def find_correspondences(structure, symmetry, tolerance):
"""
Map each symmetry operation to a permutation over the atoms in
structure.
"""
natoms = structure.get_number_of_atoms()
operations = symmetry.get_symmetry_operations()
translations = operations["translations"]
rotations = operations["rotations"]
correspondences = []
positions = structure.get_scaled_positions()
nsym = len(translations)
for isym in range(nsym):
remaining = list(range(natoms))
perm = []
for iatom in range(natoms):
dest = np.dot(rotations[isym, :, :],
positions[iatom, :]) + translations[isym, :]
dest %= 1.
for jatom in remaining:
delta = dest - positions[jatom, :]
delta -= np.round(delta)
if np.allclose(delta, 0., atol=tolerance):
remaining.remove(jatom)
perm.append(jatom)
break
else:
raise ValueError(
"the structure must have the specified symmetry")
correspondences.append(perm)
return tuplify(correspondences)
def get_crotations(structure, symmetry):
"""
Return the matrices representing the rotations in Cartesian
coordinates.
"""
lattvec = structure.cell.T
operations = symmetry.get_symmetry_operations()
rotations = operations["rotations"]
nruter = []
for r in rotations:
crotation = (np.dot(np.linalg.solve(lattvec.T, r.T), lattvec.T)).T
nruter.append(crotation * (np.fabs(crotation) >= 1e-12))
return nruter
def get_symmetry_information(sposcar_file):
"""
Obtain the symmetry information useful to compute the 2nd order force
constants irreducible elements.
"""
logging.basicConfig(level=0)
SYMPREC = 1e-5
if not os.path.isfile(sposcar_file):
sys.exit("The specified SPOSCAR file does not exist.")
supercell_matrix = np.diag([1, 1, 1])
structure = phonopy.interface.read_crystal_structure(sposcar_file,
"vasp")[0]
natoms = structure.get_number_of_atoms()
symmetry = phonopy.structure.symmetry.Symmetry(structure, symprec=SYMPREC)
dataset = symmetry.get_dataset()
print("Space group {0} ({1}) detected".format(dataset["international"],
dataset["number"]))
crotations = get_crotations(structure, symmetry)
operations = symmetry.get_symmetry_operations()
translations = operations["translations"]
rotations = operations["rotations"]
logging.debug("About to classify atom pairs")
permutations = find_correspondences(structure, symmetry, SYMPREC)
print("permutations: " + str(permutations))
equivalences = classify_pairs(structure, permutations)
logging.debug("{0} equivalence classes found".format(len(equivalences)))
for i, eq in enumerate(equivalences):
logging.debug("Equivalence class #{0}".format(i))
for il, l in enumerate(eq):
logging.debug("\t{0}. {1}".format(il + 1, l))
kernels = []
irreducible = []
for i, eq in enumerate(equivalences):
logging.debug("Representative of equivalence class #{0}".format(i))
invariances = find_invariances(eq[0][0], permutations)
logging.debug("is left invariant by {0} operations".format(
len(invariances)))
for iinv, inv in enumerate(invariances):
logging.debug("\t{0}. {1}".format(iinv, inv))
logging.debug("About to build the constraint matrix")
coefficients = get_constraints(
[crotations[inv] for inv in invariances])
rank = np.linalg.matrix_rank(coefficients)
logging.debug("{0} constraints".format(coefficients.shape[0]))
logging.debug(
"{0} independent components in this equivalence class:".format(
9 - rank))
if (rank > 0):
v = sp.linalg.svd(coefficients, full_matrices=False)[2].T
kernels.append(v[:, rank - 9:])
irreducible.append(complete_constraints(coefficients))
else:
kernels.append(np.identity(9))
irreducible.append([0, 1, 2, 3, 4, 5, 6, 7, 8])
for iirr, irr in enumerate(irreducible[-1]):
c1, c2 = np.unravel_index(irr, (3, 3))
logging.debug("\t{0}. {1}{2},{3}{4}".format(
iirr, eq[0][0][0], "xyz"[c1], eq[0][0][1], "xyz"[c2]))
irreducible = tuplify(irreducible)
todo = []
for eq, irr in zip(equivalences, irreducible):
a1, a2 = eq[0][0]
for i in irr:
print("a1", a1, "a2", a2, "i", np.unravel_index(i, (3, 3)))
todo += [dof2dof(a1, a2, i, natoms) for i in irr]
todo = tuplify(todo)
with open('out_sym', 'a') as file:
file.write("2nd order todo list before acoustic sum rule: " +
str(todo) + "\n")
file.write(
"number of irreducible elements before acoustic sum rule: " +
str(len(todo)) + "\n")
return [natoms, crotations, equivalences, kernels, irreducible, todo]