PROOUT

This file contains the projection of the wavefunctions [math]\displaystyle{ |\phi_{n\mathbf{k}}\rangle }[/math] onto [math]\displaystyle{ |\beta^\alpha_{lm}\rangle }[/math]

[math]\displaystyle{ 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}}} }[/math]

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

[math]\displaystyle{ S = 1+\sum_{ij} |p_i\rangle Q_{ij} \langle p_j| }[/math]

The angular part of the functions [math]\displaystyle{ \beta^\alpha_{lm}(\mathbf{r}) }[/math] is described by spherical harmonics [math]\displaystyle{ Y^\alpha_{lm}(\hat{\mathbf{r}}) }[/math] and the radial part by a linear combination of spherical bessel functions parametrized to be non-zero within a radius determined by RWIGS.

[math]\displaystyle{ \beta^\alpha_{lm}(\mathbf{r}) = Y^\alpha_{lm}(\hat{\mathbf{r}})\sum_n \phi_n(r) }[/math]

it so happens that the [math]\displaystyle{ |p_i\rangle }[/math] functions have a similar structure to [math]\displaystyle{ |\beta^\alpha_{lm}\rangle }[/math] which simplifies the computations above.

Available from VASP version 3.2 and upwards.

The PROOUT file is only written out if the LORBIT=5 flag is set with an appropriate RWIGS flag in the INCAR file.

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 [math]\displaystyle{ P^{\text{SOFT},\alpha}_{lmn\mathbf{k}} }[/math] and the real part of the augmentation part [math]\displaystyle{ P^{\text{AUG},\alpha}_{lmn\mathbf{k}} }[/math].
• The PROCAR file contains the information on the square, [math]\displaystyle{ P^\alpha_{lmn\mathbf{k}} (P^\alpha_{lmn\mathbf{k}})^{*} }[/math], whereas the PROOUT file describes [math]\displaystyle{ P^\alpha_{lmn\mathbf{k}} }[/math].
• 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 [math]\displaystyle{ - }[/math] ...: Real and imaginary part of [math]\displaystyle{ P^{\text{SOFT},\alpha}_{lmn\mathbf{k}} }[/math] 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 [math]\displaystyle{ P^{\text{AUG},\alpha}_{lmn\mathbf{k}} }[/math] 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).

Warning: This file is not correctly written when LNONCOLLINEAR = .TRUE. for versions of VASP <= 6.2.1

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