dft_tools/doc/guide/plovasp.rst

.. _plovasp:

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 :math:`l`, :math:`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:

#. **[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.
#. **[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.
#. **[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 :file:`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 :file:`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): :math:`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 :math:`2 l + 1`, with :math:`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 :ref:`below <transformation_file>`.

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.


.. _transformation_file:

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 :math:`N_{orb}` (in this case the transformation matrices
are assumed to be real) or to :math:`2 N_{orb}` (for the complex transformation matrices).
The total number of lines :math:`N` must be a multiple of the number of ions :math:`N_{ion}`
and the ratio :math:`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 :math:`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