LAECHG: Difference between revisions

Latest revision as of 14:56, 17 October 2024

LAECHG = .TRUE. | .FALSE.
Default: LAECHG = .FALSE.

Description: when LAECHG=.TRUE. the all-electron charge density will be reconstructed explicitly and written to files.

If LAECHG=.TRUE. is set VASP will reconstruct the all-electron charge density on the so-called "fine" FFT-grid. This "fine" FFT-grid consists of NGXF×NGYF×NGZF points in real space (i.e., the grid that is used to represent the augmented pseudo charge densities of the USPP and PAW methods).

In fact, for LAECHG=.TRUE., VASP will reconstruct three distinct all-electron densities:

the core density.
the proto-atomic valence density (overlapping atomic charge densities).
the self-consistent valence density.

These are written to the files AECCAR0, AECCAR1, and AECCAR2, respectively. The first two of these files are written at the start of the run, whereas the last is written at the end after self-consistency has been reached.

N.B.: In the language of the PAW method an "all-electron" density does not refer to the density of all electrons, instead it denotes a density that includes all the nodal features near the nucleus associated with the true (as opposed to the pseudized) one-electron orbitals. Within the PAW method, the all-electron density arising from the one-electron pseudo orbitals $\{ \widetilde{\psi}_{n\mathbf{k}} \}$ is given by:

{\displaystyle n(\mathbf{r})= \sum_{n{\mathbf{k}}} f_{n{\mathbf{k}}} \langle \widetilde{\psi}_{n\mathbf{k}}| \mathbf{r}\rangle\langle \mathbf{r}| \widetilde{\psi}_{n\mathbf{k}} \rangle + \sum_{\alpha, \beta} ( \phi^\ast_\alpha(\mathbf{r}) \phi_\beta (\mathbf{r}) - \widetilde{\phi}^\ast_\alpha(\mathbf{r}) \widetilde{\phi}_\beta (\mathbf{r}) ) \sum_{n{\mathbf{k}}} f_{n{\mathbf{k}}} \langle\widetilde{\psi}_{n\mathbf{k}}|\widetilde{p}_\alpha\rangle \langle\widetilde{p}_\beta| \widetilde{\psi}_{n\mathbf{k}}\rangle }

Normally one does not attempt to reconstruct all-electron densities explicitly since the second term on the right-hand side varies rapidly near the nuclei and is too costly to expand in-plane waves (see the bit about augmentation and compensation charges). For LAECHG=.TRUE., however, this reconstruction is exactly the thing that is done.

@@ Line 1: / Line 1: @@
 {{TAGDEF|LAECHG|.TRUE. {{!}} .FALSE. |.FALSE.}}
-Description: when {{TAG|LAECHG}}=.TRUE. the ''all-electron'' charge density will be reconstructed explicitly and written out to file.
+Description: when {{TAG|LAECHG}}=.TRUE. the ''all-electron'' charge density will be reconstructed explicitly and written to files.
 ----
 If {{TAG|LAECHG}}=.TRUE. is set VASP will reconstruct the ''all-electron'' charge density on the so-called "fine" FFT-grid.
@@ Line 13: / Line 13: @@
 These are written to the files {{FILE|AECCAR0}}, {{FILE|AECCAR1}}, and {{FILE|AECCAR2}}, respectively.
+The first two of these files are written at the start of the run, whereas the last is written at the end after self-consistency has been reached.
-'''N.B.:''' In the language of the [[PAW method]] an "all-electron" density does '''not''' refer to the ''density of all electrons'', instead it denotes a density that includes all the nodal features near the nucleus associated with the ''true'' (as opposed to the ''pseudized'') one-electron orbitals.
+'''N.B.:''' In the language of the [[Projector-augmented-wave_formalism|PAW method]] an "all-electron" density does '''not''' refer to the ''density of all electrons'', instead it denotes a density that includes all the nodal features near the nucleus associated with the ''true'' (as opposed to the ''pseudized'') one-electron orbitals.
-Within the PAW method, the ''all-electron'' density arising from a one-electron pseudo orbital <math>\widetilde{\psi}_{n\mathbf{k}}</math> is given by:
+Within the PAW method, the ''all-electron'' density arising from the one-electron pseudo orbitals <math>\{ \widetilde{\psi}_{n\mathbf{k}} \}</math> is given by:
 :<math>
-n(\mathbf{r})= \langle \widetilde{\psi}_{n\mathbf{k}}| \mathbf{r}\rangle\langle  \mathbf{r}
+n(\mathbf{r})=
-| \widetilde{\psi}_{n\mathbf{k}} \rangle + \sum_{\alpha, \beta}
+\sum_{n{\mathbf{k}}} f_{n{\mathbf{k}}}
+\langle \widetilde{\psi}_{n\mathbf{k}}| \mathbf{r}\rangle\langle  \mathbf{r}| \widetilde{\psi}_{n\mathbf{k}} \rangle +
+\sum_{\alpha, \beta}
 (
-                                       \phi^\ast_\alpha(\mathbf{r})
+  \phi^\ast_\alpha(\mathbf{r})
-                                       \phi_\beta (\mathbf{r})
+  \phi_\beta (\mathbf{r})
   -
-                                       \widetilde{\phi}^\ast_\alpha(\mathbf{r})
+  \widetilde{\phi}^\ast_\alpha(\mathbf{r})
-                                       \widetilde{\phi}_\beta (\mathbf{r})
+  \widetilde{\phi}_\beta (\mathbf{r})
 )
-                                      \langle\widetilde{\psi}_{n\mathbf{k}}|\widetilde{p}_\alpha\rangle
+\sum_{n{\mathbf{k}}} f_{n{\mathbf{k}}}
-                                       \langle\widetilde{p}_\beta| \widetilde{\psi}_{n\mathbf{k}}\rangle
+\langle\widetilde{\psi}_{n\mathbf{k}}|\widetilde{p}_\alpha\rangle
+\langle\widetilde{p}_\beta| \widetilde{\psi}_{n\mathbf{k}}\rangle
 </math>
-Normally one does not attempt to reconstruct ''all-electron'' densities explicitly since the second term on the right hand side varies rapidly near the nuclei and is too costly to expand in plane waves (see the bit about [[PAW method#The compensation or augmentation density|augmentation and compensation charges]]). For {{TAG|LAECHG}}=.TRUE., however, this reconstruction is exactly the thing that is done.
+Normally one does not attempt to reconstruct ''all-electron'' densities explicitly since the second term on the right-hand side varies rapidly near the nuclei and is too costly to expand in-plane waves (see the bit about [[Projector-augmented-wave_formalism|augmentation and compensation charges]]). For {{TAG|LAECHG}}=.TRUE., however, this reconstruction is exactly the thing that is done.
-== Related Tags and Sections ==
+== Related tags and articles ==
 {{FILE|AECCAR0}}, {{FILE|AECCAR1}}, {{FILE|AECCAR2}}
 {{sc|LAECHG|Examples|Examples that use this tag}}
 ----
-[[The_VASP_Manual|Contents]]
-[[Category:INCAR]]
+[[Category:INCAR tag]][[Category:Projector-augmented-wave method]][[Category: Charge density]]