PLOVasp

The general purpose of the PLOVasp tool is to transform raw, non-normalized projectors generated by VASP into normalized projectors corresponding to user-defined projected localized orbitals (PLO). The PLOs can then be used for DFT+DMFT calculations with or without charge self-consistency. PLOVasp also provides some utilities for basic analysis of the generated projectors, such as outputting density matrices, local Hamiltonians, and projected density of states.

PLOs are determined by the energy window in which the raw projectors are normalized. This allows to define either atomic-like strongly localized Wannier functions (large energy window) or extended Wannier functions focusing on selected low-energy states (small energy window).

In PLOVasp, all projectors sharing the same energy window are combined into a projector group. Technically, this allows one to define several groups with different energy windows for the same set of raw projectors. Note, however, that DFTtools does not support projector groups at the moment but this feature might appear in future releases.

A set of projectors defined on sites related to each other either by symmetry or by an atomic sort, along with a set of \(l\), \(m\) quantum numbers, forms a projector shell. There could be several projectors shells in a projector group, implying that they will be normalized within the same energy window.

Projector shells and groups are specified by a user-defined input file whose format is described below.

Input file format

The input file is written in the standard config-file format. Parameters (or ‘options’) are grouped into sections specified as [Section name]. All parameters must be defined inside some section.

A PLOVasp input file can contain three types of sections:

  1. [General]: includes parameters that are independent of a particular projector set, such as the Fermi level, additional output (e.g. the density of states), etc.
  2. [Group <Ng>]: describes projector groups, i.e. a set of projectors sharing the same energy window and normalization type. At the moment, DFTtools support only one projector group, therefore there should be no more than one projector group.
  3. [Shell <Ns>]: contains parameters of a projector shell labelled with <Ns>. If there is only one group section and one shell section, the group section can be omitted but in this case, the group required parameters must be provided inside the shell section.

Section [General]

The entire section is optional and it contains three parameters:

  • BASENAME (string): provides a base name for output files. Default filenames are vasp.*.
  • DOSMESH ([float float] integer): if this parameter is given, the projected density of states for each projected orbital will be evaluated and stored to files pdos_<n>.dat, where n is the orbital index. The energy mesh is defined by three numbers: EMIN EMAX NPOINTS. The first two can be omitted in which case they are taken to be equal to the projector energy window. Important note: at the moment this option works only if the tetrahedron integration method (ISMEAR = -4 or -5) is used in VASP to produce LOCPROJ.
  • EFERMI (float): provides the Fermi level. This value overrides the one extracted from VASP output files.

There are no required parameters in this section.

Section [Shell]

This section specifies a projector shell. Each [Shell] section must be labeled by an index, e.g. [Shell 1]. These indices can then be referenced in a [Group] section.

In each [Shell] section two parameters are required:

  • IONS (list of integer): indices of sites included in the shell. The sites can be given either by a list of integers IONS = 5 6 7 8 or by a range IONS = 5..8. The site indices must be compatible with the POSCAR file.
  • LSHELL (integer): \(l\) quantum number of the desired local states.

It is important that a given combination of site indices and local states given by LSHELL must be present in the LOCPROJ file.

There are additional optional parameters that allow one to transform the local states:

  • TRANSFORM (matrix): local transformation matrix applied to all states in the projector shell. The matrix is defined by a (multiline) block of floats, with each line corresponding to a row. The number of columns must be equal to \(2 l + 1\), with \(l\) given by LSHELL. Only real matrices are allowed. This parameter can be useful to select certain subset of orbitals or perform a simple global rotation.
  • TRANSFILE (string): name of the file containing transformation matrices for each site. This option allows for a full-fledged functionality when it comes to local state transformations. The format of this file is described below.

Section [Group]

Each defined projector shell must be part of a projector group. In the current implementation of DFTtools only a single group (labelled by any integer, e.g. [Group 1]) is supported. This implies that all projector shells must be included in this group.

Required parameters for any group are the following:

  • SHELLS (list of integers): indices of projector shells included in the group. All defined shells must be grouped.
  • EWINDOW (float float): the energy window specified by two floats: bottom and top. All projectors in the current group are going to be normalized within this window. Note: This option must be specified inside the [Shell] section if only one shell is defined and the [Group] section is omitted.

Optional group parameters:

  • NORMALIZE (True/False): specifies whether projectors in the group are to be normalized. The default value is True.
  • NORMION (True/False): specifies whether projectors are normalized on a per-site (per-ion) basis. That is, if NORMION = True, the orthogonality condition will be enforced on each site separately but the Wannier functions on different sites will not be orthogonal. If NORMION = False, the Wannier functions on different sites included in the group will be orthogonal to each other.

File of transformation matrices

Warning

The description below applies only to collinear cases (i.e., without spin-orbit coupling). In this case, the matrices are spin-independent.

The file specified by option TRANSFILE contains transformation matrices for each ion. Each line must contain a series of floats whose number is either equal to the number of orbitals \(N_{orb}\) (in this case the transformation matrices are assumed to be real) or to \(2 N_{orb}\) (for the complex transformation matrices). The total number of lines \(N\) must be a multiple of the number of ions \(N_{ion}\) and the ratio \(N / N_{ion}\), then, gives the dimension of the transformed orbital space. The lines with floats can be separated by any number of empty or comment lines (starting from #), which are ignored.

A very simple example is a transformation matrix that selects the \(t_{2g}\) manifold. For two correlated sites, one can define the file as follows:

# Site 1
  1.0   0.0   0.0   0.0   0.0
  0.0   1.0   0.0   0.0   0.0
  0.0   0.0   0.0   1.0   0.0

# Site 2
  1.0   0.0   0.0   0.0   0.0
  0.0   1.0   0.0   0.0   0.0
  0.0   0.0   0.0   1.0   0.0