LOCPROJ

LOCPROJ = <sites> : <functions-Ylm-specs> : <functions-radial-specs>
Default: LOCPROJ = None 

Description: The LOCPROJ tag specifies local functions on which the orbitals are projected. These projections are written to the PROJCAR, LOCPROJ, and vasprun.xml files.

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Mind: LOCPROJ is an INCAR tag and a file. The file is described at the end of this page.

When the LOCPROJ tag is set, VASP performs 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

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

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

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

The radial and the angular part of $\beta^\alpha_{lm}(\mathbf{r})$ are described by the LOCPROJ tag, which comprises three parts separated by colons that are denoted as <sites>, <functions-Ylm-specs>, and <functions-radial-specs>. For instance, to perform the projection onto a hydrogen-like 1s function on the first ionic position specified in the POSCAR file, the tag reads

LOCPROJ = 1 : s : Hy

Specifying the local basis

• <sites>: The sites on which the local functions are centered.

It is specified either using the index of the ionic positions as defined in the POSCAR file, or in terms of direct coordinates of the real space lattice. For instance, 1 2 6-8 will select sites 1, 2, 6, 7, and 8 as defined in the POSCAR file. On the other hand, (0.5, 0, 0) specifies the position in terms of direct coordinates of the real space lattice. The modes of the specification can be mixed as well, e.g., 1 (0.5, 0, 0) 8.

• <functions-Ylm-specs>: The angular character of the local functions on the specified sites.

Possible specifications are presented in the table below.

s
p	py	pz	px
d	dxy	dyz	dz2	dxz	dx2-y2
f	fy(3x2-y2)	fxyz	fyz2	fz3	fxz2	fz(x2-y2)	fx(x2-3y2)
sp	sp-1	sp-2
sp2	sp2-1	sp2-2	sp2-3
sp3	sp3-1	sp3-2	sp3-3	sp3-4
sp3d	sp3d-1	sp3d-2	sp3d-3	sp3d-4	sp3d-5
sp3d2	sp3d2-1	sp3d2-2	sp3d2-3	sp3d2-4	sp3d2-5	sp3d2-6

For more details, have a look at the section on angular functions. These functions are consistent with the definition of the initial guesses used by WANNIER90 (see section 3.4 of the WANNIER90 manual).

It is possible to select multiple characters by creating a list separated by spaces, e.g., p sp-1 dxy performs a projection for all p functions (≡ p_x, p_y, and p_z), an sp-1 function, and a d_xy function on all sites specified by <sites>.

• <functions-radial-specs>: The radial dependency of the local functions.

There are three options:

Pr: use the PAW projectors

Ps: use the PAW pseudo partial waves

Hy: use hydrogen-like (Slater type) functions (see section 3.4 of the WANNIER90 manual)

Mind: For Pr or Ps, which are radial functions derived from the PAW datasets, one can only specify spherical harmonics with the same angular moment l in the <functions-Ylm-specs> part. This means, s, p, d, f, and/or their respective separate constituents.

The radial specifiers can optionally be modified using the following modification statements:

Pr [ n^th-of-l [ species-number ] ]

n^th-of-l: Uses the radial function of the n^th projector with the angular moment specified in <functions-Ylm-specs>. The local basis of our PAW datasets typically contains 2 projectors per angular moment. By default, the projector that corresponds to the highest bound state of the relevant angular moment will be used.

species-number: Specifies from which PAW dataset in the current POTCAR file the radial functions should be derived. When the positions of the local functions are specified using the ionic site indices of the POSCAR file, the code will default to the corresponding atomic types.

Ps [ n^th-of-l [ species-number ] ]

n^th-of-l: Uses the radial function of the n^th pseudo partial wave with the angular moment specified in <functions-Ylm-specs>. The local basis of our PAW datasets typically contains 2 pseudo partial waves per angular moment. By default, the pseudo partial wave that corresponds to the highest bound state of the relevant angular moment is used.

species-number: Specifies from which PAW dataset in the current POTCAR file the radial functions should be derived. When the positions of the local functions are specified using the ionic site indices of the POSCAR file, the default is the corresponding atomic type.

Hy [ n [ α ] ]

n: Main quantum number of the hydrogen-like radial functions. Default: n=1.

α: controls the diffusivity of the radial functions ( α=Z/a₀ in Å^-1). Default: α=1.0 Å^-1.

ns type Hydrogen radial wave functions

$n$	$R(r)$
$1$	$2\alpha^{3/2}\exp(-\alpha r)$
$2$	$\frac{1}{2\sqrt 2}\alpha^{3/2}(2-\alpha r)\exp(-\alpha r /2)$
$3$	${\sqrt \frac{4}{27}}\alpha^{3/2}(1-2\alpha r/3+2\alpha^2 r^2/27)\exp(-\alpha r /3)$

This is consistent with the definition of the initial guesses used by WANNIER90 (section 3.4 of the WANNIER90 manual).

Important: Different projections have to be specified in multiple lines, as the LOCPROJ tag can only be set once.

For instance,

LOCPROJ = "1 : s : Hy 2
           1 3 : dxy : Ps 2 3"

performs the projection onto a hydrogen-like 2s function and a d_xy pseudo partial wave (2^nd d channel of atomic species 3) on ionic site 1, and a d_xy pseudo partial wave (identical type) on site 3.

Deprecated: For VASP versions <= 6.1.x, multiple occurrences of the LOCPROJ tag are allowed and taken into account.

For other tags, the second instance of a tag in the INCAR is normally ignored. However, here

LOCPROJ = 1 : s : Hy 2
LOCPROJ = 1 3 : dxy : Ps 2 3

is possible.

Example for LOCPROJ tag

As mentioned above, to put a hydrogen-like 1s function on the first ionic position specified in the POSCAR file, the tag reads

LOCPROJ = 1 : s : Hy

in the INCAR file. To change this into a 2s function, specify

LOCPROJ = 1 : s : Hy 2

To project the orbitals onto the PAW projectors of the valence atomic d_xy-states of the atoms on sites 1 and 3, write

LOCPROJ = 1 3 : dxy : Pr

This will only work if the atoms on these sites have valence atomic d-states. Otherwise, the necessary projectors will not be available in the relevant PAW datasets, and the code will exit in error at startup.

To forcibly use the radial function of the second d channel, write

LOCPROJ = 1 3 : dxy : Pr 2

Again, provided the PAW dataset(s) contain more than one d channel. Similarly, one can project onto the pseudo partial waves of the second d channel in the PAW dataset(s) by writing

LOCPROJ = 1 3 : dxy : Ps 2

To project onto the functions of the third PAW dataset in the POTCAR file, specify

LOCPROJ = 1 3 : dxy : Ps 2 3

LOCPROJ file

The LOCPROJ file contains information about the projections of the Bloch states onto the localized orbitals specified with the LOCPROJ tag described above.

The file contains a header with the information about all projections:

• ISITE: Index of the site in the POSCAR file.
• R: Position in fractional coordinates.
• Radial type: Is one of "PAW projector","PS partial wave", "Hydrogen-like" depending on the choice of Pr, Ps or Hy, respectively.
• Angular type: Angular character of the local functions, as presented in the table above in <functions-Ylm-specs>.

Each Kohn-Sham orbital is identified by the spin, k point, band index, eigenvalue, and occupation. For each of these Kohn-Sham orbitals, VASP writes the real and imaginary part of the projection onto localized orbitals $\langle \beta_{lm}^{\alpha}|S|\psi_{n\mathbf{k}}\rangle$. Note that for vasp_gam only the real part exists.

Related tags and articles

LORBIT, PROJCAR

Examples that use this tag

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