PROOUT: Difference between revisions

Revision as of 10:24, 23 November 2021

This file contains the projection of the wavefunctions onto $\beta^\alpha_{lm}(\mathbf{r})$

${\displaystyle P^\alpha_{lmn\mathbf{k}} \equiv \langle \beta_{lm}^{\alpha}|S|\phi_{n\mathbf{k}}\rangle = \underbrace{\langle \beta_{lm}^{\alpha}|\phi_{n\mathbf{k}}\rangle}_{P^{\text{SOFT},\alpha}_{lmn\mathbf{k}}} + \underbrace{\sum_{ij} \langle \beta^\alpha_{lm}|p_i\rangle Q_{ij} \langle p_j | \phi_{n\mathbf{k}}\rangle}_{P^{\text{AUG},\alpha}_{lmn\mathbf{k}}} }$

with the two terms on the right-hand side being called soft and augmentation part respectively and S the overlap matrix

$S = 1+\sum_{ij} |p_i\rangle Q_{ij} \langle p_j|$

The angular part of the functions $\beta^\alpha_{lm}(\mathbf{r})$ is described by spherical harmonics $Y^\alpha_{lm}(\hat{\mathbf{r}})$ and the radial part by a linear combination of spherical bessel functions parametrized to be non-zero within a radius determined by RWIGS.

${\displaystyle \beta^\alpha_{lm}(\mathbf{r}) = Y^\alpha_{lm}(\hat{\mathbf{r}})\sum_n \phi_n(r) }$

it so happens that the $|p_i\rangle$ functions have a similar structure to $|\beta^\alpha_{lm}\rangle$ which simplifies the computations above.

Available from VASP version 3.2 and upwards.

The PROOUT file is only written out if the LORBIT=5 flag is set with an appropriate RWIGS flag in the INCAR file.

The PROOUT file is similar in information to the PROCAR file but the following differences exist:

The PROOUT file writes the real and imaginary parts of $P^{\text{SOFT},\alpha}_{lmn\mathbf{k}}$ and the real part of the augmentation part $P^{\text{AUG},\alpha}_{lmn\mathbf{k}}$ .
The PROCAR file contains the information on the square, $P^\alpha_{lmn\mathbf{k}} (P^\alpha_{lmn\mathbf{k}})^{*}$ , whereas the PROOUT file describes $P^\alpha_{lmn\mathbf{k}}$ .
The arrangement of the output is very different in both files.

Format

line 1: PROOUT
line 2: Number of kpoints, bands and ions
line 3: Twice the number of types followed by the number of ions for each type
line 4: The Fermi weights for each kpoint (inner loop) and band (outer loop)
line 5 $-$ ...: Real and imaginary part of $P^{\text{SOFT},\alpha}_{lmn\mathbf{k}}$ for every lm-quantum number (inner loop), band, ion per type, kpoint and ion-type (outer loop)
below : augmentation part
last line: real part of $P^{\text{AUG},\alpha}_{lmn\mathbf{k}}$ for every lm-quantum number (inner loop), ion per type, ion-type, band and k point (outer loop)

This information makes it possible to construct e.g. partial DOS projected onto bonding and anti-bonding molecular orbitals or the so-called coop (crystal overlap population function).

Warning: This file is not correctly written when LNONCOLLINEAR = .TRUE. for versions of VASP <= 6.2.1

@@ Line 1: / Line 1: @@
-This file contains the projection of the wavefunctions onto spherical harmonics that are non zero within spheres of a radius {{TAG|RWIGS}} centered at each ion (<math>P_{Nlmn\mathbf{k}} \equiv \langle Y_{lm}^{N}|\phi_{n\mathbf{k}}\rangle</math>).
+This file contains the projection of the wavefunctions onto <math>\beta^\alpha_{lm}(\mathbf{r})</math>
+<math>
+P^\alpha_{lmn\mathbf{k}}
+\equiv \langle \beta_{lm}^{\alpha}|S|\phi_{n\mathbf{k}}\rangle
+= \underbrace{\langle \beta_{lm}^{\alpha}|\phi_{n\mathbf{k}}\rangle}_{P^{\text{SOFT},\alpha}_{lmn\mathbf{k}}} +
+\underbrace{\sum_{ij} \langle \beta^\alpha_{lm}|p_i\rangle Q_{ij} \langle p_j | \phi_{n\mathbf{k}}\rangle}_{P^{\text{AUG},\alpha}_{lmn\mathbf{k}}}
+</math>
+with the two terms on the right-hand side being called soft and augmentation part respectively and S the overlap matrix
+<math>S = 1+\sum_{ij} |p_i\rangle Q_{ij} \langle p_j|</math>
+The angular part of the functions <math>\beta^\alpha_{lm}(\mathbf{r})</math> is described by spherical harmonics <math>Y^\alpha_{lm}(\hat{\mathbf{r}})</math> and the radial part by a linear combination of spherical bessel functions parametrized to be non-zero within a radius determined by {{TAG|RWIGS}}.
+<math>
+\beta^\alpha_{lm}(\mathbf{r}) =
+Y^\alpha_{lm}(\hat{\mathbf{r}})\sum_n \phi_n(r)
+</math>
+it so happens that the <math>|p_i\rangle</math> functions have a similar structure to <math>|\beta^\alpha_{lm}\rangle</math> which simplifies the computations above.
 Available from VASP version 3.2 and upwards.
-The {{TAG|PROOUT}} file is only written out if the {{TAG|LORBIT}} flag is set with an appropriate {{TAG|RWIGS}} flag in the {{TAG|INCAR}} file.
+The {{TAG|PROOUT}} file is only written out if the {{TAG|LORBIT}}=5 flag is set with an appropriate {{TAG|RWIGS}} flag in the {{TAG|INCAR}} file.
 The {{TAG|PROOUT}} file is similar in information to the {{TAG|PROCAR}} file but the following differences exist:
-*The {{TAG|PROOUT}} file writes the real and imaginary parts of <math>P_{Nlmn\mathbf{k}}</math>, whereas the {{TAG|PROCAR}} file contains only the real part.
+*The {{TAG|PROOUT}} file writes the real and imaginary parts of <math>P^{\text{SOFT},\alpha}_{lmn\mathbf{k}}</math> and the real part of the augmentation part <math>P^{\text{AUG},\alpha}_{lmn\mathbf{k}}</math>.
-*The {{TAG|PROCAR}} file contains the information on the square, <math>P_{Nlmn\mathbf{k}} (P_{Nlmn\mathbf{k}})^{*}</math>, whereas the {{TAG|PROOUT}} file describes <math>P_{Nlmn\mathbf{k}}</math>.
+*The {{TAG|PROCAR}} file contains the information on the square, <math>P^\alpha_{lmn\mathbf{k}} (P^\alpha_{lmn\mathbf{k}})^{*}</math>, whereas the {{TAG|PROOUT}} file describes <math>P^\alpha_{lmn\mathbf{k}}</math>.
 *The arrangement of the output is very different in both files.
@@ Line 15: / Line 35: @@
 *line 3: Twice the number of types followed by the number of ions for each type
 *line 4: The Fermi weights for each kpoint (inner loop) and band (outer loop)
-*line 5 <math>-</math> ...: Real and imaginary part of the projection <math>P_{Nlmn\mathbf{k}}</math> for every lm-quantum number (inner loop), band, ion per type, kpoint and ion-type (outer loop)
+*line 5 <math>-</math> ...: Real and imaginary part of <math>P^{\text{SOFT},\alpha}_{lmn\mathbf{k}}</math> for every lm-quantum number (inner loop), band, ion per type, kpoint and ion-type (outer loop)
-*below : Augmentation part
+*below : augmentation part
-*last line: The corresponding augmentation part of the projections for every lm-quantum number (inner loop), ion per type, ion-type, band and k point (outer loop)
+*last line: real part of <math>P^{\text{AUG},\alpha}_{lmn\mathbf{k}}</math> for every lm-quantum number (inner loop), ion per type, ion-type, band and k point (outer loop)
-This information makes it possible to construct e.g. partial DOS projected onto bonding and anti-bonding molecular orbitals or the so-called coop ( crystal overlap population function).
+This information makes it possible to construct e.g. partial DOS projected onto bonding and anti-bonding molecular orbitals or the so-called coop (crystal overlap population function).
 {{NB|warning|This file is not correctly written when {{TAG|LNONCOLLINEAR}} {{=}} .TRUE. for versions of VASP <{{=}} 6.2.1 }}