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# fmt: off
import math
from typing import List, Optional, Tuple, Union
import numpy as np
from ase import Atoms
from ase.cell import Cell
class CellTooSmall(Exception):
pass
class VolumeNotDefined(Exception):
pass
def get_rdf(atoms: Atoms, rmax: float, nbins: int,
distance_matrix: Optional[np.ndarray] = None,
elements: Optional[Union[List[int], Tuple]] = None,
no_dists: Optional[bool] = False,
volume: Optional[float] = None):
"""Returns two numpy arrays; the radial distribution function
and the corresponding distances of the supplied atoms object.
If no_dists = True then only the first array is returned.
Note that the rdf is computed following the standard solid state
definition which uses the cell volume in the normalization.
This may or may not be appropriate in cases where one or more
directions is non-periodic.
Parameters:
rmax : float
The maximum distance that will contribute to the rdf.
The unit cell should be large enough so that it encloses a
sphere with radius rmax in the periodic directions.
nbins : int
Number of bins to divide the rdf into.
distance_matrix : numpy.array
An array of distances between atoms, typically
obtained by atoms.get_all_distances().
Default None meaning that it will be calculated.
elements : list or tuple
List of two atomic numbers. If elements is not None the partial
rdf for the supplied elements will be returned.
no_dists : bool
If True then the second array with rdf distances will not be returned.
volume : float or None
Optionally specify the volume of the system. If specified, the volume
will be used instead atoms.cell.volume.
"""
# First check whether the cell is sufficiently large
vol = atoms.cell.volume if volume is None else volume
if vol < 1.0e-10:
raise VolumeNotDefined
check_cell_and_r_max(atoms, rmax)
dm = distance_matrix
if dm is None:
dm = atoms.get_all_distances(mic=True)
rdf = np.zeros(nbins + 1)
dr = float(rmax / nbins)
indices = np.asarray(np.ceil(dm / dr), dtype=int)
natoms = len(atoms)
if elements is None:
# Coefficients to use for normalization
phi = natoms / vol
norm = 2.0 * math.pi * dr * phi * len(atoms)
indices_triu = np.triu(indices)
for index in range(nbins + 1):
rdf[index] = np.count_nonzero(indices_triu == index)
else:
i_indices = np.where(atoms.numbers == elements[0])[0]
phi = len(i_indices) / vol
norm = 4.0 * math.pi * dr * phi * natoms
for i in i_indices:
for j in np.where(atoms.numbers == elements[1])[0]:
index = indices[i, j]
if index <= nbins:
rdf[index] += 1
rr = np.arange(dr / 2, rmax, dr)
rdf[1:] /= norm * (rr * rr + (dr * dr / 12))
if no_dists:
return rdf[1:]
return rdf[1:], rr
def check_cell_and_r_max(atoms: Atoms, rmax: float) -> None:
cell = atoms.get_cell()
pbc = atoms.get_pbc()
vol = atoms.cell.volume
for i in range(3):
if pbc[i]:
axb = np.cross(cell[(i + 1) % 3, :], cell[(i + 2) % 3, :])
h = vol / np.linalg.norm(axb)
if h < 2 * rmax:
recommended_r_max = get_recommended_r_max(cell, pbc)
raise CellTooSmall(
'The cell is not large enough in '
f'direction {i}: {h:.3f} < 2*rmax={2 * rmax: .3f}. '
f'Recommended rmax = {recommended_r_max}')
def get_recommended_r_max(cell: Cell, pbc: List[bool]) -> float:
recommended_r_max = 5.0
vol = cell.volume
for i in range(3):
if pbc[i]:
axb = np.cross(cell[(i + 1) % 3, :], # type: ignore[index]
cell[(i + 2) % 3, :]) # type: ignore[index]
h = vol / np.linalg.norm(axb)
assert isinstance(h, float) # mypy
recommended_r_max = min(h / 2 * 0.99, recommended_r_max)
return recommended_r_max
def get_containing_cell_length(atoms: Atoms) -> np.ndarray:
atom2xyz = atoms.get_positions()
return np.amax(atom2xyz, axis=0) - np.amin(atom2xyz, axis=0) + 2.0
def get_volume_estimate(atoms: Atoms) -> float:
return np.prod(get_containing_cell_length(atoms))
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