def symm_ops(gpname, axes=None):
if axes is not None:
raise PointGroupSymmetryError('TODO: non-standard orientation')
op1 = numpy.eye(3)
opi = -1
opc2z = -numpy.eye(3)
opc2z[2, 2] = 1
opc2x = -numpy.eye(3)
opc2x[0, 0] = 1
opc2y = -numpy.eye(3)
opc2y[1, 1] = 1
opcsz = numpy.dot(opc2z, opi)
opcsx = numpy.dot(opc2x, opi)
opcsy = numpy.dot(opc2y, opi)
opdic = {
'E': op1,
'C2z': opc2z,
'C2x': opc2x,
'C2y': opc2y,
'i': opi,
'sz': opcsz,
'sx': opcsx,
'sy': opcsy,
}
return opdic
def as_subgroup(topgroup, axes, subgroup=None):
from pyscf.symm import std_symb
from pyscf.symm.param import SUBGROUP
groupname, axes = get_subgroup(topgroup, axes)
if isinstance(subgroup, (str, unicode)):
subgroup = std_symb(subgroup)
if groupname == 'C2v' and subgroup == 'Cs':
axes = numpy.einsum('ij,kj->ki',
rotation_mat(axes[1], numpy.pi / 2), axes)
elif (groupname == 'D2' and re.search(r'D\d+d', topgroup)
and subgroup in ('C2v', 'Cs')):
# Special treatment for D2d, D4d, .... get_subgroup gives D2 by
# default while C2v is also D2d's subgroup.
groupname = 'C2v'
axes = numpy.einsum('ij,kj->ki',
rotation_mat(axes[2], numpy.pi / 4), axes)
elif topgroup in ('Td', 'T', 'Th') and subgroup == 'C2v':
x, y, z = axes
x = _normalize(x + y)
y = numpy.cross(z, x)
axes = numpy.array((x, y, z))
elif subgroup not in SUBGROUP[groupname]:
raise PointGroupSymmetryError('%s not in Ablien subgroup of %s' %
(subgroup, topgroup))
groupname = subgroup
return groupname, axes
def symm_identical_atoms(gpname, atoms):
''' Requires '''
from pyscf import gto
# Dooh Coov for linear molecule
if gpname == 'Dooh':
coords = numpy.array([a[1] for a in atoms], dtype=float)
idx0 = argsort_coords(coords)
coords0 = coords[idx0]
opdic = symm_ops(gpname)
newc = numpy.dot(coords, opdic['sz'])
idx1 = argsort_coords(newc)
dup_atom_ids = numpy.sort((idx0, idx1), axis=0).T
uniq_idx = numpy.unique(dup_atom_ids[:, 0], return_index=True)[1]
eql_atom_ids = dup_atom_ids[uniq_idx]
eql_atom_ids = [list(sorted(set(i))) for i in eql_atom_ids]
return eql_atom_ids
elif gpname == 'Coov':
eql_atom_ids = [[i] for i, a in enumerate(atoms)]
return eql_atom_ids
coords = numpy.array([a[1] for a in atoms])
# charges = numpy.array([gto.charge(a[0]) for a in atoms])
# center = numpy.einsum('z,zr->r', charges, coords)/charges.sum()
# if not numpy.allclose(center, 0, atol=TOLERANCE):
# sys.stderr.write('WARN: Molecular charge center %s is not on (0,0,0)\n'
# % center)
opdic = symm_ops(gpname)
ops = [opdic[op] for op in OPERATOR_TABLE[gpname]]
idx = argsort_coords(coords)
coords0 = coords[idx]
dup_atom_ids = []
for op in ops:
newc = numpy.dot(coords, op)
idx = argsort_coords(newc)
if not numpy.allclose(coords0, newc[idx], atol=TOLERANCE):
raise PointGroupSymmetryError('Symmetry identical atoms not found')
dup_atom_ids.append(idx)
dup_atom_ids = numpy.sort(dup_atom_ids, axis=0).T
uniq_idx = numpy.unique(dup_atom_ids[:, 0], return_index=True)[1]
eql_atom_ids = dup_atom_ids[uniq_idx]
eql_atom_ids = [list(sorted(set(i))) for i in eql_atom_ids]
return eql_atom_ids
def linearmole_irrep_symb2id(gpname, symb):
if gpname == 'Dooh':
if symb in DOOH_IRREP_ID_TABLE:
return DOOH_IRREP_ID_TABLE[symb]
else:
n = int(''.join([i for i in symb if i.isdigit()]))
if n % 2:
return (n // 2) * 10 + DOOH_IRREP_ID_TABLE['_odd' + symb[-2:]]
else:
return (n // 2) * 10 + DOOH_IRREP_ID_TABLE['_even' + symb[-2:]]
elif gpname == 'Coov':
if symb in COOV_IRREP_ID_TABLE:
return COOV_IRREP_ID_TABLE[symb]
else:
n = int(''.join([i for i in symb if i.isdigit()]))
if n % 2:
return (n // 2) * 10 + COOV_IRREP_ID_TABLE['_odd' + symb[-1]]
else:
return (n // 2) * 10 + COOV_IRREP_ID_TABLE['_even' + symb[-1]]
else:
raise PointGroupSymmetryError('%s is not proper for linear molecule.' %
gpname)
def dump_symm_adapted_basis(mol, so):
raise PointGroupSymmetryError('TODO')
def irrep_name(pgname, irrep_id):
raise PointGroupSymmetryError(
'This function was obsoleted. Use irrep_id2name')