def test_nao(self):
c = nao.nao(mol, mf)
s = mf.get_ovlp()
self.assertTrue(numpy.allclose(reduce(numpy.dot, (c.T, s, c)),
numpy.eye(s.shape[0])))
self.assertAlmostEqual(numpy.linalg.norm(c), 8.982385484322208, 9)
self.assertAlmostEqual(abs(c).sum(), 90.443872916389637, 6)
c = nao.nao(mol1, mf1)
s = mf1.get_ovlp()
self.assertTrue(numpy.allclose(reduce(numpy.dot, (c.T, s, c)),
numpy.eye(s.shape[0])))
self.assertAlmostEqual(numpy.linalg.norm(c), 9.4629575662640129, 9)
self.assertAlmostEqual(abs(c).sum(), 100.24554485355642, 6)
def orth_ao(mol, method='meta_lowdin', pre_orth_ao=None, scf_method=None,
s=None):
'''Orthogonalize AOs
Kwargs:
method : str
One of
| lowdin : Symmetric orthogonalization
| meta-lowdin : Lowdin orth within core, valence, virtual space separately (JCTC, 10, 3784)
| NAO
'''
from pyscf.lo import nao
if s is None:
s = mol.intor_symmetric('cint1e_ovlp_sph')
if pre_orth_ao is None:
# pre_orth_ao = numpy.eye(mol.nao_nr())
pre_orth_ao = project_to_atomic_orbitals(mol, 'ANO')
if method.lower() == 'lowdin':
s1 = reduce(numpy.dot, (pre_orth_ao.T, s, pre_orth_ao))
c_orth = numpy.dot(pre_orth_ao, lowdin(s1))
elif method.lower() == 'nao':
c_orth = nao.nao(mol, scf_method, s)
else: # meta_lowdin: divide ao into core, valence and Rydberg sets,
# orthogonalizing within each set
weight = numpy.ones(pre_orth_ao.shape[0])
c_orth = nao._nao_sub(mol, weight, pre_orth_ao, s)
# adjust phase
for i in range(c_orth.shape[1]):
if c_orth[i,i] < 0:
c_orth[:,i] *= -1
return c_orth
def test_nao(self):
c = nao.nao(mol, mf)
s = mf.get_ovlp()
self.assertTrue(numpy.allclose(reduce(numpy.dot, (c.T, s, c)),
numpy.eye(s.shape[0])))
self.assertAlmostEqual(numpy.linalg.norm(c), 10.967144073462256, 9)
self.assertAlmostEqual(abs(c).sum(), 110.03099712555559, 7)
def orth_ao(mol, method='meta_lowdin', pre_orth_ao=None, scf_method=None,
s=None):
'''Orthogonalize AOs
Kwargs:
method : str
One of
| lowdin : Symmetric orthogonalization
| meta-lowdin : Lowdin orth within core, valence, virtual space separately (JCTC, 10, 3784)
| NAO
'''
from pyscf.lo import nao
if s is None:
s = mol.intor_symmetric('int1e_ovlp')
if pre_orth_ao is None:
# pre_orth_ao = numpy.eye(mol.nao_nr())
pre_orth_ao = project_to_atomic_orbitals(mol, 'ANO')
if method.lower() == 'lowdin':
s1 = reduce(numpy.dot, (pre_orth_ao.T, s, pre_orth_ao))
c_orth = numpy.dot(pre_orth_ao, lowdin(s1))
elif method.lower() == 'nao':
c_orth = nao.nao(mol, scf_method, s)
else: # meta_lowdin: divide ao into core, valence and Rydberg sets,
# orthogonalizing within each set
weight = numpy.ones(pre_orth_ao.shape[0])
c_orth = nao._nao_sub(mol, weight, pre_orth_ao, s)
# adjust phase
for i in range(c_orth.shape[1]):
if c_orth[i,i] < 0:
c_orth[:,i] *= -1
return c_orth
def orth_ao(mf_or_mol, method=ORTH_METHOD, pre_orth_ao=None, scf_method=None,
s=None):
'''Orthogonalize AOs
Kwargs:
method : str
One of
| lowdin : Symmetric orthogonalization
| meta-lowdin : Lowdin orth within core, valence, virtual space separately (JCTC, 10, 3784)
| NAO
pre_orth_ao: numpy.ndarray
Coefficients to restore AO characters for arbitrary basis. If not
given, the coefficients are generated based on ANO basis. You can
skip this by setting pre_orth_ao to identity matrix, e.g. np.eye(mol.nao).
'''
from pyscf.lo import nao
mf = scf_method
if isinstance(mf_or_mol, gto.Mole):
mol = mf_or_mol
else:
mol = mf_or_mol.mol
if mf is None:
mf = mf_or_mol
if s is None:
if getattr(mol, 'pbc_intor', None): # whether mol object is a cell
s = mol.pbc_intor('int1e_ovlp', hermi=1)
else:
s = mol.intor_symmetric('int1e_ovlp')
if pre_orth_ao is None:
pre_orth_ao = project_to_atomic_orbitals(mol, REF_BASIS)
if method.lower() == 'lowdin':
s1 = reduce(numpy.dot, (pre_orth_ao.conj().T, s, pre_orth_ao))
c_orth = numpy.dot(pre_orth_ao, lowdin(s1))
elif method.lower() == 'nao':
assert(mf is not None)
c_orth = nao.nao(mol, mf, s)
else:
# meta_lowdin: partition AOs into core, valence and Rydberg sets,
# orthogonalizing within each set
weight = numpy.ones(pre_orth_ao.shape[0])
c_orth = nao._nao_sub(mol, weight, pre_orth_ao, s)
# adjust phase
for i in range(c_orth.shape[1]):
if c_orth[i,i] < 0:
c_orth[:,i] *= -1
return c_orth
def orth_ao(mf_or_mol,
method=ORTH_METHOD,
pre_orth_ao=None,
scf_method=None,
s=None):
'''Orthogonalize AOs
Kwargs:
method : str
One of
| lowdin : Symmetric orthogonalization
| meta-lowdin : Lowdin orth within core, valence, virtual space separately (JCTC, 10, 3784)
| NAO
'''
from pyscf.lo import nao
mf = scf_method
if isinstance(mf_or_mol, gto.Mole):
mol = mf_or_mol
else:
mol = mf_or_mol.mol
if mf is None:
mf = mf_or_mol
if s is None:
if getattr(mol, 'pbc_intor', None): # whether mol object is a cell
s = mol.pbc_intor('int1e_ovlp', hermi=1)
else:
s = mol.intor_symmetric('int1e_ovlp')
if pre_orth_ao is None:
# pre_orth_ao = numpy.eye(mol.nao_nr())
pre_orth_ao = project_to_atomic_orbitals(mol, REF_BASIS)
if method.lower() == 'lowdin':
s1 = reduce(numpy.dot, (pre_orth_ao.conj().T, s, pre_orth_ao))
c_orth = numpy.dot(pre_orth_ao, lowdin(s1))
elif method.lower() == 'nao':
assert (mf is not None)
c_orth = nao.nao(mol, mf, s)
else: # meta_lowdin: divide ao into core, valence and Rydberg sets,
# orthogonalizing within each set
weight = numpy.ones(pre_orth_ao.shape[0])
c_orth = nao._nao_sub(mol, weight, pre_orth_ao, s)
# adjust phase
for i in range(c_orth.shape[1]):
if c_orth[i, i] < 0:
c_orth[:, i] *= -1
return c_orth
def orth_ao(mf_or_mol, method=ORTH_METHOD, pre_orth_ao=None, scf_method=None,
s=None):
'''Orthogonalize AOs
Kwargs:
method : str
One of
| lowdin : Symmetric orthogonalization
| meta-lowdin : Lowdin orth within core, valence, virtual space separately (JCTC, 10, 3784)
| NAO
'''
from pyscf.lo import nao
mf = scf_method
if isinstance(mf_or_mol, gto.Mole):
mol = mf_or_mol
else:
mol = mf_or_mol.mol
if mf is None:
mf = mf_or_mol
if s is None:
if getattr(mol, 'pbc_intor', None): # whether mol object is a cell
s = mol.pbc_intor('int1e_ovlp', hermi=1)
else:
s = mol.intor_symmetric('int1e_ovlp')
if pre_orth_ao is None:
# pre_orth_ao = numpy.eye(mol.nao_nr())
pre_orth_ao = project_to_atomic_orbitals(mol, REF_BASIS)
if method.lower() == 'lowdin':
s1 = reduce(numpy.dot, (pre_orth_ao.conj().T, s, pre_orth_ao))
c_orth = numpy.dot(pre_orth_ao, lowdin(s1))
elif method.lower() == 'nao':
assert(mf is not None)
c_orth = nao.nao(mol, mf, s)
else: # meta_lowdin: divide ao into core, valence and Rydberg sets,
# orthogonalizing within each set
weight = numpy.ones(pre_orth_ao.shape[0])
c_orth = nao._nao_sub(mol, weight, pre_orth_ao, s)
# adjust phase
for i in range(c_orth.shape[1]):
if c_orth[i,i] < 0:
c_orth[:,i] *= -1
return c_orth
def orth_ao(mol, method='meta_lowdin', pre_orth_ao=None, scf_method=None,
s=None):
from pyscf.lo import nao
if s is None:
s = mol.intor_symmetric('cint1e_ovlp_sph')
if pre_orth_ao is None:
# pre_orth_ao = numpy.eye(mol.nao_nr())
pre_orth_ao = pre_orth_project_ano(mol, 'ANO')
if method == 'lowdin':
s1 = reduce(numpy.dot, (pre_orth_ao.T, s, pre_orth_ao))
c_orth = numpy.dot(pre_orth_ao, lowdin(s1))
elif method == 'nao':
c_orth = nao.nao(mol, scf_method)
else: # meta_lowdin: divide ao into core, valence and Rydberg sets,
# orthogonalizing within each set
weight = numpy.ones(pre_orth_ao.shape[0])
c_orth = nao._nao_sub(mol, weight, pre_orth_ao)
# adjust phase
for i in range(c_orth.shape[1]):
if c_orth[i,i] < 0:
c_orth[:,i] *= -1
return c_orth
def orth_ao(mf_or_mol, method=ORTH_METHOD, pre_orth_ao=REF_BASIS, s=None):
'''Orthogonalize AOs
Kwargs:
method : str
One of
| lowdin : Symmetric orthogonalization
| meta-lowdin : Lowdin orth within core, valence, virtual space separately (JCTC, 10, 3784)
| NAO
pre_orth_ao: numpy.ndarray or basis str or basis dict
Basis functions may not have AO characters. This variable is the
coefficients to restore AO characters for arbitrary basis. If a
string of basis name (can be the filename of a basis set) or a
dict of basis sets are given, they are interpreted as the
reference basis (by default ANO basis) that the projection
coefficients are generated based on. Skip this projection step by
setting this variable to None.
'''
from pyscf import scf
from pyscf.lo import nao
if isinstance(mf_or_mol, gto.Mole):
mol = mf_or_mol
mf = None
else:
assert (isinstance(mf_or_mol, scf.hf.SCF))
mol = mf_or_mol.mol
mf = mf_or_mol
if s is None:
if getattr(mol, 'pbc_intor', None): # whether mol object is a cell
s = mol.pbc_intor('int1e_ovlp', hermi=1)
else:
s = mol.intor_symmetric('int1e_ovlp')
if method.lower() == 'lowdin':
if pre_orth_ao is None:
c_orth = lowdin(s1)
else:
if not isinstance(pre_orth_ao, numpy.ndarray):
pre_orth_ao = restore_ao_character(mol, pre_orth_ao)
s1 = reduce(numpy.dot, (pre_orth_ao.conj().T, s, pre_orth_ao))
c_orth = numpy.dot(pre_orth_ao, lowdin(s1))
elif method.lower() == 'nao':
assert (mf is not None)
c_orth = nao.nao(mol, mf, s)
else: # meta_lowdin: partition AOs into core, valence and Rydberg sets,
# orthogonalizing within each set
if pre_orth_ao is None:
pre_orth_ao = numpy.eye(mol.nao)
elif not isinstance(pre_orth_ao, numpy.ndarray):
pre_orth_ao = restore_ao_character(mol, pre_orth_ao)
weight = numpy.ones(pre_orth_ao.shape[0])
c_orth = nao._nao_sub(mol, weight, pre_orth_ao, s)
# adjust phase
for i in range(c_orth.shape[1]):
if c_orth[i, i] < 0:
c_orth[:, i] *= -1
return c_orth
