def aug_etb_for_dfbasis(mol, dfbasis='weigend', beta=2.3, start_at='Rb'):
'''augment weigend basis with even tempered gaussian basis
exps = alpha*beta^i for i = 1..N
'''
nuc_start = gto.mole._charge(start_at)
uniq_atoms = set([a[0] for a in mol._atom])
newbasis = {}
for symb in uniq_atoms:
nuc_charge = gto.mole._charge(symb)
if nuc_charge < nuc_start:
newbasis[symb] = dfbasis
#?elif symb in mol._ecp:
else:
conf = lib.parameters.ELEMENTS[nuc_charge][2]
max_shells = 4 - conf.count(0)
emin_by_l = [1e99] * 8
emax_by_l = [0] * 8
for b in mol._basis[symb]:
l = b[0]
if l >= max_shells + 1:
continue
if isinstance(b[1], int):
e_c = numpy.array(b[2:])
else:
e_c = numpy.array(b[1:])
es = e_c[:, 0]
cs = e_c[:, 1:]
es = es[abs(cs).max(axis=1) > 1e-3]
emax_by_l[l] = max(es.max(), emax_by_l[l])
emin_by_l[l] = min(es.min(), emin_by_l[l])
l_max = 8 - emax_by_l.count(0)
emin_by_l = numpy.array(emin_by_l[:l_max])
emax_by_l = numpy.array(emax_by_l[:l_max])
# Estimate the exponents ranges by geometric average
emax = numpy.sqrt(numpy.einsum('i,j->ij', emax_by_l, emax_by_l))
emin = numpy.sqrt(numpy.einsum('i,j->ij', emin_by_l, emin_by_l))
liljsum = numpy.arange(l_max)[:, None] + numpy.arange(l_max)
emax_by_l = [
emax[liljsum == ll].max() for ll in range(l_max * 2 - 1)
]
emin_by_l = [
emin[liljsum == ll].min() for ll in range(l_max * 2 - 1)
]
# Tune emin and emax
emin_by_l = numpy.array(
emin_by_l) * 2 # *2 for alpha+alpha on same center
emax_by_l = numpy.array(
emax_by_l) * 2 #/ (numpy.arange(l_max*2-1)*.5+1)
ns = numpy.log(
(emax_by_l + emin_by_l) / emin_by_l) / numpy.log(beta)
etb = [(l, max(n, 1), emin_by_l[l], beta)
for l, n in enumerate(numpy.ceil(ns).astype(int))]
newbasis[symb] = gto.expand_etbs(etb)
return newbasis
def aug_etb_for_dfbasis(mol, dfbasis=DFBASIS, beta=ETB_BETA,
start_at=FIRST_ETB_ELEMENT):
'''augment weigend basis with even-tempered gaussian basis
exps = alpha*beta^i for i = 1..N
'''
nuc_start = gto.charge(start_at)
uniq_atoms = set([a[0] for a in mol._atom])
newbasis = {}
for symb in uniq_atoms:
nuc_charge = gto.charge(symb)
if nuc_charge < nuc_start:
newbasis[symb] = dfbasis
#?elif symb in mol._ecp:
else:
conf = elements.CONFIGURATION[nuc_charge]
max_shells = 4 - conf.count(0)
emin_by_l = [1e99] * 8
emax_by_l = [0] * 8
l_max = 0
for b in mol._basis[symb]:
l = b[0]
l_max = max(l_max, l)
if l >= max_shells+1:
continue
if isinstance(b[1], int):
e_c = numpy.array(b[2:])
else:
e_c = numpy.array(b[1:])
es = e_c[:,0]
cs = e_c[:,1:]
es = es[abs(cs).max(axis=1) > 1e-3]
emax_by_l[l] = max(es.max(), emax_by_l[l])
emin_by_l[l] = min(es.min(), emin_by_l[l])
l_max1 = l_max + 1
emin_by_l = numpy.array(emin_by_l[:l_max1])
emax_by_l = numpy.array(emax_by_l[:l_max1])
# Estimate the exponents ranges by geometric average
emax = numpy.sqrt(numpy.einsum('i,j->ij', emax_by_l, emax_by_l))
emin = numpy.sqrt(numpy.einsum('i,j->ij', emin_by_l, emin_by_l))
liljsum = numpy.arange(l_max1)[:,None] + numpy.arange(l_max1)
emax_by_l = [emax[liljsum==ll].max() for ll in range(l_max1*2-1)]
emin_by_l = [emin[liljsum==ll].min() for ll in range(l_max1*2-1)]
# Tune emin and emax
emin_by_l = numpy.array(emin_by_l) * 2 # *2 for alpha+alpha on same center
emax_by_l = numpy.array(emax_by_l) * 2 #/ (numpy.arange(l_max1*2-1)*.5+1)
ns = numpy.log((emax_by_l+emin_by_l)/emin_by_l) / numpy.log(beta)
etb = []
for l, n in enumerate(numpy.ceil(ns).astype(int)):
if n > 0:
etb.append((l, n, emin_by_l[l], beta))
newbasis[symb] = gto.expand_etbs(etb)
return newbasis
def build_nuc_mole(self, atom_index, frac=None):
'''
Return a Mole object for specified quantum nuclei.
Nuclear basis:
H: PB4-D J. Chem. Phys. 152, 244123 (2020)
D: scaled PB4-D
other atoms: 12s12p12d, alpha=2*sqrt(2)*mass, beta=sqrt(3)
'''
nuc = gto.Mole() # a Mole object for quantum nuclei
nuc.atom_index = atom_index
nuc.super_mol = self
dirnow = os.path.realpath(os.path.join(__file__, '..'))
if self.atom_symbol(atom_index) == 'H@2':
basis = gto.basis.parse(open(os.path.join(dirnow, 'basis/s-pb4d.dat')).read())
elif self.atom_pure_symbol(atom_index) == 'H':
basis = gto.basis.parse(open(os.path.join(dirnow, 'basis/pb4d.dat')).read())
#alpha = 2 * numpy.sqrt(2) * self.mass[atom_index]
#beta = numpy.sqrt(2)
#n = 8
#basis = gto.expand_etbs([(0, n, alpha, beta), (1, n, alpha, beta), (2, n, alpha, beta)])
else:
# even-tempered basis
alpha = 2 * numpy.sqrt(2) * self.mass[atom_index]
beta = numpy.sqrt(3)
n = 12
basis = gto.expand_etbs([(0, n, alpha, beta), (1, n, alpha, beta), (2, n, alpha, beta)])
#logger.info(self, 'Nuclear basis for %s: n %s alpha %s beta %s' %(self.atom_symbol(atom_index), n, alpha, beta))
nuc.build(atom = self.atom, basis={self.atom_symbol(atom_index): basis},
charge = self.charge, cart = self.cart, spin = self.spin)
# set all quantum nuclei to have zero charges
quantum_nuclear_charge = 0
for i in range(self.natm):
if self.quantum_nuc[i] is True:
quantum_nuclear_charge -= nuc._atm[i, 0]
nuc._atm[i, 0] = 0 # set nuclear charges of quantum nuclei to 0
nuc.charge += quantum_nuclear_charge
# avoid UHF
nuc.spin = 0
nuc.nelectron = 2
# fractional
if frac is not None:
nuc.nnuc = frac
else:
nuc.nnuc = 1
return nuc
def aug_etb_for_dfbasis(mol, dfbasis='weigend', beta=2.3, start_at='Rb'):
'''augment weigend basis with even tempered gaussian basis
exps = alpha*beta^i for i = 1..N
'''
nuc_start = gto.mole._charge(start_at)
uniq_atoms = set([a[0] for a in mol._atom])
newbasis = {}
for symb in uniq_atoms:
nuc_charge = gto.mole._charge(symb)
if nuc_charge < nuc_start:
newbasis[symb] = dfbasis
#?elif symb in mol._ecp:
else:
conf = lib.parameters.ELEMENTS[nuc_charge][2]
max_shells = 4 - conf.count(0)
emin_by_l = [1e99] * 8
emax_by_l = [0] * 8
for b in mol._basis[symb]:
l = b[0]
if l >= max_shells+1:
continue
if isinstance(b[1], int):
e_c = numpy.array(b[2:])
else:
e_c = numpy.array(b[1:])
es = e_c[:,0]
cs = e_c[:,1:]
es = es[abs(cs).max(axis=1) > 1e-3]
emax_by_l[l] = max(es.max(), emax_by_l[l])
emin_by_l[l] = min(es.min(), emin_by_l[l])
l_max = 8 - emax_by_l.count(0)
emin_by_l = numpy.array(emin_by_l[:l_max])
emax_by_l = numpy.array(emax_by_l[:l_max])
# Estimate the exponents ranges by geometric average
emax = numpy.sqrt(numpy.einsum('i,j->ij', emax_by_l, emax_by_l))
emin = numpy.sqrt(numpy.einsum('i,j->ij', emin_by_l, emin_by_l))
liljsum = numpy.arange(l_max)[:,None] + numpy.arange(l_max)
emax_by_l = [emax[liljsum==ll].max() for ll in range(l_max*2-1)]
emin_by_l = [emin[liljsum==ll].min() for ll in range(l_max*2-1)]
# Tune emin and emax
emin_by_l = numpy.array(emin_by_l) * 2 # *2 for alpha+alpha on same center
emax_by_l = numpy.array(emax_by_l) * 2 #/ (numpy.arange(l_max*2-1)*.5+1)
ns = numpy.log((emax_by_l+emin_by_l)/emin_by_l) / numpy.log(beta)
etb = [(l, max(n,1), emin_by_l[l], beta)
for l, n in enumerate(numpy.ceil(ns).astype(int))]
newbasis[symb] = gto.expand_etbs(etb)
return newbasis
O SP
5.0331513 -0.09996723 0.15591627
1.1695961 0.39951283 0.60768372
0.3803890 0.70011547 0.39195739
'''),
'H1': gto.load(basis_file_from_user, 'H'),
'H2': gto.load('sto-3g', 'He') # or use basis of another atom
}
)
mol = gto.M(
atom = '''O 0 0 0; H1 0 1 0; H2 0 0 1''',
basis = {'O': 'unc-ccpvdz', # prefix "unc-" will uncontract the ccpvdz basis.
# It is equivalent to assigning
# 'O': gto.uncontract(gto.load('ccpvdz', 'O')),
'H': 'ccpvdz' # H1 H2 will use the same basis ccpvdz
}
)
mol = gto.M(
atom = '''O 0 0 0; H1 0 1 0; H2 0 0 1''',
basis = {'H': 'sto3g',
# even-temper gaussians alpha*beta^i, where i = 0,..,n
# (l, n, alpha, beta)
'O': gto.expand_etbs([(0, 4, 1.5, 2.2), # s-function
(1, 2, 0.5, 2.2)]) # p-function
}
)
# better resolution of auxiliary basis) is the use of function gto.expand_etbs.
#
# Note the PBC Gaussian DF module will automatically remove diffused Gaussian
# fitting functions. It is controlled by the parameter eta. The default value is
# 0.2 which removes all Gaussians whose exponents are smaller than 0.2.
# When your input DF basis has diffused functions, you need to reduce the
# value of mf.with_df.eta to reserve the diffused functions. However,
# keeping diffused functions occasionally lead numerical noise in the GDF
# method.
#
auxbasis = {
'C':
# (l, N, alpha, beta)
mol_gto.expand_etbs([
(0, 25, 0.15, 1.6), # 25s
(1, 20, 0.15, 1.6), # 20p
(2, 10, 0.15, 1.6), # 10d
(3, 5, 0.15, 1.6), # 5f
])
}
mf = scf.RHF(cell).density_fit(auxbasis=auxbasis)
mf.with_df.eta = 0.1
mf.kernel()
#
# The 3-index density fitting tensor can be loaded from the _cderi file.
# Using the 3-index tensor, the 4-center integrals can be constructed:
# (pq|rs) = \sum_L A_lpq A_lrs
#
# The 3-index tensor for gamma point can be accessed with the code snippet
# below. Assuming in the first pass, the GDF 3-index tensors are saved with
# the following code
mf = scf.RHF(mol)
mf.kernel()
#
# First method is to explicit call the functions provided by molden.py
#
with open("C6H6mo.molden", "w") as f1:
molden.header(mol, f1)
molden.orbital_coeff(mol, f1, mf.mo_coeff, ene=mf.mo_energy, occ=mf.mo_occ)
#
# Second method is to simply call from_mo function to write the orbitals
#
c_loc_orth = lo.orth.orth_ao(mol)
molden.from_mo(mol, "C6H6loc.molden", c_loc_orth)
#
# Molden format does not support high angular momentum basis. To handle the
# orbitals which have l>=5 functions, a hacky way is to call molden.remove_high_l
# function. However, the resultant orbitals may not be orthnormal.
#
mol = gto.M(atom="He 0 0 0", basis={"He": gto.expand_etbs(((0, 3, 1.0, 2.0), (5, 2, 1.0, 2.0)))})
mf = scf.RHF(mol).run()
try:
molden.from_mo(mol, "He_without_h.molden", mf.mo_coeff)
except RuntimeError:
print(" Found l=5 in basis.")
molden.from_mo(mol, "He_without_h.molden", mf.mo_coeff, ignore_h=True)
import numpy as np
from pyscf import gto, scf
from kspies import wy
mol = gto.M(atom='N 0 0 0 ; N 1.1 0 0', basis='cc-pVDZ')
mf = scf.RHF(mol).run()
dm_tar = mf.make_rdm1()
PBS = gto.expand_etbs([(0, 13, 2**-4, 2), (1, 3, 2**-2, 2)])
mw = wy.RWY(mol, dm_tar, pbas=PBS)
#Note that for this designed-to-be ill-conditioned problem,
#Hessian-based optimization algorithms are problematic.
mw.method = 'bfgs'
mw.tol = 2e-7
mw.run()
mw.info()
Ws_fin = mw.Ws
etas = [2.**(-a) for a in np.linspace(5., 27., 45)]
v = np.zeros(len(etas))
W = np.zeros(len(etas))
for i, eta in enumerate(etas):
mw.reg = eta
mw.run()
v[i] = mw.Dvb()
W[i] = mw.Ws
mw.info()
import matplotlib.pyplot as plt
fig, ax = plt.subplots(2)
ax[0].scatter(np.log10(Ws_fin - W), np.log10(v))
mf.kernel()
#
# First method is to explicit call the functions provided by molden.py
#
with open('C6H6mo.molden', 'w') as f1:
molden.header(mol, f1)
molden.orbital_coeff(mol, f1, mf.mo_coeff, ene=mf.mo_energy, occ=mf.mo_occ)
#
# Second method is to simply call from_mo function to write the orbitals
#
c_loc_orth = lo.orth.orth_ao(mol)
molden.from_mo(mol, 'C6H6loc.molden', c_loc_orth)
#
# Molden format does not support high angular momentum basis. To handle the
# orbitals which have l>=5 functions, a hacky way is to call molden.remove_high_l
# function. However, the resultant orbitals may not be orthnormal.
#
mol = gto.M(
atom = 'He 0 0 0',
basis = {'He': gto.expand_etbs(((0, 3, 1., 2.), (5, 2, 1., 2.)))})
mf = scf.RHF(mol).run()
try:
molden.from_mo(mol, 'He_without_h.molden', mf.mo_coeff)
except RuntimeError:
print(' Found l=5 in basis.')
molden.from_mo(mol, 'He_without_h.molden', mf.mo_coeff, ignore_h=True)
# Another straightforward way to input even-tempered Gaussian basis (for
# better resolution of auxiliary basis) is the use of function gto.expand_etbs.
#
# Note the PBC Gaussian DF module will automatically remove diffused Gaussian
# fitting functions. It is controlled by the parameter eta. The default value is
# 0.2 which removes all Gaussians whose exponents are smaller than 0.2.
# When your input DF basis has diffused functions, you need to reduce the
# value of mf.with_df.eta to reserve the diffused functions. However,
# keeping diffused functions occasionally lead numerical noise in the GDF
# method.
#
auxbasis = {'C':
# (l, N, alpha, beta)
mol_gto.expand_etbs([(0, 25, 0.15, 1.6), # 25s
(1, 20, 0.15, 1.6), # 20p
(2, 10, 0.15, 1.6), # 10d
(3, 5 , 0.15, 1.6), # 5f
])
}
mf = scf.RHF(cell).density_fit(auxbasis=auxbasis)
mf.with_df.eta = 0.1
mf.kernel()
#
# The 3-index density fitting tensor can be loaded from the _cderi file.
# Using the 3-index tensor, the 4-center integrals can be constructed:
# (pq|rs) = \sum_L A_lpq A_lrs
#
# The 3-index tensor for gamma point can be accessed with the code snippet
# below. Assuming in the first pass, the GDF 3-index tensors are saved with