PROOUT

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

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

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

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

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

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

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

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 $P^{\text{SOFT},\alpha}_{lmn\mathbf{k}}$ 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.

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 $-$ ...: 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).

Related Tags and Sections

LORBIT LOCPROJ PROJCAR

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