The current implementation of minimum_image_displacement converts a displacement to fractional coordinates and rounds each periodic component independently:
dr_frac -= torch.where(pbc, torch.round(dr_frac), torch.zeros_like(dr_frac))
Component-wise rounding finds the minimum image for orthogonal cells, but not for a general triclinic cell. In a non-orthogonal lattice, minimizing each fractional component independently does not necessarily minimize the Cartesian norm.
Minimal example
import torch
from torch_sim.transforms import minimum_image_displacement
cell = torch.tensor(
[
[1.0, 0.9, 0.0],
[0.0, 0.1, 0.0],
[0.0, 0.0, 1.0],
],
dtype=torch.float64,
)
frac = torch.tensor([0.49, 0.49, 0.0], dtype=torch.float64)
dr = cell @ frac
mic = minimum_image_displacement(
dr=dr,
cell=cell,
pbc=torch.tensor([True, True, False]),
)
# The current implementation rounds frac to [0, 0, 0].
print(mic, torch.linalg.vector_norm(mic))
# tensor([0.9310, 0.0490, 0.0000]) tensor(0.9323)
# The image shifted by the second lattice vector is much closer.
closer_image = dr - cell[:, 1]
print(closer_image, torch.linalg.vector_norm(closer_image))
# tensor([ 0.0310, -0.0510, 0.0000]) tensor(0.0597)The minimum-image problem for a general cell is instead the closest-vector problem
n* = argmin_{n in Z^3} ||dr - cell @ n||
over shifts along the periodic lattice directions.
Would it make sense to use lattice reduction followed by enumeration of nearby images, or another bounded closest-vector implementation? Checking only the 27 images adjacent in fractional coordinates is sufficient for suitable reduced cells, but is not guaranteed for an arbitrary unreduced, highly skewed basis. If support is intentionally limited to orthogonal cells, documenting and validating that restriction would also prevent silently incorrect distances.
The current implementation of
minimum_image_displacementconverts a displacement to fractional coordinates and rounds each periodic component independently:Component-wise rounding finds the minimum image for orthogonal cells, but not for a general triclinic cell. In a non-orthogonal lattice, minimizing each fractional component independently does not necessarily minimize the Cartesian norm.
Minimal example
The minimum-image problem for a general cell is instead the closest-vector problem
over shifts along the periodic lattice directions.
Would it make sense to use lattice reduction followed by enumeration of nearby images, or another bounded closest-vector implementation? Checking only the 27 images adjacent in fractional coordinates is sufficient for suitable reduced cells, but is not guaranteed for an arbitrary unreduced, highly skewed basis. If support is intentionally limited to orthogonal cells, documenting and validating that restriction would also prevent silently incorrect distances.