def project_to_atomic_orbitals(mol, basname):
'''projected AO = |bas><bas|ANO>
'''
from pyscf.scf.addons import project_mo_nr2nr
from pyscf.scf import atom_hf
from pyscf.gto.ecp import core_configuration
def search_atm_l(atm, l):
bas_ang = atm._bas[:, gto.ANG_OF]
ao_loc = atm.ao_loc_nr()
idx = []
for ib in numpy.where(bas_ang == l)[0]:
idx.extend(range(ao_loc[ib], ao_loc[ib + 1]))
return idx
# Overlap of ANO and ECP basis
def ecp_ano_det_ovlp(atm_ecp, atm_ano, ecpcore):
ecp_ao_loc = atm_ecp.ao_loc_nr()
ano_ao_loc = atm_ano.ao_loc_nr()
ecp_ao_dim = ecp_ao_loc[1:] - ecp_ao_loc[:-1]
ano_ao_dim = ano_ao_loc[1:] - ano_ao_loc[:-1]
ecp_bas_l = [[atm_ecp.bas_angular(i)] * d
for i, d in enumerate(ecp_ao_dim)]
ano_bas_l = [[atm_ano.bas_angular(i)] * d
for i, d in enumerate(ano_ao_dim)]
ecp_bas_l = numpy.hstack(ecp_bas_l)
ano_bas_l = numpy.hstack(ano_bas_l)
nelec_core = 0
ecp_occ_tmp = []
ecp_idx = []
ano_idx = []
for l in range(4):
nocc, frac = atom_hf.frac_occ(stdsymb, l)
l_occ = [2] * ((nocc - ecpcore[l]) * (2 * l + 1))
if frac > 1e-15:
l_occ.extend([frac] * (2 * l + 1))
nocc += 1
if nocc == 0:
break
nelec_core += 2 * ecpcore[l] * (2 * l + 1)
i0 = ecpcore[l] * (2 * l + 1)
i1 = nocc * (2 * l + 1)
ecp_idx.append(numpy.where(ecp_bas_l == l)[0][:i1 - i0])
ano_idx.append(numpy.where(ano_bas_l == l)[0][i0:i1])
ecp_occ_tmp.append(l_occ[:i1 - i0])
ecp_idx = numpy.hstack(ecp_idx)
ano_idx = numpy.hstack(ano_idx)
ecp_occ = numpy.zeros(atm_ecp.nao_nr())
ecp_occ[ecp_idx] = numpy.hstack(ecp_occ_tmp)
nelec_valence_left = int(
gto.charge(stdsymb) - nelec_core - sum(ecp_occ[ecp_idx]))
if nelec_valence_left > 0:
logger.warn(
mol, 'Characters of %d valence electrons are not identified.\n'
'It can affect the "meta-lowdin" localization method '
'and the population analysis of SCF method.\n'
'Adjustment to the core/valence partition may be needed '
'(see function lo.nao.set_atom_conf)\nto get reasonable '
'local orbitals or Mulliken population.\n', nelec_valence_left)
# Return 0 to force the projection to ANO basis
return 0
else:
s12 = gto.intor_cross('int1e_ovlp', atm_ecp,
atm_ano)[ecp_idx][:, ano_idx]
return numpy.linalg.det(s12)
nelec_ecp_dic = {}
for ia in range(mol.natm):
symb = mol.atom_symbol(ia)
if symb not in nelec_ecp_dic:
nelec_ecp_dic[symb] = mol.atom_nelec_core(ia)
aos = {}
atm = gto.Mole()
atmp = gto.Mole()
for symb in mol._basis.keys():
stdsymb = gto.mole._std_symbol(symb)
atm._atm, atm._bas, atm._env = \
atm.make_env([[stdsymb,(0,0,0)]], {stdsymb:mol._basis[symb]}, [])
atm.cart = mol.cart
atm._built = True
s0 = atm.intor_symmetric('int1e_ovlp')
if gto.is_ghost_atom(symb):
aos[symb] = numpy.diag(1. / numpy.sqrt(s0.diagonal()))
continue
basis_add = gto.basis.load(basname, stdsymb)
atmp._atm, atmp._bas, atmp._env = \
atmp.make_env([[stdsymb,(0,0,0)]], {stdsymb:basis_add}, [])
atmp.cart = mol.cart
atmp._built = True
if symb in nelec_ecp_dic and nelec_ecp_dic[symb] > 0:
# If ECP basis has good atomic character, ECP basis can be used in the
# localization/population analysis directly. Otherwise project ECP
# basis to ANO basis.
if not PROJECT_ECP_BASIS:
continue
ecpcore = core_configuration(nelec_ecp_dic[symb])
# Comparing to ANO valence basis, to check whether the ECP basis set has
# reasonable AO-character contraction. The ANO valence AO should have
# significant overlap to ECP basis if the ECP basis has AO-character.
if abs(ecp_ano_det_ovlp(atm, atmp, ecpcore)) > .1:
aos[symb] = numpy.diag(1. / numpy.sqrt(s0.diagonal()))
continue
else:
ecpcore = [0] * 4
# MINAO for heavier elements needs to be used with pseudo potential
if (basname.upper() == 'MINAO' and gto.charge(stdsymb) > 36
and symb not in nelec_ecp_dic):
raise RuntimeError(
'Basis MINAO has to be used with ecp for heavy elements')
ano = project_mo_nr2nr(atmp, numpy.eye(atmp.nao_nr()), atm)
rm_ano = numpy.eye(ano.shape[0]) - reduce(numpy.dot, (ano, ano.T, s0))
c = rm_ano.copy()
for l in range(param.L_MAX):
idx = numpy.asarray(search_atm_l(atm, l))
nbf_atm_l = len(idx)
if nbf_atm_l == 0:
break
idxp = numpy.asarray(search_atm_l(atmp, l))
if l < 4:
idxp = idxp[ecpcore[l]:]
nbf_ano_l = len(idxp)
if mol.cart:
degen = (l + 1) * (l + 2) // 2
else:
degen = l * 2 + 1
if nbf_atm_l > nbf_ano_l > 0:
# For angular l, first place the projected ANO, then the rest AOs.
sdiag = reduce(
numpy.dot,
(rm_ano[:, idx].T, s0, rm_ano[:, idx])).diagonal()
nleft = (nbf_atm_l - nbf_ano_l) // degen
shell_average = numpy.einsum('ij->i', sdiag.reshape(-1, degen))
shell_rest = numpy.argsort(-shell_average)[:nleft]
idx_rest = []
for k in shell_rest:
idx_rest.extend(idx[k * degen:(k + 1) * degen])
c[:, idx[:nbf_ano_l]] = ano[:, idxp]
c[:, idx[nbf_ano_l:]] = rm_ano[:, idx_rest]
elif nbf_ano_l >= nbf_atm_l > 0: # More ANOs than the mol basis functions
c[:, idx] = ano[:, idxp[:nbf_atm_l]]
sdiag = numpy.einsum('pi,pq,qi->i', c, s0, c)
c *= 1. / numpy.sqrt(sdiag)
aos[symb] = c
nao = mol.nao_nr()
c = numpy.zeros((nao, nao))
p1 = 0
for ia in range(mol.natm):
symb = mol.atom_symbol(ia)
if symb in mol._basis:
ano = aos[symb]
else:
ano = aos[mol.atom_pure_symbol(ia)]
p0, p1 = p1, p1 + ano.shape[1]
c[p0:p1, p0:p1] = ano
return c
def project_to_atomic_orbitals(mol, basname):
'''projected AO = |bas><bas|ANO>
'''
from pyscf.scf.addons import project_mo_nr2nr
from pyscf.scf import atom_hf
from pyscf.gto.ecp import core_configuration
def search_atm_l(atm, l):
bas_ang = atm._bas[:,gto.ANG_OF]
ao_loc = atm.ao_loc_nr()
idx = []
for ib in numpy.where(bas_ang == l)[0]:
idx.extend(range(ao_loc[ib], ao_loc[ib+1]))
return idx
# Overlap of ANO and ECP basis
def ecp_ano_det_ovlp(atm_ecp, atm_ano, ecpcore):
ecp_ao_loc = atm_ecp.ao_loc_nr()
ano_ao_loc = atm_ano.ao_loc_nr()
ecp_ao_dim = ecp_ao_loc[1:] - ecp_ao_loc[:-1]
ano_ao_dim = ano_ao_loc[1:] - ano_ao_loc[:-1]
ecp_bas_l = [[atm_ecp.bas_angular(i)]*d for i,d in enumerate(ecp_ao_dim)]
ano_bas_l = [[atm_ano.bas_angular(i)]*d for i,d in enumerate(ano_ao_dim)]
ecp_bas_l = numpy.hstack(ecp_bas_l)
ano_bas_l = numpy.hstack(ano_bas_l)
nelec_core = 0
ecp_occ_tmp = []
ecp_idx = []
ano_idx = []
for l in range(4):
nocc, frac = atom_hf.frac_occ(stdsymb, l)
l_occ = [2] * ((nocc-ecpcore[l])*(2*l+1))
if frac > 1e-15:
l_occ.extend([frac] * (2*l+1))
nocc += 1
if nocc == 0:
break
nelec_core += 2 * ecpcore[l] * (2*l+1)
i0 = ecpcore[l] * (2*l+1)
i1 = nocc * (2*l+1)
ecp_idx.append(numpy.where(ecp_bas_l==l)[0][:i1-i0])
ano_idx.append(numpy.where(ano_bas_l==l)[0][i0:i1])
ecp_occ_tmp.append(l_occ[:i1-i0])
ecp_idx = numpy.hstack(ecp_idx)
ano_idx = numpy.hstack(ano_idx)
ecp_occ = numpy.zeros(atm_ecp.nao_nr())
ecp_occ[ecp_idx] = numpy.hstack(ecp_occ_tmp)
nelec_valence_left = int(gto.mole.charge(stdsymb) - nelec_core
- sum(ecp_occ[ecp_idx]))
if nelec_valence_left > 0:
logger.warn(mol, 'Characters of %d valence electrons are not identified.\n'
'It can affect the "meta-lowdin" localization method '
'and the population analysis of SCF method.\n'
'Adjustment to the core/valence partition may be needed '
'(see function lo.nao.set_atom_conf)\nto get reasonable '
'local orbitals or Mulliken population.\n',
nelec_valence_left)
# Return 0 to force the projection to ANO basis
return 0
else:
s12 = gto.intor_cross('int1e_ovlp', atm_ecp, atm_ano)[ecp_idx][:,ano_idx]
return numpy.linalg.det(s12)
nelec_ecp_dic = {}
for ia in range(mol.natm):
symb = mol.atom_symbol(ia)
if symb not in nelec_ecp_dic:
nelec_ecp_dic[symb] = mol.atom_nelec_core(ia)
aos = {}
atm = gto.Mole()
atmp = gto.Mole()
for symb in mol._basis.keys():
stdsymb = gto.mole._std_symbol(symb)
atm._atm, atm._bas, atm._env = \
atm.make_env([[stdsymb,(0,0,0)]], {stdsymb:mol._basis[symb]}, [])
atm.cart = mol.cart
atm._built = True
s0 = atm.intor_symmetric('int1e_ovlp')
if gto.is_ghost_atom(symb):
aos[symb] = numpy.diag(1./numpy.sqrt(s0.diagonal()))
continue
basis_add = gto.basis.load(basname, stdsymb)
atmp._atm, atmp._bas, atmp._env = \
atmp.make_env([[stdsymb,(0,0,0)]], {stdsymb:basis_add}, [])
atmp.cart = mol.cart
atmp._built = True
if symb in nelec_ecp_dic and nelec_ecp_dic[symb] > 0:
if not PROJECT_ECP_BASIS:
# If ECP basis has good atomic character, ECP basis can be used in the
# localization/population analysis directly. Otherwise project ECP basis to
# ANO basis.
continue
ecpcore = core_configuration(nelec_ecp_dic[symb])
# Comparing to ANO valence basis, to check whether the ECP basis set has
# reasonable AO-character contraction. The ANO valence AO should have
# significant overlap to ECP basis if the ECP basis has AO-character.
if abs(ecp_ano_det_ovlp(atm, atmp, ecpcore)) > .1:
aos[symb] = numpy.diag(1./numpy.sqrt(s0.diagonal()))
continue
else:
ecpcore = [0] * 4
ano = project_mo_nr2nr(atmp, numpy.eye(atmp.nao_nr()), atm)
rm_ano = numpy.eye(ano.shape[0]) - reduce(numpy.dot, (ano, ano.T, s0))
c = rm_ano.copy()
for l in range(param.L_MAX):
idx = numpy.asarray(search_atm_l(atm, l))
nbf_atm_l = len(idx)
if nbf_atm_l == 0:
break
idxp = numpy.asarray(search_atm_l(atmp, l))
if l < 4:
idxp = idxp[ecpcore[l]:]
nbf_ano_l = len(idxp)
if mol.cart:
degen = (l + 1) * (l + 2) // 2
else:
degen = l * 2 + 1
if nbf_atm_l > nbf_ano_l > 0:
# For angular l, first place the projected ANO, then the rest AOs.
sdiag = reduce(numpy.dot, (rm_ano[:,idx].T, s0, rm_ano[:,idx])).diagonal()
nleft = (nbf_atm_l - nbf_ano_l) // degen
shell_average = numpy.einsum('ij->i', sdiag.reshape(-1,degen))
shell_rest = numpy.argsort(-shell_average)[:nleft]
idx_rest = []
for k in shell_rest:
idx_rest.extend(idx[k*degen:(k+1)*degen])
c[:,idx[:nbf_ano_l]] = ano[:,idxp]
c[:,idx[nbf_ano_l:]] = rm_ano[:,idx_rest]
elif nbf_ano_l >= nbf_atm_l > 0: # More ANOs than the mol basis functions
c[:,idx] = ano[:,idxp[:nbf_atm_l]]
sdiag = numpy.einsum('pi,pq,qi->i', c, s0, c)
c *= 1./numpy.sqrt(sdiag)
aos[symb] = c
nao = mol.nao_nr()
c = numpy.zeros((nao,nao))
p1 = 0
for ia in range(mol.natm):
symb = mol.atom_symbol(ia)
if symb in mol._basis:
ano = aos[symb]
else:
ano = aos[mol.atom_pure_symbol(ia)]
p0, p1 = p1, p1 + ano.shape[1]
c[p0:p1,p0:p1] = ano
return c