NMAXFOCKAE - Revision history

Huebsch at 05:51, 9 September 2026

2026-09-09T05:51:56Z

← Older revision		Revision as of 05:51, 9 September 2026
Line 5:		Line 5:
	In [[Projector-augmented-wave formalism#Shape restoration\|shape restoration]], radial functions with vanishing multipole moment are added to the PAW compensation charge for each angular momentum quantum number <math>L</math>. {{TAG\|LMAXFOCKAE}} sets the maximum <math>L</math>; {{TAG\|NMAXFOCKAE}} sets how many functions are used per <math>L</math>, and thereby the wave vectors at which the all-electron density is matched:		In [[Projector-augmented-wave formalism#Shape restoration\|shape restoration]], radial functions with vanishing multipole moment are added to the PAW compensation charge for each angular momentum quantum number <math>L</math>. {{TAG\|LMAXFOCKAE}} sets the maximum <math>L</math>; {{TAG\|NMAXFOCKAE}} sets how many functions are used per <math>L</math>, and thereby the wave vectors at which the all-electron density is matched:

	* {{TAG\|NMAXFOCKAE\|1}}: one function per <math>L</math>, matched at 6 Å<sup>-1</sup>, which corresponds to a plane-wave energy of approximately 140 eV.		* {{TAG\|NMAXFOCKAE\|1}}: one function per <math>L</math>, matched at {{TAG\|QMAXFOCKAE}} (default 6 Å<sup>-1</sup>, which corresponds to a plane-wave energy of approximately 140 eV).
	* {{TAG\|NMAXFOCKAE\|2}}: two functions per <math>L</math>, matched at 5 and 10 Å<sup>-1</sup>, corresponding to approximately 95 eV and 380 eV.		* {{TAG\|NMAXFOCKAE\|2}}: two functions per <math>L</math>, matched at {{TAG\|QMAXFOCKAE}} and twice {{TAG\|QMAXFOCKAE}} (default 5 and 10 Å<sup>-1</sup>, corresponding to approximately 95 eV and 380 eV).

	~~These~~ wave vectors are the points at which the density is fitted, not a guarantee of the accuracy reached at a given cutoff~~. They can be changed with {{TAG\|QMAXFOCKAE}}, which replaces the first value; the second follows at twice the first~~.		The wave vectors {{TAG\|QMAXFOCKAE}} are the points at which the density is fitted, not a guarantee of the accuracy reached at a given cutoff.

	~~Only~~ the values 1 and 2 ~~are accepted~~. Values outside that range are corrected to the nearest allowed one, so a larger number does not give a finer expansion.		{{TAG\|NMAXFOCKAE}} only accepts the values 1 and 2. Values outside that range are corrected to the nearest allowed one, so a larger number does not give a finer expansion.
			{{NB\|mind\|Whenever {{TAG\|LMAXFOCKAE\|-1}} is set — the default for DFT and Hartree-Fock — shape restoration is inactive and {{TAG\|NMAXFOCKAE}} has no effect. Shape restoration applies only to the Fock exchange and to [[:Category:Many-body perturbation theory\|many-body perturbation theory]], i.e., [[GW approximation of Hedin's equations\|GW]], [[ACFDT/RPA calculations\|RPA]] and [[MP2]].}}
	{{NB\|mind\|Whenever {{TAG\|LMAXFOCKAE\|-1}} is set — the default for DFT and Hartree-Fock — shape restoration is inactive and {{TAG\|NMAXFOCKAE}} has no effect. Shape restoration applies only to the Fock exchange and to [[:Category:Many-body perturbation theory\|many-body perturbation theory]], i.e., [[GW approximation of Hedin's equations\|GW]], [[ACFDT/RPA calculations\|RPA]] and [[MP2]].\|:}}
	{{NB\|important\|The total energies of calculations that differ in {{TAG\|NMAXFOCKAE}} and/or {{TAG\|LMAXFOCKAE}} cannot be compared.}}		{{NB\|important\|The total energies of calculations that differ in {{TAG\|NMAXFOCKAE}} and/or {{TAG\|LMAXFOCKAE}} cannot be compared.}}

Huebsch: De-duplicate against LMAXFOCKAE; link shape restoration to the PAW formalism page; correct the fit wave vectors (approx. 140 eV and 95/380 eV, not 150/400); attribute the accuracy statements to the literature; note the clamp to 1 or 2

2026-09-09T05:26:52Z

De-duplicate against LMAXFOCKAE; link shape restoration to the PAW formalism page; correct the fit wave vectors (approx. 140 eV and 95/380 eV, not 150/400); attribute the accuracy statements to the literature; note the clamp to 1 or 2

← Older revision		Revision as of 05:26, 9 September 2026
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	{{TAGDEF\|NMAXFOCKAE\|1{{!}}2\|1}}		{{TAGDEF\|NMAXFOCKAE\|1{{!}}2\|1}}

	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~~]].		Description: Sets the number of shape-restoring functions used for each angular momentum quantum number <math>L</math> in [[Projector-augmented-wave formalism#Shape restoration\|shape restoration]].
	----		----
	{{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~~}}.		In [[Projector-augmented-wave formalism#Shape restoration\|shape restoration]], radial functions with vanishing multipole moment are added to the PAW compensation charge for each angular momentum quantum number <math>L</math>. {{TAG\|LMAXFOCKAE}} sets the maximum <math>L</math>; {{TAG\|NMAXFOCKAE}} sets how many functions are used per <math>L</math>, and thereby the wave vectors at which the all-electron density is matched:
	{{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~~}}.}}
	~~{{NB\|mind\|This tag 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~~.).}}		* {{TAG\|NMAXFOCKAE\|1}}: one function per <math>L</math>, matched at 6 Å<sup>-1</sup>, which corresponds to a plane-wave energy of approximately 140 eV.
			* {{TAG\|NMAXFOCKAE\|2}}: two functions per <math>L</math>, matched at 5 and 10 Å<sup>-1</sup>, corresponding to approximately 95 eV and 380 eV.

			These wave vectors are the points at which the density is fitted, not a guarantee of the accuracy reached at a given cutoff. They can be changed with {{TAG\|QMAXFOCKAE}}, which replaces the first value; the second follows at twice the first.

			Only the values 1 and 2 are accepted. Values outside that range are corrected to the nearest allowed one, so a larger number does not give a finer expansion.

			{{NB\|mind\|Whenever {{TAG\|LMAXFOCKAE\|-1}} is set — the default for DFT and Hartree-Fock — shape restoration is inactive and {{TAG\|NMAXFOCKAE}} has no effect. Shape restoration applies only to the Fock exchange and to [[:Category:Many-body perturbation theory\|many-body perturbation theory]], i.e., [[GW approximation of Hedin's equations\|GW]], [[ACFDT/RPA calculations\|RPA]] and [[MP2]].\|:}}
			{{NB\|important\|The total energies of calculations that differ in {{TAG\|NMAXFOCKAE}} and/or {{TAG\|LMAXFOCKAE}} cannot be compared.}}

	== Recommendations ==		== 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 tag~~ 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.~~		{{TAG\|NMAXFOCKAE\|1}}, the default, is sufficient in most cases and balances accuracy against computational cost. Refs. {{cite\|shishkin:prb:2006}} and {{cite\|unzog:prb:2022}} report accurate energy differences and quasiparticle energies at this setting.
	**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 consistent settings 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~~.~~\|::}}~~		{{TAG\|NMAXFOCKAE\|2}} is reported to give very accurate results for post-DFT methods, including for the 3''d'' elements where the one-center error is largest{{cite\|unzog:prb:2022}}. It is not free: the noise and the egg-box effects grow with {{TAG\|NMAXFOCKAE}}, and two shape-restoring functions per <math>L</math> need a fine FFT grid. Set {{TAG\|NGX}}, {{TAG\|NGY}} and {{TAG\|NGZ}} explicitly when using it. VASP issues an alert to that effect whenever two functions are requested. We recommend using it only after tests that establish the higher accuracy is needed for your application.

			Two specific expectations from the literature:
			* For [[GW approximation of Hedin's equations\|GW calculations]], going from {{TAG\|NMAXFOCKAE\|1}} to {{TAG\|NMAXFOCKAE\|2}} may shift quasiparticle energies by 100 to 200 meV for 3''d'' and late 4''d'' and 5''d'' elements{{cite\|unzog:prb:2022}}.
			* For [[ACFDT/RPA calculations\|RPA]] and [[MP2]] total energies, the two settings usually differ little in energy ''differences'', even though the absolute correlation energies change{{cite\|unzog:prb:2022}}.

			The two tags are coupled: see {{TAG\|LMAXFOCKAE}} for the consistency requirement that applies when energy differences are compared, and for how to read both values back from the {{FILE\|OUTCAR}} file.

	== Related tags and articles ==		== Related tags and articles ==
	{{TAG\|LMAXFOCKAE}}, {{TAG\|LMAXFOCK}}, {{TAG\|QMAXFOCKAE}}, {{TAG\|LFOCKAEDFT}}, {{TAG\|LFOCKSTD}}		{{TAG\|LMAXFOCKAE}}, {{TAG\|LMAXFOCK}}, {{TAG\|QMAXFOCKAE}}, {{TAG\|LFOCKAEDFT}}, {{TAG\|LFOCKSTD}}, [[Projector-augmented-wave formalism]]

	{{sc\|NMAXFOCKAE\|~~Examples~~\|~~Examples~~ that use this tag}}		{{sc\|NMAXFOCKAE\|Howto\|Workflows that use this tag}}

	== References ==		== References ==
			<references/>

	[[Category:INCAR tag]]		[[Category:INCAR tag]]
	[[Category:ACFDT]]		[[Category:ACFDT]]

Csheldon: /* Recommendations */

2026-09-04T10:27:34Z

Recommendations

← Older revision		Revision as of 10:27, 4 September 2026
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	*{{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 tag 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.		*{{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 tag 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 [[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 [[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 consistent settings 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.\|::}}

	== Related tags and articles ==		== Related tags and articles ==

Csheldon at 10:25, 4 September 2026

2026-09-04T10:25:58Z

← Older revision		Revision as of 10:25, 4 September 2026
Line 5:		Line 5:
	{{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}}.		{{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}}.
	{{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}}.}}		{{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}}.}}
	{{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.).}}		{{NB\|mind\|This tag 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.).}}

	== Recommendations ==		== 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\|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.		*{{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 tag 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 [[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 [[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.\|::}}

Csheldon: /* Related tags and articles */

2026-09-04T10:25:23Z

Csheldon: Removed redirect to NMAXFOCKAE and LMAXFOCKAE

2026-07-22T13:41:45Z

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\|NMAXFOCKAE\|1{{!}}2\|1}}

			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]].
			----
			{{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}}.
			{{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}}.}}
			{{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.).}}

			== 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.\|::}}

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

			{{sc\|NMAXFOCKAE\|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"

2025-02-28T10:21:12Z

Replaced content with "#REDIRECT NMAXFOCKAE and LMAXFOCKAE"

← Older revision		Revision as of 10:21, 28 February 2025
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	#REDIRECT [[NMAXFOCKAE and LMAXFOCKAE]]		#REDIRECT [[NMAXFOCKAE and LMAXFOCKAE]]

	~~{{TAGDEF\|NMAXFOCKAE\|1{{!}}2\|1}}~~

	~~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.). Details can be found in the section {{TAG\|LMAXFOCKAE}}.~~

	~~----~~


	~~== Related tags and articles ==~~
	~~{{TAG\|LMAXFOCK}}, {{TAG\|LMAXFOCKAE}}, {{TAG\|LFOCKAEDFT}}~~
	~~----~~
	~~[[The_VASP_Manual\|Contents]]~~

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

Karsai: /* Related Tags and Sections */

2022-04-08T14:49:51Z

Related Tags and Sections

← Older revision		Revision as of 14:49, 8 April 2022
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	== Related ~~Tags~~ and ~~Sections~~ ==		== Related tags and articles ==
	{{TAG\|LMAXFOCK}}, {{TAG\|LMAXFOCKAE}}, {{TAG\|LFOCKAEDFT}}		{{TAG\|LMAXFOCK}}, {{TAG\|LMAXFOCKAE}}, {{TAG\|LFOCKAEDFT}}
	----		----
	[[The_VASP_Manual\|Contents]]		[[The_VASP_Manual\|Contents]]

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

Vaspmaster at 12:04, 15 March 2017

2017-03-15T12:04:19Z

← Older revision		Revision as of 12:04, 15 March 2017
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	#REDIRECT [[NMAXFOCKAE and LMAXFOCKAE]]		#REDIRECT [[NMAXFOCKAE and LMAXFOCKAE]]

	{{TAGDEF\|NMAXFOCKAE\|1{{!}}2\|1}}		{{TAGDEF\|NMAXFOCKAE\|1{{!}}2\|1}}

Vaspmaster: Redirected page to NMAXFOCKAE and LMAXFOCKAE

2017-03-15T11:57:51Z

Redirected page to NMAXFOCKAE and LMAXFOCKAE

← Older revision		Revision as of 11:57, 15 March 2017
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			#REDIRECT [[NMAXFOCKAE and LMAXFOCKAE]]
	{{TAGDEF\|NMAXFOCKAE\|1{{!}}2\|1}}		{{TAGDEF\|NMAXFOCKAE\|1{{!}}2\|1}}

← Older revision		Revision as of 05:51, 9 September 2026
Line 5:		Line 5:
	In [[Projector-augmented-wave formalism#Shape restoration\|shape restoration]], radial functions with vanishing multipole moment are added to the PAW compensation charge for each angular momentum quantum number <math>L</math>. {{TAG\|LMAXFOCKAE}} sets the maximum <math>L</math>; {{TAG\|NMAXFOCKAE}} sets how many functions are used per <math>L</math>, and thereby the wave vectors at which the all-electron density is matched:		In [[Projector-augmented-wave formalism#Shape restoration\|shape restoration]], radial functions with vanishing multipole moment are added to the PAW compensation charge for each angular momentum quantum number <math>L</math>. {{TAG\|LMAXFOCKAE}} sets the maximum <math>L</math>; {{TAG\|NMAXFOCKAE}} sets how many functions are used per <math>L</math>, and thereby the wave vectors at which the all-electron density is matched:

	* {{TAG\|NMAXFOCKAE\|1}}: one function per <math>L</math>, matched at 6 Å<sup>-1</sup>, which corresponds to a plane-wave energy of approximately 140 eV.		* {{TAG\|NMAXFOCKAE\|1}}: one function per <math>L</math>, matched at {{TAG\|QMAXFOCKAE}} (default 6 Å<sup>-1</sup>, which corresponds to a plane-wave energy of approximately 140 eV).
	* {{TAG\|NMAXFOCKAE\|2}}: two functions per <math>L</math>, matched at 5 and 10 Å<sup>-1</sup>, corresponding to approximately 95 eV and 380 eV.		* {{TAG\|NMAXFOCKAE\|2}}: two functions per <math>L</math>, matched at {{TAG\|QMAXFOCKAE}} and twice {{TAG\|QMAXFOCKAE}} (default 5 and 10 Å<sup>-1</sup>, corresponding to approximately 95 eV and 380 eV).

	~~These~~ wave vectors are the points at which the density is fitted, not a guarantee of the accuracy reached at a given cutoff~~. They can be changed with {{TAG\|QMAXFOCKAE}}, which replaces the first value; the second follows at twice the first~~.		The wave vectors {{TAG\|QMAXFOCKAE}} are the points at which the density is fitted, not a guarantee of the accuracy reached at a given cutoff.

	~~Only~~ the values 1 and 2 ~~are accepted~~. Values outside that range are corrected to the nearest allowed one, so a larger number does not give a finer expansion.		{{TAG\|NMAXFOCKAE}} only accepts the values 1 and 2. Values outside that range are corrected to the nearest allowed one, so a larger number does not give a finer expansion.
			{{NB\|mind\|Whenever {{TAG\|LMAXFOCKAE\|-1}} is set — the default for DFT and Hartree-Fock — shape restoration is inactive and {{TAG\|NMAXFOCKAE}} has no effect. Shape restoration applies only to the Fock exchange and to [[:Category:Many-body perturbation theory\|many-body perturbation theory]], i.e., [[GW approximation of Hedin's equations\|GW]], [[ACFDT/RPA calculations\|RPA]] and [[MP2]].}}
	{{NB\|mind\|Whenever {{TAG\|LMAXFOCKAE\|-1}} is set — the default for DFT and Hartree-Fock — shape restoration is inactive and {{TAG\|NMAXFOCKAE}} has no effect. Shape restoration applies only to the Fock exchange and to [[:Category:Many-body perturbation theory\|many-body perturbation theory]], i.e., [[GW approximation of Hedin's equations\|GW]], [[ACFDT/RPA calculations\|RPA]] and [[MP2]].\|:}}
	{{NB\|important\|The total energies of calculations that differ in {{TAG\|NMAXFOCKAE}} and/or {{TAG\|LMAXFOCKAE}} cannot be compared.}}		{{NB\|important\|The total energies of calculations that differ in {{TAG\|NMAXFOCKAE}} and/or {{TAG\|LMAXFOCKAE}} cannot be compared.}}

← Older revision		Revision as of 05:26, 9 September 2026
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	{{TAGDEF\|NMAXFOCKAE\|1{{!}}2\|1}}		{{TAGDEF\|NMAXFOCKAE\|1{{!}}2\|1}}

	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~~]].		Description: Sets the number of shape-restoring functions used for each angular momentum quantum number <math>L</math> in [[Projector-augmented-wave formalism#Shape restoration\|shape restoration]].
	----		----
	{{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~~}}.		In [[Projector-augmented-wave formalism#Shape restoration\|shape restoration]], radial functions with vanishing multipole moment are added to the PAW compensation charge for each angular momentum quantum number <math>L</math>. {{TAG\|LMAXFOCKAE}} sets the maximum <math>L</math>; {{TAG\|NMAXFOCKAE}} sets how many functions are used per <math>L</math>, and thereby the wave vectors at which the all-electron density is matched:
	{{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~~}}.}}
	~~{{NB\|mind\|This tag 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~~.).}}		* {{TAG\|NMAXFOCKAE\|1}}: one function per <math>L</math>, matched at 6 Å<sup>-1</sup>, which corresponds to a plane-wave energy of approximately 140 eV.
			* {{TAG\|NMAXFOCKAE\|2}}: two functions per <math>L</math>, matched at 5 and 10 Å<sup>-1</sup>, corresponding to approximately 95 eV and 380 eV.

			These wave vectors are the points at which the density is fitted, not a guarantee of the accuracy reached at a given cutoff. They can be changed with {{TAG\|QMAXFOCKAE}}, which replaces the first value; the second follows at twice the first.

			Only the values 1 and 2 are accepted. Values outside that range are corrected to the nearest allowed one, so a larger number does not give a finer expansion.

			{{NB\|mind\|Whenever {{TAG\|LMAXFOCKAE\|-1}} is set — the default for DFT and Hartree-Fock — shape restoration is inactive and {{TAG\|NMAXFOCKAE}} has no effect. Shape restoration applies only to the Fock exchange and to [[:Category:Many-body perturbation theory\|many-body perturbation theory]], i.e., [[GW approximation of Hedin's equations\|GW]], [[ACFDT/RPA calculations\|RPA]] and [[MP2]].\|:}}
			{{NB\|important\|The total energies of calculations that differ in {{TAG\|NMAXFOCKAE}} and/or {{TAG\|LMAXFOCKAE}} cannot be compared.}}

	== Recommendations ==		== 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 tag~~ 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.~~		{{TAG\|NMAXFOCKAE\|1}}, the default, is sufficient in most cases and balances accuracy against computational cost. Refs. {{cite\|shishkin:prb:2006}} and {{cite\|unzog:prb:2022}} report accurate energy differences and quasiparticle energies at this setting.
	**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 consistent settings 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~~.~~\|::}}~~		{{TAG\|NMAXFOCKAE\|2}} is reported to give very accurate results for post-DFT methods, including for the 3''d'' elements where the one-center error is largest{{cite\|unzog:prb:2022}}. It is not free: the noise and the egg-box effects grow with {{TAG\|NMAXFOCKAE}}, and two shape-restoring functions per <math>L</math> need a fine FFT grid. Set {{TAG\|NGX}}, {{TAG\|NGY}} and {{TAG\|NGZ}} explicitly when using it. VASP issues an alert to that effect whenever two functions are requested. We recommend using it only after tests that establish the higher accuracy is needed for your application.

			Two specific expectations from the literature:
			* For [[GW approximation of Hedin's equations\|GW calculations]], going from {{TAG\|NMAXFOCKAE\|1}} to {{TAG\|NMAXFOCKAE\|2}} may shift quasiparticle energies by 100 to 200 meV for 3''d'' and late 4''d'' and 5''d'' elements{{cite\|unzog:prb:2022}}.
			* For [[ACFDT/RPA calculations\|RPA]] and [[MP2]] total energies, the two settings usually differ little in energy ''differences'', even though the absolute correlation energies change{{cite\|unzog:prb:2022}}.

			The two tags are coupled: see {{TAG\|LMAXFOCKAE}} for the consistency requirement that applies when energy differences are compared, and for how to read both values back from the {{FILE\|OUTCAR}} file.

	== Related tags and articles ==		== Related tags and articles ==
	{{TAG\|LMAXFOCKAE}}, {{TAG\|LMAXFOCK}}, {{TAG\|QMAXFOCKAE}}, {{TAG\|LFOCKAEDFT}}, {{TAG\|LFOCKSTD}}		{{TAG\|LMAXFOCKAE}}, {{TAG\|LMAXFOCK}}, {{TAG\|QMAXFOCKAE}}, {{TAG\|LFOCKAEDFT}}, {{TAG\|LFOCKSTD}}, [[Projector-augmented-wave formalism]]

	{{sc\|NMAXFOCKAE\|~~Examples~~\|~~Examples~~ that use this tag}}		{{sc\|NMAXFOCKAE\|Howto\|Workflows that use this tag}}

	== References ==		== References ==
			<references/>

	[[Category:INCAR tag]]		[[Category:INCAR tag]]
	[[Category:ACFDT]]		[[Category:ACFDT]]

← Older revision		Revision as of 10:25, 4 September 2026
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	{{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}}.		{{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}}.
	{{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}}.}}		{{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}}.}}
	{{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.).}}		{{NB\|mind\|This tag 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.).}}

	== Recommendations ==		== 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\|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.		*{{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 tag 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 [[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 [[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.\|::}}

← Older revision		Revision as of 10:25, 4 September 2026
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	== Related tags and articles ==		== Related tags and articles ==
	{{TAG\|~~NMAXFOCKAE~~}}, {{TAG\|LMAXFOCK}}, {{TAG\|QMAXFOCKAE}}, {{TAG\|LFOCKAEDFT}}, {{TAG\|LFOCKSTD}}		{{TAG\|LMAXFOCKAE}}, {{TAG\|LMAXFOCK}}, {{TAG\|QMAXFOCKAE}}, {{TAG\|LFOCKAEDFT}}, {{TAG\|LFOCKSTD}}

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