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| == Related Tags and Sections == | | == Related Tags and Sections == |
| {{TAG|LMAXFOCK}} {{TAG|LMAXFOCKAE}} | | {{TAG|LMAXFOCK}} {{TAG|LMAXFOCKAE}} |
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| [[The_VASP_Manual|Contents]]
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| [[Category:INCAR]][[Category:Hybrids]]
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| ----
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| In the PAW method, the difference between the charge density of the all-electron partial waves and
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| the pseudo partial waves
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| <math>
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| Q_{\alpha\beta}(r)= \phi^*_\alpha(r)\phi_\beta(r) - \tilde \phi^*_\alpha(r)\tilde \phi_\beta(r)
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| </math>
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| is usually restored on spherical grids centered at each atom
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| (one-center terms inside the PAW spheres). To describe long range electrostatic terms, the
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| the ''moments'' of the differences of the all-electron and pseudo charge density are usually
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| also added on the plane wave grid up to a certain l quantum number (see {{TAG|LMAXFOCK}}).
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| These augmentation charges restore the moments of the all-electron density on the plane wave
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| grid.
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| For the RPA, GW, and most post DFT methods, the one-center terms are presently,
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| however, not implemented. Depending on the material, this can cause sizable errors
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| in particular for 3d and (to a lesser extent) 2p, 4d and 5d elements.
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| To correct for this error, an alternative treatment is implemented
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| on the plane wave grid. This allows to restore the all-electron densities accurately on the plane wave grid
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| instead of the one-center grids by specifying the flags {{TAG|LMAXFOCKAE}} and {{TAG|NMAXFOCKAE}}.
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|
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| 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
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| in a set of orthogonal functions localized at each atomic site. These augmentation charges
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| are then added to the pseudo charge densities on the plane wave grid.
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| 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
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| since the one-center terms are implemented.
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| 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
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| to which this more accurate treatment is used. The default is {{TAG|LMAXFOCKAE}}=4, for post DFT methods.
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| If no accurate augmentation is desired by the user, simply set {{TAG|LMAXFOCKAE}}=-1 in the INCAR file.
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| 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
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| to which this more accurate treatment is used. {{TAG|NMAXFOCKAE}}=2 yields very accurate results for
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| 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
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| {{TAG|NMAXFOCKAE}} and {{TAG|LMAXFOCKAE}}, if energy differences are calculated.
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| 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.
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| 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.
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| For instance for sp elements, {{TAG|LMAXFOCKAE}} = 2 suffices. For d elements, {{TAG|LMAXFOCKAE}} = 4 suffices
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| (a d electron can create charge densities with ''l''-quantum numbers up to 4), whereas for f elements, users
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| should test whether {{TAG|LMAXFOCKAE}} = 6 is required.
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| In summary, usefully manual setting of {{TAG|NMAXFOCKAE}} and {{TAG|LMAXFOCKAE}} are:
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| * {{TAG|LMAXFOCKAE}}=-1, to switch off the accurate augmentation altogether
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| * {{TAG|LMAXFOCKAE}}=4 (or larger) to force an accurate treatment for the HF part even in Hartree-Fock calculations
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| * {{TAG|NMAXFOCKAE}}=2, to select the very accurate augmentation. Please check whether the VASP default setting for {{TAG|LMAXFOCKAE}} suffices (OUTCAR file).
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| == Related Tags and Sections ==
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| {{TAG|LMAXFOCK}} {{TAG|QMAXFOCKAE}}
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| ---- | | ---- |
| [[The_VASP_Manual|Contents]] | | [[The_VASP_Manual|Contents]] |
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| [[Category:INCAR]][[Category:Hybrids]] | | [[Category:INCAR]][[Category:Hybrids]] |
NMAXFOCKAE = 1|2
Default: NMAXFOCKAE = 1
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.). Details can be found in the section LMAXFOCKAE.
Related Tags and Sections
LMAXFOCK LMAXFOCKAE
Contents
