def test_orth_ao(self):
c0 = orth.pre_orth_ao(mol, method='scf')
self.assertAlmostEqual(abs(c0).sum(), 33.48215772351, 8)
c = orth.orth_ao(mol, 'lowdin', c0)
self.assertAlmostEqual(abs(c).sum(), 94.21571091299639, 8)
c = orth.orth_ao(mol, 'meta_lowdin', c0)
self.assertAlmostEqual(abs(c).sum(), 92.15697348744733, 8)
def test_pre_orth_ao_with_ecp(self):
mol = gto.M(atom='Cu 0. 0. 0.; H 0. 0. -1.56; H 0. 0. 1.56',
basis={'Cu':'lanl2dz', 'H':'ccpvdz'},
ecp = {'cu':'lanl2dz'},
charge=-1,
verbose=0)
c0 = orth.pre_orth_ao(mol, method='ano')
self.assertAlmostEqual(numpy.linalg.norm(c0), 5.9621174285790959, 9)
def test_pre_orth_ao_with_ecp(self):
mol = gto.M(atom='Cu 0. 0. 0.; H 0. 0. -1.56; H 0. 0. 1.56',
basis={'Cu':'lanl2dz', 'H':'ccpvdz'},
ecp = {'cu':'lanl2dz'},
charge=-1,
verbose=0)
c0 = orth.pre_orth_ao(mol, method='ano')
self.assertAlmostEqual(numpy.linalg.norm(c0), 5.9621174285790959, 9)
def test_orth_ao(self):
c0 = orth.pre_orth_ao(mol, method='scf')
self.assertAlmostEqual(numpy.linalg.norm(c0), 7.2617698799320358, 9)
self.assertAlmostEqual(abs(c0).sum(), 40.116080631662804, 8)
c = orth.orth_ao(mol, 'lowdin', c0)
self.assertAlmostEqual(numpy.linalg.norm(c), 10.967144073462256, 9)
self.assertAlmostEqual(abs(c).sum(), 112.23459140302003, 8)
c = orth.orth_ao(mol, 'meta_lowdin', c0)
self.assertAlmostEqual(numpy.linalg.norm(c), 10.967144073462256, 9)
self.assertAlmostEqual(abs(c).sum(), 111.61017124719302, 8)
def test_orth_ao(self):
c0 = orth.pre_orth_ao(mol, method='scf')
self.assertAlmostEqual(numpy.linalg.norm(c0), 5.7742626195362039, 9)
self.assertAlmostEqual(abs(c0).sum(), 33.461490657433551, 8)
c = orth.orth_ao(mol, 'lowdin', c0)
self.assertAlmostEqual(numpy.linalg.norm(c), 8.9823854843222257, 9)
self.assertAlmostEqual(abs(c).sum(), 94.933979307106767, 8)
c = orth.orth_ao(mol, 'meta_lowdin', c0)
self.assertAlmostEqual(numpy.linalg.norm(c), 8.9823854843222257, 9)
self.assertAlmostEqual(abs(c).sum(), 93.029386338534394, 8)
def test_orth_ao(self):
c0 = orth.pre_orth_ao(mol, method='scf')
self.assertAlmostEqual(numpy.linalg.norm(c0), 5.7742626195362039, 9)
self.assertAlmostEqual(abs(c0).sum(), 33.461490657433551, 8)
c = orth.orth_ao(mol, 'lowdin', c0)
self.assertAlmostEqual(numpy.linalg.norm(c), 8.9823854843222257, 9)
self.assertAlmostEqual(abs(c).sum(), 94.933979307106767, 8)
c = orth.orth_ao(mol, 'meta_lowdin', c0)
self.assertAlmostEqual(numpy.linalg.norm(c), 8.9823854843222257, 9)
self.assertAlmostEqual(abs(c).sum(), 93.029386338534394, 8)
def test_orth_ao(self):
c0 = orth.pre_orth_ao(mol, method='scf')
self.assertAlmostEqual(abs(c0).sum(), 33.48215772351, 8)
c = orth.orth_ao(mol, 'lowdin', c0)
self.assertAlmostEqual(abs(c).sum(), 94.21571091299639, 8)
c = orth.orth_ao(mol, 'meta_lowdin', c0)
self.assertAlmostEqual(abs(c).sum(), 92.15697348744733, 8)
c = orth.orth_ao(mol, 'meta_lowdin', 'sto-3g')
self.assertAlmostEqual(abs(c).sum(), 90.12324660084619, 8)
c = orth.orth_ao(mol, 'meta_lowdin', None)
self.assertAlmostEqual(abs(c).sum(), 83.71349158130113, 8)
def mulliken_pop_meta_lowdin_ao(mol, dm_ao, verbose=logger.DEBUG,
pre_orth_method='ANO'):
'''Mulliken population analysis, based on meta-Lowdin AOs.
'''
from pyscf.lo import orth
if isinstance(verbose, logger.Logger):
log = verbose
else:
log = logger.Logger(mol.stdout, verbose)
c = orth.pre_orth_ao(mol, pre_orth_method)
orth_coeff = orth.orth_ao(mol, 'meta_lowdin', pre_orth_ao=c)
c_inv = numpy.linalg.inv(orth_coeff)
dm_a = reduce(numpy.dot, (c_inv, dm_ao[0], c_inv.T.conj()))
dm_b = reduce(numpy.dot, (c_inv, dm_ao[1], c_inv.T.conj()))
log.info(' ** Mulliken pop alpha/beta on meta-lowdin orthogonal AOs **')
return mulliken_pop(mol, (dm_a,dm_b), numpy.eye(orth_coeff.shape[0]), log)
def mulliken_meta(mol,
dm,
verbose=logger.DEBUG,
pre_orth_method='ANO',
s=None):
'''Mulliken population analysis, based on meta-Lowdin AOs.
In the meta-lowdin, the AOs are grouped in three sets: core, valence and
Rydberg, the orthogonalization are carreid out within each subsets.
Args:
mol : an instance of :class:`Mole`
dm : ndarray or 2-item list of ndarray
Density matrix. ROHF dm is a 2-item list of 2D array
Kwargs:
verbose : int or instance of :class:`lib.logger.Logger`
pre_orth_method : str
Pre-orthogonalization, which localized GTOs for each atom.
To obtain the occupied and unoccupied atomic shells, there are
three methods
| 'ano' : Project GTOs to ANO basis
| 'minao' : Project GTOs to MINAO basis
| 'scf' : Fraction-averaged RHF
'''
from pyscf.lo import orth
if s is None:
s = get_ovlp(mol)
if isinstance(verbose, logger.Logger):
log = verbose
else:
log = logger.Logger(mol.stdout, verbose)
c = orth.pre_orth_ao(mol, pre_orth_method)
orth_coeff = orth.orth_ao(mol, 'meta_lowdin', pre_orth_ao=c, s=s)
c_inv = numpy.dot(orth_coeff.T, s)
if isinstance(dm, numpy.ndarray) and dm.ndim == 2:
dm = reduce(numpy.dot, (c_inv, dm, c_inv.T.conj()))
else: # ROHF
dm = reduce(numpy.dot, (c_inv, dm[0] + dm[1], c_inv.T.conj()))
log.info(' ** Mulliken pop on meta-lowdin orthogonal AOs **')
return mulliken_pop(mol, dm, numpy.eye(orth_coeff.shape[0]), log)
def mulliken_meta(mol, dm, verbose=logger.DEBUG, pre_orth_method='ANO',
s=None):
'''Mulliken population analysis, based on meta-Lowdin AOs.
In the meta-lowdin, the AOs are grouped in three sets: core, valence and
Rydberg, the orthogonalization are carreid out within each subsets.
Args:
mol : an instance of :class:`Mole`
dm : ndarray or 2-item list of ndarray
Density matrix. ROHF dm is a 2-item list of 2D array
Kwargs:
verbose : int or instance of :class:`lib.logger.Logger`
pre_orth_method : str
Pre-orthogonalization, which localized GTOs for each atom.
To obtain the occupied and unoccupied atomic shells, there are
three methods
| 'ano' : Project GTOs to ANO basis
| 'minao' : Project GTOs to MINAO basis
| 'scf' : Fraction-averaged RHF
'''
from pyscf.lo import orth
if s is None:
s = get_ovlp(mol)
if isinstance(verbose, logger.Logger):
log = verbose
else:
log = logger.Logger(mol.stdout, verbose)
c = orth.pre_orth_ao(mol, pre_orth_method)
orth_coeff = orth.orth_ao(mol, 'meta_lowdin', pre_orth_ao=c, s=s)
c_inv = numpy.dot(orth_coeff.T, s)
if isinstance(dm, numpy.ndarray) and dm.ndim == 2:
dm = reduce(numpy.dot, (c_inv, dm, c_inv.T.conj()))
else: # ROHF
dm = reduce(numpy.dot, (c_inv, dm[0]+dm[1], c_inv.T.conj()))
log.info(' ** Mulliken pop on meta-lowdin orthogonal AOs **')
return mulliken_pop(mol, dm, numpy.eye(orth_coeff.shape[0]), log)
def mulliken_meta(mol, dm_ao, verbose=logger.DEBUG, pre_orth_method='ANO',
s=None):
'''Mulliken population analysis, based on meta-Lowdin AOs.
'''
from pyscf.lo import orth
if s is None:
s = hf.get_ovlp(mol)
if isinstance(verbose, logger.Logger):
log = verbose
else:
log = logger.Logger(mol.stdout, verbose)
if isinstance(dm_ao, numpy.ndarray) and dm_ao.ndim == 2:
dm_ao = numpy.array((dm_ao*.5, dm_ao*.5))
c = orth.pre_orth_ao(mol, pre_orth_method)
orth_coeff = orth.orth_ao(mol, 'meta_lowdin', pre_orth_ao=c, s=s)
c_inv = numpy.dot(orth_coeff.T, s)
dm_a = reduce(numpy.dot, (c_inv, dm_ao[0], c_inv.T.conj()))
dm_b = reduce(numpy.dot, (c_inv, dm_ao[1], c_inv.T.conj()))
log.note(' ** Mulliken pop alpha/beta on meta-lowdin orthogonal AOs **')
return mulliken_pop(mol, (dm_a,dm_b), numpy.eye(orth_coeff.shape[0]), log)
def mulliken_meta(mol, dm_ao, verbose=logger.DEBUG, pre_orth_method='ANO',
s=None):
'''Mulliken population analysis, based on meta-Lowdin AOs.
'''
from pyscf.lo import orth
if s is None:
s = hf.get_ovlp(mol)
if isinstance(verbose, logger.Logger):
log = verbose
else:
log = logger.Logger(mol.stdout, verbose)
if isinstance(dm_ao, numpy.ndarray) and dm_ao.ndim == 2:
dm_ao = numpy.array((dm_ao*.5, dm_ao*.5))
c = orth.pre_orth_ao(mol, pre_orth_method)
orth_coeff = orth.orth_ao(mol, 'meta_lowdin', pre_orth_ao=c, s=s)
c_inv = numpy.dot(orth_coeff.T, s)
dm_a = reduce(numpy.dot, (c_inv, dm_ao[0], c_inv.T.conj()))
dm_b = reduce(numpy.dot, (c_inv, dm_ao[1], c_inv.T.conj()))
log.note(' ** Mulliken pop alpha/beta on meta-lowdin orthogonal AOs **')
return mulliken_pop(mol, (dm_a,dm_b), numpy.eye(orth_coeff.shape[0]), log)
def mulliken_meta(mol,
dm_ao,
verbose=logger.DEBUG,
pre_orth_method='ANO',
s=None):
'''Mulliken population analysis, based on meta-Lowdin AOs.
'''
from pyscf.lo import orth
if s is None:
s = hf.get_ovlp(mol)
log = logger.new_logger(mf, verbose)
log.note('Analyze output for the gamma point')
log.note("KUHF mulliken_meta")
dm_ao_gamma = dm_ao[:, 0, :, :].real.copy()
s_gamma = s[0, :, :].real.copy()
c = orth.pre_orth_ao(mol, pre_orth_method)
orth_coeff = orth.orth_ao(mol, 'meta_lowdin', pre_orth_ao=c, s=s_gamma)
c_inv = np.dot(orth_coeff.T, s_gamma)
dm_a = reduce(np.dot, (c_inv, dm_ao_gamma[0], c_inv.T.conj()))
dm_b = reduce(np.dot, (c_inv, dm_ao_gamma[1], c_inv.T.conj()))
log.note(' ** Mulliken pop alpha/beta on meta-lowdin orthogonal AOs **')
return uhf.mulliken_pop(mol, (dm_a, dm_b), np.eye(orth_coeff.shape[0]),
log)