def mulliken_meta(cell,
dm_ao_kpts,
verbose=logger.DEBUG,
pre_orth_method=PRE_ORTH_METHOD,
s=None):
'''A modified Mulliken population analysis, based on meta-Lowdin AOs.
Note this function only computes the Mulliken population for the gamma
point density matrix.
'''
from pyscf.lo import orth
if s is None:
s = khf.get_ovlp(cell)
log = logger.new_logger(cell, verbose)
log.note('Analyze output for *gamma point*.')
log.info(' To include the contributions from k-points, transform to a '
'supercell then run the population analysis on the supercell\n'
' from pyscf.pbc.tools import k2gamma\n'
' k2gamma.k2gamma(mf).mulliken_meta()')
log.note("KUHF mulliken_meta")
dm_ao_gamma = dm_ao_kpts[:, 0, :, :].real
s_gamma = s[0, :, :].real
c = orth.restore_ao_character(cell, pre_orth_method)
orth_coeff = orth.orth_ao(cell, '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 mol_uhf.mulliken_pop(cell, (dm_a, dm_b),
np.eye(orth_coeff.shape[0]), log)
def mulliken_meta(cell,
dm_ao_kpts,
verbose=logger.DEBUG,
pre_orth_method='ANO',
s=None):
'''Mulliken population analysis, based on meta-Lowdin AOs.
Note this function only computes the Mulliken population for the gamma
point density matrix.
'''
from pyscf.lo import orth
if s is None:
s = khf.get_ovlp(cell)
log = logger.new_logger(cell, verbose)
log.note('Analyze output for the gamma point')
log.note("KUHF mulliken_meta")
dm_ao_gamma = dm_ao_kpts[:, 0, :, :].real
s_gamma = s[0, :, :].real
c = orth.restore_ao_character(cell, pre_orth_method)
orth_coeff = orth.orth_ao(cell, '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 mol_uhf.mulliken_pop(cell, (dm_a, dm_b),
np.eye(orth_coeff.shape[0]), log)
def mulliken_meta(cell, dm_ao_kpts, verbose=logger.DEBUG,
pre_orth_method=PRE_ORTH_METHOD, s=None):
'''A modified Mulliken population analysis, based on meta-Lowdin AOs.
Note this function only computes the Mulliken population for the gamma
point density matrix.
'''
from pyscf.lo import orth
if s is None:
s = khf.get_ovlp(cell)
log = logger.new_logger(cell, verbose)
log.note('Analyze output for *gamma point*.')
log.info(' To include the contributions from k-points, transform to a '
'supercell then run the population analysis on the supercell\n'
' from pyscf.pbc.tools import k2gamma\n'
' k2gamma.k2gamma(mf).mulliken_meta()')
log.note("KUHF mulliken_meta")
dm_ao_gamma = dm_ao_kpts[:,0,:,:].real
s_gamma = s[0,:,:].real
c = orth.restore_ao_character(cell, pre_orth_method)
orth_coeff = orth.orth_ao(cell, '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 mol_uhf.mulliken_pop(cell, (dm_a,dm_b), np.eye(orth_coeff.shape[0]), log)
def mulliken_pop(mol, dm, s=None, verbose=logger.DEBUG):
'''Mulliken population analysis
'''
nao = mol.nao_nr()
dma = dm[:nao,:nao]
dmb = dm[nao:,nao:]
if s is not None:
assert(s.size == nao**2 or numpy.allclose(s[:nao,:nao], s[nao:,nao:]))
s = s[:nao,:nao]
return uhf.mulliken_pop(mol, (dma,dmb), s, verbose)
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)
