LMAXFOCKAE - Revision history

Csheldon at 13:46, 22 July 2026

2026-07-22T13:46:13Z

← Older revision		Revision as of 13:46, 22 July 2026
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	For [[GW approximation of Hedin's equations\|GW]], [[ACFDT/RPA calculations\|RPA]], and [[:Category:Many-body perturbation theory\|post-DFT]] methods, the one-center terms are, however, presently not implemented, which can cause sizable errors, particularly for 3''d'' and (to a lesser extent) 2''p'', 4''d'', and 5''d'' elements. To correct for this error, an alternative treatment is implemented on the plane-wave grid for the exchange and correlation contributions, allowing for accurate restoration of the all-electron densities.		For [[GW approximation of Hedin's equations\|GW]], [[ACFDT/RPA calculations\|RPA]], and [[:Category:Many-body perturbation theory\|post-DFT]] methods, the one-center terms are, however, presently not implemented, which can cause sizable errors, particularly for 3''d'' and (to a lesser extent) 2''p'', 4''d'', and 5''d'' elements. To correct for this error, an alternative treatment is implemented on the plane-wave grid for the exchange and correlation contributions, allowing for accurate restoration of the all-electron densities.

	This improved treatment — termed ''shape restoration'' — is available for exchange as well as many-body correlation contributions. For exchange, the exact one-center terms are also implemented (cf. {{TAG\|LFOCKSTD}}); this means shape restoration is not required and should not change the results. More details on shape restoration are explained in Ref. {{cite\|shishkin:prb:2006}} and {{cite\|unzog:prb:2022}}.		This improved treatment — termed ''shape restoration'' — is available for exchange as well as many-body correlation contributions. <!--For exchange, the exact one-center terms are also implemented (cf. {{TAG\|LFOCKSTD}}); this means shape restoration is not required and should not change the results.--> More details on shape restoration are explained in Ref. {{cite\|shishkin:prb:2006}} and {{cite\|unzog:prb:2022}}.

	Shape restoration allows restoration of the all-electron densities accurately already on the plane-wave grid by specifying the tags {{TAG\|LMAXFOCKAE}} and {{TAG\|NMAXFOCKAE}}. This accurate augmentation charge <math>\hat n</math> is calculated for the total orbital and angular momentum quantum numbers <math>L</math> (up to {{TAG\|LMAXFOCKAE}}) and <math>M</math> using shape-restoring radial functions <math>\Delta g_L(r)</math> with coefficients <math>c^L_{nm}</math> to be determined:		Shape restoration allows restoration of the all-electron densities accurately already on the plane-wave grid by specifying the tags {{TAG\|LMAXFOCKAE}} and {{TAG\|NMAXFOCKAE}}. This accurate augmentation charge <math>\hat n</math> is calculated for the total orbital and angular momentum quantum numbers <math>L</math> (up to {{TAG\|LMAXFOCKAE}}) and <math>M</math> using shape-restoring radial functions <math>\Delta g_L(r)</math> with coefficients <math>c^L_{nm}</math> to be determined:

Csheldon: Removed redirect to NMAXFOCKAE and LMAXFOCKAE

2026-07-22T13:41:17Z

Removed redirect to NMAXFOCKAE and LMAXFOCKAE

← Older revision		Revision as of 13:41, 22 July 2026
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	~~#REDIRECT~~ [[NMAXFOCKAE and LMAXFOCKAE]]		{{TAGDEF\|LMAXFOCKAE\|[integer]}}

			{{DEF\|LMAXFOCKAE\|-1\|DFT, Hartree-Fock\|4\|post-DFT methods}}

			Description: Specifies the maximum spherical angular momentum quantum number (<math>L</math>) up to which augmentation charges are accurately restored on the plane-wave grid. This parameter controls the quality of shape restoration for the [[Projector-augmented-wave_formalism\|PAW method]].
			----
			In the [[Projector-augmented-wave_formalism\|PAW method]], the difference between the charge density of the all-electron partial waves <math>\phi_n</math> and the pseudo partial waves <math>\tilde \phi_n</math>

			<math>
			Q_{nm}({\mathbf r})= \phi^_n({\mathbf r})\phi_m({\mathbf r}) - \tilde \phi^_n({\mathbf r})\tilde \phi_m({\mathbf r})
			</math>

			is usually treated on spherical grids centered at each atom
			(one-center terms inside the PAW spheres, see [[Projector-augmented-wave_formalism\|PAW method]] method and more detailed description for {{TAG\|LMAXFOCK}}). To describe long-range electrostatic effects, the ''moments'' of the differences of the all-electron and pseudo charge density also need to be added on the plane wave grid (compensation density, see [[Projector-augmented-wave_formalism\|PAW method]]). These compensation charges exactly restore the moments of the all-electron density on the plane wave grid. For the Fock exchange the maximum ''L'' quantum number up to which the augmentation is done is controlled by {{TAG\|LMAXFOCK}}.

			For [[GW approximation of Hedin's equations\|GW]], [[ACFDT/RPA calculations\|RPA]], and [[:Category:Many-body perturbation theory\|post-DFT]] methods, the one-center terms are, however, presently not implemented, which can cause sizable errors, particularly for 3''d'' and (to a lesser extent) 2''p'', 4''d'', and 5''d'' elements. To correct for this error, an alternative treatment is implemented on the plane-wave grid for the exchange and correlation contributions, allowing for accurate restoration of the all-electron densities.

			This improved treatment — termed ''shape restoration'' — is available for exchange as well as many-body correlation contributions. For exchange, the exact one-center terms are also implemented (cf. {{TAG\|LFOCKSTD}}); this means shape restoration is not required and should not change the results. More details on shape restoration are explained in Ref. {{cite\|shishkin:prb:2006}} and {{cite\|unzog:prb:2022}}.

			Shape restoration allows restoration of the all-electron densities accurately already on the plane-wave grid by specifying the tags {{TAG\|LMAXFOCKAE}} and {{TAG\|NMAXFOCKAE}}. This accurate augmentation charge <math>\hat n</math> is calculated for the total orbital and angular momentum quantum numbers <math>L</math> (up to {{TAG\|LMAXFOCKAE}}) and <math>M</math> using shape-restoring radial functions <math>\Delta g_L(r)</math> with coefficients <math>c^L_{nm}</math> to be determined:

			<math>
			\hat n=\sum_{LM\atop n,m}\rho_{LM}\!\left[q^{LM}_{nm}Y_{LM}(\Omega)+c^L_{nm}\,\Delta g_L(r)Y_{LM}(\Omega)\right]
			</math>

			where <math>Y_{LM}(\Omega)</math> are the spherical harmonics and <math>q^{LM}_{nm}</math> are the moments of the charge difference.

			{{TAG\|NMAXFOCKAE}} controls how accurately this compensation is performed by specifying the maximum expansion order of spherical Bessel functions <math>j_L</math> with carefully chosen coefficients <math>\alpha_{\beta L}</math> and <math>q_{\beta L}</math> (cf. Appendix of Ref. {{cite\|unzog:prb:2022}} for details).

			<math>
			\;\Delta g_L(r)=\sum_{\beta=1}^{NMAXFOCKAE}\alpha_{\beta L}\, j_L\!\left(q_{\beta L}\, r\right)
			</math>
			{{NB\|mind\|This tag generally only applies to the Fock-exchange and [[:Category:Many-body perturbation theory\|many-body perturbation theory]] (MBPT) (GW, RPA, [[MP2]], etc). The default for DFT and Hartree-Fock, {{TAG\|LMAXFOCKAE\|-1}}, restores only the moments of the all-electron charge densities on the plane-wave grid. For Hartree-Fock, the setting is very precise since the one-center terms are implemented in radial grids as for DFT.
			}}

			== Recommendations ==
			=== Element-Dependent ===
			The setting for {{TAG\|LMAXFOCKAE}} should be chosen based on the elements in the calculation:
			* '''''s'' and ''p'' elements''': {{TAG\|LMAXFOCKAE\|2}}
			* '''''d'' elements''': {{TAG\|LMAXFOCKAE\|4}} (a ''d'' electron can create charge densities with L-quantum numbers up to 4)
			* '''''f'' elements''': {{TAG\|LMAXFOCKAE\|6}} may be required - test for each case

			The general rule is to set {{TAG\|LMAXFOCKAE}} to approximately twice the maximum ''l'' quantum number found in the {{FILE\|POTCAR}} file.

			=== General ===
			* Setting {{TAG\|LMAXFOCKAE\|4}} (or larger) forces an accurate treatment for charge augmentation on the plane-wave grid. This can be selected even in Hartree-Fock-type calculations, but causes some additional noise.
			*If no accurate augmentation is desired set {{TAG\|LMAXFOCKAE\|-1}}, which will reduce the noise in the correlation energies.
			* For DFT calculations, the exact one-center terms are implemented. This means shape restoration is not required and should not change the results. For post-DFT calculations, shape restoration significantly improves accuracy.

			=== Relationship with NMAXFOCKAE ===
			{{TAG\|LMAXFOCKAE}} and {{TAG\|NMAXFOCKAE}} are strongly coupled. It is vital to use consistent settings for both when comparing energy differences.
			* {{TAG\|NMAXFOCKAE\|1}} and {{TAG\|LMAXFOCKAE\|0\|op=≥}}: Charge density is restored up to approximately 150 eV (controlled by {{TAG\|QMAXFOCKAE}}).
			* {{TAG\|NMAXFOCKAE\|2}} and {{TAG\|LMAXFOCKAE\|0\|op=≥}}: Charge density is restored up to approximately 400 eV.
			{{NB\|important\|{{TAG\|NMAXFOCKAE\|2}} is for very accurate augmentation on the plane-wave grid. Use {{TAG\|NMAXFOCKAE\|2}} only with care, as it can result in very noisy data for coarse FFT grids.\|:}}

			== Related tags and articles ==
			{{TAG\|NMAXFOCKAE}}, {{TAG\|LMAXFOCK}}, {{TAG\|QMAXFOCKAE}}, {{TAG\|LFOCKAEDFT}}, {{TAG\|LFOCKSTD}}

			{{sc\|LMAXFOCKAE\|Examples\|Examples that use this tag}}

			== 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]]

Huebsch: Replaced content with "#REDIRECT NMAXFOCKAE and LMAXFOCKAE"

2025-02-28T10:20:44Z

Replaced content with "#REDIRECT NMAXFOCKAE and LMAXFOCKAE"

← Older revision		Revision as of 10:20, 28 February 2025
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	#REDIRECT [[NMAXFOCKAE and LMAXFOCKAE]]		#REDIRECT [[NMAXFOCKAE and LMAXFOCKAE]]

	~~{{TAGDEF\|LMAXFOCKAE\|[integer]}}~~
	~~{{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.).~~

	~~----~~
	~~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 <math>\tilde \phi_\beta</math>~~
	~~<math>~~
	~~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 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 {{TAG\|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 {{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.~~


	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
	~~since the one-center terms are implemented.~~

	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 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 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~~
	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, 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 articles ==~~
	~~{{TAG\|LMAXFOCK}}, {{TAG\|NMAXFOCKAE}}, {{TAG\|QMAXFOCKAE}}, {{TAG\|LFOCKAEDFT}}~~
	~~----~~

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

Karsai: /* Related Tags and Sections */

2022-04-08T14:38:52Z

Related Tags and Sections

← Older revision		Revision as of 14:38, 8 April 2022
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	== Related ~~Tags~~ and ~~Sections~~ ==		== Related tags and articles ==
	{{TAG\|LMAXFOCK}}, {{TAG\|NMAXFOCKAE}}, {{TAG\|QMAXFOCKAE}}, {{TAG\|LFOCKAEDFT}}		{{TAG\|LMAXFOCK}}, {{TAG\|NMAXFOCKAE}}, {{TAG\|QMAXFOCKAE}}, {{TAG\|LFOCKAEDFT}}
	----		----
	~~[[The_VASP_Manual\|Contents]]~~

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

Vaspmaster: Redirected page to NMAXFOCKAE and LMAXFOCKAE

2017-03-15T12:06:12Z

Redirected page to NMAXFOCKAE and LMAXFOCKAE

← Older revision		Revision as of 12:06, 15 March 2017
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			#REDIRECT [[NMAXFOCKAE and LMAXFOCKAE]]

	{{TAGDEF\|LMAXFOCKAE\|[integer]}}		{{TAGDEF\|LMAXFOCKAE\|[integer]}}
	{{DEF\|LMAXFOCKAE\|-1\|for Hartree-Fock and hybrid functionals \| 4 \| for post DFT methods}}		{{DEF\|LMAXFOCKAE\|-1\|for Hartree-Fock and hybrid functionals \| 4 \| for post DFT methods}}

Kresse at 16:22, 14 March 2017

2017-03-14T16:22:11Z

← Older revision		Revision as of 16:22, 14 March 2017
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	----		----
	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 ''moments'' of the differences of the all-electron and pseudo charge density ~~are usually~~		(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 added on the plane wave grid up to a certain ''l'' quantum number ~~(see {{TAG\|LMAXFOCK}})~~.		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 restore the moments of the all-electron density on the plane wave		These augmentation charges exactly restore the moments of the all-electron density on the plane wave
	grid.		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

Kresse: /* Related Tags and Sections */

2017-03-14T15:27:45Z

Related Tags and Sections

← Older revision		Revision as of 15:27, 14 March 2017
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	== Related Tags and Sections ==		== Related Tags and Sections ==
	{{TAG\|LMAXFOCK}}, {{TAG\|NMAXFOCKAE}}, {{TAG\|QMAXFOCKAE}}		{{TAG\|LMAXFOCK}}, {{TAG\|NMAXFOCKAE}}, {{TAG\|QMAXFOCKAE}}, {{TAG\|LFOCKAEDFT}}
	----		----
	[[The_VASP_Manual\|Contents]]		[[The_VASP_Manual\|Contents]]

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

Kresse at 15:25, 14 March 2017

2017-03-14T15:25:01Z

← Older revision		Revision as of 15:25, 14 March 2017
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	In summary, useful manual settings of {{TAG\|NMAXFOCKAE}} and {{TAG\|LMAXFOCKAE}} are:		In summary, useful manual settings of {{TAG\|NMAXFOCKAE}} and {{TAG\|LMAXFOCKAE}} are:
	* {{TAG\|LMAXFOCKAE}}=-1, to switch off the accurate augmentation altogether		* {{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\|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. Please check whether the VASP default setting for {{TAG\|LMAXFOCKAE}} suffices (OUTCAR file).		* {{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).

Kresse at 15:23, 14 March 2017

2017-03-14T15:23:52Z

← Older revision		Revision as of 15:23, 14 March 2017
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	should test whether {{TAG\|LMAXFOCKAE}} = 6 is required.		should test whether {{TAG\|LMAXFOCKAE}} = 6 is required.

	In summary, ~~usefully~~ manual settings of {{TAG\|NMAXFOCKAE}} and {{TAG\|LMAXFOCKAE}} are:		In summary, useful manual settings of {{TAG\|NMAXFOCKAE}} and {{TAG\|LMAXFOCKAE}} are:
	* {{TAG\|LMAXFOCKAE}}=-1, to switch off the accurate augmentation altogether		* {{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\|LMAXFOCKAE}}=4 (or larger) to force an accurate treatment for the HF part even in Hartree-Fock calculations

Kresse at 15:22, 14 March 2017

2017-03-14T15:22:25Z

← Older revision		Revision as of 15:22, 14 March 2017
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	If no accurate augmentation is desired by the user, simply set {{TAG\|LMAXFOCKAE}}=-1 in the INCAR file.		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 energy 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

← Older revision		Revision as of 13:46, 22 July 2026
Line 16:		Line 16:
	For [[GW approximation of Hedin's equations\|GW]], [[ACFDT/RPA calculations\|RPA]], and [[:Category:Many-body perturbation theory\|post-DFT]] methods, the one-center terms are, however, presently not implemented, which can cause sizable errors, particularly for 3''d'' and (to a lesser extent) 2''p'', 4''d'', and 5''d'' elements. To correct for this error, an alternative treatment is implemented on the plane-wave grid for the exchange and correlation contributions, allowing for accurate restoration of the all-electron densities.		For [[GW approximation of Hedin's equations\|GW]], [[ACFDT/RPA calculations\|RPA]], and [[:Category:Many-body perturbation theory\|post-DFT]] methods, the one-center terms are, however, presently not implemented, which can cause sizable errors, particularly for 3''d'' and (to a lesser extent) 2''p'', 4''d'', and 5''d'' elements. To correct for this error, an alternative treatment is implemented on the plane-wave grid for the exchange and correlation contributions, allowing for accurate restoration of the all-electron densities.

	This improved treatment — termed ''shape restoration'' — is available for exchange as well as many-body correlation contributions. For exchange, the exact one-center terms are also implemented (cf. {{TAG\|LFOCKSTD}}); this means shape restoration is not required and should not change the results. More details on shape restoration are explained in Ref. {{cite\|shishkin:prb:2006}} and {{cite\|unzog:prb:2022}}.		This improved treatment — termed ''shape restoration'' — is available for exchange as well as many-body correlation contributions. <!--For exchange, the exact one-center terms are also implemented (cf. {{TAG\|LFOCKSTD}}); this means shape restoration is not required and should not change the results.--> More details on shape restoration are explained in Ref. {{cite\|shishkin:prb:2006}} and {{cite\|unzog:prb:2022}}.

	Shape restoration allows restoration of the all-electron densities accurately already on the plane-wave grid by specifying the tags {{TAG\|LMAXFOCKAE}} and {{TAG\|NMAXFOCKAE}}. This accurate augmentation charge <math>\hat n</math> is calculated for the total orbital and angular momentum quantum numbers <math>L</math> (up to {{TAG\|LMAXFOCKAE}}) and <math>M</math> using shape-restoring radial functions <math>\Delta g_L(r)</math> with coefficients <math>c^L_{nm}</math> to be determined:		Shape restoration allows restoration of the all-electron densities accurately already on the plane-wave grid by specifying the tags {{TAG\|LMAXFOCKAE}} and {{TAG\|NMAXFOCKAE}}. This accurate augmentation charge <math>\hat n</math> is calculated for the total orbital and angular momentum quantum numbers <math>L</math> (up to {{TAG\|LMAXFOCKAE}}) and <math>M</math> using shape-restoring radial functions <math>\Delta g_L(r)</math> with coefficients <math>c^L_{nm}</math> to be determined:

← Older revision		Revision as of 15:25, 14 March 2017
Line 51:		Line 51:
	In summary, useful manual settings of {{TAG\|NMAXFOCKAE}} and {{TAG\|LMAXFOCKAE}} are:		In summary, useful manual settings of {{TAG\|NMAXFOCKAE}} and {{TAG\|LMAXFOCKAE}} are:
	* {{TAG\|LMAXFOCKAE}}=-1, to switch off the accurate augmentation altogether		* {{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\|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. Please check whether the VASP default setting for {{TAG\|LMAXFOCKAE}} suffices (OUTCAR file).		* {{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).

← Older revision		Revision as of 15:23, 14 March 2017
Line 49:		Line 49:
	should test whether {{TAG\|LMAXFOCKAE}} = 6 is required.		should test whether {{TAG\|LMAXFOCKAE}} = 6 is required.

	In summary, ~~usefully~~ manual settings of {{TAG\|NMAXFOCKAE}} and {{TAG\|LMAXFOCKAE}} are:		In summary, useful manual settings of {{TAG\|NMAXFOCKAE}} and {{TAG\|LMAXFOCKAE}} are:
	* {{TAG\|LMAXFOCKAE}}=-1, to switch off the accurate augmentation altogether		* {{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\|LMAXFOCKAE}}=4 (or larger) to force an accurate treatment for the HF part even in Hartree-Fock calculations

← Older revision		Revision as of 15:22, 14 March 2017
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	If no accurate augmentation is desired by the user, simply set {{TAG\|LMAXFOCKAE}}=-1 in the INCAR file.		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 energy 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