def _expand_fc2(fc2_alm,
supercell,
pure_trans,
rotations,
symprec=1e-5,
verbose=True):
natom = supercell.get_number_of_atoms()
fc2 = np.zeros((natom, natom, 3, 3), dtype='double', order='C')
(fc_values, elem_indices) = fc2_alm
first_atoms = np.unique(elem_indices[:, 0] // 3)
for (fc, indices) in zip(fc_values, elem_indices):
v1 = indices[0] // 3
c1 = indices[0] % 3
v2 = indices[1] // 3
c2 = indices[1] % 3
fc2[v1, v2, c1, c2] = fc
lattice = np.array(supercell.get_cell().T, dtype='double', order='C')
positions = supercell.get_scaled_positions()
permutations = compute_all_sg_permutations(positions, rotations,
pure_trans, lattice, symprec)
distribute_force_constants(fc2, first_atoms, lattice, rotations,
permutations)
return fc2
def run_phonon_solver_with_eigvec_rotation(self):
"""Phonons at ir-grid-points are copied by proper rotations.
Some phonons that are not covered by rotations are solved.
The following data are updated.
self._frequencies
self._eigenvectors
self._phonon_done
"""
self._phonon_done[:] = 0
ir_grid_points, _, _ = get_ir_grid_points(self._bz_grid)
ir_bz_grid_points = self._bz_grid.grg2bzg[ir_grid_points]
self.run_phonon_solver(grid_points=ir_bz_grid_points)
d2r_map = self._get_reciprocal_rotations_in_space_group_operations()
# perms.shape = (len(spg_ops), len(primitive)), dtype='intc'
perms = compute_all_sg_permutations(
self._primitive.scaled_positions,
self._bz_grid.symmetry_dataset["rotations"],
self._bz_grid.symmetry_dataset["translations"],
np.array(self._primitive.cell.T, dtype="double", order="C"),
symprec=self._symprec,
)
for d_i, r_i in enumerate(d2r_map):
r = self._bz_grid.rotations[r_i]
r_cart = self._bz_grid.rotations_cartesian[r_i]
for irgp in ir_bz_grid_points:
bzgp = get_grid_points_by_rotations(
irgp,
self._bz_grid,
reciprocal_rotations=[
r,
],
with_surface=True,
)[0]
if self._phonon_done[bzgp]:
continue
self._rotate_eigvecs(irgp, bzgp, r_cart, perms[d_i], d_i)
bz_grid_points_solved = self._get_phonons_at_minus_q()
if bz_grid_points_solved:
print("DEBUG: BZ-grid points additionally solved "
"than ir-grid-points.")
qpoints = np.dot(
self._bz_grid.addresses[bz_grid_points_solved] /
self._bz_grid.D_diag.astype("double"),
self._bz_grid.Q.T,
)
distances = np.linalg.norm(np.dot(
qpoints,
np.linalg.inv(self._primitive.cell).T),
axis=1)
for qpt, dist in zip(qpoints, distances):
print(qpt, dist)
def get_constrained_fc2(supercell,
dataset_second_atoms,
atom1,
forces1,
reduced_site_sym,
symprec):
"""
dataset_second_atoms: [{'number': 7,
'displacement': [],
'forces': []}, ...]
"""
lattice = supercell.get_cell().T
positions = supercell.get_scaled_positions()
num_atom = supercell.get_number_of_atoms()
fc2 = np.zeros((num_atom, num_atom, 3, 3), dtype='double')
atom_list = np.unique([x['number'] for x in dataset_second_atoms])
for atom2 in atom_list:
disps2 = []
sets_of_forces = []
for disps_second in dataset_second_atoms:
if atom2 != disps_second['number']:
continue
bond_sym = get_bond_symmetry(
reduced_site_sym,
lattice,
positions,
atom1,
atom2,
symprec)
disps2.append(disps_second['displacement'])
sets_of_forces.append(disps_second['forces'] - forces1)
solve_force_constants(fc2,
atom2,
disps2,
sets_of_forces,
supercell,
bond_sym,
symprec)
# Shift positions according to set atom1 is at origin
pos_center = positions[atom1].copy()
positions -= pos_center
rotations = np.array(reduced_site_sym, dtype='intc', order='C')
translations = np.zeros((len(reduced_site_sym), 3),
dtype='double', order='C')
permutations = compute_all_sg_permutations(positions,
rotations,
translations,
lattice,
symprec)
distribute_force_constants(fc2,
atom_list,
lattice,
rotations,
permutations)
return fc2
def _set_atomic_permutations(self):
positions = self._cell.scaled_positions
lattice = np.array(self._cell.cell.T, dtype='double', order='C')
rotations = self._symmetry_operations['rotations']
translations = self._symmetry_operations['translations']
self._atomic_permutations = compute_all_sg_permutations(
positions, # scaled positions
rotations, # scaled
translations, # scaled
lattice, # column vectors
self._symprec)
def _set_atomic_permutations(self):
positions = self._cell.scaled_positions
lattice = np.array(self._cell.cell.T, dtype="double", order="C")
rotations = self._symmetry_operations["rotations"]
translations = self._symmetry_operations["translations"]
self._atomic_permutations = compute_all_sg_permutations(
positions, # scaled positions
rotations, # scaled
translations, # scaled
lattice, # column vectors
self._symprec,
)
def get_atomic_permutations(self):
if self._atomic_permutations is None:
positions = self._cell.get_scaled_positions()
lattice = np.array(self._cell.get_cell().T,
dtype='double', order='C')
rotations = self._symmetry_operations['rotations']
translations = self._symmetry_operations['translations']
self._atomic_permutations = compute_all_sg_permutations(
positions, # scaled positions
rotations, # scaled
translations, # scaled
lattice, # column vectors
self._symprec)
return self._atomic_permutations
def _test_compute_permutation(ph: Phonopy):
symmetry = ph.primitive_symmetry
ppos = ph.primitive.scaled_positions
plat = ph.primitive.cell.T
symprec = symmetry.tolerance
rots = symmetry.symmetry_operations["rotations"]
trans = symmetry.symmetry_operations["translations"]
perms = compute_all_sg_permutations(ppos, rots, trans, plat, symprec)
for i, (r, t) in enumerate(zip(rots, trans)):
ppos_rot = np.dot(ppos, r.T) + t
perm = compute_permutation_for_rotation(ppos, ppos_rot, plat, symprec)
np.testing.assert_array_equal(perms[i], perm)
diff = ppos[perm] - ppos_rot
diff -= np.rint(diff)
assert ((np.dot(diff, plat)**2).sum(axis=1) < symprec).all()
def _get_constrained_fc2(supercell, dataset_second_atoms, atom1, forces1,
reduced_site_sym, symprec):
"""Return fc2 under reduced (broken) site symmetry by first displacement.
dataset_second_atoms: [{'number': 7,
'displacement': [],
'forces': []}, ...]
"""
lattice = supercell.cell.T
positions = supercell.scaled_positions
num_atom = len(supercell)
fc2 = np.zeros((num_atom, num_atom, 3, 3), dtype="double")
atom_list = np.unique([x["number"] for x in dataset_second_atoms])
for atom2 in atom_list:
disps2 = []
sets_of_forces = []
for disps_second in dataset_second_atoms:
if atom2 != disps_second["number"]:
continue
bond_sym = get_bond_symmetry(reduced_site_sym, lattice, positions,
atom1, atom2, symprec)
disps2.append(disps_second["displacement"])
sets_of_forces.append(disps_second["forces"] - forces1)
solve_force_constants(fc2, atom2, disps2, sets_of_forces, supercell,
bond_sym, symprec)
# Shift positions according to set atom1 is at origin
pos_center = positions[atom1].copy()
positions -= pos_center
rotations = np.array(reduced_site_sym, dtype="intc", order="C")
translations = np.zeros((len(reduced_site_sym), 3),
dtype="double",
order="C")
permutations = compute_all_sg_permutations(positions, rotations,
translations, lattice, symprec)
distribute_force_constants(fc2, atom_list, lattice, rotations,
permutations)
return fc2
def _expand_fc3(fc3_alm,
supercell,
pure_trans,
rotations,
symprec=1e-5,
verbose=True):
(fc_values, elem_indices) = fc3_alm
natom = supercell.get_number_of_atoms()
fc3 = np.zeros((natom, natom, natom, 3, 3, 3), dtype='double', order='C')
first_atoms = np.unique(elem_indices[:, 0] // 3)
for (fc, indices) in zip(fc_values, elem_indices):
v1, v2, v3 = indices // 3
c1, c2, c3 = indices % 3
fc3[v1, v2, v3, c1, c2, c3] = fc
fc3[v1, v3, v2, c1, c3, c2] = fc
lattice = np.array(supercell.get_cell().T, dtype='double', order='C')
positions = supercell.get_scaled_positions()
s2compact = np.arange(supercell.get_number_of_atoms(), dtype='intc')
target_atoms = [i for i in s2compact if i not in first_atoms]
permutations = compute_all_sg_permutations(positions, rotations,
pure_trans, lattice, symprec)
if verbose:
print("Expanding fc3")
distribute_fc3(fc3,
first_atoms,
target_atoms,
lattice,
rotations,
permutations,
s2compact,
verbose=verbose)
return fc3