PROOUT

This file is written when LORBIT=5 and RWIGS tags are set in the INCAR file and contains the projection of the wavefunctions $|\phi _{n\mathbf {k} }\rangle$ onto $|\beta _{lm}^{\alpha }\rangle$ which can be written as

$P_{lmn\mathbf {k} }^{\alpha }\equiv \langle \beta _{lm}^{\alpha }|S|\phi _{n\mathbf {k} }\rangle =\underbrace {\langle \beta _{lm}^{\alpha }|\phi _{n\mathbf {k} }\rangle } _{P_{lmn\mathbf {k} }^{{\text{SOFT}},\alpha }}+\underbrace {\sum _{ij}\langle \beta _{lm}^{\alpha }|p_{i}\rangle Q_{ij}\langle p_{j}|\phi _{n\mathbf {k} }\rangle } _{P_{lmn\mathbf {k} }^{{\text{AUG}},\alpha }}$

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

$\beta _{lm}^{\alpha }(\mathbf {r} )=Y_{lm}^{\alpha }({\hat {\mathbf {r} }})\sum _{n}\phi _{n}(r).$

It so happens that the $|p_{i}\rangle$ functions have a similar structure to $|\beta _{lm}^{\alpha }\rangle$ which simplifies the computations above.

For the case of spin-polarized ISPIN=2 or noncollinear calculations LNONCOLLINEAR=.TRUE., two files are produced PROCAR.1 and PROCAR.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 $P_{lmn\mathbf {k} }^{{\text{SOFT}},\alpha }$ and the real part of the augmentation part $P_{lmn\mathbf {k} }^{{\text{AUG}},\alpha }$.
• The PROCAR file contains the information on the square, $P_{lmn\mathbf {k} }^{\alpha }(P_{lmn\mathbf {k} }^{\alpha })^{*}$, whereas the PROOUT file describes $P_{lmn\mathbf {k} }^{\alpha }$.
• 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 $P_{lmn\mathbf {k} }^{{\text{SOFT}},\alpha }$ 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 $P_{lmn\mathbf {k} }^{{\text{AUG}},\alpha }$ 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).

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