|
|
| (6 intermediate revisions by 2 users not shown) |
| Line 1: |
Line 1: |
| | #REDIRECT [[NMAXFOCKAE and LMAXFOCKAE]] |
| | |
| {{TAGDEF|NMAXFOCKAE|1{{!}}2|1}} | | {{TAGDEF|NMAXFOCKAE|1{{!}}2|1}} |
|
| |
|
| Line 8: |
Line 10: |
|
| |
|
|
| |
|
| == Related Tags and Sections == | | == Related tags and articles == |
| {{TAG|LMAXFOCK}} {{TAG|LMAXFOCKAE}} | | {{TAG|LMAXFOCK}}, {{TAG|LMAXFOCKAE}}, {{TAG|LFOCKAEDFT}} |
| ----
| |
| [[The_VASP_Manual|Contents]]
| |
| | |
| [[Category:INCAR]][[Category:Hybrids]]
| |
| | |
| | |
| ----
| |
| In the PAW method, the difference between the charge density of the all-electron partial waves and
| |
| the pseudo partial waves
| |
| <math>
| |
| Q_{\alpha\beta}(r)= \phi^*_\alpha(r)\phi_\beta(r) - \tilde \phi^*_\alpha(r)\tilde \phi_\beta(r)
| |
| </math>
| |
| is usually restored on spherical grids centered at each atom
| |
| (one-center terms inside the PAW spheres). To describe long range electrostatic terms, the
| |
| the ''moments'' of the differences of the all-electron and pseudo charge density are usually
| |
| also added on the plane wave grid up to a certain l quantum number (see {{TAG|LMAXFOCK}}).
| |
| These augmentation charges restore the moments of the all-electron density on the plane wave
| |
| grid.
| |
| | |
| For the RPA, GW, and most post DFT methods, the one-center terms are presently,
| |
| however, not implemented. Depending on the material, this can cause sizable errors
| |
| in particular for 3d and (to a lesser extent) 2p, 4d and 5d elements.
| |
| To correct for this error, an alternative treatment is implemented
| |
| on the plane wave grid. This allows to restore the all-electron densities accurately on the plane wave grid
| |
| instead of the one-center grids by specifying the flags {{TAG|LMAXFOCKAE}} and {{TAG|NMAXFOCKAE}}.
| |
| | |
| 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
| |
| in a set of orthogonal functions localized at each atomic site. These augmentation charges
| |
| are then added to the pseudo charge densities on the plane wave grid.
| |
| | |
| | |
| 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
| |
| since the one-center terms are implemented.
| |
| | |
| 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
| |
| to which this more accurate treatment is used. The default is {{TAG|LMAXFOCKAE}}=4, for post DFT methods.
| |
| If no accurate augmentation is desired by the user, simply set {{TAG|LMAXFOCKAE}}=-1 in the INCAR file.
| |
| | |
| 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
| |
| to which this more accurate treatment is used. {{TAG|NMAXFOCKAE}}=2 yields very accurate results for
| |
| 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
| |
| {{TAG|NMAXFOCKAE}} and {{TAG|LMAXFOCKAE}}, if energy differences are calculated.
| |
| 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.
| |
| | |
| | |
| 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.
| |
| For instance for sp elements, {{TAG|LMAXFOCKAE}} = 2 suffices. For d elements, {{TAG|LMAXFOCKAE}} = 4 suffices
| |
| (a d electron can create charge densities with ''l''-quantum numbers up to 4), whereas for f elements, users
| |
| should test whether {{TAG|LMAXFOCKAE}} = 6 is required.
| |
| | |
| In summary, usefully manual setting of {{TAG|NMAXFOCKAE}} and {{TAG|LMAXFOCKAE}} are:
| |
| * {{TAG|LMAXFOCKAE}}=-1, to switch off the accurate augmentation altogether
| |
| * {{TAG|LMAXFOCKAE}}=4 (or larger) to force an accurate treatment for the HF part even in Hartree-Fock calculations
| |
| * {{TAG|NMAXFOCKAE}}=2, to select the very accurate augmentation. Please check whether the VASP default setting for {{TAG|LMAXFOCKAE}} suffices (OUTCAR file).
| |
| | |
| | |
| == Related Tags and Sections ==
| |
| {{TAG|LMAXFOCK}} {{TAG|QMAXFOCKAE}}
| |
| ---- | | ---- |
| [[The_VASP_Manual|Contents]] | | [[The_VASP_Manual|Contents]] |
|
| |
|
| [[Category:INCAR]][[Category:Hybrids]] | | [[Category:INCAR tag]][[Category:Hybrids]][[Category:GW]] |
