LMAXFOCKAE: Difference between revisions

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{{TAGDEF|LMAXFOCKAE|[integer]|-1}}
#REDIRECT [[NMAXFOCKAE and LMAXFOCKAE]]
{{DEF|ICHARG|2|if {{TAG|ISTART}}{{=}}0|0|else}}


{{TAGDEF|NMAXFOCKAE|0{{!}}1{{!}}2}}
{{TAGDEF|LMAXFOCKAE|[integer]}}
{{DEF|NMAXFOCKAE|0|density functional theory|1|post DFT methods}}
{{DEF|LMAXFOCKAE|-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.).


Description: {{TAG|LMAXFOCKAE}} and {{TAG|LMAXFOCKAE}} describes the maximum angular momentum quantum number ''l'' and the number of channels for an "accurate" augmentation of charge densities in Hartree-Fock type routines.
----
----
In the PAW method the difference between the charge density of the all-electron partial waves and
In the PAW method, the difference between the charge density of the all-electron partial waves <math>\phi_\beta</math> and
the pseudo partial waves  
the pseudo partial waves <math>\tilde \phi_\beta</math>
<math>
<math>
Q_{\alpha\beta}(r)= \phi^*_\alpha(r)\phi_\beta(r)  - \tilde \phi^*_\alpha(r)\tilde \phi_\beta(r)
Q_{\alpha\beta}(r)= \phi^*_\alpha(r)\phi_\beta(r)  - \tilde \phi^*_\alpha(r)\tilde \phi_\beta(r)
</math>
</math>
is usually restored on spherical grids centered at each atom
is usually restored on spherical grids centered at each atom
(one-center terms inside the PAW spheres). To describe long range electrostatic terms, the
(one-center terms inside the PAW spheres). To describe long range electrostatic effect, the ''moments'' of the differences of the all-electron and pseudo charge density  
the ''moments'' of the differences of the all-electron and pseudo charge density are also
also need to added to the pseudo density on the plane wave grid. This is done up to a certain ''l'' quantum number.
restored on the plane wave grid up to a certain ''l'' quantum number (see {{TAG|LMAXFOCK}}).
These augmentation charges exactly restore the moments of the all-electron density on the plane wave
grid. For the charge densities used in the Hartree and DFT term,
this augmentation is done exactly up to the maximum ''l'' quantum number required by the POTCAR files,
whereas for the Fock exchange,  the augmentation on the plane wave grid is controlled by {{TAG|LMAXFOCK}}.


For the RPA, GW, and most post DFT methods, the one-center terms are presently,
For the RPA, GW, and most post DFT methods, the one-center terms are, however, presently
however, not implemented. Depending on the material, this can cause sizable errors
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.
in particular for 3d and (to a lesser extent) 2p, 4d and 5d elements.
To correct for this error, an alternative treatment is implemented
To correct for this error, an alternative treatment is implemented
on the plane wave grid. This  allows to restore the ''shape'' of the charge density difference accurately on the plane wave grid, using the flags {{TAG|LMAXFOCKAE}} and {{TAG|NMAXFOCKAE}}.
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, <math> Q_{\alpha\beta}(r) </math> is Fourier transformed  
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
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
in a set of orthogonal functions localized at each atomic site.
are then added to the pseudo charge densities on the plane wave grid.




If the {{TAG|NMAXFOCKAE}}=0 (the default for DFT and Hartree-Fock calculations), only the moment and 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
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  
as hybrid functionals, since the one-center terms are implemented.
since the one-center terms are implemented.  


If the {{TAG|NMAXFOCKAE}}=1 is set, the moments of the all-electron charge density are stored 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.  {{TAG|LMAXFOCKAE}} can be used to specify the maximum spherical (l) quantum number up  
If {{TAG|LMAXFOCKAE}} is set to values 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  
to which this more accurate treatment is used. The default for {{TAG|LMAXFOCKAE}} is 4.
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|NMAXFOCKAE}}=2 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,  {{TAG|LMAXFOCKAE}} can be used to specify the maximum spherical (l) quantum number up  
If {{TAG|LMAXFOCKAE}} is set to values larger than -1 and {{TAG|NMAXFOCKAE}}=2, the charge density is restored accurately on the plane wave grid up to a typical plane wave energy 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  
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
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.  
{{TAG|NMAXFOCKAE}} and {{TAG|LMAXFOCKAE}}, if energy differences are calculated.  
For GW calculations, increasing  {{TAG|NMAXFOCKAE}}=1 to {{TAG|NMAXFOCKAE}}=2 might change QP energies by 100-200 meV for 3d and late 4d and 5d elements.
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.




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


In summary, useful manual settings 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 charge augmentation on the plane wave grid (can be selected even in Hartree-Fock type calculations).
* {{TAG|NMAXFOCKAE}}=2, to select the very accurate augmentation on the plane wave grid. Please check whether the VASP default setting for {{TAG|LMAXFOCKAE}} suffices (OUTCAR file).


== Related Tags and Sections ==
 
{{TAG|LMAXFOCK}}
== Related tags and articles ==
{{TAG|LMAXFOCK}}, {{TAG|NMAXFOCKAE}}, {{TAG|QMAXFOCKAE}}, {{TAG|LFOCKAEDFT}}
----
----
[[The_VASP_Manual|Contents]]


[[Category:INCAR]][[Category:Hybrids]]
[[Category:INCAR tag]][[Category:Hybrids]][[Category:GW]]

Latest revision as of 14:38, 8 April 2022

LMAXFOCKAE = [integer] 

Default: LMAXFOCKAE = -1 for Hartree-Fock and hybrid functionals
= 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. 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 the pseudo partial waves is usually restored on spherical grids centered at each atom (one-center terms inside the PAW spheres). To describe long range electrostatic effect, the moments of the differences of the all-electron and pseudo charge density also need to added to the pseudo density on the plane wave grid. This is done up to a certain l quantum number. These augmentation charges exactly restore the moments of the all-electron density on the plane wave grid. For the charge densities used in the Hartree and DFT term, this augmentation is done exactly up to the maximum l quantum number required by the POTCAR files, whereas for the Fock exchange, the augmentation on the plane wave grid is controlled by LMAXFOCK.

For the RPA, GW, and most post DFT methods, the one-center terms are, however, presently 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 LMAXFOCKAE and NMAXFOCKAE.

To achieve this improved treatment on the plane wave grid, is Fourier transformed to reciprocal space 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.


For 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 since the one-center terms are implemented.

If LMAXFOCKAE is set to values larger than -1 (and 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. 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 LMAXFOCKAE is set to values larger than -1 and NMAXFOCKAE=2, the charge density is restored accurately on the plane wave grid up to a typical plane wave energy 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.


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 numbers up to 4), whereas for f elements, users should test whether LMAXFOCKAE = 6 is required.

In summary, useful manual settings of NMAXFOCKAE and LMAXFOCKAE are:

  • LMAXFOCKAE=-1, to switch off the accurate augmentation altogether
  • LMAXFOCKAE=4 (or larger) to force an accurate treatment for the charge augmentation on the plane wave grid (can be selected even in Hartree-Fock type calculations).
  • NMAXFOCKAE=2, to select the very accurate augmentation on the plane wave grid. Please check whether the VASP default setting for LMAXFOCKAE suffices (OUTCAR file).


Related tags and articles

LMAXFOCK, NMAXFOCKAE, QMAXFOCKAE, LFOCKAEDFT