Source code for hiphive.core.structure_alignment

import itertools
from typing import Union
import ase
import numpy as np
import spglib as spg
from . import atoms as atoms_module
from ..input_output.logging_tools import logger
from .utilities import ase_atoms_to_spglib_tuple

logger = logger.getChild('relate_structures')


[docs] def align_supercell( supercell: ase.Atoms, prim: ase.Atoms, symprec: float = None, ) -> tuple[ase.Atoms, np.ndarray, np.ndarray]: """Rotates and translates a supercell configuration such that it is aligned with the target primitive cell. Parameters ---------- supercell Supercell configuration. prim Target primitive configuration. symprec Precision parameter forwarded to spglib. Returns ------- Aligned supercell configuration as well as rotation matrix (`3x3` array) and translation vector (`3x1` array) that relate the input to the aligned supercell configuration. """ # TODO: Make sure the input is what we expect # find rotation and translation R, T = relate_structures(supercell, prim, symprec=symprec) # Create the aligned system aligned_supercell = rotate_atoms(supercell, R) aligned_supercell.translate(T) aligned_supercell.wrap() return aligned_supercell, R, T
[docs] def relate_structures( reference: ase.Atoms, target: ase.Atoms, symprec: float = 1e-5, ) -> tuple[np.ndarray, np.ndarray]: """Finds rotation and translation operations that align two structures with periodic boundary conditions. The rotation and translation in Cartesian coordinates will map the reference structure onto the target. Aligning the reference with the target structure can be achieved via the transformations:: R, T = relate_structures(atoms_ref, atoms_target) atoms_ref_rotated = rotate_atoms(atoms_ref, R) atoms_ref_rotated.translate(T) atoms_ref_rotated.wrap() atoms_ref_rotated == atoms_target Parameters ---------- reference Reference structure to be mapped. target Target structure. Returns ------- A tuple comprising the rotation matrix in Cartesian coordinates (`3x3` array) and the translation vector in Cartesian coordinates. """ logger.debug('Reference atoms:') _debug_log_atoms(reference) reference_primitive_cell = get_primitive_cell(reference, symprec=symprec) logger.debug('Reference primitive cell') _debug_log_atoms(reference_primitive_cell) logger.debug('Target atoms:') _debug_log_atoms(target) target_primitive_cell = get_primitive_cell(target, symprec=symprec) logger.debug('Target primitive cell') _debug_log_atoms(target_primitive_cell) logger.debug('Sane check that primitive cells can match...') _assert_structures_match(reference_primitive_cell, target_primitive_cell) logger.debug('Finding rotations...') rotations = _find_rotations(reference_primitive_cell.cell, target_primitive_cell.cell) logger.debug('Finding transformations...') for R in rotations: rotated_reference_primitive_cell = \ rotate_atoms(reference_primitive_cell, R) T = _find_translation(rotated_reference_primitive_cell, target_primitive_cell) if T is not None: break else: raise Exception(('Found no translation!\n' 'Reference primitive cell basis:\n' '{}\n' 'Target primitive cell basis:\n' '{}') .format(reference_primitive_cell.basis, target_primitive_cell.basis)) logger.debug(('Found rotation\n' '{}\n' 'and translation\n' '{}') .format(R, T)) return R, T
[docs] def is_rotation(R: np.ndarray, cell_metric: np.ndarray = None): """Checks if a rotation matrix is orthonormal. A cell metric can be passed if the rotation matrix is in scaled coordinates Parameters ---------- R Rotation matrix (`3x3` array). cell_metric Cell metric if the rotation is in scaled coordinates. """ if not cell_metric: cell_metric = np.eye(3) V = cell_metric V_inv = np.linalg.inv(V) lhs = np.linalg.multi_dot([V_inv, R.T, V, V.T, R, V_inv.T]) return np.allclose(lhs, np.eye(3), atol=1e-4) # TODO: tol
def _find_rotations(reference_cell_metric, target_cell_metric): """ Generates all proper and improper rotations aligning two cell metrics. """ rotations = [] V1 = reference_cell_metric for perm in itertools.permutations([0, 1, 2]): # Make sure the improper rotations are included for inv in itertools.product([1, -1], repeat=3): V2 = np.diag(inv) @ target_cell_metric[perm, :] R = np.linalg.solve(V1, V2).T # Make sure the rotation is orthonormal if is_rotation(R): for R_tmp in rotations: if np.allclose(R, R_tmp): # TODO: tol break else: rotations.append(R) assert rotations, ('Found no rotations! Reference cell metric:\n' '{}\n' 'Target cell metric:\n' '{}').format(reference_cell_metric, target_cell_metric) logger.debug('Found {} rotations'.format(len(rotations))) return rotations def _assert_structures_match(ref, prim): """ Asserts the structures are compatible with respect to number of atoms, atomic numbers and volume. TODO: tol """ if len(ref) != len(prim): raise ValueError( 'Number of atoms in reference primitive cell {} does not match ' 'target primitive {}'.format(len(ref), len(prim))) if sorted(ref.numbers) != sorted(prim.numbers): raise ValueError('Atomic numbers do not match\nReference: {}\nTarget:' ' {}\n'.format(ref.numbers, prim.numbers)) if not np.isclose(ref.get_volume(), prim.get_volume()): raise ValueError( 'Volume for reference primitive cell {} does not match target ' 'primitive cell {}\n'.format(ref.get_volume(), prim.get_volume()))
[docs] def get_primitive_cell( atoms: ase.Atoms, to_primitive: bool = True, no_idealize: bool = True, symprec: float = 1e-5, ) -> atoms_module.Atoms: """ Returns primitive cell obtained using spglib. Parameters ---------- atoms Atomic structure. to_primitive Passed to spglib. no_idealize Passed to spglib. symprec Numerical tolerance; passed to spglib. """ if not all(atoms.pbc): raise ValueError('atoms must have pbc.') atoms_as_tuple = ase_atoms_to_spglib_tuple(atoms) spg_primitive_cell = spg.standardize_cell(atoms_as_tuple, to_primitive=True, no_idealize=True, symprec=symprec) primitive_cell = atoms_module.Atoms(cell=spg_primitive_cell[0], scaled_positions=spg_primitive_cell[1], numbers=spg_primitive_cell[2], pbc=True) return primitive_cell
def _debug_log_atoms(atoms): logger.debug('cell:\n{}'.format(atoms.cell)) logger.debug('spos:\n{}'.format(atoms.get_scaled_positions())) logger.debug('pos:\n{}'.format(atoms.positions)) logger.debug('numbers:\n{}'.format(atoms.numbers))
[docs] def rotate_atoms( atoms: Union[ase.Atoms, atoms_module.Atoms], rotation: np.ndarray, ) -> atoms_module.Atoms: """Rotates the cell and positions of `atoms` and returns a copy. Parameters ---------- atoms Atomic structure. rotation Rotation matrix (`3x3` array). """ cell = np.dot(rotation, atoms.cell.T).T positions = np.dot(rotation, atoms.positions.T).T return atoms_module.Atoms(cell=cell, positions=positions, numbers=atoms.numbers, pbc=atoms.pbc)
def _find_translation(reference, target): """Returns the translation between two compatible atomic structures. The two structures must describe the same structure when infinitely repeated but differ by a translation. Parameters ---------- reference : ase.Atoms target : ase.Atoms Returns ------- numpy.ndarray or None translation vector or `None` if structures are incompatible """ atoms = atoms_module.Atoms(cell=target.cell, positions=reference.positions, numbers=reference.numbers, pbc=True) atoms.wrap() atoms_atom_0 = atoms[0] for atom in target: if atoms_atom_0.symbol != atom.symbol: continue T = atom.position - atoms_atom_0.position atoms_copy = atoms.copy() atoms_copy.positions += T if are_nonpaired_configurations_equal(atoms_copy, target): return T return None
[docs] def are_nonpaired_configurations_equal( atoms1: ase.Atoms, atoms2: ase.Atoms, ) -> bool: """ Checks whether two configurations are identical. To be considered equal the structures must have the same cell metric, elemental occupation, scaled positions (modulo one), and periodic boundary conditions. Unlike the ``__eq__`` operator of :class:`ase.Atoms` the order of the atoms does not matter. Parameters ---------- atoms1 atoms2 Returns ------- True if atoms are equal, False otherwise """ # TODO: add tolerance n_atoms = len(atoms1) if not (np.allclose(atoms1.cell, atoms2.cell, atol=1e-4) and n_atoms == len(atoms2) and sorted(atoms1.numbers) == sorted(atoms2.numbers) and all(atoms1.pbc == atoms2.pbc)): return False new_cell = (atoms1.cell + atoms2.cell) / 2 pos = [a.position for a in atoms1] + [a.position for a in atoms2] num = [a.number for a in atoms1] + [a.number for a in atoms2] s3 = atoms_module.Atoms(cell=new_cell, positions=pos, numbers=num, pbc=True) for i in range(n_atoms): for j in range(n_atoms, len(s3)): d = s3.get_distance(i, j, mic=True) if abs(d) < 1e-4: # TODO: tol if s3[i].number != s3[j].number: return False break else: return False return True