def get_fourth_order_displacements(cell,
symmetry,
is_plusminus='auto',
is_diagonal=False):
# Atoms 1, 2, and 3 are defined as follows:
#
# Atom 1: The first displaced atom. Fourth order force constant
# between Atoms 1, 2, 3, and 4 is calculated.
# Atom 2: The second displaced atom. Third order force constant
# between Atoms 2, 3, and 4 is calculated.
# Atom 3: The third displaced atom. Second order force constant
# between Atoms 3 and 4 is calculated.
# Atom 4: Force is mesuared on this atom.
# Least displacements for third order force constants
#
# Data structure
# [{'number': atom1,
# 'displacement': [0.00000, 0.007071, 0.007071],
# 'second_atoms': [ {'number': atom2,
# 'displacement': [0.007071, 0.000000, 0.007071],
# 'third_atoms': [ {'number': atom3,
# 'displacements':
# [[-0.007071, 0.000000, -0.007071],
# ,...]}, {...}, ... ]},
# Least displacements of first atoms (Atom 1) are searched by
# using respective site symmetries of the original crystal.
disps_first = get_least_displacements(symmetry,
is_plusminus=is_plusminus,
is_diagonal=False)
symprec = symmetry.get_symmetry_tolerance()
dds = []
for disp in disps_first:
atom1 = disp[0]
disp1 = disp[1:4]
site_sym = symmetry.get_site_symmetry(atom1)
dds_atom1 = {'number': atom1, 'direction': disp1, 'second_atoms': []}
reduced_site_sym = get_reduced_site_symmetry(site_sym, disp1, symprec)
second_atoms = get_least_orbits(atom1, cell, reduced_site_sym, symprec)
for atom2 in second_atoms:
reduced_bond_sym = get_bond_symmetry(reduced_site_sym,
cell.get_scaled_positions(),
atom1, atom2, symprec)
for disp2 in _get_displacements_second(reduced_bond_sym, symprec,
is_diagonal):
dds_atom2 = _get_second_displacements(atom2, disp2, cell,
reduced_bond_sym,
symprec, is_diagonal)
dds_atom1['second_atoms'].append(dds_atom2)
dds.append(dds_atom1)
write_supercells_with_three_displacements(cell, dds)
return dds
def _get_second_displacements(atom2,
disp2,
cell,
reduced_bond_sym,
symprec,
is_diagonal):
positions = cell.get_scaled_positions()
dds_atom2 = {'number': atom2,
'direction': disp2,
'third_atoms': []}
reduced_bond_sym2 = get_reduced_site_symmetry(reduced_bond_sym,
disp2,
symprec)
third_atoms = get_least_orbits(atom2,
cell,
reduced_bond_sym2,
symprec)
for atom3 in third_atoms:
reduced_plane_sym = get_bond_symmetry(
reduced_bond_sym2,
cell.get_scaled_positions(),
atom2,
atom3,
symprec)
dds_atom3 = get_next_displacements(atom2,
atom3,
reduced_plane_sym,
positions,
symprec,
is_diagonal)
dds_atom2['third_atoms'].append(dds_atom3)
return dds_atom2
def _get_reduced_bond_sym(self, reduced_site_sym, first_atom_num,
second_atom_num, disp2):
bond_sym = get_bond_symmetry(reduced_site_sym, self._positions,
first_atom_num, second_atom_num,
self._symprec)
direction = np.dot(np.linalg.inv(self._lattice), disp2)
reduced_bond_sym = get_reduced_site_symmetry(bond_sym, direction,
self._symprec)
return reduced_bond_sym
def get_constrained_fc2(
supercell,
dataset_second_atoms,
atom1,
reduced_site_sym,
translational_symmetry_type,
is_permutation_symmetry,
symprec,
):
"""
dataset_second_atoms: [{'number': 7,
'displacement': [],
'delta_forces': []}, ...]
"""
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, supercell.get_scaled_positions(), atom1, atom2, symprec)
disps2.append(disps_second["displacement"])
sets_of_forces.append(disps_second["delta_forces"])
solve_force_constants(fc2, atom2, disps2, sets_of_forces, supercell, bond_sym, symprec)
# Shift positions according to set atom1 is at origin
lattice = supercell.get_cell().T
positions = supercell.get_scaled_positions()
pos_center = positions[atom1].copy()
positions -= pos_center
distribute_force_constants(
fc2,
range(num_atom),
atom_list,
lattice,
positions,
np.array(reduced_site_sym, dtype="intc", order="C"),
np.zeros((len(reduced_site_sym), 3), dtype="double"),
symprec,
)
if translational_symmetry_type:
set_translational_invariance(fc2, translational_symmetry_type=translational_symmetry_type)
if is_permutation_symmetry:
set_permutation_symmetry(fc2)
return fc2
def get_fourth_order_displacements(cell, symmetry, is_plusminus="auto", is_diagonal=False):
# Atoms 1, 2, and 3 are defined as follows:
#
# Atom 1: The first displaced atom. Fourth order force constant
# between Atoms 1, 2, 3, and 4 is calculated.
# Atom 2: The second displaced atom. Third order force constant
# between Atoms 2, 3, and 4 is calculated.
# Atom 3: The third displaced atom. Second order force constant
# between Atoms 3 and 4 is calculated.
# Atom 4: Force is mesuared on this atom.
# Least displacements for third order force constants
#
# Data structure
# [{'number': atom1,
# 'displacement': [0.00000, 0.007071, 0.007071],
# 'second_atoms': [ {'number': atom2,
# 'displacement': [0.007071, 0.000000, 0.007071],
# 'third_atoms': [ {'number': atom3,
# 'displacements':
# [[-0.007071, 0.000000, -0.007071],
# ,...]}, {...}, ... ]},
# Least displacements of first atoms (Atom 1) are searched by
# using respective site symmetries of the original crystal.
disps_first = get_least_displacements(symmetry, is_plusminus=is_plusminus, is_diagonal=False)
symprec = symmetry.get_symmetry_tolerance()
dds = []
for disp in disps_first:
atom1 = disp[0]
disp1 = disp[1:4]
site_sym = symmetry.get_site_symmetry(atom1)
dds_atom1 = {"number": atom1, "direction": disp1, "second_atoms": []}
reduced_site_sym = get_reduced_site_symmetry(site_sym, disp1, symprec)
second_atoms = get_least_orbits(atom1, cell, reduced_site_sym, symprec)
for atom2 in second_atoms:
reduced_bond_sym = get_bond_symmetry(reduced_site_sym, cell.get_scaled_positions(), atom1, atom2, symprec)
for disp2 in _get_displacements_second(reduced_bond_sym, symprec, is_diagonal):
dds_atom2 = _get_second_displacements(atom2, disp2, cell, reduced_bond_sym, symprec, is_diagonal)
dds_atom1["second_atoms"].append(dds_atom2)
dds.append(dds_atom1)
write_supercells_with_three_displacements(cell, dds)
return dds
def _get_reduced_bond_sym(self,
reduced_site_sym,
first_atom_num,
second_atom_num,
disp2):
bond_sym = get_bond_symmetry(
reduced_site_sym,
self._positions,
first_atom_num,
second_atom_num,
self._symprec)
direction = np.dot(np.linalg.inv(self._lattice), disp2)
reduced_bond_sym = get_reduced_site_symmetry(
bond_sym, direction, self._symprec)
return reduced_bond_sym
def get_constrained_fc2(supercell, dataset_second_atoms, atom1,
reduced_site_sym, translational_symmetry_type,
is_permutation_symmetry, symprec):
"""
dataset_second_atoms: [{'number': 7,
'displacement': [],
'delta_forces': []}, ...]
"""
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])
atom_list_done = []
for atom2 in atom_list:
disps2 = []
sets_of_forces = []
for disps_second in dataset_second_atoms:
if atom2 != disps_second['number']:
continue
atom_list_done.append(atom2)
bond_sym = get_bond_symmetry(reduced_site_sym,
supercell.get_scaled_positions(),
atom1, atom2, symprec)
disps2.append(disps_second['displacement'])
sets_of_forces.append(disps_second['delta_forces'])
solve_force_constants(fc2, atom2, disps2, sets_of_forces, supercell,
bond_sym, symprec)
# Shift positions according to set atom1 is at origin
lattice = supercell.get_cell().T
positions = supercell.get_scaled_positions()
pos_center = positions[atom1].copy()
positions -= pos_center
distribute_force_constants(
fc2, range(num_atom), atom_list_done, lattice, positions,
np.array(reduced_site_sym, dtype='intc', order='C'),
np.zeros((len(reduced_site_sym), 3), dtype='double'), symprec)
if translational_symmetry_type:
set_translational_invariance(
fc2, translational_symmetry_type=translational_symmetry_type)
if is_permutation_symmetry:
set_permutation_symmetry(fc2)
return fc2
def _get_second_displacements(atom2, disp2, cell, reduced_bond_sym, symprec,
is_diagonal):
positions = cell.get_scaled_positions()
dds_atom2 = {'number': atom2, 'direction': disp2, 'third_atoms': []}
reduced_bond_sym2 = get_reduced_site_symmetry(reduced_bond_sym, disp2,
symprec)
third_atoms = get_least_orbits(atom2, cell, reduced_bond_sym2, symprec)
for atom3 in third_atoms:
reduced_plane_sym = get_bond_symmetry(reduced_bond_sym2,
cell.get_scaled_positions(),
atom2, atom3, symprec)
dds_atom3 = get_next_displacements(atom2, atom3, reduced_plane_sym,
positions, symprec, is_diagonal)
dds_atom2['third_atoms'].append(dds_atom3)
return dds_atom2
def _get_constrained_fc3(supercell, displacements, reduced_site_sym,
translational_symmetry_type, is_permutation_symmetry,
symprec, verbose):
"""
Two displacements and force constants calculation (e.g. DFPT)
displacements = {'number': 3,
'displacement': [0.01, 0.00, 0.01]
'second_atoms': [{'number': 7,
'displacement': [],
'delta_fc2': }]}
Three displacements and force calculation
displacements = {'number': 3,
'displacement': [0.01, 0.00, 0.01]
'second_atoms': [{'number': 7,
'displacement': [],
'third_atoms': ... }]}
third_atoms is like:
'third_atoms': [{'number': 56,
'displacement': [],
'delta_forces': ... }]}
"""
num_atom = supercell.get_number_of_atoms()
atom1 = displacements['number']
disp1 = displacements['displacement']
delta_fc3 = np.zeros((num_atom, num_atom, num_atom, 3, 3, 3),
dtype='double')
if 'delta_forces' in displacements['second_atoms'][0]:
fc2_with_one_disp = get_constrained_fc2(
supercell, displacements['second_atoms'], atom1, reduced_site_sym,
translational_symmetry_type, is_permutation_symmetry, symprec)
atom_list = np.unique([x['number'] for x in displacements['second_atoms']])
for atom2 in atom_list:
bond_sym = get_bond_symmetry(reduced_site_sym,
supercell.get_scaled_positions(), atom1,
atom2, symprec)
disps2 = []
delta_fc2s = []
for disps_second in displacements['second_atoms']:
if atom2 != disps_second['number']:
continue
disps2.append(disps_second['displacement'])
if 'delta_fc2' in disps_second:
delta_fc2s.append(disps_second['delta_fc2'])
else:
direction = np.dot(disps_second['displacement'],
np.linalg.inv(supercell.get_cell()))
reduced_bond_sym = get_reduced_site_symmetry(
bond_sym, direction, symprec)
delta_fc2s.append(
get_delta_fc2(disps_second['third_atoms'], atom2,
fc2_with_one_disp, supercell,
reduced_bond_sym,
translational_symmetry_type,
is_permutation_symmetry, symprec))
if verbose > 1:
print("Second displacements for fc4[ %d, %d, x, x ]" %
(atom1 + 1, atom2 + 1))
for i, v in enumerate(disps2):
print " [%7.4f %7.4f %7.4f]" % tuple(v)
solve_fc3(delta_fc3,
atom2,
supercell,
bond_sym,
disps2,
delta_fc2s,
symprec=symprec,
verbose=False)
# Shift positions according to set atom1 is at origin
lattice = supercell.get_cell().T
positions = supercell.get_scaled_positions()
pos_center = positions[atom1].copy()
positions -= pos_center
if verbose:
print "Expanding delta fc3"
distribute_fc3(delta_fc3,
atom_list,
lattice,
positions,
np.array(reduced_site_sym, dtype='intc', order='C'),
np.zeros((len(reduced_site_sym), 3), dtype='double'),
symprec,
verbose=verbose)
if translational_symmetry_type > 0:
set_translational_invariance_fc3_per_index(delta_fc3)
if is_permutation_symmetry:
set_permutation_symmetry_fc3(delta_fc3)
return delta_fc3
def _get_constrained_fc3(supercell,
displacements,
reduced_site_sym,
is_translational_symmetry,
is_permutation_symmetry,
symprec,
verbose):
"""
Two displacements and force constants calculation (e.g. DFPT)
displacements = {'number': 3,
'displacement': [0.01, 0.00, 0.01]
'second_atoms': [{'number': 7,
'displacement': [],
'delta_fc2': }]}
Three displacements and force calculation
displacements = {'number': 3,
'displacement': [0.01, 0.00, 0.01]
'second_atoms': [{'number': 7,
'displacement': [],
'third_atoms': ... }]}
third_atoms is like:
'third_atoms': [{'number': 56,
'displacement': [],
'delta_forces': ... }]}
"""
num_atom = supercell.get_number_of_atoms()
atom1 = displacements['number']
disp1 = displacements['displacement']
fc3 = np.zeros((num_atom, num_atom, num_atom, 3, 3, 3), dtype='double')
atom_list_done = []
if 'delta_forces' in displacements['second_atoms'][0]:
fc2_with_one_disp = get_constrained_fc2(supercell,
displacements['second_atoms'],
atom1,
reduced_site_sym,
is_translational_symmetry,
is_permutation_symmetry,
symprec)
atom_list = np.unique([x['number'] for x in displacements['second_atoms']])
for atom2 in atom_list:
disps2 = []
delta_fc2s = []
for disps_second in displacements['second_atoms']:
if atom2 != disps_second['number']:
continue
atom_list_done.append(atom2)
bond_sym = get_bond_symmetry(
reduced_site_sym,
supercell.get_scaled_positions(),
atom1,
atom2,
symprec)
disps2.append(disps_second['displacement'])
if 'delta_fc2' in disps_second:
delta_fc2s.append(disps_second['delta_fc2'])
else:
direction = np.dot(disps_second['displacement'],
np.linalg.inv(supercell.get_cell()))
reduced_bond_sym = get_reduced_site_symmetry(
bond_sym, direction, symprec)
delta_fc2s.append(get_delta_fc2(
disps_second['third_atoms'],
atom2,
fc2_with_one_disp,
supercell,
reduced_bond_sym,
is_translational_symmetry,
is_permutation_symmetry,
symprec))
if verbose > 1:
print ("Second displacements for fc4[ %d, %d, x, x ]" %
(atom1 + 1, atom2 + 1))
for i, v in enumerate(disps2):
print " [%7.4f %7.4f %7.4f]" % tuple(v)
solve_fc3(fc3,
atom2,
supercell,
bond_sym,
disps2,
delta_fc2s,
symprec=symprec)
# Shift positions according to set atom1 is at origin
lattice = supercell.get_cell().T
positions = supercell.get_scaled_positions()
pos_center = positions[atom1].copy()
positions -= pos_center
if verbose:
print "(Copying delta fc3...)"
distribute_fc3(fc3,
atom_list_done,
lattice,
positions,
np.intc(reduced_site_sym).copy(),
np.zeros((len(reduced_site_sym), 3), dtype='double'),
symprec,
verbose)
if is_translational_symmetry:
set_translational_invariance_fc3_per_index(fc3)
if is_permutation_symmetry:
set_permutation_symmetry_fc3(fc3)
return fc3
