LMAXFOCK: Difference between revisions

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Description: {{TAG|LMAXFOCK}} sets the maximum angular momentum quantum number ''l'' for the augmentation of charge densities in Hartree-Fock type routines.
Description: {{TAG|LMAXFOCK}} sets the maximum angular momentum quantum number ''l'' for the 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
In the PAW method, the difference between the charge density of the all-electron partial waves <math>\phi_\beta</math> and
the pseudo partial waves  
the pseudo partial waves <math>\tilde \phi_\beta</math>
<math>
<math>
Q_{\alpha\beta}(r)= \phi^*_\alpha(r)\phi_\beta(r)  - \tilde \phi^*_\alpha(r)\tilde \phi_\beta(r)
Q_{\alpha\beta}(r)= \phi^*_\alpha(r)\phi_\beta(r)  - \tilde \phi^*_\alpha(r)\tilde \phi_\beta(r)
</math>
</math>
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 effect, the ''moments'' of the differences of the all-electron and pseudo charge density  
(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 exactly 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 densities used in the Hartree and DFT term,  
''l'' quantum number required for the POTCAR files, whereas for the Fock exchange,  
this augmentation is done exactly up to the maximum ''l'' quantum number required by the POTCAR files,  
the augmentation is controlled by {{TAG|LMAXFOCK}}.
whereas for the Fock exchange, the augmentation on the plane wave grid is controlled by {{TAG|LMAXFOCK}}.


Specifically, the exchange potential is given by
Specifically, when the exchange energy is evaluated
<span>
 
<math>
<span id="ExFock">
V_{\mathrm{x}}\left(\mathbf{r},\mathbf{r}'\right)
:<math>
= -\frac{e^2}{2}\sum_{\mathbf{q}m}f_{\mathbf{q}m}
E_{\mathrm{x}}= -\frac{e^2}{2}\sum_{\mathbf{k}n,\mathbf{q}m}
e^{-i\mathbf{q}\cdot\mathbf{r}'}
f_{\mathbf{k}n} f_{\mathbf{q}m} \times
\frac{u_{\mathbf{q}m}^{*}(\mathbf{r}')u_{\mathbf{q}m}(\mathbf{r})}
\int\int d^3\mathbf{r} d^3\mathbf{r}'
\frac{\psi_{\mathbf{k}n}^{*}(\mathbf{r})\psi_{\mathbf{q}m}^{*}(\mathbf{r}')
\psi_{\mathbf{k}n}(\mathbf{r}')\psi_{\mathbf{q}m}(\mathbf{r})}
{\vert \mathbf{r}-\mathbf{r}' \vert}
{\vert \mathbf{r}-\mathbf{r}' \vert}
e^{i\mathbf{q}\cdot\mathbf{r}}
</math>
</math>
</span>
</span>
When the densit


This flag determines the treatment on the plane wave grid for
the overlap density <math> \psi_{\mathbf{k}n}^{*}(\mathbf{r})\psi_{\mathbf{q}m}(\mathbf{r}) </math>
the exact exchange.  
between two Bloch orbitals needs to be calculated on the plane wave grid. The tag {{TAG|LMAXFOCK}}
To compensate resulting errors, the contributions from the one-center terms are evaluated for the pseudo orbitals also only up to ''l''={{TAG|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 {{TAG|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 {{TAG|LMAXFOCK}}=4.
controls up to which ''l'' quantum number, augmentation charges are added on the plane wave grid.
To accelerate convergence with respect to {{TAG|LMAXFOCK}}, VASP uses a small trick: the contributions from the Hartree-Fock one-center terms are evaluated for the pseudo orbitals also only up to ''l''={{TAG|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 {{TAG|LMAXFOCK}}=4, and it might be necessary 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 {{TAG|LMAXFOCK}}=4.


To be compatible w.r.t. old releases, VASP also reads the flag {{TAG|HFLMAX}} to the same effect as {{TAG|LMAXFOCK}}.
To be compatible w.r.t. old releases, VASP also reads the flag {{TAG|HFLMAX}} to the same effect as {{TAG|LMAXFOCK}}.

Revision as of 16:18, 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 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 exactly restore the moments of the all-electron density on the plane wave grid. For the charge densities used in the Hartree and DFT term, this augmentation is done exactly up to the maximum l quantum number required by the POTCAR files, whereas for the Fock exchange, the augmentation on the plane wave grid is controlled by LMAXFOCK.

Specifically, when the exchange energy is evaluated

the overlap density between two Bloch orbitals needs to be calculated on the plane wave grid. The tag LMAXFOCK controls up to which l quantum number, augmentation charges are added on the plane wave grid. To accelerate convergence with respect to LMAXFOCK, VASP uses a small trick: the contributions from the Hartree-Fock 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 necessary 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.

Related Tags and Sections

HFLMAX, LMAXFOCKAE


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