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| {{TAGDEF|LMAXFOCKAE|[integer]|-1}} | | {{TAGDEF|LMAXFOCKAE|[integer]}} |
| {{DEF|ICHARG|2|if {{TAG|ISTART}}{{=}}0|0|else}} | | {{DEF|LAXMFOCKAE|-1|for DFT, Hartree-Fock | 4 | for post DFT methods}} |
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| {{TAGDEF|NMAXFOCKAE|0{{!}}1{{!}}2}} | | Description: {{TAG|LMAXFOCKAE}} determines whether |
| {{DEF|NMAXFOCKAE|0|density functional theory|1|post DFT methods}} | | the overlap densities in the Fock exchange and correlated wave function methods are accurately reconstructed on the plane wave grid or not. Details can be found in the section {{TAG|NMAXFOCKAE}}. |
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| Description: {{TAG|LMAXFOCKAE}} and {{TAG|LMAXFOCKAE}} describes the maximum angular momentum quantum number ''l'' and the number of channels for an "accurate" augmentation of charge densities in Hartree-Fock type routines.
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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 Sections == |
| {{TAG|LMAXFOCK}} | | {{TAG|LMAXFOCK}} {{TAG|NMAXFOCKAE}} |
| ---- | | ---- |
| [[The_VASP_Manual|Contents]] | | [[The_VASP_Manual|Contents]] |
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| [[Category:INCAR]][[Category:Hybrids]] | | [[Category:INCAR]][[Category:Hybrids]] |
