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
• 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 [email protected]: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.