LMAXFOCK

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.

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In the PAW method, the difference between the charge density of the all-electron partial waves $\phi_\beta$ and the pseudo partial waves $\tilde \phi_\beta$ $Q_{\alpha\beta}(r)= \phi^*_\alpha(r)\phi_\beta(r) - \tilde \phi^*_\alpha(r)\tilde \phi_\beta(r)$ is usually restored on spherical grids centered at each atom (one-center terms inside the PAW spheres). To describe long range electrostatic 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, the 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

$E_{\mathrm{x}}= -\frac{e^2}{2}\sum_{\mathbf{k}n,\mathbf{q}m} f_{\mathbf{k}n} f_{\mathbf{q}m} \times \int\int d^3\mathbf{r} d^3\mathbf{r}' \frac{\psi_{\mathbf{k}n}^{*}(\mathbf{r})\psi_{\mathbf{q}m}^{*}(\mathbf{r}') \psi_{\mathbf{k}n}(\mathbf{r}')\psi_{\mathbf{q}m}(\mathbf{r})} {\vert \mathbf{r}-\mathbf{r}' \vert}$

the overlap density $\psi_{\mathbf{k}n}^{*}(\mathbf{r})\psi_{\mathbf{q}m}(\mathbf{r})$ 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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