`structure.get_reduced_structure(reduction_algo="niggli")` returns a reflected structure

[vsimkus]

Python version

Python 3.11.12

Pymatgen version

2025.2.18

Operating system version

MacOS 24.5.0

Current behavior

Hi, thanks for such a great package! I am having some trouble with the Niggli reduction, and unless I am misunderstanding something I think there is a bug in the final mapping.

The issue: Running structure.get_reduced_structure(reduction_algo="niggli") sometimes returns a reflected version of the original system. The core issue is in the final mapping at the following lines:

pymatgen/src/pymatgen/core/lattice.py

Lines 1274 to 1278 in f9d9fe8

	mapped = self.find_mapping(lattice, e, skip_rotation_matrix=True)
	if mapped is not None:
	if np.linalg.det(mapped[0].matrix) > 0:
	return mapped[0] # type:ignore[return-value]
	return type(self)(-mapped[0].matrix)

If you switchskip_rotation_matrix=False and check the determinant of the rotation matrix, you'll get -1, corresponding to a reflection matrix.

Let me know if I'm misunderstanding something and this is an intended behavior!

Below I've provided a snippet that shows the source of the issue: the find_mapping method returns a reflection mapping, even when the source and target lattices are the same!

Thanks again!

Expected Behavior

I would expect that find_mapping returns a rotated lattice but not a reflection. While a reflected system has the same energy, it's physical properties can be different.

Minimal example

import ase
import ase.io
import numpy as np
from pymatgen.io.ase import AseAtomsAdaptor


def get_atoms():
    atoms = ase.Atoms(
        positions=np.array(
            [
                [0.00000000e00, 0.00000000e00, 0.00000000e00],
                [2.32160500e00, -2.55395379e-10, 2.62836300e00],
                [-2.55396948e-10, 2.32160500e00, 2.62836300e00],
                [2.32160500e00, 2.32160500e00, -6.87146875e-17],
                [2.85942205e-10, -2.85941836e-10, 2.94272573e00],
                [-4.80245259e-10, 2.32160500e00, 3.14362728e-01],
                [2.32160500e00, 2.32160500e00, 2.31400027e00],
                [-3.05465285e-11, 2.32160500e00, 4.94236327e00],
            ]
        ),
        numbers=np.array([11, 11, 65, 65, 8, 8, 8, 8]),
        cell=[
            [4.643209998612975, 0.0, 0.0],
            [-1.0215833248797727e-09, 4.643209998612975, 0.0],
            [-2.3216049982849043, -2.3216049998172785, 5.2567259980108245],
        ],
        pbc=True,
    )
    return atoms


if __name__ == "__main__":
    atoms = get_atoms()
    ase.io.write("original.png", atoms)
    ase.io.write("original.cif", atoms)

    structure = AseAtomsAdaptor.get_structure(atoms)
    # structure = structure.get_reduced_structure(reduction_algo="niggli")
    tol = 1e-5
    e = tol * structure._lattice.volume ** (1 / 3)
    # Compute a lattice mapping between it and itself
    mapping, rotation_matrix, translation_vector = structure._lattice.find_mapping(
        structure._lattice, e, skip_rotation_matrix=False
    )
    print(np.linalg.det(rotation_matrix)).    # ----> prints -1, corresponding to a reflection!
    structure_mapped = type(structure)(
        mapping,
        structure.species_and_occu,
        structure.cart_coords,
        coords_are_cartesian=True,
        to_unit_cell=True,
        site_properties=structure.site_properties,
        labels=structure.labels,
        charge=structure._charge,
    )
    atoms_mapped = AseAtomsAdaptor.get_atoms(structure_mapped)
    ase.io.write("mapped.png", atoms_mapped)
    ase.io.write("mapped.cif", atoms_mapped)

Relevant files to reproduce this bug

No response