def _core_val_ryd_list(mol):
from pyscf.gto.ecp import core_configuration
count = numpy.zeros((mol.natm, 9), dtype=int)
core_lst = []
val_lst = []
rydbg_lst = []
k = 0
for ib in range(mol.nbas):
ia = mol.bas_atom(ib)
# Avoid calling mol.atom_charge because we should include ECP core electrons here
nuc = mole._charge(mol.atom_symbol(ia))
l = mol.bas_angular(ib)
nc = mol.bas_nctr(ib)
symb = mol.atom_symbol(ia)
nelec_ecp = mol.atom_nelec_core(ia)
ecpcore = core_configuration(nelec_ecp)
coreshell = [int(x) for x in AOSHELL[nuc][0][::2]]
cvshell = [int(x) for x in AOSHELL[nuc][1][::2]]
for n in range(nc):
if l > 3:
rydbg_lst.extend(range(k, k+(2*l+1)))
elif ecpcore[l]+count[ia,l]+n < coreshell[l]:
core_lst.extend(range(k, k+(2*l+1)))
elif ecpcore[l]+count[ia,l]+n < cvshell[l]:
val_lst.extend(range(k, k+(2*l+1)))
else:
rydbg_lst.extend(range(k, k+(2*l+1)))
k = k + 2*l+1
count[ia,l] += nc
return core_lst, val_lst, rydbg_lst
def __init__(self, atoms, basis=None):
self.atomtypes = mole.atom_types(atoms, basis)
# fake systems, which treates the atoms of different basis as different atoms.
# the fake systems do not have the same symmetry as the potential
# it's only used to determine the main (Z-)axis
chg1 = numpy.pi - 2
coords = []
fake_chgs = []
idx = []
for k, lst in self.atomtypes.items():
idx.append(lst)
coords.append([atoms[i][1] for i in lst])
ksymb = mole._rm_digit(k)
if ksymb != k or ksymb == 'GHOST':
fake_chgs.append([chg1] * len(lst))
chg1 *= numpy.pi-2
else:
fake_chgs.append([mole._charge(ksymb)] * len(lst))
coords = numpy.array(numpy.vstack(coords), dtype=float)
fake_chgs = numpy.hstack(fake_chgs)
self.charge_center = numpy.einsum('i,ij->j', fake_chgs, coords)/fake_chgs.sum()
coords = coords - self.charge_center
self.im = numpy.einsum('i,ij,ik->jk', fake_chgs, coords, coords)/fake_chgs.sum()
idx = numpy.argsort(numpy.hstack(idx))
self.atoms = numpy.hstack((fake_chgs.reshape(-1,1), coords))[idx]
def para(mol, mo1, mo_coeff, mo_occ, hfc_nuc=None):
if hfc_nuc is None:
hfc_nuc = range(mol.natm)
effspin = mol.spin * .5
mu_B = 1 # lib.param.BOHR_MAGNETON
mu_N = lib.param.PROTON_MASS * mu_B
fac = lib.param.ALPHA / 2 / effspin
fac *= lib.param.G_ELECTRON * mu_B * mu_N
occidxa = mo_occ[0] > 0
occidxb = mo_occ[1] > 0
orboa = mo_coeff[0][:, occidxa]
orbob = mo_coeff[1][:, occidxb]
nao = mo_coeff[0].shape[0]
dm10 = numpy.empty((3, nao, nao))
for i in range(3):
dm10[i] = reduce(numpy.dot, (mo_coeff[0], mo1[0][i], orboa.conj().T))
dm10[i] += reduce(numpy.dot, (mo_coeff[1], mo1[1][i], orbob.conj().T))
para = numpy.empty((len(hfc_nuc), 3, 3))
for n, atm_id in enumerate(hfc_nuc):
Z = mole._charge(mol.atom_symbol(atm_id))
nuc_spin, g_nuc = parameters.ISOTOPE[Z][1:3]
gyromag = 1e-6 / (
2 * numpy.pi) * parameters.g_factor_to_gyromagnetic_ratio(g_nuc)
mol.set_rinv_origin(mol.atom_coord(atm_id))
h01 = mol.intor_asymmetric('int1e_prinvxp', 3)
para[n] = numpy.einsum('xji,yij->yx', dm10, h01) * 2
para[n] *= fac * gyromag
return para
def get_inertia_momentum(atoms, basis):
charge = numpy.array([mole._charge(a[0]) for a in atoms])
coords = numpy.array([a[1] for a in atoms], dtype=float)
rbar = numpy.einsum('i,ij->j', charge, coords)/charge.sum()
coords = coords - rbar
im = numpy.einsum('i,ij,ik->jk', charge, coords, coords)/charge.sum()
return im
def _core_val_ryd_list(mol):
from pyscf.gto.ecp import core_configuration
count = numpy.zeros((mol.natm, 9), dtype=int)
core_lst = []
val_lst = []
rydbg_lst = []
k = 0
for ib in range(mol.nbas):
ia = mol.bas_atom(ib)
# Avoid calling mol.atom_charge because we should include ECP core electrons here
nuc = mole._charge(mol.atom_symbol(ia))
l = mol.bas_angular(ib)
nc = mol.bas_nctr(ib)
symb = mol.atom_symbol(ia)
nelec_ecp = mol.atom_nelec_core(ia)
ecpcore = core_configuration(nelec_ecp)
coreshell = [int(x) for x in AOSHELL[nuc][0][::2]]
cvshell = [int(x) for x in AOSHELL[nuc][1][::2]]
for n in range(nc):
if l > 3:
rydbg_lst.extend(range(k, k + (2 * l + 1)))
elif ecpcore[l] + count[ia, l] + n < coreshell[l]:
core_lst.extend(range(k, k + (2 * l + 1)))
elif ecpcore[l] + count[ia, l] + n < cvshell[l]:
val_lst.extend(range(k, k + (2 * l + 1)))
else:
rydbg_lst.extend(range(k, k + (2 * l + 1)))
k = k + 2 * l + 1
count[ia, l] += nc
return core_lst, val_lst, rydbg_lst
def __init__(self, atoms, basis=None):
self.atomtypes = mole.atom_types(atoms, basis)
# fake systems, which treates the atoms of different basis as different atoms.
# the fake systems do not have the same symmetry as the potential
# it's only used to determine the main (Z-)axis
chg1 = numpy.pi - 2
coords = []
fake_chgs = []
idx = []
for k, lst in self.atomtypes.items():
idx.append(lst)
coords.append([atoms[i][1] for i in lst])
ksymb = mole._rm_digit(k)
if ksymb != k or ksymb == 'GHOST':
# Put random charges on the decorated atoms
fake_chgs.append([chg1] * len(lst))
chg1 *= numpy.pi-2
else:
fake_chgs.append([mole._charge(ksymb)] * len(lst))
coords = numpy.array(numpy.vstack(coords), dtype=float)
fake_chgs = numpy.hstack(fake_chgs)
self.charge_center = numpy.einsum('i,ij->j', fake_chgs, coords)/fake_chgs.sum()
coords = coords - self.charge_center
self.im = numpy.einsum('i,ij,ik->jk', fake_chgs, coords, coords)/fake_chgs.sum()
idx = numpy.argsort(numpy.hstack(idx))
self.atoms = numpy.hstack((fake_chgs.reshape(-1,1), coords))[idx]
def __init__(self, atoms, basis=None):
self.atomtypes = mole.atom_types(atoms, basis)
# fake systems, which treates the atoms of different basis as different atoms.
# the fake systems do not have the same symmetry as the potential
# it's only used to determine the main (Z-)axis
chg1 = numpy.pi - 2
coords = []
fake_chgs = []
idx = []
for k, lst in self.atomtypes.items():
idx.append(lst)
coords.append([atoms[i][1] for i in lst])
ksymb = mole._rm_digit(k)
if ksymb != k:
# Put random charges on the decorated atoms
fake_chgs.append([chg1] * len(lst))
chg1 *= numpy.pi - 2
elif 'GHOST' in ksymb:
ksymb = mole._remove_prefix_ghost(ksymb)
fake_chgs.append([mole._charge(ksymb) + .3] * len(lst))
else:
fake_chgs.append([mole._charge(ksymb)] * len(lst))
coords = numpy.array(numpy.vstack(coords), dtype=float)
fake_chgs = numpy.hstack(fake_chgs)
self.charge_center = numpy.einsum('i,ij->j', fake_chgs,
coords) / fake_chgs.sum()
coords = coords - self.charge_center
idx = numpy.argsort(numpy.hstack(idx))
self.atoms = numpy.hstack((fake_chgs.reshape(-1, 1), coords))[idx]
self.group_atoms_by_distance = []
decimals = int(-numpy.log10(TOLERANCE)) - 1
for index in self.atomtypes.values():
index = numpy.asarray(index)
c = self.atoms[index, 1:]
dists = numpy.around(norm(c, axis=1), decimals)
u, idx = numpy.unique(dists, return_inverse=True)
for i, s in enumerate(u):
self.group_atoms_by_distance.append(index[idx == i])
def dia(gobj, mol, dm0, hfc_nuc=None, verbose=None):
log = logger.new_logger(gobj, verbose)
if hfc_nuc is None:
hfc_nuc = range(mol.natm)
if isinstance(dm0, numpy.ndarray) and dm0.ndim == 2: # RHF DM
return numpy.zeros((3, 3))
dma, dmb = dm0
spindm = dma - dmb
effspin = mol.spin * .5
mu_B = 1 # lib.param.BOHR_MAGNETON
mu_N = lib.param.PROTON_MASS * mu_B
fac = lib.param.ALPHA / 2 / effspin
fac *= lib.param.G_ELECTRON * mu_B * mu_N
coords = mol.atom_coords()
ao = numint.eval_ao(mol, coords)
nao = dma.shape[0]
dia = []
for i, atm_id in enumerate(hfc_nuc):
Z = mole._charge(mol.atom_symbol(atm_id))
nuc_spin, g_nuc = parameters.ISOTOPE[Z][1:3]
# g factor of other isotopes can be found in file nuclear_g_factor.dat
gyromag = 1e-6 / (
2 * numpy.pi) * parameters.g_factor_to_gyromagnetic_ratio(g_nuc)
log.info(
'Atom %d %s nuc-spin %g nuc-g-factor %g gyromagnetic ratio %g (in MHz)',
atm_id, mol.atom_symbol(atm_id), nuc_spin, g_nuc, gyromag)
mol.set_rinv_origin(mol.atom_coord(atm_id))
# a01p[mu,sigma] the imaginary part of integral <vec{r}/r^3 cross p>
# mu = gN * I * mu_N
a01p = mol.intor('int1e_sa01sp', 12).reshape(3, 4, nao, nao)
h11 = a01p[:, 1:] - a01p[:, 1:].transpose(0, 1, 3, 2)
e11 = numpy.einsum('xyij,ji->xy', h11, spindm)
e11 *= fac * gyromag
# e11 includes fermi-contact and spin-dipolar contriutions and a rank-2 contact
# term. We ignore the contribution of rank-2 contact term, view it as part of
# SD contribution. See also TCA, 73, 173
fermi_contact = (
4 * numpy.pi / 3 * fac * gyromag *
numpy.einsum('i,j,ji', ao[atm_id], ao[atm_id], spindm))
dip = e11 - numpy.eye(3) * fermi_contact
log.info('FC %s', fermi_contact)
if gobj.verbose >= logger.INFO:
_write(gobj, dip, 'SD')
dia.append(e11)
return numpy.asarray(dia)
def set_atom_conf(element, description):
'''Change the default atomic core and valence configuration to the one
given by "description".
See lo.nao.AOSHELL for the default configuration.
Args:
element : str or int
Element symbol or nuclear charge
description : str or a list of str
| "double p" : double p shell
| "double d" : double d shell
| "double f" : double f shell
| "polarize" : add one polarized shell
| "1s1d" : keep core unchanged and set 1 s 1 d shells for valence
| ("3s2p","1d") : 3 s, 2 p shells for core and 1 d shells for valence
'''
charge = mole._charge(element)
def to_conf(desc):
desc = desc.replace(' ', '').replace('-', '').replace('_', '').lower()
if "doublep" in desc:
desc = '2p'
elif "doubled" in desc:
desc = '2d'
elif "doublef" in desc:
desc = '2f'
elif "polarize" in desc:
loc = AOSHELL[charge][1].find('0')
desc = '1' + AOSHELL[charge][1][loc + 1]
return desc
if isinstance(description, str):
c_desc, v_desc = AOSHELL[charge][0], to_conf(description)
else:
c_desc, v_desc = to_conf(description[0]), to_conf(description[1])
ncore = [int(x) for x in AOSHELL[charge][0][::2]]
ncv = [int(x) for x in AOSHELL[charge][1][::2]]
for i, s in enumerate(('s', 'p', 'd', 'f')):
if s in c_desc:
ncore[i] = int(c_desc.split(s)[0][-1])
if s in v_desc:
ncv[i] = ncore[i] + int(v_desc.split(s)[0][-1])
c_conf = '%ds%dp%dd%df' % tuple(ncore)
cv_conf = '%ds%dp%dd%df' % tuple(ncv)
AOSHELL[charge] = [c_conf, cv_conf]
sys.stderr.write('Update %s conf: core %s core+valence %s\n' %
(element, c_conf, cv_conf))
def set_atom_conf(element, description):
"""Change the default atomic core and valence configuration to the one
given by "description".
See lo.nao.AOSHELL for the default configuration.
Args:
element : str or int
Element symbol or nuclear charge
description : str or a list of str
| "double p" : double p shell
| "double d" : double d shell
| "double f" : double f shell
| "polarize" : add one polarized shell
| "1s1d" : keep core unchanged and set 1 s 1 d shells for valence
| ("3s2p","1d") : 3 s, 2 p shells for core and 1 d shells for valence
"""
charge = mole._charge(element)
def to_conf(desc):
desc = desc.replace(" ", "").replace("-", "").replace("_", "").lower()
if "doublep" in desc:
desc = "2p"
elif "doubled" in desc:
desc = "2d"
elif "doublef" in desc:
desc = "2f"
elif "polarize" in desc:
loc = AOSHELL[charge][1].find("0")
desc = "1" + AOSHELL[charge][1][loc + 1]
return desc
if isinstance(description, str):
c_desc, v_desc = AOSHELL[charge][0], to_conf(description)
else:
c_desc, v_desc = to_conf(description[0]), to_conf(description[1])
ncore = [int(x) for x in AOSHELL[charge][0][::2]]
ncv = [int(x) for x in AOSHELL[charge][1][::2]]
for i, s in enumerate(("s", "p", "d", "f")):
if s in c_desc:
ncore[i] = int(c_desc.split(s)[0][-1])
if s in v_desc:
ncv[i] = ncore[i] + int(v_desc.split(s)[0][-1])
c_conf = "%ds%dp%dd%df" % tuple(ncore)
cv_conf = "%ds%dp%dd%df" % tuple(ncv)
AOSHELL[charge] = [c_conf, cv_conf]
sys.stderr.write("Update %s conf: core %s core+valence %s\n" % (element, c_conf, cv_conf))
def __init__(self, atoms, basis=None):
self.atomtypes = mole.atom_types(atoms, basis)
# fake systems, which treates the atoms of different basis as different atoms.
# the fake systems do not have the same symmetry as the potential
# it's only used to determine the main (Z-)axis
chg1 = numpy.pi - 2
coords = []
fake_chgs = []
idx = []
for k, lst in self.atomtypes.items():
idx.append(lst)
coords.append([atoms[i][1] for i in lst])
ksymb = mole._rm_digit(k)
if ksymb != k or ksymb == 'GHOST':
# Put random charges on the decorated atoms
fake_chgs.append([chg1] * len(lst))
chg1 *= numpy.pi-2
else:
fake_chgs.append([mole._charge(ksymb)] * len(lst))
coords = numpy.array(numpy.vstack(coords), dtype=float)
fake_chgs = numpy.hstack(fake_chgs)
self.charge_center = numpy.einsum('i,ij->j', fake_chgs, coords)/fake_chgs.sum()
coords = coords - self.charge_center
idx = numpy.argsort(numpy.hstack(idx))
self.atoms = numpy.hstack((fake_chgs.reshape(-1,1), coords))[idx]
self.group_atoms_by_distance = []
decimals = int(-numpy.log10(TOLERANCE)) - 1
for index in self.atomtypes.values():
index = numpy.asarray(index)
c = self.atoms[index,1:]
dists = numpy.around(norm(c, axis=1), decimals)
u, idx = numpy.unique(dists, return_inverse=True)
for i, s in enumerate(u):
self.group_atoms_by_distance.append(index[idx == i])
def get_mass_center(atoms):
mass = numpy.array([pyscf.lib.parameters.ELEMENTS[mole._charge(a[0])][1]
for a in atoms])
coords = numpy.array([a[1] for a in atoms], dtype=float)
rbar = numpy.einsum('i,ij->j', mass, coords)/mass.sum()
return rbar
def get_charge_center(atoms):
charge = numpy.array([mole._charge(a[0]) for a in atoms])
coords = numpy.array([a[1] for a in atoms], dtype=float)
rbar = numpy.einsum('i,ij->j', charge, coords)/charge.sum()
return rbar
def get_nuc_g_factor(symb, mass=None):
Z = mole._charge(symb)
# g factor of other isotopes can be found in file nuclear_g_factor.dat
nuc_spin, g_nuc = ISOTOPE[Z][1:3]
#gyromag = g_factor_to_gyromagnetic_ratio(g_nuc)
return g_nuc
