LMAXFOCKAE

LMAXFOCKAE = [integer]
Default: LMAXFOCKAE = -1

NMAXFOCKAE = [integer]
Default: NMAXFOCKAE = 0

Description: LMAXFOCKAE and 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.

In the PAW method the difference between the charge density of the all-electron partial waves and the pseudo partial waves $Q_{\alpha \beta }(r)=\phi _{\alpha }^{*}(r)\phi _{\beta }(r)-{\tilde {\phi }}_{\alpha }^{*}(r){\tilde {\phi }}_{\beta }(r)$ 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 also restored on the plane wave grid up to a certain l quantum number (see LMAXFOCK).

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 shape of the charge density difference accurately on the plane wave grid, using the flags LMAXFOCKAE and NMAXFOCKAE.

To achieve this, $Q_{\alpha \beta }(r)$ is Fourier transformed to reciprocal space $Q_{\alpha \beta }(q)$ and then expanded in a set of orthogonal functions localized at each atomic site.

If the 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 as hybrid functionals, since the one-center terms are implemented.

If the 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. LMAXFOCKAE can be used to specify the maximum spherical (l) quantum number up to which this more accurate treatment is used. The default for LMAXFOCKAE is 4.

If 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, LMAXFOCKAE can be used to specify the maximum spherical (l) quantum number up to which this more accurate treatment is used. 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 NMAXFOCKAE=1 and 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 NMAXFOCKAE and LMAXFOCKAE, if energy differences are calculated. For GW calculations, increasing NMAXFOCKAE=1 to NMAXFOCKAE=2 might change QP energies by 100-200 meV for 3d and late 4d and 5d elements.

If NMAXFOCKAE is used, the setting for LMAXFOCKAE should be also checked. Generally, it suffices to set LMAXFOCKAE to twice the maximum l quantum number found in the POTCAR file. For instance for sp elements, {TAG|LMAXFOCKAE}} = 2 suffices. For d elements, {TAG|LMAXFOCKAE}} = 4 suffices (a d electron can create a density with l-quantum number of 4), whereas for f elements, users should test whether {TAG|LMAXFOCKAE}} = 4 is required.

Related Tags and Sections

LMAXFOCK

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