffices to set LMAXFOCKAE to twice the maximum l quantum number found in the POTCAR file. For instance for sp elements, LMAXFOCKAE = 2 suffices. For d elements, LMAXFOCKAE = 4 suffices (a d electron can create charge densities with l-quantum number of 4), whereas for f elements, users should test whether LMAXFOCKAE = 6 is required.

In summary, usefully manual setting of NMAXFOCKAE and LMAXFOCKAE are:

• LMAXFOCKAE=-1, to switch off the accurate augmentation altogether (fall back to the DFT treatment)
• LMAXFOCKAE=4 (or larger) to force an accurate treatment for the HF part even in Hartree-Fock calculations
• NMAXFOCKAE=2, to select the very accurate augmentation. Please check whether the VASP default setting for LMAXFOCKAE suffices (OUTCAR file).

Related Tags and Sections

LMAXFOCK

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