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 $|\beta^\alpha_{lm}\rangle$ which can be written as

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

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

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).

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