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 $|\psi_{n\mathbf{k}}\rangle$ onto a localized orbitals basis $|\beta^\alpha_{lm}\rangle$ which can be written as

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

Here, the two terms on the right-hand side are called soft and augmentation part, respectively, and $S$ is the overlap matrix,

$S = 1+\sum_{ij} |\tilde{p}_i\rangle Q_{ij} \langle \tilde{p}_j|.$

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

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

The spherical bessel functions $\phi_n(r)$ are parametrized to be non-zero within a radius determined by RWIGS. In addition, it so happens that $|\tilde{p}_i\rangle$ has a similar form as $|\beta^\alpha_{lm}\rangle$ 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 $P^{\text{SOFT},\alpha}_{lmn\mathbf{k}}$, and the real part of the augmentation part $P^{\text{AUG},\alpha}_{lmn\mathbf{k}}$.
• The PROCAR file contains the information of the squared projection, $P^\alpha_{lmn\mathbf{k}} (P^\alpha_{lmn\mathbf{k}})^{*}$, whereas the PROOUT file contains $P^\alpha_{lmn\mathbf{k}}$.
• 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 $-$ ...: Real and imaginary part of $P^{\text{SOFT},\alpha}_{lmn\mathbf{k}}$ for every $lm$-quantum number (inner loop), band, ion per type, k point 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).

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

Related Tags and Sections

LORBIT, LOCPROJ, PROJCAR, PROCAR

---