def auxmol_set(self, mol, auxbas="weigend"):
"""
Generate 2c/3c electron integral (eri2c,eri3c)
Generate ovlp matrix (S), and AO to Lowdin AO matrix transformation matrix (X)
Args:
mol: Mole class
Default is ks.mol
Kwargs:
auxbas: str
auxilliary basis for 2c/3c eri. Default is weigend
Returns:
eri3c: float
3 center eri. shape: (AO,AO,AUX)
eri2c: float
2 center eri. shape: (AUX,AUX)
"""
auxmol = gto.Mole()
auxmol.atom = mol.atom
auxmol.basis = auxbas
auxmol.build()
self.auxmol = auxmol
atm, bas, env = gto.conc_env(mol._atm, mol._bas, mol._env, auxmol._atm,\
auxmol._bas, auxmol._env)
eri3c = df.incore.aux_e2(mol, auxmol, intor="cint3c2e_sph", aosym="s1",\
comp=1 )
eri2c = df.incore.fill_2c2e(mol, auxmol)
self.eri3c = eri3c.copy()
self.eri2c = eri2c.copy()
return eri3c, eri2c
def fuse_auxcell(mydf, auxcell):
chgcell = make_modchg_basis(auxcell, mydf.eta)
fused_cell = copy.copy(auxcell)
fused_cell._atm, fused_cell._bas, fused_cell._env = \
gto.conc_env(auxcell._atm, auxcell._bas, auxcell._env,
chgcell._atm, chgcell._bas, chgcell._env)
fused_cell.rcut = max(auxcell.rcut, chgcell.rcut)
aux_loc = auxcell.ao_loc_nr()
naux = aux_loc[-1]
modchg_offset = -numpy.ones((chgcell.natm, 8), dtype=int)
smooth_loc = chgcell.ao_loc_nr()
for i in range(chgcell.nbas):
ia = chgcell.bas_atom(i)
l = chgcell.bas_angular(i)
modchg_offset[ia, l] = smooth_loc[i]
def fuse(Lpq):
Lpq, chgLpq = Lpq[:naux], Lpq[naux:]
for i in range(auxcell.nbas):
l = auxcell.bas_angular(i)
ia = auxcell.bas_atom(i)
p0 = modchg_offset[ia, l]
if p0 >= 0:
nd = (aux_loc[i + 1] - aux_loc[i]) // auxcell.bas_nctr(i)
for i0, i1 in lib.prange(aux_loc[i], aux_loc[i + 1], nd):
Lpq[i0:i1] -= chgLpq[p0:p0 + nd]
return Lpq
return fused_cell, fuse
def int_ket(_bas, intor):
if len(_bas) == 0:
return []
atm, bas, env = gto.conc_env(cell._atm, cell._bas, cell._env,
fakecell._atm, _bas, fakecell._env)
atm = numpy.asarray(atm, dtype=numpy.int32)
bas = numpy.asarray(bas, dtype=numpy.int32)
env = numpy.asarray(env, dtype=numpy.double)
natm = len(atm)
nbas = len(bas)
shls_slice = (cell.nbas, nbas, 0, cell.nbas)
ao_loc = gto.moleintor.make_loc(bas, intor)
ni = ao_loc[shls_slice[1]] - ao_loc[shls_slice[0]]
nj = ao_loc[shls_slice[3]] - ao_loc[shls_slice[2]]
out = [numpy.zeros((ni,nj), order='F', dtype=numpy.complex128)
for k in range(nkpts)]
out_ptrs = (ctypes.c_void_p*nkpts)(
*[x.ctypes.data_as(ctypes.c_void_p) for x in out])
comp = 1
fintor = getattr(gto.moleintor.libcgto, intor)
ptr_coords = numpy.asarray(atm[:cell.natm,gto.PTR_COORD],
dtype=numpy.int32, order='C')
drv = libpbc.PBCnr2c_drv
drv(fintor, fill, out_ptrs, xyz.ctypes.data_as(ctypes.c_void_p),
ptr_coords.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(cell.natm),
Ls.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(len(Ls)),
expLk.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(nkpts),
ctypes.c_int(comp), (ctypes.c_int*4)(*(shls_slice[:4])),
ao_loc.ctypes.data_as(ctypes.c_void_p), intopt,
atm.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(natm),
bas.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(nbas),
env.ctypes.data_as(ctypes.c_void_p))
return out
def test_aux_e2_diff_bra_ket(self):
mol1 = mol.copy()
mol1.basis = 'sto3g'
mol1.build(0, 0, verbose=0)
atm1, bas1, env1 = gto.conc_env(atm, bas, env,
mol1._atm, mol1._bas, mol1._env)
ao_loc = gto.moleintor.make_loc(bas1, 'int3c2e_sph')
shls_slice = (0, mol.nbas,
mol.nbas+auxmol.nbas, mol.nbas+auxmol.nbas+mol1.nbas,
mol.nbas, mol.nbas+auxmol.nbas)
j3c = gto.moleintor.getints3c('int3c2e_sph', atm1, bas1, env1, comp=1,
shls_slice=shls_slice, aosym='s1', ao_loc=ao_loc)
nao = mol.nao_nr()
naoj = mol1.nao_nr()
naoaux = auxmol.nao_nr()
eri0 = numpy.empty((nao,naoj,naoaux))
pi = 0
for i in range(mol.nbas):
pj = 0
for j in range(mol.nbas+auxmol.nbas, len(bas1)):
pk = 0
for k in range(mol.nbas, mol.nbas+auxmol.nbas):
shls = (i, j, k)
buf = gto.moleintor.getints_by_shell('int3c2e_sph',
shls, atm1, bas1, env1)
di, dj, dk = buf.shape
eri0[pi:pi+di,pj:pj+dj,pk:pk+dk] = buf
pk += dk
pj += dj
pi += di
self.assertTrue(numpy.allclose(eri0, j3c))
def _int_nuc_vloc(mydf, nuccell, kpts, intor='int3c2e_sph'):
'''Vnuc - Vloc'''
cell = mydf.cell
nkpts = len(kpts)
# Use the 3c2e code with steep s gaussians to mimic nuclear density
fakenuc = _fake_nuc(cell)
fakenuc._atm, fakenuc._bas, fakenuc._env = \
gto.conc_env(nuccell._atm, nuccell._bas, nuccell._env,
fakenuc._atm, fakenuc._bas, fakenuc._env)
kptij_lst = numpy.hstack((kpts, kpts)).reshape(-1, 2, 3)
buf = incore.aux_e2(cell, fakenuc, intor, aosym='s2', kptij_lst=kptij_lst)
charge = cell.atom_charges()
charge = numpy.append(charge,
-charge) # (charge-of-nuccell, charge-of-fakenuc)
nao = cell.nao_nr()
nchg = len(charge)
nao_pair = nao * (nao + 1) // 2
buf = buf.reshape(nkpts, nao_pair, nchg)
mat = numpy.einsum('kxz,z->kx', buf, charge)
if cell.dimension == 3:
nucbar = sum([
z / nuccell.bas_exp(i)[0]
for i, z in enumerate(cell.atom_charges())
])
nucbar *= numpy.pi / cell.vol
ovlp = cell.pbc_intor('int1e_ovlp_sph', 1, lib.HERMITIAN, kpts)
for k in range(nkpts):
s = lib.pack_tril(ovlp[k])
mat[k] += nucbar * s
return mat
def fuse_auxcell(mydf, auxcell):
chgcell = make_modchg_basis(auxcell, mydf.eta)
fused_cell = copy.copy(auxcell)
fused_cell._atm, fused_cell._bas, fused_cell._env = \
gto.conc_env(auxcell._atm, auxcell._bas, auxcell._env,
chgcell._atm, chgcell._bas, chgcell._env)
aux_loc = auxcell.ao_loc_nr()
naux = aux_loc[-1]
modchg_offset = -numpy.ones((chgcell.natm,8), dtype=int)
smooth_loc = chgcell.ao_loc_nr()
for i in range(chgcell.nbas):
ia = chgcell.bas_atom(i)
l = chgcell.bas_angular(i)
modchg_offset[ia,l] = smooth_loc[i]
def fuse(Lpq):
Lpq, chgLpq = Lpq[:naux], Lpq[naux:]
for i in range(auxcell.nbas):
l = auxcell.bas_angular(i)
ia = auxcell.bas_atom(i)
p0 = modchg_offset[ia,l]
if p0 >= 0:
nd = (aux_loc[i+1] - aux_loc[i]) // auxcell.bas_nctr(i)
for i0, i1 in lib.prange(aux_loc[i], aux_loc[i+1], nd):
Lpq[i0:i1] -= chgLpq[p0:p0+nd]
return Lpq
return fused_cell, fuse
def hellmann_feynman_df(mol, ia):
"""
Outputs the integral
Z_I*<i|(r-R_I)/|r-R_I|^3|j>
of only one Gaussian using as second Gaussian
an 1s basis funtion of an He atom with
alpha=1e-15 and coeff=1.00000. The result
is divided by the norm of the He function.
"""
# Creating auxiliar Molecule
intmol = gto.Mole()
intmol.atom = '''He 0. 0. 0.'''
intmol.basis = He_flat_basis
intmol.build()
# Merging molecules
atm_x, bas_x, env_x = gto.conc_env(intmol._atm, intmol._bas, intmol._env,\
mol._atm, mol._bas, mol._env)
PTR_RINV_ORIG = 4
env_x[PTR_RINV_ORIG:PTR_RINV_ORIG + 3] = mol.atom_coord(ia)
HF_partial = gto.moleintor.getints('cint1e_drinv_sph',
atm_x,
bas_x,
env_x,
comp=3,
hermi=0,
aosym='s1',
out=None)
return -mol.atom_charge(ia)*\
np.hstack(HF_partial[:,:,:1])[1:]/gto.gto_norm(0,He_exp_flt)
def integral_one_gaussian_polarization(mol):
"""
Outputs the integral <i|r|j> with the only-one-Gaussian trick
using as second Gaussian an 1s basis funtion of an He atom with
alpha=1e-15 and coeff=1.00000. The result is divided by the
norm of the 'dummy' He function.
"""
# Creating auxiliar Molecule
intmol = gto.Mole()
intmol.atom = '''He 0. 0. 0.'''
intmol.basis = He_flat_basis
intmol.build()
# Merging molecules
atm_x, bas_x, env_x = gto.conc_env(intmol._atm, intmol._bas, intmol._env,
mol._atm, mol._bas, mol._env)
# Computing the overlap
PTR_COMMON_ORIG = 1
env_x[PTR_COMMON_ORIG:PTR_COMMON_ORIG + 3] = (
0., 0., 0.) #(mol.atom_coord(1)-mol.atom_coord(0))/2.
#mol.set_common_orig((1.,0.,0.))
HF_partial = gto.moleintor.getints('cint1e_r_sph',
atm_x,
bas_x,
env_x,
comp=3,
hermi=0,
aosym='s1',
out=None)
return np.hstack(HF_partial[:, :, :1])[1:] / gto.gto_norm(0, He_exp_flt)
def int_ket(_bas, intor):
if len(_bas) == 0:
return []
intor = cell._add_suffix(intor)
atm, bas, env = gto.conc_env(cell._atm, cell._bas, cell._env,
fakecell._atm, _bas, fakecell._env)
atm = numpy.asarray(atm, dtype=numpy.int32)
bas = numpy.asarray(bas, dtype=numpy.int32)
env = numpy.asarray(env, dtype=numpy.double)
natm = len(atm)
nbas = len(bas)
shls_slice = (cell.nbas, nbas, 0, cell.nbas)
ao_loc = gto.moleintor.make_loc(bas, intor)
ni = ao_loc[shls_slice[1]] - ao_loc[shls_slice[0]]
nj = ao_loc[shls_slice[3]] - ao_loc[shls_slice[2]]
out = numpy.empty((nkpts, ni, nj), dtype=numpy.complex128)
comp = 1
fintor = getattr(gto.moleintor.libcgto, intor)
drv = libpbc.PBCnr2c_drv
drv(fintor, fill, out.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(nkpts), ctypes.c_int(comp), ctypes.c_int(nimgs),
Ls.ctypes.data_as(ctypes.c_void_p),
expkL.ctypes.data_as(ctypes.c_void_p),
(ctypes.c_int * 4)(*(shls_slice[:4])),
ao_loc.ctypes.data_as(ctypes.c_void_p), intopt, lib.c_null_ptr(),
atm.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(natm),
bas.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(nbas),
env.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(env.size))
return out
def test_aux_e2_diff_bra_ket(self):
mol1 = mol.copy()
mol1.basis = 'sto3g'
mol1.build(0, 0, verbose=0)
j3c = df.incore.aux_e2(mol, auxmol, intor='cint3c2e_sph', aosym='s1',
mol1=mol1)
nao = mol.nao_nr()
naoj = mol1.nao_nr()
naoaux = auxmol.nao_nr()
j3c = j3c.reshape(nao,naoj,naoaux)
atm1, bas1, env1 = gto.conc_env(atm, bas, env,
mol1._atm, mol1._bas, mol1._env)
eri0 = numpy.empty((nao,naoj,naoaux))
pi = 0
for i in range(mol.nbas):
pj = 0
for j in range(mol.nbas+auxmol.nbas, len(bas1)):
pk = 0
for k in range(mol.nbas, mol.nbas+auxmol.nbas):
shls = (i, j, k)
buf = gto.moleintor.getints_by_shell('cint3c2e_sph',
shls, atm1, bas1, env1)
di, dj, dk = buf.shape
eri0[pi:pi+di,pj:pj+dj,pk:pk+dk] = buf
pk += dk
pj += dj
pi += di
self.assertTrue(numpy.allclose(eri0, j3c))
def auxmol_set(self, mol, auxbas = "weigend"):
"""
Generate 2c/3c electron integral (eri2c,eri3c)
Generate ovlp matrix (S), and AO to Lowdin AO matrix transformation matrix (X)
Args:
mol: Mole class
Default is ks.mol
Kwargs:
auxbas: str
auxilliary basis for 2c/3c eri. Default is weigend
Returns:
eri3c: float
3 center eri. shape: (AO,AO,AUX)
eri2c: float
2 center eri. shape: (AUX,AUX)
"""
auxmol = gto.Mole()
auxmol.atom = mol.atom
auxmol.basis = auxbas
auxmol.build()
self.auxmol = auxmol
nao = mol.nao_nr()
naux = auxmol.nao_nr()
atm, bas, env = gto.conc_env(mol._atm, mol._bas, mol._env, auxmol._atm,\
auxmol._bas, auxmol._env)
eri3c = df.incore.aux_e2(mol, auxmol, intor="cint3c2e_sph", aosym="s1",\
comp=1 )
eri2c = df.incore.fill_2c2e(mol,auxmol)
self.eri3c = eri3c.copy()
self.eri2c = eri2c.copy()
return eri3c, eri2c
def ft_ao(mol,
Gv,
shls_slice=None,
b=numpy.eye(3),
gxyz=None,
Gvbase=None,
verbose=None):
''' FT transform AO
'''
if shls_slice is None:
shls_slice = (0, mol.nbas)
nGv = Gv.shape[0]
if (gxyz is None or b is None or Gvbase is None
# backward compatibility for pyscf-1.2, in which the argument Gvbase is gs
or (Gvbase is not None and isinstance(Gvbase[0],
(int, numpy.integer)))):
GvT = numpy.asarray(Gv.T, order='C')
p_gxyzT = lib.c_null_ptr()
p_gs = (ctypes.c_int * 3)(0, 0, 0)
p_b = (ctypes.c_double * 1)(0)
eval_gz = 'GTO_Gv_general'
else:
if abs(b - numpy.diag(b.diagonal())).sum() < 1e-8:
eval_gz = 'GTO_Gv_orth'
else:
eval_gz = 'GTO_Gv_nonorth'
GvT = numpy.asarray(Gv.T, order='C')
gxyzT = numpy.asarray(gxyz.T, order='C', dtype=numpy.int32)
p_gxyzT = gxyzT.ctypes.data_as(ctypes.c_void_p)
b = numpy.hstack((b.ravel(), numpy.zeros(3)) + Gvbase)
p_b = b.ctypes.data_as(ctypes.c_void_p)
p_gs = (ctypes.c_int * 3)(*[len(x) for x in Gvbase])
fn = libcgto.GTO_ft_ovlp_mat
intor = getattr(libcgto, 'GTO_ft_ovlp_sph')
eval_gz = getattr(libcgto, eval_gz)
fill = getattr(libcgto, 'GTO_ft_fill_s1')
ghost_atm = numpy.array([[0, 0, 0, 0, 0, 0]], dtype=numpy.int32)
ghost_bas = numpy.array([[0, 0, 1, 1, 0, 0, 3, 0]], dtype=numpy.int32)
ghost_env = numpy.zeros(4)
ghost_env[3] = numpy.sqrt(4 * numpy.pi) # s function spherical norm
atm, bas, env = gto.conc_env(mol._atm, mol._bas, mol._env, ghost_atm,
ghost_bas, ghost_env)
ao_loc = mol.ao_loc_nr()
nao = ao_loc[mol.nbas]
ao_loc = numpy.asarray(numpy.hstack((ao_loc, [nao + 1])),
dtype=numpy.int32)
ni = ao_loc[shls_slice[1]] - ao_loc[shls_slice[0]]
mat = numpy.zeros((nGv, ni), order='F', dtype=numpy.complex)
shls_slice = shls_slice + (mol.nbas, mol.nbas + 1)
fn(intor, eval_gz, fill,
mat.ctypes.data_as(ctypes.c_void_p), (ctypes.c_int * 4)(*shls_slice),
ao_loc.ctypes.data_as(ctypes.c_void_p), ctypes.c_double(0),
GvT.ctypes.data_as(ctypes.c_void_p), p_b, p_gxyzT, p_gs,
ctypes.c_int(nGv), atm.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(len(atm)), bas.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(len(bas)), env.ctypes.data_as(ctypes.c_void_p))
return mat
def int_ket(_bas, intor):
if len(_bas) == 0:
return []
intor = cell._add_suffix(intor)
atm, bas, env = gto.conc_env(cell._atm, cell._bas, cell._env,
fakecell._atm, _bas, fakecell._env)
atm = numpy.asarray(atm, dtype=numpy.int32)
bas = numpy.asarray(bas, dtype=numpy.int32)
env = numpy.asarray(env, dtype=numpy.double)
natm = len(atm)
nbas = len(bas)
shls_slice = (cell.nbas, nbas, 0, cell.nbas)
ao_loc = gto.moleintor.make_loc(bas, intor)
ni = ao_loc[shls_slice[1]] - ao_loc[shls_slice[0]]
nj = ao_loc[shls_slice[3]] - ao_loc[shls_slice[2]]
out = numpy.empty((nkpts,ni,nj), dtype=numpy.complex128)
comp = 1
fintor = getattr(gto.moleintor.libcgto, intor)
drv = libpbc.PBCnr2c_drv
drv(fintor, fill, out.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(nkpts), ctypes.c_int(comp), ctypes.c_int(nimgs),
Ls.ctypes.data_as(ctypes.c_void_p),
expkL.ctypes.data_as(ctypes.c_void_p),
(ctypes.c_int*4)(*(shls_slice[:4])),
ao_loc.ctypes.data_as(ctypes.c_void_p), intopt, lib.c_null_ptr(),
atm.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(natm),
bas.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(nbas),
env.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(env.size))
return out
def test_aux_e2_diff_bra_ket(self):
mol1 = mol.copy()
mol1.basis = 'sto3g'
mol1.build(0, 0, verbose=0)
atm1, bas1, env1 = gto.conc_env(atm, bas, env,
mol1._atm, mol1._bas, mol1._env)
ao_loc = gto.moleintor.make_loc(bas1, 'cint3c2e_sph')
shls_slice = (0, mol.nbas,
mol.nbas+auxmol.nbas, mol.nbas+auxmol.nbas+mol1.nbas,
mol.nbas, mol.nbas+auxmol.nbas)
j3c = _ri.nr_auxe2('cint3c2e_sph', atm1, bas1, env1, shls_slice,
ao_loc, 's1', 1)
nao = mol.nao_nr()
naoj = mol1.nao_nr()
naoaux = auxmol.nao_nr()
eri0 = numpy.empty((nao,naoj,naoaux))
pi = 0
for i in range(mol.nbas):
pj = 0
for j in range(mol.nbas+auxmol.nbas, len(bas1)):
pk = 0
for k in range(mol.nbas, mol.nbas+auxmol.nbas):
shls = (i, j, k)
buf = gto.moleintor.getints_by_shell('cint3c2e_sph',
shls, atm1, bas1, env1)
di, dj, dk = buf.shape
eri0[pi:pi+di,pj:pj+dj,pk:pk+dk] = buf
pk += dk
pj += dj
pi += di
self.assertTrue(numpy.allclose(eri0.reshape(-1,naoaux), j3c))
def integral_one_gaussian_from_overlap(mol):
"""
Outputs the integral of only one Gaussian
using as second Gaussian in <i|j> an 1s
basis funtion of an He atom with
alpha=1e-15 and coeff=1.00000. The result
is divided by the norm of the He function.
"""
# Creating auxiliar Molecule
intmol = gto.Mole()
intmol.atom = '''He 0. 0. 0.'''
intmol.basis = He_flat_basis
intmol.build()
# Merging molecules
atm_x, bas_x, env_x = gto.conc_env(intmol._atm, intmol._bas, intmol._env,
mol._atm, mol._bas, mol._env)
# Computing the overlap
HF_partial = gto.moleintor.getints('cint1e_ovlp_sph',
atm_x,
bas_x,
env_x,
comp=1,
hermi=0,
aosym='s1',
out=None)
return np.hstack(HF_partial[:, :1])[1:] / gto.gto_norm(0, He_exp_flt)
def aux_e2(mol, auxmol, intor='cint3c2e_spinor', aosym='s1', comp=1, hermi=0):
atm, bas, env = \
gto.conc_env(mol._atm, mol._bas, mol._env,
auxmol._atm, auxmol._bas, auxmol._env)
c_atm = numpy.asarray(atm, dtype=numpy.int32, order='C')
c_bas = numpy.asarray(bas, dtype=numpy.int32, order='C')
c_env = numpy.asarray(env, dtype=numpy.double, order='C')
natm = ctypes.c_int(mol.natm+auxmol.natm)
nbas = ctypes.c_int(mol.nbas)
nao = mol.nao_2c()
naoaux = auxmol.nao_nr()
if aosym == 's1':
eri = numpy.empty((nao*nao,naoaux), dtype=numpy.complex)
fill = getattr(libri, 'RIfill_r_s1_auxe2')
else:
eri = numpy.empty((nao*(nao+1)//2,naoaux), dtype=numpy.complex)
fill = getattr(libri, 'RIfill_r_s2ij_auxe2')
fintor = getattr(libri, intor)
cintopt = _vhf.make_cintopt(c_atm, c_bas, c_env, intor)
libri.RIr_3c2e_auxe2_drv(fintor, fill,
eri.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(0), ctypes.c_int(mol.nbas),
ctypes.c_int(mol.nbas), ctypes.c_int(auxmol.nbas),
ctypes.c_int(1), cintopt,
c_atm.ctypes.data_as(ctypes.c_void_p), natm,
c_bas.ctypes.data_as(ctypes.c_void_p), nbas,
c_env.ctypes.data_as(ctypes.c_void_p))
return eri
def ft_ao(mol, Gv, shls_slice=None,
invh=None, gxyz=None, gs=None, verbose=None):
''' FT transform AO
'''
if shls_slice is None:
shls_slice = (0, mol.nbas)
nGv = Gv.shape[0]
if gxyz is None or invh is None or gs is None:
GvT = numpy.asarray(Gv.T, order='C')
p_gxyzT = lib.c_null_ptr()
p_gs = (ctypes.c_int*3)(0,0,0)
p_invh = (ctypes.c_double*1)(0)
eval_gz = 'GTO_Gv_general'
else:
GvT = numpy.asarray(Gv.T, order='C')
gxyzT = numpy.asarray(gxyz.T, order='C', dtype=numpy.int32)
p_gxyzT = gxyzT.ctypes.data_as(ctypes.c_void_p)
p_gs = (ctypes.c_int*3)(*gs)
# Guess what type of eval_gz to use
if isinstance(invh, numpy.ndarray) and invh.shape == (3,3):
p_invh = invh.ctypes.data_as(ctypes.c_void_p)
if numpy.allclose(invh-numpy.diag(invh.diagonal()), 0):
eval_gz = 'GTO_Gv_uniform_orth'
else:
eval_gz = 'GTO_Gv_uniform_nonorth'
else:
invh = numpy.hstack(invh)
p_invh = invh.ctypes.data_as(ctypes.c_void_p)
eval_gz = 'GTO_Gv_nonuniform_orth'
fn = libcgto.GTO_ft_ovlp_mat
intor = getattr(libcgto, 'GTO_ft_ovlp_sph')
eval_gz = getattr(libcgto, eval_gz)
fill = getattr(libcgto, 'GTO_ft_fill_s1')
ghost_atm = numpy.array([[0,0,0,0,0,0]], dtype=numpy.int32)
ghost_bas = numpy.array([[0,0,1,1,0,0,3,0]], dtype=numpy.int32)
ghost_env = numpy.zeros(4)
ghost_env[3] = numpy.sqrt(4*numpy.pi) # s function spheric norm
atm, bas, env = gto.conc_env(mol._atm, mol._bas, mol._env,
ghost_atm, ghost_bas, ghost_env)
ao_loc = mol.ao_loc_nr()
nao = ao_loc[mol.nbas]
ao_loc = numpy.asarray(numpy.hstack((ao_loc, [nao+1])), dtype=numpy.int32)
ni = ao_loc[shls_slice[1]] - ao_loc[shls_slice[0]]
mat = numpy.zeros((nGv,ni), order='F', dtype=numpy.complex)
shls_slice = shls_slice + (mol.nbas, mol.nbas+1)
fn(intor, eval_gz, fill, mat.ctypes.data_as(ctypes.c_void_p),
(ctypes.c_int*4)(*shls_slice),
ao_loc.ctypes.data_as(ctypes.c_void_p),
ctypes.c_double(0),
GvT.ctypes.data_as(ctypes.c_void_p),
p_invh, p_gxyzT, p_gs, ctypes.c_int(nGv),
atm.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(len(atm)),
bas.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(len(bas)),
env.ctypes.data_as(ctypes.c_void_p))
return mat
def ft_ao(mol, Gv, shls_slice=None, b=numpy.eye(3),
gxyz=None, Gvbase=None, verbose=None):
''' FT transform AO
'''
if shls_slice is None:
shls_slice = (0, mol.nbas)
nGv = Gv.shape[0]
if (gxyz is None or b is None or Gvbase is None
# backward compatibility for pyscf-1.2, in which the argument Gvbase is gs
or (Gvbase is not None and isinstance(Gvbase[0], (int, numpy.integer)))):
GvT = numpy.asarray(Gv.T, order='C')
p_gxyzT = lib.c_null_ptr()
p_gs = (ctypes.c_int*3)(0,0,0)
p_b = (ctypes.c_double*1)(0)
eval_gz = 'GTO_Gv_general'
else:
if abs(b-numpy.diag(b.diagonal())).sum() < 1e-8:
eval_gz = 'GTO_Gv_orth'
else:
eval_gz = 'GTO_Gv_nonorth'
GvT = numpy.asarray(Gv.T, order='C')
gxyzT = numpy.asarray(gxyz.T, order='C', dtype=numpy.int32)
p_gxyzT = gxyzT.ctypes.data_as(ctypes.c_void_p)
b = numpy.hstack((b.ravel(), numpy.zeros(3)) + Gvbase)
p_b = b.ctypes.data_as(ctypes.c_void_p)
p_gs = (ctypes.c_int*3)(*[len(x) for x in Gvbase])
fn = libcgto.GTO_ft_fill_drv
if mol.cart:
intor = getattr(libcgto, 'GTO_ft_ovlp_cart')
else:
intor = getattr(libcgto, 'GTO_ft_ovlp_sph')
eval_gz = getattr(libcgto, eval_gz)
fill = getattr(libcgto, 'GTO_ft_fill_s1')
ghost_atm = numpy.array([[0,0,0,0,0,0]], dtype=numpy.int32)
ghost_bas = numpy.array([[0,0,1,1,0,0,3,0]], dtype=numpy.int32)
ghost_env = numpy.zeros(4)
ghost_env[3] = numpy.sqrt(4*numpy.pi) # s function spherical norm
atm, bas, env = gto.conc_env(mol._atm, mol._bas, mol._env,
ghost_atm, ghost_bas, ghost_env)
ao_loc = mol.ao_loc_nr()
nao = ao_loc[mol.nbas]
ao_loc = numpy.asarray(numpy.hstack((ao_loc, [nao+1])), dtype=numpy.int32)
ni = ao_loc[shls_slice[1]] - ao_loc[shls_slice[0]]
mat = numpy.zeros((nGv,ni), order='F', dtype=numpy.complex)
shls_slice = shls_slice + (mol.nbas, mol.nbas+1)
fn(intor, eval_gz, fill, mat.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(1), (ctypes.c_int*4)(*shls_slice),
ao_loc.ctypes.data_as(ctypes.c_void_p),
ctypes.c_double(0),
GvT.ctypes.data_as(ctypes.c_void_p),
p_b, p_gxyzT, p_gs, ctypes.c_int(nGv),
atm.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(len(atm)),
bas.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(len(bas)),
env.ctypes.data_as(ctypes.c_void_p))
return mat
def _int_nuc_vloc(mydf, nuccell, kpts, intor='cint3c2e_sph'):
'''Vnuc - Vloc'''
cell = mydf.cell
rcut = max(cell.rcut, nuccell.rcut)
Ls = cell.get_lattice_Ls(rcut=rcut)
expLk = numpy.asarray(numpy.exp(1j * numpy.dot(Ls, kpts.T)), order='C')
nkpts = len(kpts)
# Use the 3c2e code with steep s gaussians to mimic nuclear density
fakenuc = _fake_nuc(cell)
fakenuc._atm, fakenuc._bas, fakenuc._env = \
gto.conc_env(nuccell._atm, nuccell._bas, nuccell._env,
fakenuc._atm, fakenuc._bas, fakenuc._env)
nao = cell.nao_nr()
buf = [
numpy.zeros((nao, nao, fakenuc.natm),
order='F',
dtype=numpy.complex128) for k in range(nkpts)
]
ints = incore._wrap_int3c(cell, fakenuc, intor, 1, Ls, buf)
atm, bas, env = ints._envs[:3]
c_shls_slice = (ctypes.c_int * 6)(0, cell.nbas, cell.nbas, cell.nbas * 2,
cell.nbas * 2,
cell.nbas * 2 + fakenuc.natm)
xyz = numpy.asarray(cell.atom_coords(), order='C')
ptr_coordL = atm[:cell.natm, gto.PTR_COORD]
ptr_coordL = numpy.vstack(
(ptr_coordL, ptr_coordL + 1, ptr_coordL + 2)).T.copy('C')
for l, L1 in enumerate(Ls):
env[ptr_coordL] = xyz + L1
exp_Lk = numpy.einsum('k,ik->ik', expLk[l].conj(), expLk[:l + 1])
exp_Lk = numpy.asarray(exp_Lk, order='C')
exp_Lk[l] = .5
ints(exp_Lk, c_shls_slice)
charge = cell.atom_charges()
charge = numpy.append(charge,
-charge) # (charge-of-nuccell, charge-of-fakenuc)
for k in range(nkpts):
v = numpy.einsum('ijz,z->ij', buf[k], charge)
buf[k] = lib.pack_tril(v + v.T.conj())
if cell.dimension == 3:
nucbar = sum([
z / nuccell.bas_exp(i)[0]
for i, z in enumerate(cell.atom_charges())
])
nucbar *= numpy.pi / cell.vol
ovlp = cell.pbc_intor('cint1e_ovlp_sph', 1, lib.HERMITIAN, kpts)
for k in range(nkpts):
s = lib.pack_tril(ovlp[k])
buf[k] += nucbar * s
return buf
def _int_nuc_vloc(mydf, nuccell, kpts, intor='int3c2e', aosym='s2', comp=1):
'''Vnuc - Vloc'''
cell = mydf.cell
nkpts = len(kpts)
# Use the 3c2e code with steep s gaussians to mimic nuclear density
fakenuc = _fake_nuc(cell)
fakenuc._atm, fakenuc._bas, fakenuc._env = \
gto.conc_env(nuccell._atm, nuccell._bas, nuccell._env,
fakenuc._atm, fakenuc._bas, fakenuc._env)
kptij_lst = numpy.hstack((kpts, kpts)).reshape(-1, 2, 3)
buf = incore.aux_e2(cell,
fakenuc,
intor,
aosym=aosym,
comp=comp,
kptij_lst=kptij_lst)
charge = cell.atom_charges()
charge = numpy.append(charge,
-charge) # (charge-of-nuccell, charge-of-fakenuc)
nao = cell.nao_nr()
nchg = len(charge)
if aosym == 's1':
nao_pair = nao**2
else:
nao_pair = nao * (nao + 1) // 2
if comp == 1:
buf = buf.reshape(nkpts, nao_pair, nchg)
mat = numpy.einsum('kxz,z->kx', buf, charge)
else:
buf = buf.reshape(nkpts, comp, nao_pair, nchg)
mat = numpy.einsum('kcxz,z->kcx', buf, charge)
# vbar is the interaction between the background charge
# and the compensating function. 0D, 1D, 2D do not have vbar.
if cell.dimension == 3 and intor in ('int3c2e', 'int3c2e_sph',
'int3c2e_cart'):
assert (comp == 1)
charge = -cell.atom_charges()
nucbar = sum([z / nuccell.bas_exp(i)[0] for i, z in enumerate(charge)])
nucbar *= numpy.pi / cell.vol
ovlp = cell.pbc_intor('int1e_ovlp', 1, lib.HERMITIAN, kpts)
for k in range(nkpts):
if aosym == 's1':
mat[k] -= nucbar * ovlp[k].reshape(nao_pair)
else:
mat[k] -= nucbar * lib.pack_tril(ovlp[k])
return mat
def test_rinv_with_zeta(self):
with mol.with_rinv_orig((.2,.3,.4)), mol.with_rinv_zeta(2.2):
v1 = mol.intor('int1e_rinv_sph')
pmol = gto.M(atom='Ghost .2 .3 .4', unit='b', basis={'Ghost':[[0,(2.2*.5, 1)]]})
pmol._atm, pmol._bas, pmol._env = \
gto.conc_env(mol._atm, mol._bas, mol._env,
pmol._atm, pmol._bas, pmol._env)
shls_slice = (pmol.nbas-1,pmol.nbas, pmol.nbas-1,pmol.nbas,
0, pmol.nbas, 0, pmol.nbas)
v0 = pmol.intor('int2e_sph', shls_slice=shls_slice)
nao = pmol.nao_nr()
v0 = v0.reshape(nao,nao)[:-1,:-1]
self.assertTrue(numpy.allclose(v0, v1))
def auxmol_set(self, auxbas="weigend"):
print "GENERATING INTEGRALS"
auxmol = gto.Mole()
auxmol.atom = self.mol.atom
auxmol.basis = auxbas
auxmol.build()
mol = self.mol
nao = self.n_ao = mol.nao_nr()
naux = self.n_aux = auxmol.nao_nr()
#print nao
#print naux
atm, bas, env = gto.conc_env(mol._atm, mol._bas, mol._env, auxmol._atm,
auxmol._bas, auxmol._env)
eri3c = np.empty((nao, nao, naux))
pi = 0
for i in range(mol.nbas):
pj = 0
for j in range(mol.nbas):
pk = 0
for k in range(mol.nbas, mol.nbas + auxmol.nbas):
shls = (i, j, k)
buf = gto.getints_by_shell('cint3c2e_sph', shls, atm, bas,
env)
di, dj, dk = buf.shape
eri3c[pi:pi + di, pj:pj + dj, pk:pk + dk] = buf
pk += dk
pj += dj
pi += di
print "ERI3C INTEGRALS GENERATED"
eri2c = np.empty((naux, naux))
pk = 0
for k in range(mol.nbas, mol.nbas + auxmol.nbas):
pl = 0
for l in range(mol.nbas, mol.nbas + auxmol.nbas):
shls = (k, l)
buf = gto.getints_by_shell('cint2c2e_sph', shls, atm, bas, env)
dk, dl = buf.shape
eri2c[pk:pk + dk, pl:pl + dl] = buf
pl += dl
pk += dk
print "ERI2C INTEGRALS GENERATED"
self.eri3c = eri3c
self.eri2c = eri2c
RSinv = MatrixPower(eri2c, -0.5)
with sess.as_default():
self.B = tf.einsum(
'ijp,pq->ijq', self.toTF(eri3c), self.toTF(RSinv)
).eval(
) #self.B = np.einsum('ijp,pq->ijq', self.eri3c, RSinv) # (AO,AO,n_aux)
return
def setUpModule():
global mol, auxmol, atm, bas, env
mol = gto.Mole()
mol.build(
verbose = 0,
atom = '''O 0 0. 0.
1 0 -0.757 0.587
1 0 0.757 0.587''',
basis = 'cc-pvdz',
)
auxmol = df.addons.make_auxmol(mol, 'weigend')
atm, bas, env = gto.conc_env(mol._atm, mol._bas, mol._env,
auxmol._atm, auxmol._bas, auxmol._env)
def _int_nuc_vloc(mydf, nuccell, kpts, intor='int3c2e_sph'):
'''Vnuc - Vloc'''
cell = mydf.cell
nkpts = len(kpts)
# Use the 3c2e code with steep s gaussians to mimic nuclear density
fakenuc = aft._fake_nuc(cell)
fakenuc._atm, fakenuc._bas, fakenuc._env = \
gto.conc_env(nuccell._atm, nuccell._bas, nuccell._env,
fakenuc._atm, fakenuc._bas, fakenuc._env)
kptij_lst = numpy.hstack((kpts, kpts)).reshape(-1, 2, 3)
ishs = mpi.work_balanced_partition(numpy.arange(cell.nbas),
costs=numpy.arange(1, cell.nbas + 1))
if len(ishs) > 0:
ish0, ish1 = ishs[0], ishs[-1] + 1
buf = incore.aux_e2(cell,
fakenuc,
intor,
aosym='s2',
kptij_lst=kptij_lst,
shls_slice=(ish0, ish1, 0, cell.nbas, 0,
fakenuc.nbas))
else:
buf = numpy.zeros(0)
charge = cell.atom_charges()
charge = numpy.append(charge,
-charge) # (charge-of-nuccell, charge-of-fakenuc)
nao = cell.nao_nr()
nchg = len(charge)
nao_pair = nao * (nao + 1) // 2
buf = buf.reshape(nkpts, -1, nchg)
# scaled by 1./mpi.pool.size because nuc is mpi.reduced in get_nuc function
buf = numpy.einsum('kxz,z->kx', buf, 1. / mpi.pool.size * charge)
mat = numpy.empty((nkpts, nao_pair), dtype=numpy.complex128)
for k in range(nkpts):
mat[k] = mpi.allgather(buf[k])
if rank == 0 and cell.dimension == 3:
nucbar = sum([
z / nuccell.bas_exp(i)[0]
for i, z in enumerate(cell.atom_charges())
])
nucbar *= numpy.pi / cell.vol
ovlp = cell.pbc_intor('int1e_ovlp_sph', 1, lib.HERMITIAN, kpts)
for k in range(nkpts):
s = lib.pack_tril(ovlp[k])
mat[k] += nucbar * s
return mat
def _int_nuc_vloc(mydf, nuccell, kpts, intor='int3c2e_sph', aosym='s2', comp=1):
'''Vnuc - Vloc'''
cell = mydf.cell
nkpts = len(kpts)
# Use the 3c2e code with steep s gaussians to mimic nuclear density
fakenuc = aft._fake_nuc(cell)
fakenuc._atm, fakenuc._bas, fakenuc._env = \
gto.conc_env(nuccell._atm, nuccell._bas, nuccell._env,
fakenuc._atm, fakenuc._bas, fakenuc._env)
kptij_lst = numpy.hstack((kpts,kpts)).reshape(-1,2,3)
ishs = mpi.work_balanced_partition(numpy.arange(cell.nbas),
costs=numpy.arange(1, cell.nbas+1))
if len(ishs) > 0:
ish0, ish1 = ishs[0], ishs[-1]+1
buf = incore.aux_e2(cell, fakenuc, intor, aosym='s2', kptij_lst=kptij_lst,
shls_slice=(ish0,ish1,0,cell.nbas,0,fakenuc.nbas))
else:
buf = numpy.zeros(0)
charge = cell.atom_charges()
charge = numpy.append(charge, -charge) # (charge-of-nuccell, charge-of-fakenuc)
nao = cell.nao_nr()
nchg = len(charge)
nao_pair = nao*(nao+1)//2
buf = buf.reshape(nkpts,-1,nchg)
# scaled by 1./mpi.pool.size because nuc is mpi.reduced in get_nuc function
buf = numpy.einsum('kxz,z->kx', buf, 1./mpi.pool.size*charge)
mat = numpy.empty((nkpts,nao_pair), dtype=numpy.complex128)
for k in range(nkpts):
mat[k] = mpi.allgather(buf[k])
if (rank == 0 and
cell.dimension == 3 and intor in ('int3c2e', 'int3c2e_sph',
'int3c2e_cart')):
assert(comp == 1)
charges = cell.atom_charges()
nucbar = sum([z/nuccell.bas_exp(i)[0] for i,z in enumerate(charges)])
nucbar *= numpy.pi/cell.vol
ovlp = cell.pbc_intor('int1e_ovlp_sph', 1, lib.HERMITIAN, kpts)
for k in range(nkpts):
if aosym == 's1':
mat[k] += nucbar * ovlp[k].reshape(nao_pair)
else:
mat[k] += nucbar * lib.pack_tril(ovlp[k])
return mat
def test_rinv_with_zeta(self):
with mol.with_rinv_orig((.2, .3, .4)), mol.with_rinv_zeta(2.2):
v1 = mol.intor('int1e_rinv_sph')
pmol = gto.M(atom='Ghost .2 .3 .4',
unit='b',
basis={'Ghost': [[0, (2.2 * .5, 1)]]})
pmol._atm, pmol._bas, pmol._env = \
gto.conc_env(mol._atm, mol._bas, mol._env,
pmol._atm, pmol._bas, pmol._env)
shls_slice = (pmol.nbas - 1, pmol.nbas, pmol.nbas - 1, pmol.nbas, 0,
pmol.nbas, 0, pmol.nbas)
v0 = pmol.intor('int2e_sph', shls_slice=shls_slice)
nao = pmol.nao_nr()
v0 = v0.reshape(nao, nao)[:-1, :-1]
self.assertTrue(numpy.allclose(v0, v1))
def test_rinv_with_zeta(self):
mol.set_rinv_orig_((.2,.3,.4))
mol.set_rinv_zeta_(2.2)
v1 = mol.intor('cint1e_rinv_sph')
mol.set_rinv_zeta_(0)
pmol = gto.M(atom='Ghost .2 .3 .4', unit='b', basis={'Ghost':[[0,(2.2*.5, 1)]]})
pmol._atm, pmol._bas, pmol._env = \
gto.conc_env(mol._atm, mol._bas, mol._env,
pmol._atm, pmol._bas, pmol._env)
pmol.natm = len(pmol._atm)
pmol.nbas = len(pmol._bas)
v0 = pmol.intor('cint2e_sph', bras=[pmol.nbas-1], kets=[pmol.nbas-1])
nao = pmol.nao_nr()
v0 = v0.reshape(nao,nao)[:-1,:-1]
self.assertTrue(numpy.allclose(v0, v1))
def _int_nuc_vloc(mydf, nuccell, kpts, intor='int3c2e', aosym='s2', comp=1):
'''Vnuc - Vloc'''
cell = mydf.cell
nkpts = len(kpts)
# Use the 3c2e code with steep s gaussians to mimic nuclear density
fakenuc = _fake_nuc(cell)
fakenuc._atm, fakenuc._bas, fakenuc._env = \
gto.conc_env(nuccell._atm, nuccell._bas, nuccell._env,
fakenuc._atm, fakenuc._bas, fakenuc._env)
kptij_lst = numpy.hstack((kpts,kpts)).reshape(-1,2,3)
buf = incore.aux_e2(cell, fakenuc, intor, aosym=aosym, comp=comp,
kptij_lst=kptij_lst)
charge = cell.atom_charges()
charge = numpy.append(charge, -charge) # (charge-of-nuccell, charge-of-fakenuc)
nao = cell.nao_nr()
nchg = len(charge)
if aosym == 's1':
nao_pair = nao**2
else:
nao_pair = nao*(nao+1)//2
if comp == 1:
buf = buf.reshape(nkpts,nao_pair,nchg)
mat = numpy.einsum('kxz,z->kx', buf, charge)
else:
buf = buf.reshape(nkpts,comp,nao_pair,nchg)
mat = numpy.einsum('kcxz,z->kcx', buf, charge)
# vbar is the interaction between the background charge
# and the compensating function. 0D, 1D, 2D do not have vbar.
if cell.dimension == 3 and intor in ('int3c2e', 'int3c2e_sph',
'int3c2e_cart'):
assert(comp == 1)
charge = -cell.atom_charges()
nucbar = sum([z/nuccell.bas_exp(i)[0] for i,z in enumerate(charge)])
nucbar *= numpy.pi/cell.vol
ovlp = cell.pbc_intor('int1e_ovlp', 1, lib.HERMITIAN, kpts)
for k in range(nkpts):
if aosym == 's1':
mat[k] -= nucbar * ovlp[k].reshape(nao_pair)
else:
mat[k] -= nucbar * lib.pack_tril(ovlp[k])
return mat
def _int_nuc_vloc(cell, nuccell, kpts):
'''Vnuc - Vloc'''
nimgs = numpy.max((cell.nimgs, nuccell.nimgs), axis=0)
Ls = numpy.asarray(cell.get_lattice_Ls(nimgs), order='C')
expLk = numpy.asarray(numpy.exp(1j * numpy.dot(Ls, kpts.T)), order='C')
nkpts = len(kpts)
# Use the 3c2e code with steep s gaussians to mimic nuclear density
fakenuc = _fake_nuc(cell)
fakenuc._atm, fakenuc._bas, fakenuc._env = \
gto.conc_env(nuccell._atm, nuccell._bas, nuccell._env,
fakenuc._atm, fakenuc._bas, fakenuc._env)
nao = cell.nao_nr()
buf = [
numpy.zeros((nao, nao, fakenuc.natm),
order='F',
dtype=numpy.complex128) for k in range(nkpts)
]
ints = incore._wrap_int3c(cell, fakenuc, 'cint3c2e_sph', 1, Ls, buf)
atm, bas, env = ints._envs[:3]
c_shls_slice = (ctypes.c_int * 6)(0, cell.nbas, cell.nbas, cell.nbas * 2,
cell.nbas * 2,
cell.nbas * 2 + fakenuc.natm)
xyz = numpy.asarray(cell.atom_coords(), order='C')
ptr_coordL = atm[:cell.natm, gto.PTR_COORD]
ptr_coordL = numpy.vstack(
(ptr_coordL, ptr_coordL + 1, ptr_coordL + 2)).T.copy('C')
for l, L1 in enumerate(Ls):
env[ptr_coordL] = xyz + L1
exp_Lk = numpy.einsum('k,ik->ik', expLk[l].conj(), expLk[:l + 1])
exp_Lk = numpy.asarray(exp_Lk, order='C')
exp_Lk[l] = .5
ints(exp_Lk, c_shls_slice)
charge = cell.atom_charges()
charge = numpy.append(charge,
-charge) # (charge-of-nuccell, charge-of-fakenuc)
for k, kpt in enumerate(kpts):
v = numpy.einsum('ijz,z->ij', buf[k], charge)
if gamma_point(kpt):
buf[k] = v.real + v.real.T
else:
buf[k] = v + v.T.conj()
return buf
def build(self, j_only=False, with_j3c=True):
log = logger.Logger(self.stdout, self.verbose)
t1 = (time.clock(), time.time())
cell = self.cell
if self.eta is None:
self.eta = estimate_eta(cell)
log.debug('Set smooth gaussian eta to %.9g', self.eta)
self.dump_flags()
auxcell = make_modrho_basis(cell, self.auxbasis, self.eta)
chgcell = make_modchg_basis(auxcell, self.eta)
self._j_only = j_only
if j_only:
kptij_lst = numpy.hstack((self.kpts,self.kpts)).reshape(-1,2,3)
else:
kptij_lst = [(ki, self.kpts[j])
for i, ki in enumerate(self.kpts) for j in range(i+1)]
kptij_lst = numpy.asarray(kptij_lst)
if not isinstance(self._cderi, str):
if isinstance(self._cderi_file, str):
self._cderi = self._cderi_file
else:
self._cderi = self._cderi_file.name
if with_j3c:
if self.approx_sr_level == 0:
build_Lpq_pbc(self, auxcell, chgcell, kptij_lst)
elif self.approx_sr_level == 1:
build_Lpq_pbc(self, auxcell, chgcell, numpy.zeros((1,2,3)))
elif self.approx_sr_level == 2:
build_Lpq_nonpbc(self, auxcell, chgcell)
elif self.approx_sr_level == 3:
build_Lpq_1c_approx(self, auxcell, chgcell)
t1 = log.timer_debug1('Lpq', *t1)
_make_j3c(self, cell, auxcell, chgcell, kptij_lst)
t1 = log.timer_debug1('j3c', *t1)
# Merge chgcell into auxcell
auxcell._atm, auxcell._bas, auxcell._env = \
gto.conc_env(auxcell._atm, auxcell._bas, auxcell._env,
chgcell._atm, chgcell._bas, chgcell._env)
self.auxcell = auxcell
return self
def calc_eri2c(mol, auxmol, Ikl):
nao = mol.nao_nr()
naux = auxmol.nao_nr()
# Merging M1 and M2 to compute the integrals.
atm, bas, env = gto.conc_env(mol._atm, mol._bas, mol._env, auxmol._atm,
auxmol._bas, auxmol._env)
eri2c = np.empty((naux, naux))
pk = 0
for k in range(mol.nbas, mol.nbas + auxmol.nbas):
pl = 0
for l in range(mol.nbas, mol.nbas + auxmol.nbas):
shls = (k, l)
buf = gto.getints_by_shell(Ikl, shls, atm, bas, env)
dk, dl = buf.shape
eri2c[pk:pk + dk, pl:pl + dl] = buf
pl += dl
pk += dk
return eri2c
def auxmol_set(self, auxbas="weigend"):
print "GENERATING INTEGRALS"
auxmol = gto.Mole()
auxmol.atom = self.mol.atom
auxmol.basis = auxbas
auxmol.build()
mol = self.mol
nao = self.n_ao = mol.nao_nr()
naux = self.n_aux = auxmol.nao_nr()
atm, bas, env = gto.conc_env(mol._atm, mol._bas, mol._env, auxmol._atm,
auxmol._bas, auxmol._env)
eri3c = df.incore.aux_e1(mol,
auxmol,
intor='cint3c2e_sph',
aosym='s1',
comp=1)
eri3c = eri3c.reshape(naux, nao, nao).T
print "ERI3C INTEGRALS GENERATED"
eri2c = np.empty((naux, naux))
pk = 0
for k in range(mol.nbas, mol.nbas + auxmol.nbas):
pl = 0
for l in range(mol.nbas, mol.nbas + auxmol.nbas):
shls = (k, l)
buf = gto.getints_by_shell('cint2c2e_sph', shls, atm, bas, env)
dk, dl = buf.shape
eri2c[pk:pk + dk, pl:pl + dl] = buf
pl += dl
pk += dk
print "ERI2C INTEGRALS GENERATED"
self.eri3c = eri3c
self.eri2c = eri2c
RSinv = MatrixPower(eri2c, -0.5)
self.B = np.einsum('ijp,pq->ijq', self.eri3c, RSinv) # (AO,AO,n_aux)
# change to (LAO,LAO,n_aux) BpqR
self.S = self.the_scf.get_ovlp() # (ao X ao)
self.X = MatrixPower(self.S, -1. / 2.) # AO, LAO
print "BpqR GENERATED"
return
def _int_nuc_vloc(cell, nuccell, kpts):
'''Vnuc - Vloc'''
nimgs = numpy.max((cell.nimgs, nuccell.nimgs), axis=0)
Ls = numpy.asarray(cell.get_lattice_Ls(nimgs), order='C')
expLk = numpy.asarray(numpy.exp(1j*numpy.dot(Ls, kpts.T)), order='C')
nkpts = len(kpts)
# Use the 3c2e code with steep s gaussians to mimic nuclear density
fakenuc = _fake_nuc(cell)
fakenuc._atm, fakenuc._bas, fakenuc._env = \
gto.conc_env(nuccell._atm, nuccell._bas, nuccell._env,
fakenuc._atm, fakenuc._bas, fakenuc._env)
nao = cell.nao_nr()
buf = [numpy.zeros((nao,nao,fakenuc.natm), order='F', dtype=numpy.complex128)
for k in range(nkpts)]
ints = incore._wrap_int3c(cell, fakenuc, 'cint3c2e_sph', 1, Ls, buf)
atm, bas, env = ints._envs[:3]
c_shls_slice = (ctypes.c_int*6)(0, cell.nbas, cell.nbas, cell.nbas*2,
cell.nbas*2, cell.nbas*2+fakenuc.natm)
xyz = numpy.asarray(cell.atom_coords(), order='C')
ptr_coordL = atm[:cell.natm,gto.PTR_COORD]
ptr_coordL = numpy.vstack((ptr_coordL,ptr_coordL+1,ptr_coordL+2)).T.copy('C')
for l, L1 in enumerate(Ls):
env[ptr_coordL] = xyz + L1
exp_Lk = numpy.einsum('k,ik->ik', expLk[l].conj(), expLk[:l+1])
exp_Lk = numpy.asarray(exp_Lk, order='C')
exp_Lk[l] = .5
ints(exp_Lk, c_shls_slice)
charge = cell.atom_charges()
charge = numpy.append(charge, -charge) # (charge-of-nuccell, charge-of-fakenuc)
for k, kpt in enumerate(kpts):
v = numpy.einsum('ijz,z->ij', buf[k], charge)
if gamma_point(kpt):
buf[k] = v.real + v.real.T
else:
buf[k] = v + v.T.conj()
return buf
def int_ket(_bas, intor):
if len(_bas) == 0:
return []
atm, bas, env = gto.conc_env(cell._atm, cell._bas, cell._env,
fakecell._atm, _bas, fakecell._env)
atm = numpy.asarray(atm, dtype=numpy.int32)
bas = numpy.asarray(bas, dtype=numpy.int32)
env = numpy.asarray(env, dtype=numpy.double)
natm = len(atm)
nbas = len(bas)
shls_slice = (cell.nbas, nbas, 0, cell.nbas)
ao_loc = gto.moleintor.make_loc(bas, intor)
ni = ao_loc[shls_slice[1]] - ao_loc[shls_slice[0]]
nj = ao_loc[shls_slice[3]] - ao_loc[shls_slice[2]]
out = [
numpy.zeros((ni, nj), order='F', dtype=numpy.complex128)
for k in range(nkpts)
]
out_ptrs = (ctypes.c_void_p *
nkpts)(*[x.ctypes.data_as(ctypes.c_void_p) for x in out])
comp = 1
fintor = getattr(gto.moleintor.libcgto, intor)
ptr_coords = numpy.asarray(atm[:cell.natm, gto.PTR_COORD],
dtype=numpy.int32,
order='C')
drv = libpbc.PBCnr2c_drv
drv(fintor, fill, out_ptrs, xyz.ctypes.data_as(ctypes.c_void_p),
ptr_coords.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(cell.natm), Ls.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(len(Ls)), expLk.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(nkpts), ctypes.c_int(comp),
(ctypes.c_int * 4)(*(shls_slice[:4])),
ao_loc.ctypes.data_as(ctypes.c_void_p), intopt,
atm.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(natm),
bas.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(nbas),
env.ctypes.data_as(ctypes.c_void_p))
return out
def calc_eri3c(mol, auxmol, IklM):
nao = mol.nao_nr()
naux = auxmol.nao_nr()
# Merging M1 and M2 to compute the integrals.
atm, bas, env = gto.conc_env(mol._atm, mol._bas, mol._env, auxmol._atm,
auxmol._bas, auxmol._env)
eri3c = np.empty((nao, nao, naux))
pi = 0
for i in range(mol.nbas):
pj = 0
for j in range(mol.nbas):
pk = 0
for k in range(mol.nbas, mol.nbas + auxmol.nbas):
shls = (i, j, k)
buf = gto.getints_by_shell(IklM, shls, atm, bas, env)
di, dj, dk = buf.shape
eri3c[pi:pi + di, pj:pj + dj, pk:pk + dk] = buf
pk += dk
pj += dj
pi += di
return eri3c
def get_jk(mols, dms, scripts=['ijkl,ji->kl'], intor='cint2e_sph',
aosym='s1', comp=1, hermi=0, shls_slice=None, verbose=logger.WARN):
'''Compute J/K matrices for the given density matrix
Args:
mols : an instance of :class:`Mole` or a list of `Mole` objects
dms : ndarray or list of ndarrays
A density matrix or a list of density matrices
Kwargs:
hermi : int
Whether J/K matrix is hermitian
| 0 : no hermitian or symmetric
| 1 : hermitian
| 2 : anti-hermitian
intor : str
2-electron integral name. See :func:`getints` for the complete
list of available 2-electron integral names
aosym : int or str
Permutation symmetry for the AO integrals
| 4 or '4' or 's4': 4-fold symmetry (default)
| '2ij' or 's2ij' : symmetry between i, j in (ij|kl)
| '2kl' or 's2kl' : symmetry between k, l in (ij|kl)
| 1 or '1' or 's1': no symmetry
| 'a4ij' : 4-fold symmetry with anti-symmetry between i, j in (ij|kl)
| 'a4kl' : 4-fold symmetry with anti-symmetry between k, l in (ij|kl)
| 'a2ij' : anti-symmetry between i, j in (ij|kl)
| 'a2kl' : anti-symmetry between k, l in (ij|kl)
comp : int
Components of the integrals, e.g. cint2e_ip_sph has 3 components.
scripts : a list of strings
Contraction description (following numpy.einsum convention) based on
letters [ijkl]. Each script will be one-to-one applied to each
entry of dms. So it must have the same number of elements as the
dms, len(scripts) == len(dms).
shls_slice : 8-element list
(ish_start, ish_end, jsh_start, jsh_end, ksh_start, ksh_end, lsh_start, lsh_end)
Returns:
Depending on the number of density matrices, the function returns one
J/K matrix or a list of J/K matrices (the same number of entries as the
input dms).
Each JK matrices may be a 2D array or 3D array if the AO integral
has multiple components.
Examples:
>>> from pyscf import gto
>>> mol = gto.M(atom='H 0 -.5 0; H 0 .5 0', basis='cc-pvdz')
>>> nao = mol.nao_nr()
>>> dm = numpy.random.random((nao,nao))
>>> # Default, Coulomb matrix
>>> vj = get_jk(mol, dm)
>>> # Coulomb matrix with 8-fold permutation symmetry for AO integrals
>>> vj = get_jk(mol, dm, 'ijkl,ji->kl', aosym='s8')
>>> # Exchange matrix with 8-fold permutation symmetry for AO integrals
>>> vk = get_jk(mol, dm, 'ijkl,jk->il', aosym='s8')
>>> # Compute coulomb and exchange matrices together
>>> vj, vk = get_jk(mol, (dm,dm), ('ijkl,ji->kl','ijkl,li->kj'), aosym='s8')
>>> # Analytical gradients for coulomb matrix
>>> j1 = get_jk(mol, dm, 'ijkl,lk->ij', intor='cint2e_ip1_sph', aosym='s2kl', comp=3)
>>> # contraction across two molecules
>>> mol1 = gto.M(atom='He 2 0 0', basis='6-31g')
>>> nao1 = mol1.nao_nr()
>>> dm1 = numpy.random.random((nao1,nao1))
>>> # Coulomb interaction between two molecules, note 4-fold symmetry can be applied
>>> jcross = get_jk((mol1,mol1,mol,mol), dm, scripts='ijkl,lk->ij', aosym='s4')
>>> ecoul = numpy.einsum('ij,ij', jcross, dm1)
>>> # Exchange interaction between two molecules, no symmetry can be used
>>> kcross = get_jk((mol1,mol,mol,mol1), dm, scripts='ijkl,jk->il')
>>> ex = numpy.einsum('ij,ji', kcross, dm1)
>>> # Analytical gradients for coulomb matrix between two molecules
>>> jcros1 = get_jk((mol1,mol1,mol,mol), dm, scripts='ijkl,lk->ij', intor='cint2e_ip1_sph', comp=3)
>>> # Analytical gradients for coulomb interaction between 1s density and the other molecule
>>> jpart1 = get_jk((mol1,mol1,mol,mol), dm, scripts='ijkl,lk->ij', intor='cint2e_ip1_sph', comp=3,
... shls_slice=(0,1,0,1,0,mol.nbas,0,mol.nbas))
'''
if isinstance(mols, (tuple, list)):
assert(len(mols) == 4)
if shls_slice is None:
shls_slice = numpy.array([(0, mol.nbas) for mol in mols])
else:
shls_slice = numpy.asarray(shls_slice).reshape(4,2)
# concatenate unique mols and build corresponding shls_slice
mol_ids = [id(mol) for mol in mols]
atm, bas, env = mols[0]._atm, mols[0]._bas, mols[0]._env
bas_start = numpy.zeros(4, dtype=int)
for m in range(1,4):
first = mol_ids.index(mol_ids[m])
if first == m: # the unique mol
bas_start[m] = bas.shape[0]
atm, bas, env = gto.conc_env(atm, bas, env, mols[m]._atm,
mols[m]._bas, mols[m]._env)
else:
bas_start[m] = bas_start[first]
shls_slice[m] += bas_start[m]
shls_slice = shls_slice.flatten()
else:
atm, bas, env = mols._atm, mols._bas, mols._env
if shls_slice is None:
shls_slice = (0, mols.nbas) * 4
if isinstance(scripts, str):
scripts = [scripts]
if isinstance(dms, numpy.ndarray) and dms.ndim == 2:
dms = [dms]
assert(len(scripts) == len(dms))
#format scripts
descript = []
for script in scripts:
dmsym, vsym = script.lower().split(',')[1].split('->')
if hermi == 0:
descript.append('->'.join((dmsym,'s1'+vsym)))
else:
descript.append('->'.join((dmsym,'s2'+vsym)))
vs = _vhf.direct_bindm(intor, aosym, descript, dms, comp, atm, bas, env,
shls_slice=shls_slice)
if hermi != 0:
for v in vs:
if v.ndim == 3:
for vi in v:
pyscf.lib.hermi_triu(vi, hermi, inplace=True)
else:
pyscf.lib.hermi_triu(v, hermi, inplace=True)
return vs
def auxmol_set(self,auxbas = "weigend"):
print "===================="
print "GENERATING INTEGRALS"
print "===================="
auxmol = gto.Mole()
auxmol.atom = self.hf1.mol.atom
auxmol.basis = auxbas
auxmol.build()
mol = self.hf1.mol
nao = self.n_ao[0] = int(mol.nao_nr())
naux = self.n_aux[0] = auxmol.nao_nr()
atm, bas, env = gto.conc_env(mol._atm, mol._bas, mol._env, auxmol._atm, auxmol._bas, auxmol._env)
eri3c = np.empty((nao,nao,naux))
pi = 0
for i in range(mol.nbas):
pj = 0
for j in range(mol.nbas):
pk = 0
for k in range(mol.nbas, mol.nbas+auxmol.nbas):
shls = (i, j, k)
buf = gto.getints_by_shell('cint3c2e_sph', shls, atm, bas, env)
di, dj, dk = buf.shape
eri3c[pi:pi+di,pj:pj+dj,pk:pk+dk] = buf
pk += dk
pj += dj
pi += di
eri2c = np.empty((naux,naux))
pk = 0
for k in range(mol.nbas, mol.nbas+auxmol.nbas):
pl = 0
for l in range(mol.nbas, mol.nbas+auxmol.nbas):
shls = (k, l)
buf = gto.getints_by_shell('cint2c2e_sph', shls, atm, bas, env)
dk, dl = buf.shape
eri2c[pk:pk+dk,pl:pl+dl] = buf
pl += dl
pk += dk
self.eri3c.append(eri3c)
self.eri2c.append(eri2c)
print "\nAA INT GENERATED"
self.eri3c.append(eri3c)
self.eri2c.append(eri2c)
RSinv = MatrixPower(eri2c,-0.5)
self.B0 = np.einsum('ijp,pq->ijq', eri3c, RSinv)
auxmol = mol = nao = naux = None
auxmol = gto.Mole()
auxmol.atom = self.hf3.mol.atom
auxmol.basis = auxbas
auxmol.build()
mol = self.hf3.mol
nao = self.n_ao[2] = int(mol.nao_nr())
naux = self.n_aux[2] = auxmol.nao_nr()
atm, bas, env = gto.conc_env(mol._atm, mol._bas, mol._env, auxmol._atm, auxmol._bas, auxmol._env)
eri3c = np.empty((nao,nao,naux))
pi = 0
for i in range(mol.nbas):
pj = 0
for j in range(mol.nbas):
pk = 0
for k in range(mol.nbas, mol.nbas+auxmol.nbas):
shls = (i, j, k)
buf = gto.getints_by_shell('cint3c2e_sph', shls, atm, bas, env)
di, dj, dk = buf.shape
eri3c[pi:pi+di,pj:pj+dj,pk:pk+dk] = buf
pk += dk
pj += dj
pi += di
eri2c = np.empty((naux,naux))
pk = 0
for k in range(mol.nbas, mol.nbas+auxmol.nbas):
pl = 0
for l in range(mol.nbas, mol.nbas+auxmol.nbas):
shls = (k, l)
buf = gto.getints_by_shell('cint2c2e_sph', shls, atm, bas, env)
dk, dl = buf.shape
eri2c[pk:pk+dk,pl:pl+dl] = buf
pl += dl
pk += dk
# if(self.hyb[0] > 0.01):
# eri3cBO = np.zeros((nao,nao,naux))
# for i in range(naux):
# eri3cBO[:,:,i] = TransMat(eri3c[:,:,i],self.U)
# eri3c = eri3cBO.copy()
print "\nWHOLE INT GENERATED"
self.eri3c.append(eri3c)
self.eri2c.append(eri2c)
RSinv = MatrixPower(eri2c,-0.5)
self.B1 = np.einsum('ijp,pq->ijq', eri3c, RSinv)
auxmol = mol = nao = naux = None
return
def get_jk(mols, dms, scripts=['ijkl,ji->kl'], intor='int2e_sph',
aosym='s1', comp=1, hermi=0, shls_slice=None, verbose=logger.WARN):
'''Compute J/K matrices for the given density matrix
Args:
mols : an instance of :class:`Mole` or a list of `Mole` objects
dms : ndarray or list of ndarrays
A density matrix or a list of density matrices
Kwargs:
hermi : int
Whether J/K matrix is hermitian
| 0 : no hermitian or symmetric
| 1 : hermitian
| 2 : anti-hermitian
intor : str
2-electron integral name. See :func:`getints` for the complete
list of available 2-electron integral names
aosym : int or str
Permutation symmetry for the AO integrals
| 4 or '4' or 's4': 4-fold symmetry (default)
| '2ij' or 's2ij' : symmetry between i, j in (ij|kl)
| '2kl' or 's2kl' : symmetry between k, l in (ij|kl)
| 1 or '1' or 's1': no symmetry
| 'a4ij' : 4-fold symmetry with anti-symmetry between i, j in (ij|kl)
| 'a4kl' : 4-fold symmetry with anti-symmetry between k, l in (ij|kl)
| 'a2ij' : anti-symmetry between i, j in (ij|kl)
| 'a2kl' : anti-symmetry between k, l in (ij|kl)
comp : int
Components of the integrals, e.g. cint2e_ip_sph has 3 components.
scripts : a list of strings
Contraction description (following numpy.einsum convention) based on
letters [ijkl]. Each script will be one-to-one applied to each
entry of dms. So it must have the same number of elements as the
dms, len(scripts) == len(dms).
shls_slice : 8-element list
(ish_start, ish_end, jsh_start, jsh_end, ksh_start, ksh_end, lsh_start, lsh_end)
Returns:
Depending on the number of density matrices, the function returns one
J/K matrix or a list of J/K matrices (the same number of entries as the
input dms).
Each JK matrices may be a 2D array or 3D array if the AO integral
has multiple components.
Examples:
>>> from pyscf import gto
>>> mol = gto.M(atom='H 0 -.5 0; H 0 .5 0', basis='cc-pvdz')
>>> nao = mol.nao_nr()
>>> dm = numpy.random.random((nao,nao))
>>> # Default, Coulomb matrix
>>> vj = get_jk(mol, dm)
>>> # Coulomb matrix with 8-fold permutation symmetry for AO integrals
>>> vj = get_jk(mol, dm, 'ijkl,ji->kl', aosym='s8')
>>> # Exchange matrix with 8-fold permutation symmetry for AO integrals
>>> vk = get_jk(mol, dm, 'ijkl,jk->il', aosym='s8')
>>> # Compute coulomb and exchange matrices together
>>> vj, vk = get_jk(mol, (dm,dm), ('ijkl,ji->kl','ijkl,li->kj'), aosym='s8')
>>> # Analytical gradients for coulomb matrix
>>> j1 = get_jk(mol, dm, 'ijkl,lk->ij', intor='int2e_ip1_sph', aosym='s2kl', comp=3)
>>> # contraction across two molecules
>>> mol1 = gto.M(atom='He 2 0 0', basis='6-31g')
>>> nao1 = mol1.nao_nr()
>>> dm1 = numpy.random.random((nao1,nao1))
>>> # Coulomb interaction between two molecules, note 4-fold symmetry can be applied
>>> jcross = get_jk((mol1,mol1,mol,mol), dm, scripts='ijkl,lk->ij', aosym='s4')
>>> ecoul = numpy.einsum('ij,ij', jcross, dm1)
>>> # Exchange interaction between two molecules, no symmetry can be used
>>> kcross = get_jk((mol1,mol,mol,mol1), dm, scripts='ijkl,jk->il')
>>> ex = numpy.einsum('ij,ji', kcross, dm1)
>>> # Analytical gradients for coulomb matrix between two molecules
>>> jcros1 = get_jk((mol1,mol1,mol,mol), dm, scripts='ijkl,lk->ij', intor='int2e_ip1_sph', comp=3)
>>> # Analytical gradients for coulomb interaction between 1s density and the other molecule
>>> jpart1 = get_jk((mol1,mol1,mol,mol), dm, scripts='ijkl,lk->ij', intor='int2e_ip1_sph', comp=3,
... shls_slice=(0,1,0,1,0,mol.nbas,0,mol.nbas))
'''
if isinstance(mols, (tuple, list)):
assert(len(mols) == 4)
assert(mols[0].cart == mols[1].cart == mols[2].cart == mols[3].cart)
if shls_slice is None:
shls_slice = numpy.array([(0, mol.nbas) for mol in mols])
else:
shls_slice = numpy.asarray(shls_slice).reshape(4,2)
# concatenate unique mols and build corresponding shls_slice
mol_ids = [id(mol) for mol in mols]
atm, bas, env = mols[0]._atm, mols[0]._bas, mols[0]._env
bas_start = numpy.zeros(4, dtype=int)
for m in range(1,4):
first = mol_ids.index(mol_ids[m])
if first == m: # the unique mol
bas_start[m] = bas.shape[0]
atm, bas, env = gto.conc_env(atm, bas, env, mols[m]._atm,
mols[m]._bas, mols[m]._env)
else:
bas_start[m] = bas_start[first]
shls_slice[m] += bas_start[m]
shls_slice = shls_slice.flatten()
else:
atm, bas, env = mols._atm, mols._bas, mols._env
if shls_slice is None:
shls_slice = (0, mols.nbas) * 4
if isinstance(scripts, str):
scripts = [scripts]
if isinstance(dms, numpy.ndarray) and dms.ndim == 2:
dms = [dms]
assert(len(scripts) == len(dms))
#format scripts
descript = []
for script in scripts:
dmsym, vsym = script.lower().split(',')[1].split('->')
if hermi == 0:
descript.append('->'.join((dmsym,'s1'+vsym)))
else:
descript.append('->'.join((dmsym,'s2'+vsym)))
vs = _vhf.direct_bindm(intor, aosym, descript, dms, comp, atm, bas, env,
shls_slice=shls_slice)
if hermi != 0:
for v in vs:
if v.ndim == 3:
for vi in v:
pyscf.lib.hermi_triu(vi, hermi, inplace=True)
else:
pyscf.lib.hermi_triu(v, hermi, inplace=True)
return vs
def _ft_aopair_kpts(cell, Gv, shls_slice=None, aosym='s1',
invh=None, gxyz=None, gs=None,
kpt=numpy.zeros(3), kptjs=numpy.zeros((2,3)), out=None):
''' FT transform AO pair
\int i(r) j(r) exp(-ikr) dr^3
for all kpt = kptj - kpti. The return list holds the AO pair array
corresponding to the kpoints given by kptjs
'''
kpt = numpy.reshape(kpt, 3)
kptjs = numpy.asarray(kptjs, order='C').reshape(-1,3)
nGv = Gv.shape[0]
Gv = Gv + kpt # kptis = kptjs - kpt
if (gxyz is None or invh is None or gs is None or (abs(kpt).sum() > 1e-9)):
GvT = numpy.asarray(Gv.T, order='C')
p_gxyzT = lib.c_null_ptr()
p_gs = (ctypes.c_int*3)(0,0,0)
p_invh = (ctypes.c_double*1)(0)
eval_gz = 'GTO_Gv_general'
else:
GvT = numpy.asarray(Gv.T, order='C')
gxyzT = numpy.asarray(gxyz.T, order='C', dtype=numpy.int32)
p_gxyzT = gxyzT.ctypes.data_as(ctypes.c_void_p)
p_gs = (ctypes.c_int*3)(*gs)
# Guess what type of eval_gz to use
if isinstance(invh, numpy.ndarray) and invh.shape == (3,3):
p_invh = invh.ctypes.data_as(ctypes.c_void_p)
if abs(invh-numpy.diag(invh.diagonal())).sum() < 1e-8:
eval_gz = 'GTO_Gv_uniform_orth'
else:
eval_gz = 'GTO_Gv_uniform_nonorth'
else:
invh = numpy.hstack(invh)
p_invh = invh.ctypes.data_as(ctypes.c_void_p)
eval_gz = 'GTO_Gv_nonuniform_orth'
drv = libpbc.PBC_ft_latsum_kpts
intor = getattr(libpbc, 'GTO_ft_ovlp_sph')
eval_gz = getattr(libpbc, eval_gz)
# make copy of atm,bas,env because they are modified in the lattice sum
atm, bas, env = gto.conc_env(cell._atm, cell._bas, cell._env,
cell._atm, cell._bas, cell._env)
ao_loc = cell.ao_loc_nr()
nao = ao_loc[cell.nbas]
ao_loc = numpy.asarray(numpy.hstack((ao_loc[:-1], ao_loc+nao)),
dtype=numpy.int32)
if shls_slice is None:
shls_slice = (0, cell.nbas, cell.nbas, cell.nbas*2)
else:
shls_slice = (shls_slice[0], shls_slice[1],
cell.nbas+shls_slice[2], cell.nbas+shls_slice[3])
ni = ao_loc[shls_slice[1]] - ao_loc[shls_slice[0]]
nj = ao_loc[shls_slice[3]] - ao_loc[shls_slice[2]]
shape = (nGv, ni, nj)
fill = getattr(libpbc, 'PBC_ft_fill_'+aosym)
if aosym == 's1hermi': # Symmetry for Gamma point
assert(abs(kpt).sum() < 1e-9 and abs(kptjs).sum() < 1e-9)
elif aosym == 's2':
i0 = ao_loc[shls_slice[0]]
i1 = ao_loc[shls_slice[1]]
nij = i1*(i1+1)//2 - i0*(i0+1)//2
shape = (nGv, nij)
if out is None:
out = [numpy.zeros(shape, order='F', dtype=numpy.complex128)
for k in range(len(kptjs))]
else:
out = [numpy.ndarray(shape, order='F', dtype=numpy.complex128,
buffer=out[k]) for k in range(len(kptjs))]
out_ptrs = (ctypes.c_void_p*len(out))(
*[x.ctypes.data_as(ctypes.c_void_p) for x in out])
xyz = numpy.asarray(cell.atom_coords(), order='C')
ptr_coord = numpy.asarray(atm[cell.natm:,gto.PTR_COORD],
dtype=numpy.int32, order='C')
Ls = numpy.asarray(cell.get_lattice_Ls(cell.nimgs), order='C')
exp_Lk = numpy.einsum('ik,jk->ij', Ls, kptjs)
exp_Lk = numpy.exp(1j * numpy.asarray(exp_Lk, order='C'))
drv(intor, eval_gz, fill, out_ptrs, xyz.ctypes.data_as(ctypes.c_void_p),
ptr_coord.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(len(xyz)),
Ls.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(len(Ls)),
exp_Lk.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(len(kptjs)),
(ctypes.c_int*4)(*shls_slice),
ao_loc.ctypes.data_as(ctypes.c_void_p),
GvT.ctypes.data_as(ctypes.c_void_p),
p_invh, p_gxyzT, p_gs, ctypes.c_int(nGv),
atm.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(cell.natm*2),
bas.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(cell.nbas*2),
env.ctypes.data_as(ctypes.c_void_p))
if aosym == 's1hermi':
for mat in out:
for i in range(1,ni):
mat[:,:i,i] = mat[:,i,:i]
return out
def __init__(self, mol, unrestricted=False):
scf.hf.SCF.__init__(self, mol)
if mol.elec.nhomo is not None:
unrestricted = True
self.unrestricted = unrestricted
self.mf_elec = None
# dm_elec will be the total density after SCF, but can be spin
# densities during the SCF procedure
self.dm_elec = None
self.mf_nuc = []
self.dm_nuc = []
self._eri_ne = []
self._eri_nn = []
# The verbosity flag is passed now instead of when creating those mol
# objects because users need time to change mol's verbose level after
# the mol object is created.
self.mol.elec.verbose = self.mol.verbose
for i in range(mol.nuc_num):
self.mol.nuc[i].verbose = self.mol.verbose
# initialize sub mf objects for electrons and quantum nuclei
# electronic part:
if unrestricted:
self.mf_elec = scf.UHF(mol.elec)
else:
self.mf_elec = scf.RHF(mol.elec)
self.mf_elec.get_hcore = self.get_hcore_elec
self.mf_elec.super_mf = self
if mol.elec.nhomo is not None:
self.mf_elec.get_occ = self.get_occ_elec(self.mf_elec)
# nuclear part
for i in range(mol.nuc_num):
self.mf_nuc.append(scf.RHF(mol.nuc[i]))
mf_nuc = self.mf_nuc[-1]
mf_nuc.occ_state = 0 # for Delta-SCF
mf_nuc.get_occ = self.get_occ_nuc(mf_nuc)
mf_nuc.get_hcore = self.get_hcore_nuc
mf_nuc.get_veff = self.get_veff_nuc_bare
mf_nuc.energy_qmnuc = self.energy_qmnuc
mf_nuc.super_mf = self
self.dm_nuc.append(None)
# build ne and nn ERIs if there is enough memory
for i in range(mol.nuc_num):
self._eri_ne.append(None)
self._eri_nn.append([None] * mol.nuc_num)
if mol.incore_anyway or self._is_mem_enough(
mol.elec.nao_nr(), mol.nuc[i].nao_nr()):
atm, bas, env = gto.conc_env(mol.nuc[i]._atm, mol.nuc[i]._bas,
mol.nuc[i]._env, mol.elec._atm,
mol.elec._bas, mol.elec._env)
self._eri_ne[i] = \
gto.moleintor.getints('int2e_sph', atm, bas, env,
shls_slice=(0, mol.nuc[i]._bas.shape[0], 0, mol.nuc[i]._bas.shape[0],
mol.nuc[i]._bas.shape[0],
mol.nuc[i]._bas.shape[0] + mol.elec._bas.shape[0],
mol.nuc[i]._bas.shape[0],
mol.nuc[i]._bas.shape[0] + mol.elec._bas.shape[0]),
aosym='s4')
for i in range(mol.nuc_num - 1):
for j in range(i + 1, mol.nuc_num):
if mol.incore_anyway or self._is_mem_enough(
mol.nuc[i].nao_nr(), mol.nuc[j].nao_nr()):
atm, bas, env = gto.conc_env(
mol.nuc[i]._atm, mol.nuc[i]._bas, mol.nuc[i]._env,
mol.nuc[j]._atm, mol.nuc[j]._bas, mol.nuc[j]._env)
self._eri_nn[i][j] = \
gto.moleintor.getints('int2e_sph', atm, bas, env,
shls_slice=(0, mol.nuc[i]._bas.shape[0], 0, mol.nuc[i]._bas.shape[0],
mol.nuc[i]._bas.shape[0],
mol.nuc[i]._bas.shape[0] + mol.nuc[j]._bas.shape[0],
mol.nuc[i]._bas.shape[0],
mol.nuc[i]._bas.shape[0] + mol.nuc[j]._bas.shape[0]),
aosym='s4')
def wrap_int3c(cell,
auxcell,
intor='int3c2e',
aosym='s1',
comp=1,
kptij_lst=numpy.zeros((1, 2, 3)),
cintopt=None,
pbcopt=None):
intor = cell._add_suffix(intor)
pcell = copy.copy(cell)
pcell._atm, pcell._bas, pcell._env = \
atm, bas, env = gto.conc_env(cell._atm, cell._bas, cell._env,
cell._atm, cell._bas, cell._env)
ao_loc = gto.moleintor.make_loc(bas, intor)
aux_loc = auxcell.ao_loc_nr(auxcell.cart or 'ssc' in intor)
ao_loc = numpy.asarray(numpy.hstack([ao_loc, ao_loc[-1] + aux_loc[1:]]),
dtype=numpy.int32)
atm, bas, env = gto.conc_env(atm, bas, env, auxcell._atm, auxcell._bas,
auxcell._env)
Ls = cell.get_lattice_Ls()
nimgs = len(Ls)
kpti = kptij_lst[:, 0]
kptj = kptij_lst[:, 1]
if gamma_point(kptij_lst):
kk_type = 'g'
dtype = numpy.double
nkpts = nkptij = 1
kptij_idx = numpy.array([0], dtype=numpy.int32)
expkL = numpy.ones(1)
elif is_zero(kpti - kptj): # j_only
kk_type = 'k'
dtype = numpy.complex128
kpts = kptij_idx = numpy.asarray(kpti, order='C')
expkL = numpy.exp(1j * numpy.dot(kpts, Ls.T))
nkpts = nkptij = len(kpts)
else:
kk_type = 'kk'
dtype = numpy.complex128
kpts = unique(numpy.vstack([kpti, kptj]))[0]
expkL = numpy.exp(1j * numpy.dot(kpts, Ls.T))
wherei = numpy.where(
abs(kpti.reshape(-1, 1, 3) - kpts).sum(axis=2) < KPT_DIFF_TOL)[1]
wherej = numpy.where(
abs(kptj.reshape(-1, 1, 3) - kpts).sum(axis=2) < KPT_DIFF_TOL)[1]
nkpts = len(kpts)
kptij_idx = numpy.asarray(wherei * nkpts + wherej, dtype=numpy.int32)
nkptij = len(kptij_lst)
fill = 'PBCnr3c_fill_%s%s' % (kk_type, aosym[:2])
drv = libpbc.PBCnr3c_drv
if cintopt is None:
cintopt = _vhf.make_cintopt(atm, bas, env, intor)
# Remove the precomputed pair data because the pair data corresponds to the
# integral of cell #0 while the lattice sum moves shls to all repeated images.
if intor[:3] != 'ECP':
libpbc.CINTdel_pairdata_optimizer(cintopt)
if pbcopt is None:
pbcopt = _pbcintor.PBCOpt(pcell).init_rcut_cond(pcell)
if isinstance(pbcopt, _pbcintor.PBCOpt):
cpbcopt = pbcopt._this
else:
cpbcopt = lib.c_null_ptr()
nbas = cell.nbas
def int3c(shls_slice, out):
shls_slice = (shls_slice[0], shls_slice[1], nbas + shls_slice[2],
nbas + shls_slice[3], nbas * 2 + shls_slice[4],
nbas * 2 + shls_slice[5])
drv(
getattr(libpbc, intor),
getattr(libpbc, fill),
out.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(nkptij),
ctypes.c_int(nkpts),
ctypes.c_int(comp),
ctypes.c_int(nimgs),
Ls.ctypes.data_as(ctypes.c_void_p),
expkL.ctypes.data_as(ctypes.c_void_p),
kptij_idx.ctypes.data_as(ctypes.c_void_p),
(ctypes.c_int * 6)(*shls_slice),
ao_loc.ctypes.data_as(ctypes.c_void_p),
cintopt,
cpbcopt,
atm.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(cell.natm),
bas.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(nbas), # need to pass cell.nbas to libpbc.PBCnr3c_drv
env.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(env.size))
return out
return int3c
def _ft_aopair_kpts(cell, Gv, shls_slice=None, aosym='s1',
b=None, gxyz=None, Gvbase=None, q=numpy.zeros(3),
kptjs=numpy.zeros((1,3)), intor='GTO_ft_ovlp', comp=1,
out=None):
r'''
FT transform AO pair
\sum_T exp(-i k_j * T) \int exp(-i(G+q)r) i(r) j(r-T) dr^3
The return array holds the AO pair
corresponding to the kpoints given by kptjs
'''
intor = cell._add_suffix(intor)
q = numpy.reshape(q, 3)
kptjs = numpy.asarray(kptjs, order='C').reshape(-1,3)
Gv = numpy.asarray(Gv, order='C').reshape(-1,3)
nGv = Gv.shape[0]
GvT = numpy.asarray(Gv.T, order='C')
GvT += q.reshape(-1,1)
if (gxyz is None or b is None or Gvbase is None or (abs(q).sum() > 1e-9)
# backward compatibility for pyscf-1.2, in which the argument Gvbase is gs
or (Gvbase is not None and isinstance(Gvbase[0], (int, numpy.integer)))):
p_gxyzT = lib.c_null_ptr()
p_mesh = (ctypes.c_int*3)(0,0,0)
p_b = (ctypes.c_double*1)(0)
eval_gz = 'GTO_Gv_general'
else:
if abs(b-numpy.diag(b.diagonal())).sum() < 1e-8:
eval_gz = 'GTO_Gv_orth'
else:
eval_gz = 'GTO_Gv_nonorth'
gxyzT = numpy.asarray(gxyz.T, order='C', dtype=numpy.int32)
p_gxyzT = gxyzT.ctypes.data_as(ctypes.c_void_p)
b = numpy.hstack((b.ravel(), q) + Gvbase)
p_b = b.ctypes.data_as(ctypes.c_void_p)
p_mesh = (ctypes.c_int*3)(*[len(x) for x in Gvbase])
Ls = cell.get_lattice_Ls()
expkL = numpy.exp(1j * numpy.dot(kptjs, Ls.T))
atm, bas, env = gto.conc_env(cell._atm, cell._bas, cell._env,
cell._atm, cell._bas, cell._env)
ao_loc = gto.moleintor.make_loc(bas, intor)
if shls_slice is None:
shls_slice = (0, cell.nbas, cell.nbas, cell.nbas*2)
else:
shls_slice = (shls_slice[0], shls_slice[1],
cell.nbas+shls_slice[2], cell.nbas+shls_slice[3])
ni = ao_loc[shls_slice[1]] - ao_loc[shls_slice[0]]
nj = ao_loc[shls_slice[3]] - ao_loc[shls_slice[2]]
nkpts = len(kptjs)
nimgs = len(Ls)
shape = (nkpts, comp, ni, nj, nGv)
# Theoretically, hermitian symmetry can be also found for kpti == kptj:
# f_ji(G) = \int f_ji exp(-iGr) = \int f_ij^* exp(-iGr) = [f_ij(-G)]^*
# hermi operation needs reordering the axis-0. It is inefficient.
if aosym == 's1hermi': # Symmetry for Gamma point
assert(is_zero(q) and is_zero(kptjs) and ni == nj)
elif aosym == 's2':
i0 = ao_loc[shls_slice[0]]
i1 = ao_loc[shls_slice[1]]
nij = i1*(i1+1)//2 - i0*(i0+1)//2
shape = (nkpts, comp, nij, nGv)
drv = libpbc.PBC_ft_latsum_drv
cintor = getattr(libpbc, intor)
eval_gz = getattr(libpbc, eval_gz)
if nkpts == 1:
fill = getattr(libpbc, 'PBC_ft_fill_nk1'+aosym)
else:
fill = getattr(libpbc, 'PBC_ft_fill_k'+aosym)
out = numpy.ndarray(shape, dtype=numpy.complex128, buffer=out)
drv(cintor, eval_gz, fill, out.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(nkpts), ctypes.c_int(comp), ctypes.c_int(nimgs),
Ls.ctypes.data_as(ctypes.c_void_p), expkL.ctypes.data_as(ctypes.c_void_p),
(ctypes.c_int*4)(*shls_slice), ao_loc.ctypes.data_as(ctypes.c_void_p),
GvT.ctypes.data_as(ctypes.c_void_p), p_b, p_gxyzT, p_mesh, ctypes.c_int(nGv),
atm.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(cell.natm),
bas.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(cell.nbas),
env.ctypes.data_as(ctypes.c_void_p))
if aosym == 's1hermi':
for i in range(1,ni):
out[:,:,:i,i] = out[:,:,i,:i]
out = numpy.rollaxis(out, -1, 2)
if comp == 1:
out = out[:,0]
return out
def _ft_aopair_kpts(cell, Gv, shls_slice=None, aosym='s1',
b=None, gxyz=None, Gvbase=None,
kpt=numpy.zeros(3), kptjs=numpy.zeros((2,3)), out=None):
''' FT transform AO pair
\int i(r) j(r) exp(-ikr) dr^3
for all kpt = kptj - kpti. The return list holds the AO pair array
corresponding to the kpoints given by kptjs
'''
kpt = numpy.reshape(kpt, 3) # kptis = kptjs - kpt
kptjs = numpy.asarray(kptjs, order='C').reshape(-1,3)
nGv = Gv.shape[0]
GvT = numpy.asarray(Gv.T, order='C')
GvT += kpt.reshape(-1,1)
if (gxyz is None or b is None or Gvbase is None or (abs(kpt).sum() > 1e-9)
# backward compatibility for pyscf-1.2, in which the argument Gvbase is gs
or (Gvbase is not None and isinstance(Gvbase[0], (int, numpy.integer)))):
p_gxyzT = lib.c_null_ptr()
p_gs = (ctypes.c_int*3)(0,0,0)
p_b = (ctypes.c_double*1)(0)
eval_gz = 'GTO_Gv_general'
else:
gxyzT = numpy.asarray(gxyz.T, order='C', dtype=numpy.int32)
p_gxyzT = gxyzT.ctypes.data_as(ctypes.c_void_p)
b = numpy.hstack((b.ravel(), kpt) + Gvbase)
p_b = b.ctypes.data_as(ctypes.c_void_p)
p_gs = (ctypes.c_int*3)(*[len(x) for x in Gvbase])
eval_gz = 'GTO_Gv_cubic'
drv = libpbc.PBC_ft_latsum_kpts
intor = getattr(libpbc, 'GTO_ft_ovlp_sph')
eval_gz = getattr(libpbc, eval_gz)
# make copy of atm,bas,env because they are modified in the lattice sum
atm, bas, env = gto.conc_env(cell._atm, cell._bas, cell._env,
cell._atm, cell._bas, cell._env)
ao_loc = cell.ao_loc_nr()
nao = ao_loc[cell.nbas]
ao_loc = numpy.asarray(numpy.hstack((ao_loc[:-1], ao_loc+nao)),
dtype=numpy.int32)
if shls_slice is None:
shls_slice = (0, cell.nbas, cell.nbas, cell.nbas*2)
else:
shls_slice = (shls_slice[0], shls_slice[1],
cell.nbas+shls_slice[2], cell.nbas+shls_slice[3])
ni = ao_loc[shls_slice[1]] - ao_loc[shls_slice[0]]
nj = ao_loc[shls_slice[3]] - ao_loc[shls_slice[2]]
shape = (nGv, ni, nj)
fill = getattr(libpbc, 'PBC_ft_fill_'+aosym)
# Theoretically, hermitian symmetry can be also found for kpti == kptj:
# f_ji(G) = \int f_ji exp(-iGr) = \int f_ij^* exp(-iGr) = [f_ij(-G)]^*
# The hermi operation needs reordering the axis-0. It is inefficient.
if aosym == 's1hermi': # Symmetry for Gamma point
assert(abs(kpt).sum() < 1e-9 and abs(kptjs).sum() < 1e-9)
elif aosym == 's2':
i0 = ao_loc[shls_slice[0]]
i1 = ao_loc[shls_slice[1]]
nij = i1*(i1+1)//2 - i0*(i0+1)//2
shape = (nGv, nij)
if out is None:
out = [numpy.zeros(shape, order='F', dtype=numpy.complex128)
for k in range(len(kptjs))]
else:
out = [numpy.ndarray(shape, order='F', dtype=numpy.complex128,
buffer=out[k]) for k in range(len(kptjs))]
out_ptrs = (ctypes.c_void_p*len(out))(
*[x.ctypes.data_as(ctypes.c_void_p) for x in out])
xyz = numpy.asarray(cell.atom_coords(), order='C')
ptr_coord = numpy.asarray(atm[cell.natm:,gto.PTR_COORD],
dtype=numpy.int32, order='C')
Ls = cell.get_lattice_Ls()
exp_Lk = numpy.einsum('ik,jk->ij', Ls, kptjs)
exp_Lk = numpy.exp(1j * numpy.asarray(exp_Lk, order='C'))
drv(intor, eval_gz, fill, out_ptrs, xyz.ctypes.data_as(ctypes.c_void_p),
ptr_coord.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(len(xyz)),
Ls.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(len(Ls)),
exp_Lk.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(len(kptjs)),
(ctypes.c_int*4)(*shls_slice),
ao_loc.ctypes.data_as(ctypes.c_void_p),
GvT.ctypes.data_as(ctypes.c_void_p),
p_b, p_gxyzT, p_gs, ctypes.c_int(nGv),
atm.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(cell.natm*2),
bas.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(cell.nbas*2),
env.ctypes.data_as(ctypes.c_void_p))
if aosym == 's1hermi':
for mat in out:
for i in range(1,ni):
mat[:,:i,i] = mat[:,i,:i]
return out
def conc_env(self):
return gto.conc_env(self.mol._atm, self.mol._bas, self.mol._env, self.Vmol._atm, self.Vmol._bas, self.Vmol._env)
def _make_j3c(mydf, cell, auxcell, chgcell, kptij_lst):
t1 = (time.clock(), time.time())
log = logger.Logger(mydf.stdout, mydf.verbose)
max_memory = max(2000, mydf.max_memory-lib.current_memory()[0])
auxcell = copy.copy(auxcell)
auxcell._atm, auxcell._bas, auxcell._env = \
gto.conc_env(auxcell._atm, auxcell._bas, auxcell._env,
chgcell._atm, chgcell._bas, chgcell._env)
outcore.aux_e2(cell, auxcell, mydf._cderi, 'cint3c2e_sph',
kptij_lst=kptij_lst, dataname='j3c', max_memory=max_memory)
t1 = log.timer_debug1('3c2e', *t1)
nao = cell.nao_nr()
naux = auxcell.nao_nr()
gs = mydf.gs
gxyz = lib.cartesian_prod((numpy.append(range(gs[0]+1), range(-gs[0],0)),
numpy.append(range(gs[1]+1), range(-gs[1],0)),
numpy.append(range(gs[2]+1), range(-gs[2],0))))
invh = numpy.linalg.inv(cell._h)
Gv = 2*numpy.pi * numpy.dot(gxyz, invh)
ngs = gxyz.shape[0]
kptis = kptij_lst[:,0]
kptjs = kptij_lst[:,1]
kpt_ji = kptjs - kptis
uniq_kpts, uniq_index, uniq_inverse = unique(kpt_ji)
# j2c ~ (-kpt_ji | kpt_ji)
j2c = auxcell.pbc_intor('cint2c2e_sph', hermi=1, kpts=uniq_kpts)
kLRs = []
kLIs = []
for k, kpt in enumerate(uniq_kpts):
aoaux = ft_ao.ft_ao(auxcell, Gv, None, invh, gxyz, gs, kpt)
coulG = tools.get_coulG(cell, kpt, gs=gs) / cell.vol
aoauxG = aoaux * coulG.reshape(-1,1)
kLRs.append(numpy.asarray(aoauxG.real, order='C'))
kLIs.append(numpy.asarray(aoauxG.imag, order='C'))
if is_zero(kpt): # kpti == kptj
j2c[k] -= lib.dot(kLRs[-1].T, numpy.asarray(aoaux.real,order='C'))
j2c[k] -= lib.dot(kLIs[-1].T, numpy.asarray(aoaux.imag,order='C'))
else:
# aoaux ~ kpt_ij, aoaux.conj() ~ kpt_kl
j2c[k] -= lib.dot(aoauxG.conj().T, aoaux)
aoaux = coulG = None
feri = h5py.File(mydf._cderi)
# Expand approx Lpq for aosym='s1'. The approx Lpq are all in aosym='s2' mode
if mydf.approx_sr_level > 0 and len(kptij_lst) > 1:
Lpq_fake = _fake_Lpq_kpts(mydf, feri, naux, nao)
def save(label, dat, col0, col1):
feri[label][:,col0:col1] = dat
def make_kpt(uniq_kptji_id): # kpt = kptj - kpti
kpt = uniq_kpts[uniq_kptji_id]
log.debug1('kpt = %s', kpt)
adapted_ji_idx = numpy.where(uniq_inverse == uniq_kptji_id)[0]
adapted_kptjs = kptjs[adapted_ji_idx]
nkptj = len(adapted_kptjs)
log.debug1('adapted_ji_idx = %s', adapted_ji_idx)
kLR = kLRs[uniq_kptji_id]
kLI = kLIs[uniq_kptji_id]
if is_zero(kpt): # kpti == kptj
aosym = 's2'
nao_pair = nao*(nao+1)//2
vbar = mydf.auxbar(auxcell)
ovlp = cell.pbc_intor('cint1e_ovlp_sph', hermi=1, kpts=adapted_kptjs)
for k, ji in enumerate(adapted_ji_idx):
ovlp[k] = lib.pack_tril(ovlp[k])
else:
aosym = 's1'
nao_pair = nao**2
max_memory = max(2000, mydf.max_memory-lib.current_memory()[0])
# nkptj for 3c-coulomb arrays plus 1 Lpq array
buflen = min(max(int(max_memory*.6*1e6/16/naux/(nkptj+1)), 1), nao_pair)
shranges = pyscf.df.outcore._guess_shell_ranges(cell, buflen, aosym)
buflen = max([x[2] for x in shranges])
# +1 for a pqkbuf
if aosym == 's2':
Gblksize = max(16, int(max_memory*.2*1e6/16/buflen/(nkptj+1)))
else:
Gblksize = max(16, int(max_memory*.4*1e6/16/buflen/(nkptj+1)))
Gblksize = min(Gblksize, ngs)
pqkRbuf = numpy.empty(buflen*Gblksize)
pqkIbuf = numpy.empty(buflen*Gblksize)
# buf for ft_aopair
buf = numpy.zeros((nkptj,buflen*Gblksize), dtype=numpy.complex128)
col1 = 0
for istep, sh_range in enumerate(shranges):
log.debug1('int3c2e [%d/%d], AO [%d:%d], ncol = %d', \
istep+1, len(shranges), *sh_range)
bstart, bend, ncol = sh_range
col0, col1 = col1, col1+ncol
j3cR = []
j3cI = []
for k, idx in enumerate(adapted_ji_idx):
v = numpy.asarray(feri['j3c/%d'%idx][:,col0:col1])
if mydf.approx_sr_level == 0:
Lpq = numpy.asarray(feri['Lpq/%d'%idx][:,col0:col1])
elif aosym == 's2':
Lpq = numpy.asarray(feri['Lpq/0'][:,col0:col1])
else:
Lpq = numpy.asarray(Lpq_fake[:,col0:col1])
lib.dot(j2c[uniq_kptji_id], Lpq, -.5, v, 1)
j3cR.append(numpy.asarray(v.real, order='C'))
if is_zero(kpt) and gamma_point(adapted_kptjs[k]):
j3cI.append(None)
else:
j3cI.append(numpy.asarray(v.imag, order='C'))
v = Lpq = None
if aosym == 's2':
shls_slice = (bstart, bend, 0, bend)
for p0, p1 in lib.prange(0, ngs, Gblksize):
ft_ao._ft_aopair_kpts(cell, Gv[p0:p1], shls_slice, aosym, invh,
gxyz[p0:p1], gs, kpt, adapted_kptjs, out=buf)
nG = p1 - p0
for k, ji in enumerate(adapted_ji_idx):
aoao = numpy.ndarray((nG,ncol), dtype=numpy.complex128,
order='F', buffer=buf[k])
pqkR = numpy.ndarray((ncol,nG), buffer=pqkRbuf)
pqkI = numpy.ndarray((ncol,nG), buffer=pqkIbuf)
pqkR[:] = aoao.real.T
pqkI[:] = aoao.imag.T
aoao[:] = 0
lib.dot(kLR[p0:p1].T, pqkR.T, -1, j3cR[k], 1)
lib.dot(kLI[p0:p1].T, pqkI.T, -1, j3cR[k], 1)
if not (is_zero(kpt) and gamma_point(adapted_kptjs[k])):
lib.dot(kLR[p0:p1].T, pqkI.T, -1, j3cI[k], 1)
lib.dot(kLI[p0:p1].T, pqkR.T, 1, j3cI[k], 1)
else:
shls_slice = (bstart, bend, 0, cell.nbas)
ni = ncol // nao
for p0, p1 in lib.prange(0, ngs, Gblksize):
ft_ao._ft_aopair_kpts(cell, Gv[p0:p1], shls_slice, aosym, invh,
gxyz[p0:p1], gs, kpt, adapted_kptjs, out=buf)
nG = p1 - p0
for k, ji in enumerate(adapted_ji_idx):
aoao = numpy.ndarray((nG,ni,nao), dtype=numpy.complex128,
order='F', buffer=buf[k])
pqkR = numpy.ndarray((ni,nao,nG), buffer=pqkRbuf)
pqkI = numpy.ndarray((ni,nao,nG), buffer=pqkIbuf)
pqkR[:] = aoao.real.transpose(1,2,0)
pqkI[:] = aoao.imag.transpose(1,2,0)
aoao[:] = 0
pqkR = pqkR.reshape(-1,nG)
pqkI = pqkI.reshape(-1,nG)
zdotCN(kLR[p0:p1].T, kLI[p0:p1].T, pqkR.T, pqkI.T,
-1, j3cR[k], j3cI[k], 1)
if is_zero(kpt):
for k, ji in enumerate(adapted_ji_idx):
if gamma_point(adapted_kptjs[k]):
for i, c in enumerate(vbar):
if c != 0:
j3cR[k][i] -= c * ovlp[k][col0:col1].real
else:
for i, c in enumerate(vbar):
if c != 0:
j3cR[k][i] -= c * ovlp[k][col0:col1].real
j3cI[k][i] -= c * ovlp[k][col0:col1].imag
for k, ji in enumerate(adapted_ji_idx):
if is_zero(kpt) and gamma_point(adapted_kptjs[k]):
save('j3c/%d'%ji, j3cR[k], col0, col1)
else:
save('j3c/%d'%ji, j3cR[k]+j3cI[k]*1j, col0, col1)
for k, kpt in enumerate(uniq_kpts):
make_kpt(k)
feri.close()
def _ft_aopair_kpts(cell,
Gv,
shls_slice=None,
aosym='s1',
b=None,
gxyz=None,
Gvbase=None,
q=numpy.zeros(3),
kptjs=numpy.zeros((1, 3)),
out=None):
''' FT transform AO pair
\int exp(-i(G+q)r) i(r) j(r) exp(-ikr) dr^3
The return list holds the AO pair array
corresponding to the kpoints given by kptjs
'''
q = numpy.reshape(q, 3)
kptjs = numpy.asarray(kptjs, order='C').reshape(-1, 3)
nGv = Gv.shape[0]
GvT = numpy.asarray(Gv.T, order='C')
GvT += q.reshape(-1, 1)
if (gxyz is None or b is None or Gvbase is None or (abs(q).sum() > 1e-9)
# backward compatibility for pyscf-1.2, in which the argument Gvbase is gs
or (Gvbase is not None and isinstance(Gvbase[0],
(int, numpy.integer)))):
p_gxyzT = lib.c_null_ptr()
p_gs = (ctypes.c_int * 3)(0, 0, 0)
p_b = (ctypes.c_double * 1)(0)
eval_gz = 'GTO_Gv_general'
else:
if abs(b - numpy.diag(b.diagonal())).sum() < 1e-8:
eval_gz = 'GTO_Gv_orth'
else:
eval_gz = 'GTO_Gv_nonorth'
gxyzT = numpy.asarray(gxyz.T, order='C', dtype=numpy.int32)
p_gxyzT = gxyzT.ctypes.data_as(ctypes.c_void_p)
Gvx = lib.cartesian_prod(Gvbase)
b = numpy.hstack((b.ravel(), q) + Gvbase)
p_b = b.ctypes.data_as(ctypes.c_void_p)
p_gs = (ctypes.c_int * 3)(*[len(x) for x in Gvbase])
drv = libpbc.PBC_ft_latsum_kpts
intor = getattr(libpbc, 'GTO_ft_ovlp_sph')
eval_gz = getattr(libpbc, eval_gz)
# make copy of atm,bas,env because they are modified in the lattice sum
atm, bas, env = gto.conc_env(cell._atm, cell._bas, cell._env, cell._atm,
cell._bas, cell._env)
ao_loc = cell.ao_loc_nr()
nao = ao_loc[cell.nbas]
ao_loc = numpy.asarray(numpy.hstack((ao_loc[:-1], ao_loc + nao)),
dtype=numpy.int32)
if shls_slice is None:
shls_slice = (0, cell.nbas, cell.nbas, cell.nbas * 2)
else:
shls_slice = (shls_slice[0], shls_slice[1], cell.nbas + shls_slice[2],
cell.nbas + shls_slice[3])
ni = ao_loc[shls_slice[1]] - ao_loc[shls_slice[0]]
nj = ao_loc[shls_slice[3]] - ao_loc[shls_slice[2]]
shape = (nGv, ni, nj)
fill = getattr(libpbc, 'PBC_ft_fill_' + aosym)
# Theoretically, hermitian symmetry can be also found for kpti == kptj:
# f_ji(G) = \int f_ji exp(-iGr) = \int f_ij^* exp(-iGr) = [f_ij(-G)]^*
# The hermi operation needs reordering the axis-0. It is inefficient.
if aosym == 's1hermi': # Symmetry for Gamma point
assert (abs(q).sum() < 1e-9 and abs(kptjs).sum() < 1e-9)
elif aosym == 's2':
i0 = ao_loc[shls_slice[0]]
i1 = ao_loc[shls_slice[1]]
nij = i1 * (i1 + 1) // 2 - i0 * (i0 + 1) // 2
shape = (nGv, nij)
if out is None:
out = [
numpy.zeros(shape, order='F', dtype=numpy.complex128)
for k in range(len(kptjs))
]
else:
out = [
numpy.ndarray(shape,
order='F',
dtype=numpy.complex128,
buffer=out[k]) for k in range(len(kptjs))
]
out_ptrs = (ctypes.c_void_p *
len(out))(*[x.ctypes.data_as(ctypes.c_void_p) for x in out])
xyz = numpy.asarray(cell.atom_coords(), order='C')
ptr_coord = numpy.asarray(atm[cell.natm:, gto.PTR_COORD],
dtype=numpy.int32,
order='C')
Ls = cell.get_lattice_Ls()
exp_Lk = numpy.einsum('ik,jk->ij', Ls, kptjs)
exp_Lk = numpy.exp(1j * numpy.asarray(exp_Lk, order='C'))
drv(intor, eval_gz, fill, out_ptrs, xyz.ctypes.data_as(ctypes.c_void_p),
ptr_coord.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(len(xyz)),
Ls.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(len(Ls)),
exp_Lk.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(len(kptjs)), (ctypes.c_int * 4)(*shls_slice),
ao_loc.ctypes.data_as(ctypes.c_void_p),
GvT.ctypes.data_as(ctypes.c_void_p), p_b, p_gxyzT, p_gs,
ctypes.c_int(nGv), atm.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(cell.natm * 2), bas.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(cell.nbas * 2), env.ctypes.data_as(ctypes.c_void_p))
if aosym == 's1hermi':
for mat in out:
for i in range(1, ni):
mat[:, :i, i] = mat[:, i, :i]
return out
from pyscf import gto
from pyscf import scf
from pyscf import ao2mo
from pyscf import df
mol = gto.Mole()
mol.build(
verbose=0,
atom='''O 0 0. 0.
1 0 -0.757 0.587
1 0 0.757 0.587''',
basis='cc-pvdz',
)
auxmol = df.addons.make_auxmol(mol, 'weigend')
atm, bas, env = gto.conc_env(mol._atm, mol._bas, mol._env, auxmol._atm,
auxmol._bas, auxmol._env)
class KnowValues(unittest.TestCase):
def test_aux_e2(self):
nao = mol.nao_nr()
naoaux = auxmol.nao_nr()
eri0 = numpy.empty((nao, nao, naoaux))
pi = 0
for i in range(mol.nbas):
pj = 0
for j in range(mol.nbas):
pk = 0
for k in range(mol.nbas, mol.nbas + auxmol.nbas):
shls = (i, j, k)
buf = gto.moleintor.getints_by_shell(
from pyscf import ao2mo
from pyscf import df
mol = gto.Mole()
mol.build(
verbose = 0,
atom = '''O 0 0. 0.
1 0 -0.757 0.587
1 0 0.757 0.587''',
basis = 'cc-pvdz',
)
libri = df.incore.libri
auxmol = df.incore.format_aux_basis(mol)
atm, bas, env = \
gto.conc_env(mol._atm, mol._bas, mol._env,
auxmol._atm, auxmol._bas, auxmol._env)
class KnowValues(unittest.TestCase):
def test_aux_e2(self):
j3c = df.incore.aux_e2(mol, auxmol, intor='cint3c2e_sph', aosym='s1')
nao = mol.nao_nr()
naoaux = auxmol.nao_nr()
j3c = j3c.reshape(nao,nao,naoaux)
eri0 = numpy.empty((nao,nao,naoaux))
pi = 0
for i in range(mol.nbas):
pj = 0
for j in range(mol.nbas):
pk = 0
for k in range(mol.nbas, mol.nbas+auxmol.nbas):
from pyscf import gto, scf
'''
Concatenate two molecule enviroments
We need the integrals from different bra and ket space, eg to prepare
initial guess from different geometry or basis, or compute the
transition properties between two states. To access These integrals, we
need concatenate the enviroments of two Mole object.
This method can be used to generate the 3-center integrals for RI integrals.
'''
mol1 = gto.M(verbose=0, atom='C 0 0 0; O 0 0 1.5', basis='ccpvdz')
mol2 = gto.M(verbose=0, atom='H 0 1 0; H 1 0 0', basis='ccpvdz')
atm3, bas3, env3 = gto.conc_env(mol1._atm, mol1._bas, mol1._env, mol2._atm,
mol2._bas, mol2._env)
nao1 = mol1.nao_nr()
nao2 = mol2.nao_nr()
s12 = numpy.empty((nao1, nao2))
pi = 0
for i in range(mol1.nbas):
pj = 0
for j in range(mol1.nbas, mol1.nbas + mol2.nbas):
shls = (i, j)
buf = gto.moleintor.getints_by_shell('cint1e_ovlp_sph', shls, atm3,
bas3, env3)
di, dj = buf.shape
s12[pi:pi + di, pj:pj + dj] = buf
pj += dj
pi += di
print('<mol1|mol2> overlap shape %s' % str(s12.shape))
def fuse_auxcell(mydf, auxcell):
chgcell = make_modchg_basis(auxcell, mydf.eta)
fused_cell = copy.copy(auxcell)
fused_cell._atm, fused_cell._bas, fused_cell._env = \
gto.conc_env(auxcell._atm, auxcell._bas, auxcell._env,
chgcell._atm, chgcell._bas, chgcell._env)
fused_cell.rcut = max(auxcell.rcut, chgcell.rcut)
aux_loc = auxcell.ao_loc_nr()
naux = aux_loc[-1]
modchg_offset = -numpy.ones((chgcell.natm,8), dtype=int)
smooth_loc = chgcell.ao_loc_nr()
for i in range(chgcell.nbas):
ia = chgcell.bas_atom(i)
l = chgcell.bas_angular(i)
modchg_offset[ia,l] = smooth_loc[i]
if auxcell.cart:
# Normalization coefficients are different in the same shell for cartesian
# basis. E.g. the d-type functions, the 5 d-type orbitals are normalized wrt
# the integral \int r^2 * r^2 e^{-a r^2} dr. The s-type 3s orbital should be
# normalized wrt the integral \int r^0 * r^2 e^{-a r^2} dr. The different
# normalization was not built in the basis. There two ways to surmount this
# problem. First is to transform the cartesian basis and scale the 3s (for
# d functions), 4p (for f functions) ... then transform back. The second is to
# remove the 3s, 4p functions. The function below is the second solution
import ctypes
c2s_fn = gto.moleintor.libcgto.CINTc2s_ket_sph
aux_loc_sph = auxcell.ao_loc_nr(cart=False)
naux_sph = aux_loc_sph[-1]
def fuse(Lpq):
Lpq, chgLpq = Lpq[:naux], Lpq[naux:]
if Lpq.ndim == 1:
npq = 1
Lpq_sph = numpy.empty(naux_sph, dtype=Lpq.dtype)
else:
npq = Lpq.shape[1]
Lpq_sph = numpy.empty((naux_sph,npq), dtype=Lpq.dtype)
if Lpq.dtype == numpy.complex:
npq *= 2 # c2s_fn supports double only, *2 to handle complex
for i in range(auxcell.nbas):
l = auxcell.bas_angular(i)
ia = auxcell.bas_atom(i)
p0 = modchg_offset[ia,l]
if p0 >= 0:
nd = (l+1) * (l+2) // 2
c0, c1 = aux_loc[i], aux_loc[i+1]
s0, s1 = aux_loc_sph[i], aux_loc_sph[i+1]
for i0, i1 in lib.prange(c0, c1, nd):
Lpq[i0:i1] -= chgLpq[p0:p0+nd]
if l < 2:
Lpq_sph[s0:s1] = Lpq[c0:c1]
else:
Lpq_cart = numpy.asarray(Lpq[c0:c1], order='C')
c2s_fn(Lpq_sph[s0:s1].ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(npq * auxcell.bas_nctr(i)),
Lpq_cart.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(l))
return Lpq_sph
else:
def fuse(Lpq):
Lpq, chgLpq = Lpq[:naux], Lpq[naux:]
for i in range(auxcell.nbas):
l = auxcell.bas_angular(i)
ia = auxcell.bas_atom(i)
p0 = modchg_offset[ia,l]
if p0 >= 0:
nd = l * 2 + 1
for i0, i1 in lib.prange(aux_loc[i], aux_loc[i+1], nd):
Lpq[i0:i1] -= chgLpq[p0:p0+nd]
return Lpq
return fused_cell, fuse
def fuse_auxcell(mydf, auxcell):
chgcell = make_modchg_basis(auxcell, mydf.eta)
fused_cell = copy.copy(auxcell)
fused_cell._atm, fused_cell._bas, fused_cell._env = \
gto.conc_env(auxcell._atm, auxcell._bas, auxcell._env,
chgcell._atm, chgcell._bas, chgcell._env)
fused_cell.rcut = max(auxcell.rcut, chgcell.rcut)
aux_loc = auxcell.ao_loc_nr()
naux = aux_loc[-1]
modchg_offset = -numpy.ones((chgcell.natm, 8), dtype=int)
smooth_loc = chgcell.ao_loc_nr()
for i in range(chgcell.nbas):
ia = chgcell.bas_atom(i)
l = chgcell.bas_angular(i)
modchg_offset[ia, l] = smooth_loc[i]
if auxcell.cart:
# Normalization coefficients are different in the same shell for cartesian
# basis. E.g. the d-type functions, the 5 d-type orbitals are normalized wrt
# the integral \int r^2 * r^2 e^{-a r^2} dr. The s-type 3s orbital should be
# normalized wrt the integral \int r^0 * r^2 e^{-a r^2} dr. The different
# normalization was not built in the basis. There two ways to surmount this
# problem. First is to transform the cartesian basis and scale the 3s (for
# d functions), 4p (for f functions) ... then transform back. The second is to
# remove the 3s, 4p functions. The function below is the second solution
c2s_fn = gto.moleintor.libcgto.CINTc2s_ket_sph
aux_loc_sph = auxcell.ao_loc_nr(cart=False)
naux_sph = aux_loc_sph[-1]
def fuse(Lpq):
Lpq, chgLpq = Lpq[:naux], Lpq[naux:]
if Lpq.ndim == 1:
npq = 1
Lpq_sph = numpy.empty(naux_sph, dtype=Lpq.dtype)
else:
npq = Lpq.shape[1]
Lpq_sph = numpy.empty((naux_sph, npq), dtype=Lpq.dtype)
if Lpq.dtype == numpy.complex:
npq *= 2 # c2s_fn supports double only, *2 to handle complex
for i in range(auxcell.nbas):
l = auxcell.bas_angular(i)
ia = auxcell.bas_atom(i)
p0 = modchg_offset[ia, l]
if p0 >= 0:
nd = (l + 1) * (l + 2) // 2
c0, c1 = aux_loc[i], aux_loc[i + 1]
s0, s1 = aux_loc_sph[i], aux_loc_sph[i + 1]
for i0, i1 in lib.prange(c0, c1, nd):
Lpq[i0:i1] -= chgLpq[p0:p0 + nd]
if l < 2:
Lpq_sph[s0:s1] = Lpq[c0:c1]
else:
Lpq_cart = numpy.asarray(Lpq[c0:c1], order='C')
c2s_fn(Lpq_sph[s0:s1].ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(npq * auxcell.bas_nctr(i)),
Lpq_cart.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(l))
return Lpq_sph
else:
def fuse(Lpq):
Lpq, chgLpq = Lpq[:naux], Lpq[naux:]
for i in range(auxcell.nbas):
l = auxcell.bas_angular(i)
ia = auxcell.bas_atom(i)
p0 = modchg_offset[ia, l]
if p0 >= 0:
nd = l * 2 + 1
for i0, i1 in lib.prange(aux_loc[i], aux_loc[i + 1], nd):
Lpq[i0:i1] -= chgLpq[p0:p0 + nd]
return Lpq
return fused_cell, fuse
def get_nuc(mydf, kpts=None):
cell = mydf.cell
if kpts is None:
kpts_lst = numpy.zeros((1,3))
else:
kpts_lst = numpy.reshape(kpts, (-1,3))
if mydf._cderi is None:
mydf.build()
log = logger.Logger(mydf.stdout, mydf.verbose)
t1 = t0 = (time.clock(), time.time())
auxcell = mydf.auxcell
nuccell = make_modchg_basis(cell, mydf.eta, 0)
nuccell._bas = numpy.asarray(nuccell._bas[nuccell._bas[:,gto.ANG_OF]==0],
dtype=numpy.int32, order='C')
charge = -cell.atom_charges()
nucbar = sum([z/nuccell.bas_exp(i)[0] for i,z in enumerate(charge)])
nucbar *= numpy.pi/cell.vol
vj = [v.ravel() for v in _int_nuc_vloc(cell, nuccell, kpts_lst)]
t1 = log.timer_debug1('vnuc pass1: analytic int', *t1)
j2c = pgto.intor_cross('cint2c2e_sph', auxcell, nuccell)
jaux = j2c.dot(charge)
kpt_allow = numpy.zeros(3)
coulG = tools.get_coulG(cell, kpt_allow, gs=mydf.gs) / cell.vol
Gv = cell.get_Gv(mydf.gs)
aoaux = ft_ao.ft_ao(nuccell, Gv)
vGR = numpy.einsum('i,xi->x', charge, aoaux.real) * coulG
vGI = numpy.einsum('i,xi->x', charge, aoaux.imag) * coulG
max_memory = mydf.max_memory - lib.current_memory()[0]
for k, pqkR, pqkI, p0, p1 \
in mydf.ft_loop(cell, mydf.gs, kpt_allow, kpts_lst, max_memory=max_memory):
# rho_ij(G) nuc(-G) / G^2
# = [Re(rho_ij(G)) + Im(rho_ij(G))*1j] [Re(nuc(G)) - Im(nuc(G))*1j] / G^2
if not gamma_point(kpts_lst[k]):
vj[k] += numpy.einsum('k,xk->x', vGR[p0:p1], pqkI) * 1j
vj[k] += numpy.einsum('k,xk->x', vGI[p0:p1], pqkR) *-1j
vj[k] += numpy.einsum('k,xk->x', vGR[p0:p1], pqkR)
vj[k] += numpy.einsum('k,xk->x', vGI[p0:p1], pqkI)
t1 = log.timer_debug1('contracting Vnuc', *t1)
# Append nuccell to auxcell, so that they can be FT together in pw_loop
# the first [:naux] of ft_ao are aux fitting functions.
nuccell._atm, nuccell._bas, nuccell._env = \
gto.conc_env(auxcell._atm, auxcell._bas, auxcell._env,
nuccell._atm, nuccell._bas, nuccell._env)
naux = auxcell.nao_nr()
aoaux = ft_ao.ft_ao(nuccell, Gv)
vG = numpy.einsum('i,xi,x->x', charge, aoaux[:,naux:], coulG)
jaux -= numpy.einsum('x,xj->j', vG.real, aoaux[:,:naux].real)
jaux -= numpy.einsum('x,xj->j', vG.imag, aoaux[:,:naux].imag)
jaux -= charge.sum() * mydf.auxbar(auxcell)
ovlp = cell.pbc_intor('cint1e_ovlp_sph', 1, lib.HERMITIAN, kpts_lst)
nao = cell.nao_nr()
nao_pair = nao * (nao+1) // 2
max_memory = max(2000, mydf.max_memory-lib.current_memory()[0])
blksize = max(16, min(int(max_memory*1e6/16/nao_pair), mydf.blockdim))
for k, kpt in enumerate(kpts_lst):
with mydf.load_Lpq((kpt,kpt)) as Lpq:
v = 0
for p0, p1 in lib.prange(0, jaux.size, blksize):
v += numpy.dot(jaux[p0:p1], numpy.asarray(Lpq[p0:p1]))
vj[k] = vj[k].reshape(nao,nao) - nucbar * ovlp[k]
if gamma_point(kpt):
vj[k] += lib.unpack_tril(numpy.asarray(v.real,order='C'))
else:
vj[k] += lib.unpack_tril(v)
if kpts is None or numpy.shape(kpts) == (3,):
vj = vj[0]
return vj