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doc/NaCl-crystal-band-NAC.png

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doc/Si-crystal-band.png

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...@@ -71,8 +71,8 @@ Choice of force calculator ...@@ -71,8 +71,8 @@ Choice of force calculator
--------------------------- ---------------------------
Currently interfaces for VASP, Wien2k, Pwscf, Abinit, and Elk are Currently interfaces for VASP, Wien2k, Pwscf, Abinit, and Elk are
prepared. Wien2k, Pwscf, Abinit and Elk interfaces are invoked with prepared. Wien2k, Pwscf, Abinit, Elk and CRYSTAL interfaces are invoked with
``--wienk2``, ``--pwscf``, ``--abinit``, and ``--elk`` options, ``--wienk2``, ``--pwscf``, ``--abinit``, ``--elk`` and ``--crystal`` options,
respectively, and if none of these options or ``--vasp`` option is respectively, and if none of these options or ``--vasp`` option is
specified, VASP mode is invoked. specified, VASP mode is invoked.
...@@ -148,7 +148,7 @@ input file that contains the unit cell crystal structure, e.g., ...@@ -148,7 +148,7 @@ input file that contains the unit cell crystal structure, e.g.,
``--elk`` ``--elk``
~~~~~~~~~~~~ ~~~~~~~~~~~~
Pwscf mode is invoked with this option. Usually this option is used Elk mode is invoked with this option. Usually this option is used
with ``--cell`` (``-c``) option or ``CELL_FILENAME`` tag to read Elk with ``--cell`` (``-c``) option or ``CELL_FILENAME`` tag to read Elk
input file that contains the unit cell crystal structure, e.g., input file that contains the unit cell crystal structure, e.g.,
...@@ -156,6 +156,19 @@ input file that contains the unit cell crystal structure, e.g., ...@@ -156,6 +156,19 @@ input file that contains the unit cell crystal structure, e.g.,
% phonopy --elk -c elk-unitcell.in band.conf % phonopy --elk -c elk-unitcell.in band.conf
.. _crystal_mode:
``--crystal``
~~~~~~~~~~~~~
CRYSTAL mode is invoked with this option. Usually this option is used
with ``--cell`` (``-c``) option or ``CELL_FILENAME`` tag to read a CRYSTAL
input file that contains the unit cell crystal structure, e.g.,
::
% phonopy --crystal -c crystal.o band.conf
.. _vasp_mode: .. _vasp_mode:
``--vasp`` ``--vasp``
...@@ -190,6 +203,7 @@ directory. The default file names for the calculators are as follows:: ...@@ -190,6 +203,7 @@ directory. The default file names for the calculators are as follows::
Abinit | unitcell.in Abinit | unitcell.in
Pwscf | unitcell.in Pwscf | unitcell.in
Elk | elk.in Elk | elk.in
CRYSTAL| crystal.o
Create ``FORCE_SETS`` Create ``FORCE_SETS``
---------------------- ----------------------
...@@ -293,6 +307,15 @@ files. ...@@ -293,6 +307,15 @@ files.
% phonopy --elk -f disp-001/INFO.OUT disp-002/INFO.OUT ... % phonopy --elk -f disp-001/INFO.OUT disp-002/INFO.OUT ...
CRYSTAL interface
^^^^^^^^^^^^^^^^^
``FORCE_SETS`` file is created from ``disp.yaml`` and CRYSTAL output
files.
::
% phonopy --crystal -f supercell-001.o supercell-002.o ...
.. _fz_force_sets_option: .. _fz_force_sets_option:
...@@ -407,7 +430,7 @@ printed out and phonopy stops without going to phonon analysis. ...@@ -407,7 +430,7 @@ printed out and phonopy stops without going to phonon analysis.
% phonopy --symmetry % phonopy --symmetry
This tag can be used together with the ``--cell`` (``-c``), This tag can be used together with the ``--cell`` (``-c``),
``--abinit``, ``--pwscf``, ``--elk``, ``--wien2k``, or ``--abinit``, ``--pwscf``, ``--elk``, ``--wien2k``, ``--crystal`` or
``--primitive_axis`` option. ``--primitive_axis`` option.
Input/Output file control Input/Output file control
......
.. _crystal_interface:
CRYSTAL & phonopy calculation
=========================================
CRYSTAL program package has a robust built-in phonon calculation
workflow. However, the Phonopy interface enables convenient access
to many phonon-related properties, such as subsequent Phono3py
calculations of lattice thermal conductivity.
Supported features
---------------------------
The CRYSTAL interface reads the unit cell from a CRYSTAL output file
(lattice vectors, conventional atomic numbers, fractional atomic positions)
For optimization outputs, the final geometry in the file is read.
If dielectric tensor and effective Born charges are present, the interface
creates a BORN file for Non-analytical correction (:ref:`nac_tag`).
The recommended strategy is to carry out a Gamma-point frequency calculation
with INTENS and INTCPHF. This produces all required quantities and also confirms that
the structure optimization has converged to a true local minimum.
If ATOMSPIN keyword is present, magnetic moments are read from it. There
is very little experience on using this feature, so be careful.
How to run
----------
The workflow for a CRYSTAL-Phonopy calculation is outlined here using the
Si example found in ``example/Si-CRYSTAL``.
In this example, the CRYSTAL output file is ``crystal.o``.
This is the default for the CRYSTAL interface, so, the ``-c crystal.o``
parameter is not needed
1) Create supercells with :ref:`crystal_mode` option::
% phonopy --crystal -d --dim="4 4 4"
In this example, 4x4x4 supercells are created. For every supercell file, the
interface creates a .d12 input file and an .ext structure file. The files
``supercell.d12/.ext`` contain the perfect supercell. The files
``supercell-xxx.d12/.ext`` (``xxx`` are numbers) contain the supercells
with displacements. File ``disp.yaml`` is also generated, containing information
about the supercell and the displacements.
In the case of the Si example, files ``supercell-001.d12`` and
``supercell-001.ext`` will be created.
2) To make valid CRYSTAL input files, there are two possible options:
a) Manually: modify the generated supercell-xxx.d12 files by replacing
the line ``Insert basis sets and parameters here`` with the
basis set and computational parameters.
b) Recommended option: before generating the supercells, include a file named
``TEMPLATE`` in the current directory. This file should contain the
basis sets and computational parameters for CRYSTAL (see the Si example).
When phonopy finds this file, it automatically generates complete
CRYSTAL input files in the step 1
Note that supercells with displacements must not be relaxed in the
force calculations, because atomic forces induced by a small atomic
displacement are what we need for phonon calculation. To get accurate
forces, TOLDEE parameter should be 10 or higher. Phonopy includes this
parameter and the necessary GRADCAL keyword automatically in the inputs.
Then, CRYSTAL supercell calculations are executed to obtain forces on
atoms, e.g., as follows::
% runcry14 supercell-001.d12
3) To create ``FORCE_SETS``, that is used by phonopy,
the following phonopy command is executed::
% phonopy --crystal -f supercell-001.o
Here ``.o`` files are the CRYSTAL output files from the force
calculations. saved text files of standard outputs of the
Pwscf calculations. All ``.o`` files corresponding to the generated
``supercell-xxx.d12`` files have to be given in the above command.
To run this command, ``disp.yaml`` has to be located in the current
directory because the information on atomic displacements stored in
``disp.yaml`` are used to generate ``FORCE_SETS``. See some more detail at
:ref:`crystal_force_sets_option`.
4) Now, Phonopy post-prcessing commands can be run. ``FORCE_SETS`` is
automatically read in. Create phonon dispersion plot with:
::
% phonopy --crystal --dim="4 4 4" -p -s band.conf
_
_ __ | |__ ___ _ __ ___ _ __ _ _
| '_ \| '_ \ / _ \| '_ \ / _ \ | '_ \| | | |
| |_) | | | | (_) | | | | (_) || |_) | |_| |
| .__/|_| |_|\___/|_| |_|\___(_) .__/ \__, |
|_| |_| |___/
1.11.6
Python version 2.7.3
Spglib version 1.9.9
Calculator interface: crystal
Band structure mode
Settings:
Supercell: [4 4 4]
Spacegroup: Fd-3m (227)
Computing force constants...
Reciprocal space paths in reduced coordinates:
[ 0.00 0.00 0.00] --> [ 0.50 0.00 0.50]
[ 0.50 0.00 0.50] --> [ 0.50 0.25 0.75]
[ 0.50 0.25 0.75] --> [ 0.37 0.38 0.75]
[ 0.38 0.38 0.75] --> [ 0.00 0.00 0.00]
[ 0.00 0.00 0.00] --> [ 0.50 0.50 0.50]
[ 0.50 0.50 0.50] --> [ 0.63 0.25 0.63]
[ 0.62 0.25 0.62] --> [ 0.50 0.25 0.75]
[ 0.50 0.25 0.75] --> [ 0.50 0.50 0.50]
[ 0.50 0.50 0.50] --> [ 0.37 0.37 0.75]
[ 0.62 0.25 0.62] --> [ 0.50 -0.00 0.50]
_
___ _ __ __| |
/ _ \ '_ \ / _` |
| __/ | | | (_| |
\___|_| |_|\__,_|
|crystal-band|
.. |crystal-band| image:: Si-crystal-band.png
:width: 33%
For further settings and command options, see the general Phonopy documentation
:ref:`setting_tags` and :ref:`command_options`, respectively, and
for examples, see :ref:`examples_link`.
Non-analytical term correction (Optional)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The workflow for a CRYSTAL-Phonopy calculation with Non-analytical correction
is outlined here using the NaCl example found in ``example/NaCl-CRYSTAL``.
In this example, the CRYSTAL output file is ``crystal.o``.
This is the default for the CRYSTAL interface, so, the ``-c crystal.o``
parameter is not needed.
To activate non-analytical term correction, :ref:`born_file` is
required. This file contains the Born effective charges
and the dielectric tensor. They can be calculated with CRYSTAL.
The recommended strategy is to carry out a Gamma-point frequency calculation
with INTENS and INTCPHF. This produces all required quantities and also confirms that
the structure optimization has converged to a true local minimum.
(see the FREQCALC-INTENS-INTCPHF block in the beginning of ``crystal.o``)
The workflow is very similar to the Si example below:
1) Create displaced supercells::
phonopy --crystal --dim="4 4 4" -d
Note that now the CRYSTAL interface automatically creates the ``BORN``
file. It should look like this::
default
1.8126 0.0000 0.0000 0.0000 1.8126 0.0000 0.0000 0.0000 1.8126
1.0238 -0.0000 -0.0000 -0.0000 1.0238 0.0000 -0.0000 0.0000 1.0238
-1.0238 0.0000 0.0000 0.0000 -1.0238 0.0000 0.0000 0.0000 -1.0238
However, if you don't want to run a FREQCALC-INTENS-INTCPHF calculation,
but have the necessary data from some other source, you can create
the ``BORN`` file manually following the ``BORN`` format
(:ref:`born_file`).
2) Run the supercell inputs with CRYSTAL
3) Collect forces::
phonopy --crystal -f supercell-*o
4) Calculate phonon dispersion data into band.yaml and save band.pdf,
using Non-analytical correction --nac::
phonopy --crystal --dim="4 4 4" -p -s --nac band.conf
|crystal-band-nac|
.. |crystal-band-nac| image:: NaCl-crystal-band-NAC.png
:width: 33%
...@@ -63,10 +63,10 @@ showing the values on the plot. Instead the values at the neighboring ...@@ -63,10 +63,10 @@ showing the values on the plot. Instead the values at the neighboring
.. _gruneisen_calculators: .. _gruneisen_calculators:
Abinit, Pwscf, and Wien2k interfaces Abinit, Pwscf, Wien2k, and CRYSTAL interfaces
------------------------------------- ---------------------------------------------
``--abinit``, ``--pwscf``, or ``--wien2k`` options can be specified ``--abinit``, ``--pwscf``, ``--wien2k``, or ``--crystal`` options can be specified
for corresponding calculators and the crystal structure file format for corresponding calculators and the crystal structure file format
should be different from that of the VASP format. An Abinit example is should be different from that of the VASP format. An Abinit example is
as follows:: as follows::
...@@ -79,7 +79,7 @@ as follows:: ...@@ -79,7 +79,7 @@ as follows::
Command options Command options
---------------- ----------------
If one of ``--abinit``, ``--pwscf``, or ``--wien2k`` options is If one of ``--abinit``, ``--pwscf``, ``--wien2k``, or ``--crystal`` options is
specified, the interface mode is changed to it. The unit conversion specified, the interface mode is changed to it. The unit conversion
factor to THz is appropriately selected and its crystal structure file factor to THz is appropriately selected and its crystal structure file
format is accepted. If none of them is specified, as the VASP format is accepted. If none of them is specified, as the VASP
......
...@@ -52,7 +52,8 @@ Selected features ...@@ -52,7 +52,8 @@ Selected features
:ref:`Siesta <siesta_interface>`, :ref:`Siesta <siesta_interface>`,
:ref:`Elk <elk_interface>`, :ref:`Elk <elk_interface>`,
:ref:`FHI-aims <FHI_aims_interface>`, :ref:`FHI-aims <FHI_aims_interface>`,
:ref:`Wien2k <wien2k_interface>` :ref:`Wien2k <wien2k_interface>`,
:ref:`CRYSTAL <crystal_interface>`
- :ref:`Python APIs <phonopy_module>` - :ref:`Python APIs <phonopy_module>`
|i0| |i1| |i2| |i3| |i0| |i1| |i2| |i3|
......
...@@ -3,7 +3,7 @@ ...@@ -3,7 +3,7 @@
Interfaces to calculators Interfaces to calculators
========================== ==========================
The interfaces for VASP, Wien2k, Pwscf, Abinit, and Elk are built in The interfaces for VASP, Wien2k, Pwscf, Abinit, Elk and CRYSTAL are built in
to the usual phonopy command. See the command options and how to to the usual phonopy command. See the command options and how to
invoke each of them at :ref:`force_calculators`. invoke each of them at :ref:`force_calculators`.
...@@ -20,8 +20,9 @@ Physical unit systems used for the calculators are as follows:: ...@@ -20,8 +20,9 @@ Physical unit systems used for the calculators are as follows::
Abinit | au (bohr) AMU eV/Angstrom eV/Angstrom.au Abinit | au (bohr) AMU eV/Angstrom eV/Angstrom.au
Siesta | au (bohr) AMU eV/Angstrom eV/Angstrom.au Siesta | au (bohr) AMU eV/Angstrom eV/Angstrom.au
elk | au (bohr) AMU hartree/au hartree/au^2 elk | au (bohr) AMU hartree/au hartree/au^2
CRYSTAL | Angstrom AMU eV/Angstrom eV/Angstrom^2
For these sets of physical properties, phonon frequency is calcualted For these sets of physical properties, phonon frequency is calculated
in THz. in THz.
Default file name, value, and conversion factor Default file name, value, and conversion factor
...@@ -39,6 +40,7 @@ used as shown below:: ...@@ -39,6 +40,7 @@ used as shown below::
Abinit | unitcell.in Abinit | unitcell.in
Siesta | input.fdf Siesta | input.fdf
Elk | elk.in Elk | elk.in
CRYSTAL | crystal.o
Default displacement distances Default displacement distances
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
...@@ -55,6 +57,7 @@ shown below:: ...@@ -55,6 +57,7 @@ shown below::
Abinit | 0.02 au (bohr) Abinit | 0.02 au (bohr)
Siesta | 0.02 au (bohr) Siesta | 0.02 au (bohr)
Elk | 0.02 au (bohr) Elk | 0.02 au (bohr)
CRYSTAL | 0.01 Angstrom
.. _nac_default_value_interfaces: .. _nac_default_value_interfaces:
...@@ -69,6 +72,7 @@ Default unit conversion factor for non-analytical term correction ...@@ -69,6 +72,7 @@ Default unit conversion factor for non-analytical term correction
Abinit | 51.422090 Abinit | 51.422090
Siesta | 51.422090 Siesta | 51.422090
Elk | 1 Elk | 1
CRYSTAL | 14.399652
Interface to force calculator Interface to force calculator
...@@ -85,6 +89,7 @@ Short tutorials for force calculators are found in the following pages. ...@@ -85,6 +89,7 @@ Short tutorials for force calculators are found in the following pages.
abinit abinit
siesta siesta
elk elk
crystal
Interface to VASP DFPT force constants Interface to VASP DFPT force constants
--------------------------------------- ---------------------------------------
......
...@@ -79,8 +79,9 @@ is 0.01.) ...@@ -79,8 +79,9 @@ is 0.01.)
The frequency unit conversion factor to THz has to be set by using the ``factor`` The frequency unit conversion factor to THz has to be set by using the ``factor``
keyword in ``Phonopy`` class. The factors are ``VaspToTHz`` for VASP, keyword in ``Phonopy`` class. The factors are ``VaspToTHz`` for VASP,
``Wien2kToTHz`` for Wien2k, ``AbinitToTHz`` for Abinit, ``Wien2kToTHz`` for Wien2k, ``AbinitToTHz`` for Abinit,
``PwscfToTHz`` for Pwscf, ``ElkToTHz`` for Elk, and ``SiestaToTHz`` ``PwscfToTHz`` for Pwscf, ``ElkToTHz`` for Elk, ``SiestaToTHz``
for Siesta. ``VaspToTHz`` is the default value. For example:: for Siesta, and ``CrystalToTHz for CRYSTAL``. ``VaspToTHz`` is the default value.
For example::
from phonopy.units import AbinitToTHz from phonopy.units import AbinitToTHz
......
...@@ -199,8 +199,8 @@ mean square displacements. ...@@ -199,8 +199,8 @@ mean square displacements.
The default values for calculators are those to convert frequency The default values for calculators are those to convert frequency
units to THz. The default conversion factors for ``wien2k``, units to THz. The default conversion factors for ``wien2k``,
``abinit``, ``pwscf``, and ``elk`` are 3.44595, 21.49068, 108.9708, ``abinit``, ``pwscf``, ``elk``, and CRYSTAL are 3.44595, 21.49068, 108.9708,
and 154.1079 respectively. These are determined following the physical 154.1079, and 15.633302 respectively. These are determined following the physical
unit systems of the calculators. How to calcualte these conversion unit systems of the calculators. How to calcualte these conversion
factors is explained at :ref:`physical_unit_conversion`. factors is explained at :ref:`physical_unit_conversion`.
......
NaCl phonon dispersions with non-analytical correction
CRYSTAL output file is crystal.o. This is the default file name
for the CRYSTAL interface, so, the -c crystal.o parameter is not needed
CRYSTAL output file crystal.o includes the Born effective
charges and the dielectric tensor
(from FREQCALC-INTENS-INTCPHF, see the input in the beginning of crystal.o)
1) Create displaced supercells:
phonopy --crystal --dim="4 4 4" -d
Complete CRYSTAL inputs can be prepared manually
or with the help of a template (see TEMPLATE)
2) Run the supercell inputs with CRYSTAL
Here supercell-001.o and supercell-002.o have been pre-calculated.
3) Collect forces:
phonopy --crystal -f supercell-*o
4) Calculate phonon dispersion data into band.yaml and save band.pdf:
phonopy --crystal --dim="4 4 4" -p -s band.conf
Take the non-analytical correction into account (see BORN file)
phonopy --crystal --dim="4 4 4" -p -s --nac band.conf
Plot the phonon dispersion in cm^{-1} units:
(factor = CrystalToTHz * THzToCm = 15.633302 * 33.356410)
phonopy --crystal --dim="4 4 4" -p -s --nac --factor=521.47083 band.conf
Create a formatted plot (here band.yaml is in cm^{-1) units):
bandplot --fmin=0 --line --ylabel="Frequency (cm\$^{-1}\$)" "--band_labels=`grep BAND_LABELS band.conf | cut -d= -f2-`" -o dispersion.pdf
11 5
0 0 5 2.0 1.0
4098.2003908 -.58535911879E-02
616.49374031 -.43647161872E-01
139.96644001 -.19431465884
39.073441051 -.48685065731
11.929847205 -.41881705137
0 0 3 2.0 1.0
20.659966030 .85949689854E-01
1.9838860978 -.56359144041
.64836323942 -.51954009048
0 0 1 1.0 1.0
0.32 1.0000000000
0 1 1 0.0 1.0
0.16 1.0 1.0
0 2 5 6.0 1.0
75.401862017 .154353625324E-01
17.274818978 .997382931840E-01
5.1842347425 .312095939659
1.6601211973 .492956748074
.51232528958 .324203983180
17 7
0 0 5 2.0 1.0
10449.827566 0.19708362484E-02
1571.7365221 0.14754727977E-01
357.12065523 0.66679112875E-01
100.25185935 0.17228924084
30.812727554 0.15883786100
0 0 3 2.0 1.0
51.923789434 -0.10009298909
5.7045760975 0.60841752753
2.3508376809 0.54352153355
0 0 1 2.0 1.0
0.49731621872 1.0000000000
0 1 1 0.0 1.0
0.21000000000 1.0 1.0
0 2 5 6.0 1.0
307.66790569 -0.87801484118E-02
72.102015515 -0.63563355471E-01
22.532680262 -0.24016428276
7.8991765444 -0.47798866557
2.8767268321 -0.38515850005
0 2 1 5.0 1.0
0.77358997479 1.0000000000
0 3 1 0.0 1.0
0.65000000000 1.0000000000
99 0
END
DFT
PBE0
END
SHRINK
1 1
TOLINTEG
8 8 8 8 16
MAXCYCLE
60
FMIXING
80
BROYDEN
0.01 50 4
NOSHIFT
EXCHSIZE
30000000
BIPOSIZE
30000000
BAND = 0 0 0 1/2 0 1/2 1/2 1/4 3/4 3/8 3/8 3/4 0 0 0 1/2 1/2 1/2 5/8 1/4 5/8 1/2 1/4 3/4 1/2 1/2 1/2 3/8 3/8 3/4, 5/8 1/4 5/8 1/2 0 1/2
BAND_LABELS = $\Gamma$ X W K $\Gamma$ L U W L K:U X
BAND_POINTS = 101
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Si phonon dispersions
CRYSTAL output file is crystal.o. This is the default file name
for the CRYSTAL interface, so, the -c crystal.o parameter is not needed
1) Create displaced supercells:
phonopy --crystal --dim="4 4 4" -d
Complete CRYSTAL inputs can be prepared manually
or with the help of a template (see TEMPLATE)
2) Run the supercell input with CRYSTAL
Here supercell-001.o has been pre-calculated.
3) Collect forces:
phonopy --crystal -f supercell-*o
4) Calculate phonon dispersion data into band.yaml and save band.pdf:
phonopy --crystal --dim="4 4 4" -p -s band.conf
Plot the phonon dispersion in cm^{-1} units:
(factor = CrystalToTHz * THzToCm = 15.633302 * 33.356410)
phonopy --crystal --dim="4 4 4" -p -s --factor=521.47083 band.conf
Create a formatted plot (here band.yaml is in cm^{-1) units):
bandplot --fmin=0 --line --ylabel="Frequency (cm\$^{-1}\$)" "--band_labels=`grep BAND_LABELS band.conf | cut -d= -f2-`" -o dispersion.pdf
14 7
0 0 5 2.0 1.0
6903.7118686 0.13373962995E-02
1038.4346419 0.99966546241E-02
235.87581480 0.44910165101E-01
66.069385169 0.11463638540
20.247945761 0.10280063858
0 0 3 2.0 1.0
34.353481730 0.70837285010E-01
3.6370788192 -0.43028836252
1.4002048599 -0.41382774969
0 0 1 2.0 1.0
0.25943211957 1.0000000000
0 1 1 0.0 1.0
0.12000000000 1.0 1.0
0 2 5 6.0 1.0
179.83907373 0.61916656462E-02
41.907258846 0.43399431982E-01
12.955294367 0.15632019351
4.4383267393 0.29419996982
1.5462247904 0.23536823814
0 2 1 2.0 1.0
0.40981363585 1.0000000000
0 3 1 0.0 1.0
0.35000000000 1.0000000000
99 0
ENDBAS
DFT
PBE0
END
SHRINK
1 1
TOLINTEG
8 8 8 8 16
MAXCYCLE
60
FMIXING
80
BROYDEN
0.01 50 4
NOSHIFT
EXCHSIZE
30000000
BIPOSIZE
30000000
BAND = 0 0 0 1/2 0 1/2 1/2 1/4 3/4 3/8 3/8 3/4 0 0 0 1/2 1/2 1/2 5/8 1/4 5/8 1/2 1/4 3/4 1/2 1/2 1/2 3/8 3/8 3/4, 5/8 1/4 5/8 1/2 0 1/2
BAND_LABELS = $\Gamma$ X W K $\Gamma$ L U W L K:U X
BAND_POINTS = 101
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