PROOUT: Difference between revisions
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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. | 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. | ||
For the case of spin-polarized {{TAG|ISPIN}}=2 or noncollinear calculations {{TAG|LNONCOLLINEAR}}=.TRUE., two files are produced | For the case of spin-polarized {{TAG|ISPIN}}=2 or noncollinear calculations {{TAG|LNONCOLLINEAR}}=.TRUE., two files are produced PROOUT.1 and PROOUT.2 referring to the up and down part of the spinor of the orbital. | ||
{{NB|warning|This file is not correctly written when {{TAG|LNONCOLLINEAR}} {{=}} .TRUE. for versions of VASP <{{=}} 6.2.1 }} | {{NB|warning|This file is not correctly written when {{TAG|LNONCOLLINEAR}} {{=}} .TRUE. for versions of VASP <{{=}} 6.2.1 }} | ||
Revision as of 11:27, 29 November 2021
This file is written when LORBIT=5 and RWIGS tags are set in the INCAR file and contains the projection of the Bloch wavefunctions Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle |\psi_{n\mathbf{k}}\rangle} onto Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle |\beta^\alpha_{lm}\rangle} which can be written as
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle P^\alpha_{lmn\mathbf{k}} \equiv \langle \beta_{lm}^{\alpha}|S|\psi_{n\mathbf{k}}\rangle = \underbrace{\langle \beta_{lm}^{\alpha}|\psi_{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 | \psi_{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
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle S = 1+\sum_{ij} |p_i\rangle Q_{ij} \langle p_j|.}
The angular part of the functions Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle \beta^\alpha_{lm}(\mathbf{r})} is described by spherical harmonics Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle 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
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle \beta^\alpha_{lm}(\mathbf{r}) = Y^\alpha_{lm}(\hat{\mathbf{r}})\sum_n \phi_n(r). }
It so happens that the Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle |p_i\rangle} functions have a similar structure to Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle |\beta^\alpha_{lm}\rangle} which simplifies the computations above.
For the case of spin-polarized ISPIN=2 or noncollinear calculations LNONCOLLINEAR=.TRUE., two files are produced PROOUT.1 and PROOUT.2 referring to the up and down part of the spinor of the orbital.
| Warning: This file is not correctly written when LNONCOLLINEAR = .TRUE. for versions of VASP <= 6.2.1 |
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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle P^{\text{SOFT},\alpha}_{lmn\mathbf{k}}} and the real part of the augmentation part Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle P^{\text{AUG},\alpha}_{lmn\mathbf{k}}} .
- The PROCAR file contains the information on the square, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle P^\alpha_{lmn\mathbf{k}} (P^\alpha_{lmn\mathbf{k}})^{*}} , whereas the PROOUT file describes Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle P^\alpha_{lmn\mathbf{k}}} .
- The arrangement of the output is very different in both files.
Depending on the intended application users might find it more practical to use the information contained in the PROJCAR and LOCPROJ files controlled by the LOCPROJ tag.
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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): - ...: Real and imaginary part of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle 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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle 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).