Spgrep

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

• GitHub: https://github.com/spglib/spgrep
• Document: https://spglib.github.io/spgrep
• 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 Python3.10+ and can be installed via PyPI:

pip install spgrep

or in local:

git clone git@github.com:spglib/spgrep.git
cd spgrep
pip install -e .

Change log

See the change log for recent changes.

How to cite spgrep

If you use spgrep in your research, please consider citing the following work:

• Kohei Shinohara, Atsushi Togo, Isao Tanaka, spgrep: On-the-fly generator of space-group irreducible representations, J. Open Source Softw. 8, 85, 5269 (2023)

@article{spgrep,
    doi = {10.21105/joss.05269},
    url = {https://doi.org/10.21105/joss.05269},
    year = {2023},
    publisher = {The Open Journal},
    volume = {8},
    number = {85},
    pages = {5269},
    author = {Shinohara, Kohei and Togo, Atsushi and Tanaka, Isao},
    title = {spgrep: On-the-fly generator of space-group irreducible representations},
    journal = {J. Open Source Softw.}
}

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.