NMAXFOCKAE: Difference between revisions

Latest revision as of 13:41, 22 July 2026

NMAXFOCKAE = 1|2
Default: NMAXFOCKAE = 1

Description: NMAXFOCKAE determines the maximum order of expansion for augmentation charges used in shape restoration for the PAW method.

NMAXFOCKAE controls how accurately this augmentation is performed by specifying the maximum expansion order. It controls the plane-wave cutoff up to which accurate charge densities are restored on the plane-wave grid. Shape restoration is only accurate up to a certain plane-wave cutoff, typically about 150 eV for NMAXFOCKAE = 1, and 400 eV for NMAXFOCKAE = 2.

Important: Shape restoration is more fully documented in the LMAXFOCKAE page. Additionally, see Ref. ^[1] and ^[2].

Mind: This flag generally only applies to the Fock-exchange and many-body perturbation theory (MBPT) methods (GW, RPA, MP2, etc.).

Recommendations

NMAXFOCKAE = 1 is sufficient in most cases and provides a good balance between accuracy and computational cost. It predicts very accurate energy differences and quite accurate quasiparticle energies.
NMAXFOCKAE = 2 should be used with great caution. Specifically, noise and egg-box effects for coarse FFT grids are introduced as NMAXFOCKAE is increased. Use this flag only after extensive tests and verification that the increased accuracy is needed for your application. It yields very accurate results for post-DFT methods (MP2, RPA, GW) even for difficult 3d elements.
- For GW calculations, increasing from NMAXFOCKAE = 1 to NMAXFOCKAE = 2 might change quasiparticle energies by 100-200 meV for 3d and late 4d and 5d elements.
- For RPA and MP2 total energy calculations, differences between NMAXFOCKAE = 1 and NMAXFOCKAE = 2 are usually small for total energy differences.

Mind: Since absolute correlation energies might change, it is vital to use the same setting for NMAXFOCKAE and LMAXFOCKAE, if energy differences are calculated. Please check whether the VASP default setting for LMAXFOCKAE suffices (OUTCAR file). Use this setting only with care, as it can result in very noisy data for coarse FFT grids.

References

[shishkin:prb:2006-1] M. Shishkin and G. Kresse, Phys. Rev. B 74, 035101 (2006).

[unzog:prb:2022-2] M. Unzog, A. Tal, G. Kresse, X-ray absorption using the projector augmented-wave method and the Bethe-Salpeter equation, Phys. Rev. B 106, 155133 (2022).

[1]

[2]

@@ Line 1: / Line 1: @@
 {{TAGDEF|NMAXFOCKAE|1{{!}}2|1}}
-{{TAGDEF|LMAXFOCKAE|[integer]}}
+Description: {{TAG|NMAXFOCKAE}} determines the maximum order of expansion for augmentation charges used in [[LMAXFOCKAE|shape restoration]] for the [[Projector-augmented-wave_formalism|PAW method]].
-{{DEF|LAXMFOCKAE|-1|for Hartree-Fock and hybrid functionals |   4 | for post DFT methods}}
-Description: {{TAG|NMAXFOCKAE}} and {{TAG|LMAXFOCKAE}} determine whether
-the overlap densities in the Fock exchange and correlated wave function methods are accurately reconstructed on the plane wave grid. This flag generally only applies to the Fock-exchange part as well as many-body
-post DFT methods (GW, RPA, MP2, etc.).
 ----
-In the PAW method, the difference between the charge density of the all-electron partial waves and
+{{TAG|NMAXFOCKAE}} controls how accurately this augmentation is performed by specifying the maximum expansion order. It controls the plane-wave cutoff up to which accurate charge densities are restored on the plane-wave grid. Shape restoration is only accurate up to a certain plane-wave cutoff, typically about 150 eV for {{TAG|NMAXFOCKAE|1}}, and 400 eV for {{TAG|NMAXFOCKAE|2}}.
-the pseudo partial waves
+{{NB|important|Shape restoration is more fully documented in the {{TAG|LMAXFOCKAE}} page. Additionally, see Ref. {{cite|shishkin:prb:2006}} and {{cite|unzog:prb:2022}}.}}
-<math>
+{{NB|mind|This flag generally only applies to the Fock-exchange and [[:Category:Many-body_perturbation_theory|many-body perturbation theory]] (MBPT) methods ([[GW approximation of Hedin's equations|GW]], [[ACFDT/RPA calculations|RPA]], [[MP2]], etc.).}}
-Q_{\alpha\beta}(r)= \phi^*_\alpha(r)\phi_\beta(r)  - \tilde \phi^*_\alpha(r)\tilde \phi_\beta(r)
-</math>
-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 {{TAG|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 densities accurately on the plane wave grid
-instead of the one-center grids by specifying the flags {{TAG|LMAXFOCKAE}} and {{TAG|NMAXFOCKAE}}.
-To achieve this improved treatment on the plane wave grid, <math> Q_{\alpha\beta}(r) </math> is Fourier transformed  to reciprocal space <math> Q_{\alpha\beta}(q) </math> and then expanded
-in a set of orthogonal functions localized at each atomic site. These augmentation charges
-are then added to the pseudo charge densities on the plane wave grid.
+== Recommendations ==
+*{{TAG|NMAXFOCKAE|1}} is sufficient in most cases and provides a good balance between accuracy and computational cost. It predicts very accurate energy differences and quite accurate quasiparticle energies.
+*{{TAG|NMAXFOCKAE|2}} should be used with great caution. Specifically, noise and egg-box effects for coarse FFT grids are introduced as {{TAG|NMAXFOCKAE}} is increased. Use this flag only after extensive tests and verification that the increased accuracy is needed for your application. It yields very accurate results for post-DFT methods (MP2, RPA, GW) even for difficult 3''d'' elements.
+**For [[GW approximation of Hedin's equations|GW calculations]], increasing from {{TAG|NMAXFOCKAE|1}} to {{TAG|NMAXFOCKAE|2}} might change quasiparticle energies by 100-200 meV for 3''d'' and late 4''d'' and 5''d'' elements.
+**For [[ACFDT/RPA calculations|RPA]] and [[MP2|MP2]] total energy calculations, differences between {{TAG|NMAXFOCKAE|1}} and {{TAG|NMAXFOCKAE|2}} are usually small for total energy differences. {{NB|mind|Since absolute correlation energies might change, it is vital to use the same setting for {{TAG|NMAXFOCKAE}} and {{TAG|LMAXFOCKAE}}, if energy differences are calculated. Please check whether the VASP default setting for {{TAG|LMAXFOCKAE}} suffices ({{FILE|OUTCAR}} file). Use this setting only with care, as it can result in very noisy data for coarse FFT grids.|::}}
-For {{TAG|LMAXFOCKAE}}=-1 (the default for DFT and Hartree-Fock calculations), only the moments of the all-electron charge densities are restored on the plane wave grid. This setting is exact for Hartree-Fock
+== Related tags and articles ==
-since the one-center terms are implemented.
+{{TAG|NMAXFOCKAE}}, {{TAG|LMAXFOCK}}, {{TAG|QMAXFOCKAE}}, {{TAG|LFOCKAEDFT}}, {{TAG|LFOCKSTD}}
-If {{TAG|LMAXFOCKAE}} is set to value larger than -1 (and {{TAG|NMAXFOCKAE}}=1), not only the moments of the all-electron charge density are restored, but also 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.  {{TAG|LMAXFOCKAE}} is used to specify the maximum spherical (l) quantum number up
+{{sc|NMAXFOCKAE|Examples|Examples that use this tag}}
-to which this more accurate treatment is used. The default is {{TAG|LMAXFOCKAE}}=4, for post DFT methods.
-If no accurate augmentation is desired by the user, simply set {{TAG|LMAXFOCKAE}}=-1 in the INCAR file.
-If {{TAG|LMAXFOCKAE}} is set to value larger than -1 and {{TAG|NMAXFOCKAE}}=2, the charge density is restored accurately on the plane wave grid up to a typical plane wave energies of 380 eV. As before,  {{TAG|LMAXFOCKAE}} can be used to specify the maximum spherical (l) quantum number up
-to which this more accurate treatment is used.  {{TAG|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 {{TAG|NMAXFOCKAE}}=1 and {{TAG|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
-{{TAG|NMAXFOCKAE}} and {{TAG|LMAXFOCKAE}}, if energy differences are calculated.
-For GW calculations, increasing  {{TAG|NMAXFOCKAE}} from 1 to 2 might change QP energies by 100-200 meV for 3d and late 4d and 5d elements.
-The setting for {{TAG|LMAXFOCKAE}} should be also considered carefully. Generally, it suffices to set {{TAG|LMAXFOCKAE}} to twice the maximum ''l'' quantum number found in the {{FILE|POTCAR}} file.
-For instance for sp elements, {{TAG|LMAXFOCKAE}} = 2 suffices. For d elements, {{TAG|LMAXFOCKAE}} = 4 suffices
-(a d electron can create charge densities with ''l''-quantum numbers up to 4), whereas for f elements, users
-should test whether  {{TAG|LMAXFOCKAE}} = 6 is required.
-In summary, usefully manual setting of {{TAG|NMAXFOCKAE}}  and {{TAG|LMAXFOCKAE}} are:
-*  {{TAG|LMAXFOCKAE}}=-1, to switch off the accurate augmentation altogether
-* {{TAG|LMAXFOCKAE}}=4 (or larger) to force an accurate treatment for the HF part even in Hartree-Fock calculations
-* {{TAG|NMAXFOCKAE}}=2, to select the very accurate augmentation. Please check whether the VASP default setting for {{TAG|LMAXFOCKAE}} suffices (OUTCAR file).
-== Related Tags and Sections ==
-{{TAG|LMAXFOCK}} {{TAG|QMAXFOCKAE}}
-----
-[[The_VASP_Manual|Contents]]
-[[Category:INCAR]][[Category:Hybrids]]
+== References ==
+[[Category:INCAR tag]]
+[[Category:ACFDT]]
+[[Category:Low-scaling GW and RPA]]
+[[Category:Exchange-correlation functionals]]
+[[Category:Hybrid functionals]]
+[[Category:Many-body perturbation theory]]
+[[Category:GW]]