def is_dihedral(self):
""" Whether or not the reflection is a sigma_d
"""
if self.principal_reflection:
return False
for atom in self.molecule:
# If there's an atom in the plane, it's a sigma_v. If there's an atom in the direction of the normal (or it's negative),
# it's sigma_v. Otherwise, it's a sigma_d. If the atom is at the origin, ignore it.
if atom.pos.is_zero():
continue
elif SymmetryOperation.is_same_axis(self.axis, atom.pos):
return False
elif SymmetryOperation.is_perpendicular(self.axis, atom.pos):
return False
return True
def is_dihedral(self):
""" Whether or not the reflection is a sigma_d
"""
if self.principal_reflection:
return False
for atom in self.molecule:
# If there's an atom in the plane, it's a sigma_v. If there's an atom in the direction of the normal (or it's negative),
# it's sigma_v. Otherwise, it's a sigma_d. If the atom is at the origin, ignore it.
if atom.pos.is_zero():
continue
elif SymmetryOperation.is_same_axis(self.axis, atom.pos):
return False
elif SymmetryOperation.is_perpendicular(self.axis, atom.pos):
return False
return True
def _name_operations(self):
""" Determines the most-likely-to-be human-readable names for the operations.
"""
# Figure out the principal reflections (sigma_h's)
principal_rotations = []
for k, g in itertools.groupby(sorted(self.rotations),
attrgetter('n', 'exponent')):
principal_rotations = list(g)
break
if len(principal_rotations) > 0:
if principal_rotations[0].n > 2:
# Mark them all as sigma_h's
for rot in principal_rotations:
for op in self.reflections:
if SymmetryOperation.is_same_axis(op.axis, rot.axis):
op.principal_reflection = True
else:
# Otherwise, just choose the Z axis
for op in self.reflections:
if SymmetryOperation.is_same_axis(
op.axis, principal_rotations[0].axis):
op.principal_reflection = True
break
self.operations.sort()
self._rotations = None
self._improper_rotations = None
self._reflections = None
self.identity_element.name = "E"
if not self.inversion is None:
self.inversion.name = 'i'
for key, rotiter in itertools.groupby(self.rotations, attrgetter('n')):
rotgrp = list(rotiter)
prime_count = 0
labels = []
order = rotgrp[0].n
if len(rotgrp) == rotgrp[0].n - 1:
# only one axis, label it simply
rotgrp[0].name = "C_" + str(order)
for i in xrange(1, len(rotgrp)):
rotgrp[i].name = "C_" + str(order) + "^" + str(
rotgrp[i].exponent)
else:
naxes = len([x for x in rotgrp if x.exponent == 1])
has_paren_label = False
for i, rot in enumerate(rotgrp):
if i < naxes:
if SymmetryOperation.is_same_axis(
rot.axis, Vector(0, 0, 1)):
labels.append("(z)")
has_paren_label = True
rot.name = "C_" + str(order) + "(z)"
elif SymmetryOperation.is_same_axis(
rot.axis, Vector(0, 1, 1)):
labels.append("(y)")
has_paren_label = True
rot.name = "C_" + str(order) + "(y)"
elif SymmetryOperation.is_same_axis(
rot.axis, Vector(1, 0, 0)):
labels.append("(x)")
has_paren_label = True
rot.name = "C_" + str(order) + "(x)"
else:
label = "'" * (prime_count +
(1 if has_paren_label else 0))
labels.append(label)
prime_count += 1
rot.name = "C_" + str(order) + label
else:
rot.name = "C_" + str(order) + labels[
i % naxes] + "^" + str(rot.exponent)
for key, rotiter in itertools.groupby(self.improper_rotations,
attrgetter('n')):
rotgrp = list(rotiter)
prime_count = 0
labels = []
order = rotgrp[0].n
if len(rotgrp) == rotgrp[0].n - 1:
# only one axis, label it simply
rotgrp[0].name = "S_" + str(order)
for i in xrange(1, len(rotgrp)):
rotgrp[i].name = "S_" + str(order) + "^" + str(
rotgrp[i].exponent)
else:
has_paren_label = False
naxes = len([x for x in rotgrp if x.exponent == 1])
for i, rot in enumerate(rotgrp):
if i < naxes:
if SymmetryOperation.is_same_axis(
rot.axis, Vector(0, 0, 1)):
labels.append("(z)")
has_paren_label = True
rot.name = "S_" + str(order) + "(z)"
elif SymmetryOperation.is_same_axis(
rot.axis, Vector(0, 1, 0)):
labels.append("(y)")
has_paren_label = True
rot.name = "S_" + str(order) + "(y)"
elif SymmetryOperation.is_same_axis(
rot.axis, Vector(1, 0, 0)):
labels.append("(x)")
has_paren_label = True
rot.name = "S_" + str(order) + "(x)"
else:
label = "'" * (prime_count +
(1 if has_paren_label else 0))
labels.append(label)
prime_count += 1
rot.name = "S_" + str(order) + label
else:
rot.name = "S_" + str(order) + labels[
i % naxes] + "^" + str(rot.exponent)
prime_count = {'v': 0, 'd': 0, 'h': 0}
has_paren_label = False
for ref in self.reflections:
subscript = ''
if ref.is_principal_reflection():
subscript = 'h'
elif ref.is_dihedral():
subscript = 'd'
else:
subscript = 'v'
if SymmetryOperation.is_same_axis(ref.axis, Vector(0, 0, 1)):
ref.name = "sigma_" + subscript + "(xy)"
has_paren_label = True
elif SymmetryOperation.is_same_axis(ref.axis, Vector(0, 1, 0)):
ref.name = "sigma_" + subscript + "(xz)"
has_paren_label = True
elif SymmetryOperation.is_same_axis(ref.axis, Vector(1, 0, 0)):
ref.name = "sigma_" + subscript + "(yz)"
has_paren_label = True
else:
label = "'" * (prime_count[subscript] +
(1 if has_paren_label else 0))
prime_count[subscript] += 1
ref.name = "sigma_" + subscript + label
self.classes.sort(key=attrgetter('first_element'))
def _name_operations(self):
""" Determines the most-likely-to-be human-readable names for the operations.
"""
# Figure out the principal reflections (sigma_h's)
principal_rotations = []
for k, g in itertools.groupby(sorted(self.rotations), attrgetter('n', 'exponent')):
principal_rotations = list(g)
break
if len(principal_rotations) > 0:
if principal_rotations[0].n > 2:
# Mark them all as sigma_h's
for rot in principal_rotations:
for op in self.reflections:
if SymmetryOperation.is_same_axis(op.axis, rot.axis):
op.principal_reflection = True
else:
# Otherwise, just choose the Z axis
for op in self.reflections:
if SymmetryOperation.is_same_axis(op.axis, principal_rotations[0].axis):
op.principal_reflection = True
break
self.operations.sort()
self._rotations = None
self._improper_rotations = None
self._reflections = None
self.identity_element.name = "E"
if not self.inversion is None:
self.inversion.name = 'i'
for key, rotiter in itertools.groupby(self.rotations, attrgetter('n')):
rotgrp = list(rotiter)
prime_count = 0
labels = []
order = rotgrp[0].n
if len(rotgrp) == rotgrp[0].n - 1:
# only one axis, label it simply
rotgrp[0].name = "C_" + str(order)
for i in xrange(1, len(rotgrp)):
rotgrp[i].name = "C_" + str(order) + "^" + str(rotgrp[i].exponent)
else:
naxes = len([x for x in rotgrp if x.exponent == 1])
has_paren_label = False
for i, rot in enumerate(rotgrp):
if i < naxes:
if SymmetryOperation.is_same_axis(rot.axis, Vector(0,0,1)):
labels.append("(z)")
has_paren_label = True
rot.name = "C_" + str(order) + "(z)"
elif SymmetryOperation.is_same_axis(rot.axis, Vector(0,1,1)):
labels.append("(y)")
has_paren_label = True
rot.name = "C_" + str(order) + "(y)"
elif SymmetryOperation.is_same_axis(rot.axis, Vector(1,0,0)):
labels.append("(x)")
has_paren_label = True
rot.name = "C_" + str(order) + "(x)"
else:
label = "'" * (prime_count + (1 if has_paren_label else 0))
labels.append(label)
prime_count += 1
rot.name = "C_" + str(order) + label
else:
rot.name = "C_" + str(order) + labels[i % naxes] + "^" + str(rot.exponent)
for key, rotiter in itertools.groupby(self.improper_rotations, attrgetter('n')):
rotgrp = list(rotiter)
prime_count = 0
labels = []
order = rotgrp[0].n
if len(rotgrp) == rotgrp[0].n - 1:
# only one axis, label it simply
rotgrp[0].name = "S_" + str(order)
for i in xrange(1, len(rotgrp)):
rotgrp[i].name = "S_" + str(order) + "^" + str(rotgrp[i].exponent)
else:
has_paren_label = False
naxes = len([x for x in rotgrp if x.exponent == 1])
for i, rot in enumerate(rotgrp):
if i < naxes:
if SymmetryOperation.is_same_axis(rot.axis, Vector(0,0,1)):
labels.append("(z)")
has_paren_label = True
rot.name = "S_" + str(order) + "(z)"
elif SymmetryOperation.is_same_axis(rot.axis, Vector(0,1,0)):
labels.append("(y)")
has_paren_label = True
rot.name = "S_" + str(order) + "(y)"
elif SymmetryOperation.is_same_axis(rot.axis, Vector(1,0,0)):
labels.append("(x)")
has_paren_label = True
rot.name = "S_" + str(order) + "(x)"
else:
label = "'" * (prime_count + (1 if has_paren_label else 0))
labels.append(label)
prime_count += 1
rot.name = "S_" + str(order) + label
else:
rot.name = "S_" + str(order) + labels[i % naxes] + "^" + str(rot.exponent)
prime_count = {'v':0, 'd':0,'h':0}
has_paren_label = False
for ref in self.reflections:
subscript = ''
if ref.is_principal_reflection():
subscript = 'h'
elif ref.is_dihedral():
subscript = 'd'
else:
subscript = 'v'
if SymmetryOperation.is_same_axis(ref.axis, Vector(0,0,1)):
ref.name = "sigma_"+ subscript + "(xy)"
has_paren_label = True
elif SymmetryOperation.is_same_axis(ref.axis, Vector(0,1,0)):
ref.name = "sigma_" + subscript + "(xz)"
has_paren_label = True
elif SymmetryOperation.is_same_axis(ref.axis, Vector(1,0,0)):
ref.name = "sigma_" + subscript + "(yz)"
has_paren_label = True
else:
label = "'" * (prime_count[subscript] + (1 if has_paren_label else 0))
prime_count[subscript] += 1
ref.name = "sigma_" + subscript + label
self.classes.sort(key=attrgetter('first_element'))
