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| {{TAGDEF|LMAXFOCKAE|[integer]}}
| | #REDIRECT [[NMAXFOCKAE and LMAXFOCKAE]] |
| {{DEF|LMAXFOCKAE|-1|for Hartree-Fock and hybrid functionals | 4 | for post DFT methods}}
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| Description: {{TAG|NMAXFOCKAE}} and {{TAG|LMAXFOCKAE}} determine whether
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| 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
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| post DFT methods (GW, RPA, MP2, etc.).
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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 ''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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| 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 values 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 values larger than -1 and {{TAG|NMAXFOCKAE}}=2, the charge density is restored accurately on the plane wave grid up to a typical plane wave energy 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 settings 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|NMAXFOCKAE}}, {{TAG|QMAXFOCKAE}}
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| ----
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| [[The_VASP_Manual|Contents]]
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| [[Category:INCAR]][[Category:Hybrids]][[Category:GW]]
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