PROOUT

This file is written if LORBIT=5 and the RWIGS tag is set in the INCAR file. It contains the projection of the Kohn-Sham orbitals 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 a localized orbitals basis 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}|\tilde{p}_i\rangle Q_{ij} \langle \tilde{p}_j | \psi_{n\mathbf{k}}\rangle}_{P^{\text{AUG},\alpha}_{lmn\mathbf{k}}}. }

Here, the two terms on the right-hand side are called soft and augmentation part, respectively, and 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/":): S is 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} |\tilde{p}_i\rangle Q_{ij} \langle \tilde{p}_j|.}

The radial and the angular 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 \beta^\alpha_{lm}(\mathbf{r})} are described by a linear combination of spherical bessel 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 \phi_n(r)} and 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}})} , respectively:

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). }

The spherical bessel 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 \phi_n(r)} are parametrized to be non-zero within a radius determined by RWIGS. In addition, it so happens that 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 |\tilde{p}_i\rangle} has a similar form 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 |\beta^\alpha_{lm}\rangle} which simplifies the computations above.

The PROOUT file contains similar information as 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 of the squared projection, 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 contains 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.

This information makes it possible to construct, e.g., partial DOS projected onto bonding and anti-bonding molecular orbitals and the so-called crystal-orbital-overlap-population (COOP) function. Depending on the application, users might find it more practical to use the information contained in the PROJCAR and LOCPROJ files. These are controlled by the LOCPROJ tag.

For spin-polarized calculations with ISPIN=2 and noncollinear calculations with LNONCOLLINEAR=.TRUE., PROOUT.1 and PROOUT.2 are written, referring to the Kohn-Sham orbitals' two spin components.

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 k point (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 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 lm} -quantum number (inner loop), band, ion per type, k point 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 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 lm} -quantum number (inner loop), ion per type, ion type, band and k point (outer loop).

Warning: For VASP version <= 6.2.1, PROOUT is not correctly written when LNONCOLLINEAR = True.

Related Tags and Sections

LORBIT, LOCPROJ, PROJCAR, PROCAR

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