def make_modchg_basis(auxcell, smooth_eta):
# * chgcell defines smooth gaussian functions for each angular momentum for
# auxcell. The smooth functions may be used to carry the charge
chgcell = copy.copy(
auxcell) # smooth model density for coulomb integral to carry charge
half_sph_norm = .5 / numpy.sqrt(numpy.pi)
chg_bas = []
chg_env = [smooth_eta]
ptr_eta = auxcell._env.size
ptr = ptr_eta + 1
l_max = auxcell._bas[:, gto.ANG_OF].max()
# gaussian_int(l*2+2) for multipole integral:
# \int (r^l e^{-ar^2} * Y_{lm}) (r^l Y_{lm}) r^2 dr d\Omega
norms = [
half_sph_norm / gto.gaussian_int(l * 2 + 2, smooth_eta)
for l in range(l_max + 1)
]
for ia in range(auxcell.natm):
for l in set(auxcell._bas[auxcell._bas[:, gto.ATOM_OF] == ia,
gto.ANG_OF]):
chg_bas.append([ia, l, 1, 1, 0, ptr_eta, ptr, 0])
chg_env.append(norms[l])
ptr += 1
chgcell._atm = auxcell._atm
chgcell._bas = numpy.asarray(chg_bas,
dtype=numpy.int32).reshape(-1, gto.BAS_SLOTS)
chgcell._env = numpy.hstack((auxcell._env, chg_env))
chgcell.rcut = _estimate_rcut(smooth_eta, l_max, 1., auxcell.precision)
logger.debug1(auxcell,
'make compensating basis, num shells = %d, num cGTOs = %d',
chgcell.nbas, chgcell.nao_nr())
logger.debug1(auxcell, 'chgcell.rcut %s', chgcell.rcut)
return chgcell
def make_modchg_basis(auxcell, smooth_eta):
# * chgcell defines smooth gaussian functions for each angular momentum for
# auxcell. The smooth functions may be used to carry the charge
chgcell = copy.copy(auxcell) # smooth model density for coulomb integral to carry charge
half_sph_norm = .5/numpy.sqrt(numpy.pi)
chg_bas = []
chg_env = [smooth_eta]
ptr_eta = auxcell._env.size
ptr = ptr_eta + 1
l_max = auxcell._bas[:,gto.ANG_OF].max()
# gaussian_int(l*2+2) for multipole integral:
# \int (r^l e^{-ar^2} * Y_{lm}) (r^l Y_{lm}) r^2 dr d\Omega
norms = [half_sph_norm/gto.gaussian_int(l*2+2, smooth_eta)
for l in range(l_max+1)]
for ia in range(auxcell.natm):
for l in set(auxcell._bas[auxcell._bas[:,gto.ATOM_OF]==ia, gto.ANG_OF]):
chg_bas.append([ia, l, 1, 1, 0, ptr_eta, ptr, 0])
chg_env.append(norms[l])
ptr += 1
chgcell._atm = auxcell._atm
chgcell._bas = numpy.asarray(chg_bas, dtype=numpy.int32).reshape(-1,gto.BAS_SLOTS)
chgcell._env = numpy.hstack((auxcell._env, chg_env))
chgcell.rcut = _estimate_rcut(smooth_eta, l_max, 1., auxcell.precision)
logger.debug1(auxcell, 'make compensating basis, num shells = %d, num cGTOs = %d',
chgcell.nbas, chgcell.nao_nr())
logger.debug1(auxcell, 'chgcell.rcut %s', chgcell.rcut)
return chgcell
def make_modrho_basis(cell, auxbasis=None, drop_eta=1.):
auxcell = copy.copy(cell)
if auxbasis is None:
auxbasis = 'weigend+etb'
if isinstance(auxbasis, str):
uniq_atoms = set([a[0] for a in cell._atom])
_basis = auxcell.format_basis(dict([(a, auxbasis)
for a in uniq_atoms]))
else:
_basis = auxcell.format_basis(auxbasis)
auxcell._basis = _basis
auxcell._atm, auxcell._bas, auxcell._env = \
auxcell.make_env(cell._atom, auxcell._basis, cell._env[:gto.PTR_ENV_START])
# Note libcint library will multiply the norm of the integration over spheric
# part sqrt(4pi) to the basis.
half_sph_norm = numpy.sqrt(.25 / numpy.pi)
steep_shls = []
ndrop = 0
rcut = []
for ib in range(len(auxcell._bas)):
l = auxcell.bas_angular(ib)
np = auxcell.bas_nprim(ib)
nc = auxcell.bas_nctr(ib)
es = auxcell.bas_exp(ib)
ptr = auxcell._bas[ib, gto.PTR_COEFF]
cs = auxcell._env[ptr:ptr + np * nc].reshape(nc, np).T
if numpy.any(es < drop_eta):
cs = cs[es >= drop_eta]
es = es[es >= drop_eta]
np, ndrop = len(es), ndrop + np - len(es)
pe = auxcell._bas[ib, gto.PTR_EXP]
auxcell._bas[ib, gto.NPRIM_OF] = np
auxcell._env[pe:pe + np] = es
if np > 0:
# int1 is the multipole value. l*2+2 is due to the radial part integral
# \int (r^l e^{-ar^2} * Y_{lm}) (r^l Y_{lm}) r^2 dr d\Omega
int1 = gto.mole._gaussian_int(l * 2 + 2, es)
s = numpy.einsum('pi,p->i', cs, int1)
# The auxiliary basis normalization factor is not a must for density expansion.
# half_sph_norm here to normalize the monopole (charge). This convention can
# simplify the formulism of \int \bar{\rho}, see function auxbar.
cs = numpy.einsum('pi,i->pi', cs, half_sph_norm / s)
auxcell._env[ptr:ptr + np * nc] = cs.T.reshape(-1)
steep_shls.append(ib)
rcut.append(_estimate_rcut(es.min(), l, 1., 20, cell.precision))
auxcell.rcut = max(rcut)
auxcell._bas = numpy.asarray(auxcell._bas[steep_shls], order='C')
auxcell._built = True
logger.debug(cell, 'Drop %d primitive fitting functions', ndrop)
logger.debug(cell, 'make aux basis, num shells = %d, num cGTOs = %d',
auxcell.nbas, auxcell.nao_nr())
logger.debug(cell, 'auxcell.rcut %s', auxcell.rcut)
return auxcell
def make_modrho_basis(cell, auxbasis=None, drop_eta=None):
auxcell = addons.make_auxmol(cell, auxbasis)
# Note libcint library will multiply the norm of the integration over spheric
# part sqrt(4pi) to the basis.
half_sph_norm = numpy.sqrt(.25 / numpy.pi)
steep_shls = []
ndrop = 0
rcut = []
_env = auxcell._env.copy()
for ib in range(len(auxcell._bas)):
l = auxcell.bas_angular(ib)
np = auxcell.bas_nprim(ib)
nc = auxcell.bas_nctr(ib)
es = auxcell.bas_exp(ib)
ptr = auxcell._bas[ib, gto.PTR_COEFF]
cs = auxcell._env[ptr:ptr + np * nc].reshape(nc, np).T
if drop_eta is not None and numpy.any(es < drop_eta):
cs = cs[es >= drop_eta]
es = es[es >= drop_eta]
np, ndrop = len(es), ndrop + np - len(es)
if np > 0:
pe = auxcell._bas[ib, gto.PTR_EXP]
auxcell._bas[ib, gto.NPRIM_OF] = np
_env[pe:pe + np] = es
# int1 is the multipole value. l*2+2 is due to the radial part integral
# \int (r^l e^{-ar^2} * Y_{lm}) (r^l Y_{lm}) r^2 dr d\Omega
int1 = gto.gaussian_int(l * 2 + 2, es)
s = numpy.einsum('pi,p->i', cs, int1)
# The auxiliary basis normalization factor is not a must for density expansion.
# half_sph_norm here to normalize the monopole (charge). This convention can
# simplify the formulism of \int \bar{\rho}, see function auxbar.
cs = numpy.einsum('pi,i->pi', cs, half_sph_norm / s)
_env[ptr:ptr + np * nc] = cs.T.reshape(-1)
steep_shls.append(ib)
r = _estimate_rcut(es, l, abs(cs).max(axis=1), cell.precision)
rcut.append(r.max())
auxcell._env = _env
auxcell.rcut = max(rcut)
auxcell._bas = numpy.asarray(auxcell._bas[steep_shls], order='C')
logger.info(cell, 'Drop %d primitive fitting functions', ndrop)
logger.info(cell, 'make aux basis, num shells = %d, num cGTOs = %d',
auxcell.nbas, auxcell.nao_nr())
logger.info(cell, 'auxcell.rcut %s', auxcell.rcut)
return auxcell
def make_modrho_basis(cell, auxbasis=None, drop_eta=None):
auxcell = addons.make_auxmol(cell, auxbasis)
# Note libcint library will multiply the norm of the integration over spheric
# part sqrt(4pi) to the basis.
half_sph_norm = numpy.sqrt(.25/numpy.pi)
steep_shls = []
ndrop = 0
rcut = []
for ib in range(len(auxcell._bas)):
l = auxcell.bas_angular(ib)
np = auxcell.bas_nprim(ib)
nc = auxcell.bas_nctr(ib)
es = auxcell.bas_exp(ib)
ptr = auxcell._bas[ib,gto.PTR_COEFF]
cs = auxcell._env[ptr:ptr+np*nc].reshape(nc,np).T
if drop_eta is not None and numpy.any(es < drop_eta):
cs = cs[es>=drop_eta]
es = es[es>=drop_eta]
np, ndrop = len(es), ndrop+np-len(es)
if np > 0:
pe = auxcell._bas[ib,gto.PTR_EXP]
auxcell._bas[ib,gto.NPRIM_OF] = np
auxcell._env[pe:pe+np] = es
# int1 is the multipole value. l*2+2 is due to the radial part integral
# \int (r^l e^{-ar^2} * Y_{lm}) (r^l Y_{lm}) r^2 dr d\Omega
int1 = gto.gaussian_int(l*2+2, es)
s = numpy.einsum('pi,p->i', cs, int1)
# The auxiliary basis normalization factor is not a must for density expansion.
# half_sph_norm here to normalize the monopole (charge). This convention can
# simplify the formulism of \int \bar{\rho}, see function auxbar.
cs = numpy.einsum('pi,i->pi', cs, half_sph_norm/s)
auxcell._env[ptr:ptr+np*nc] = cs.T.reshape(-1)
steep_shls.append(ib)
r = _estimate_rcut(es, l, abs(cs).max(axis=1), cell.precision)
rcut.append(r.max())
auxcell.rcut = max(rcut)
auxcell._bas = numpy.asarray(auxcell._bas[steep_shls], order='C')
logger.info(cell, 'Drop %d primitive fitting functions', ndrop)
logger.info(cell, 'make aux basis, num shells = %d, num cGTOs = %d',
auxcell.nbas, auxcell.nao_nr())
logger.info(cell, 'auxcell.rcut %s', auxcell.rcut)
return auxcell