LMAXFOCK: Difference between revisions
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is usually restored on spherical grids centered at each atom | is usually restored on spherical grids centered at each atom | ||
(one-center terms inside the PAW spheres). To describe long range electrostatic | (one-center terms inside the PAW spheres). To describe long range electrostatic effect, the ''moments'' of the differences of the all-electron and pseudo charge density | ||
also need to added on the plane wave grid. This is done up to a certain ''l'' quantum number. | also need to added on the plane wave grid. This is done up to a certain ''l'' quantum number. | ||
These augmentation charges restore the moments of the all-electron density on the plane wave | These augmentation charges restore the moments of the all-electron density on the plane wave | ||
grid. For the charge density, this augmentation is done exactly up to the maximum | grid. For the charge density, this augmentation is done exactly up to the maximum | ||
''l'' quantum number required for the POTCAR files. | ''l'' quantum number required for the POTCAR files, whereas for the Fock exchange, | ||
the augmentation is controlled by {{TAG|LMAXFOCK}}. | |||
Specifically, the exchange potential is given by | |||
<span> | |||
<math> | |||
V_{\mathrm{x}}\left(\mathbf{r},\mathbf{r}'\right) | |||
= -\frac{e^2}{2}\sum_{\mathbf{q}m}f_{\mathbf{q}m} | |||
e^{-i\mathbf{q}\cdot\mathbf{r}'} | |||
\frac{u_{\mathbf{q}m}^{*}(\mathbf{r}')u_{\mathbf{q}m}(\mathbf{r})} | |||
{\vert \mathbf{r}-\mathbf{r}' \vert} | |||
e^{i\mathbf{q}\cdot\mathbf{r}} | |||
</math> | |||
</span> | |||
When the densit | |||
This flag determines the treatment on the plane wave grid for | This flag determines the treatment on the plane wave grid for | ||
Revision as of 16:04, 14 March 2017
LMAXFOCK = [integer]
Default: LMAXFOCK = 4
Description: LMAXFOCK sets the maximum angular momentum quantum number l for the 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 [math]\displaystyle{ 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 effect, the moments of the differences of the all-electron and pseudo charge density also need to added on the plane wave grid. This is done up to a certain l quantum number. These augmentation charges restore the moments of the all-electron density on the plane wave grid. For the charge density, this augmentation is done exactly up to the maximum l quantum number required for the POTCAR files, whereas for the Fock exchange, the augmentation is controlled by LMAXFOCK.
Specifically, the exchange potential is given by [math]\displaystyle{ V_{\mathrm{x}}\left(\mathbf{r},\mathbf{r}'\right) = -\frac{e^2}{2}\sum_{\mathbf{q}m}f_{\mathbf{q}m} e^{-i\mathbf{q}\cdot\mathbf{r}'} \frac{u_{\mathbf{q}m}^{*}(\mathbf{r}')u_{\mathbf{q}m}(\mathbf{r})} {\vert \mathbf{r}-\mathbf{r}' \vert} e^{i\mathbf{q}\cdot\mathbf{r}} }[/math] When the densit
This flag determines the treatment on the plane wave grid for the exact exchange. To compensate resulting errors, the contributions from the one-center terms are evaluated for the pseudo orbitals also only up to l=LMAXFOCK, whereas the one-center terms for the exact all-electron orbitals are evaluated up to the maximum required l (twice the angular quantum number of the partial wave with the highest l). The default is LMAXFOCK=4, and it might be required to increase this parameter, if the system contains f-electrons. Since this increases the computational load considerably (factor 2), it is recommended to perform tests, whether the results are already reasonably converged using the default LMAXFOCK=4.
To be compatible w.r.t. old releases, VASP also reads the flag HFLMAX to the same effect as LMAXFOCK.