Spgrep#

Lines of code

Spgrep is a Python package of on-the-fly generator of space-group irreducible representations.

Github: spglib/spgrep
Document: https://spglib.github.io/spgrep
Document(develop): https://spglib.github.io/spgrep/develop/
PyPI: https://pypi.org/project/spgrep

Features#

Enumerate the following irreducible representations (irreps) of space groups from spglib’s cell and kpoints:
- Linear irreps
- Physically irreps (irreps over real numbers)
- Projective irreps for spnior
- Projective irreducible co-representations for spinor
Enumerate irreps of crystallographic point groups as well
Find symmetry-adapted basis forming given irreps
Minimal dependencies (numpy and spglib)

Usage#

from spgrep import get_spacegroup_irreps
from spgrep.representation import get_character

# Rutile structure (https://materialsproject.org/materials/mp-2657/)
# P4_2/mnm (No. 136)
a = 4.603
c = 2.969
x_4f = 0.3046
lattice = [
    [a, 0, 0],
    [0, a, 0],
    [0, 0, c],
]
positions = [
    [0, 0, 0],  # Ti(2a)
    [0.5, 0.5, 0.5],  # Ti(2a)
    [x_4f, x_4f, 0],  # O(4f)
    [-x_4f, -x_4f, 0],  # O(4f)
    [-x_4f + 0.5, x_4f + 0.5, 0.5],  # O(4f)
    [x_4f + 0.5, -x_4f + 0.5, 0.5],  # O(4f)
]
numbers = [0, 0, 1, 1, 1, 1]

kpoint = [0.5, 0, 0]  # X point
irreps, rotations, translations, mapping_little_group = get_spacegroup_irreps(
    lattice, positions, numbers, kpoint
)

# Symmetry operations by spglib
assert len(rotations) == 16
assert len(translations) == 16

# At X point, the little co-group is isomorphic to mmm (order=8)
assert len(mapping_little_group) == 8
print(mapping_little_group)  # [ 0,  1,  4,  5,  8,  9, 12, 13]

# Two two-dimensional irreps
for irrep in irreps:
    print(get_character(irrep))
# [2.+0.j 0.+0.j 0.+0.j 2.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]
# [2.+0.j 0.+0.j 0.+0.j -2.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]

See example pages for more detailed use cases and API summary for summary of functionalities.

Installation#

Spgrep works with Python3.8+ and can be installed via PyPI:

pip install spgrep

or in local:

conda create -n spgrep python=3.10 pip
conda activate spgrep
git clone git@github.com:spglib/spgrep.git
cd spgrep
pip install -e .

Change log#

See the change log for recent changes.

How to contribute#

We welcome any contributions to improve functionalities. Please open issues or create pull requests. See the development page for preparing an environment.

License#

Spgrep is released under a BSD 3-clause license.

Spgrep

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