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| {{TAGDEF|NMAXFOCKAE|1{{!}}2|1}
| | #REDIRECT [[NMAXFOCKAE and LMAXFOCKAE]] |
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| {{TAGDEF|LMAXFOCKAE|[integer]|-1}} | | {{TAGDEF|NMAXFOCKAE|1{{!}}2|1}} |
| {{DEF|ICHARG|2|if {{TAG|ISTART}}{{=}}0|0|else}} | |
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| | | Description: {{TAG|NMAXFOCKAE}} and {{TAG|LMAXFOCKAE}} determine whether |
| Description: {{TAG|LMAXFOCKAE}} and {{TAG|LMAXFOCKAE}} determines 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 |
| charge-densities and overlap densities are accurately reconstructed on the plane wave grid.
| | post DFT methods (GW, RPA, MP2, etc.). Details can be found in the section {{TAG|LMAXFOCKAE}}. |
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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 also
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| restored on the plane wave grid up to a certain ''l'' quantum number (see {{TAG|LMAXFOCK}}).
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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 ''shape'' of the charge density difference accurately on the plane wave grid, using the flags {{TAG|LMAXFOCKAE}} and {{TAG|NMAXFOCKAE}}.
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| To achieve this, <math> Q_{\alpha\beta}(r) </math> is Fourier transformed
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| 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.
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| 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
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| as hybrid functionals, since the one-center terms are implemented.
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| 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
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| to which this more accurate treatment is used. The default for {{TAG|LMAXFOCKAE}} is 4.
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| 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
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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}}=1 to {{TAG|NMAXFOCKAE}}=2 might change QP energies by 100-200 meV for 3d and late 4d and 5d elements.
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| 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.
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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 a density with l-quantum number of 4), whereas for f elements, users
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| should test whether {TAG|LMAXFOCKAE}} = 4 is required.
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| == Related Tags and Sections == | | == Related tags and articles == |
| {{TAG|LMAXFOCK}} | | {{TAG|LMAXFOCK}}, {{TAG|LMAXFOCKAE}}, {{TAG|LFOCKAEDFT}} |
| ---- | | ---- |
| [[The_VASP_Manual|Contents]] | | [[The_VASP_Manual|Contents]] |
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| [[Category:INCAR]][[Category:Hybrids]] | | [[Category:INCAR tag]][[Category:Hybrids]][[Category:GW]] |
