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NMAXFOCKAE: Difference between revisions

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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
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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.}}


Latest revision as of 05:51, 9 September 2026

NMAXFOCKAE = 1|2
Default: NMAXFOCKAE = 1 

Description: Sets the number of shape-restoring functions used for each angular momentum quantum number [math]\displaystyle{ L }[/math] in shape restoration.

In shape restoration, radial functions with vanishing multipole moment are added to the PAW compensation charge for each angular momentum quantum number [math]\displaystyle{ L }[/math]. LMAXFOCKAE sets the maximum [math]\displaystyle{ L }[/math]; NMAXFOCKAE sets how many functions are used per [math]\displaystyle{ L }[/math], and thereby the wave vectors at which the all-electron density is matched:

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

The wave vectors QMAXFOCKAE are the points at which the density is fitted, not a guarantee of the accuracy reached at a given cutoff.

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.

Mind: Whenever LMAXFOCKAE = -1 is set — the default for DFT and Hartree-Fock — shape restoration is inactive and NMAXFOCKAE has no effect. Shape restoration applies only to the Fock exchange and to many-body perturbation theory, i.e., GW, RPA and MP2.
Important: The total energies of calculations that differ in NMAXFOCKAE and/or LMAXFOCKAE cannot be compared.

Recommendations

NMAXFOCKAE = 1, the default, is sufficient in most cases and balances accuracy against computational cost. Refs. [1] and [2] report accurate energy differences and quasiparticle energies at this setting.

NMAXFOCKAE = 2 is reported to give very accurate results for post-DFT methods, including for the 3d elements where the one-center error is largest[2]. It is not free: the noise and the egg-box effects grow with NMAXFOCKAE, and two shape-restoring functions per [math]\displaystyle{ L }[/math] need a fine FFT grid. Set NGX, NGY and 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 calculations, going from NMAXFOCKAE = 1 to NMAXFOCKAE = 2 may shift quasiparticle energies by 100 to 200 meV for 3d and late 4d and 5d elements[2].
  • For RPA and MP2 total energies, the two settings usually differ little in energy differences, even though the absolute correlation energies change[2].

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

Related tags and articles

LMAXFOCKAE, LMAXFOCK, QMAXFOCKAE, LFOCKAEDFT, LFOCKSTD, Projector-augmented-wave formalism

Workflows that use this tag

References

  1. ↑ M. Shishkin and G. Kresse, Phys. Rev. B 74, 035101 (2006).
  2. ↑ a b c d 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).
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