def test_aux_e2(self):
cell = pgto.Cell()
cell.unit = 'B'
cell.a = numpy.eye(3) * 3.
cell.gs = numpy.array([20,20,20])
cell.atom = 'He 0 1 1; He 1 1 0'
cell.basis = { 'He': [[0, (0.8, 1.0)],
[0, (1.2, 1.0)]] }
cell.verbose = 0
cell.build(0, 0)
auxcell = incore.format_aux_basis(cell)
cell.nimgs = auxcell.nimgs = [3,3,3]
a1 = incore.aux_e2(cell, auxcell, 'cint3c1e_sph')
self.assertAlmostEqual(finger(a1), 0.1208944790152819, 9)
a2 = incore.aux_e2(cell, auxcell, 'cint3c1e_sph', aosym='s2ij')
self.assertTrue(numpy.allclose(a1, lib.unpack_tril(a2, axis=0).reshape(a1.shape)))
numpy.random.seed(3)
kpti_kptj = [numpy.random.random(3)]*2
a1 = incore.aux_e2(cell, auxcell, 'cint3c1e_sph', kpti_kptj=kpti_kptj)
self.assertAlmostEqual(finger(a1), -0.073719031689332651-0.054002639392614758j, 9)
a2 = incore.aux_e2(cell, auxcell, 'cint3c1e_sph', aosym='s2ij', kpti_kptj=kpti_kptj)
self.assertTrue(numpy.allclose(a1, lib.unpack_tril(a2, 1, axis=0).reshape(a1.shape)))
numpy.random.seed(1)
kpti_kptj = numpy.random.random((2,3))
a1 = incore.aux_e2(cell, auxcell, 'cint3c1e_sph', kpti_kptj=kpti_kptj)
self.assertAlmostEqual(finger(a1), 0.039329191948685879-0.039836453846241987j, 9)
def test_aux_e2(self):
tmpfile = tempfile.NamedTemporaryFile(dir=lib.param.TMPDIR)
numpy.random.seed(1)
kptij_lst = numpy.random.random((3,2,3))
kptij_lst[0] = 0
kptij_lst[1,0] = kptij_lst[1,1]
outcore.aux_e2(cell, cell, tmpfile.name, aosym='s2ij', comp=1,
kptij_lst=kptij_lst, verbose=0)
refk0 = incore.aux_e2(cell, cell, aosym='s2ij', kpti_kptj=kptij_lst[0])
refk1 = incore.aux_e2(cell, cell, aosym='s2ij', kpti_kptj=kptij_lst[1])
refk2 = incore.aux_e2(cell, cell, aosym='s2ij', kpti_kptj=kptij_lst[2])
with h5py.File(tmpfile.name, 'r') as f:
self.assertTrue(numpy.allclose(refk0, f['eri_mo/0'].value.T))
self.assertTrue(numpy.allclose(refk1, f['eri_mo/1'].value.T))
self.assertTrue(numpy.allclose(refk2, f['eri_mo/2'].value.T))
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 test_aux_e2(self):
tmpfile = tempfile.NamedTemporaryFile(dir=lib.param.TMPDIR)
numpy.random.seed(1)
kptij_lst = numpy.random.random((3, 2, 3))
kptij_lst[0] = 0
kptij_lst[1, 0] = kptij_lst[1, 1]
outcore.aux_e2(cell,
cell,
tmpfile.name,
aosym='s2ij',
comp=1,
kptij_lst=kptij_lst,
verbose=0)
refk0 = incore.aux_e2(cell, cell, aosym='s2ij', kpti_kptj=kptij_lst[0])
refk1 = incore.aux_e2(cell, cell, aosym='s2ij', kpti_kptj=kptij_lst[1])
refk2 = incore.aux_e2(cell, cell, aosym='s2ij', kpti_kptj=kptij_lst[2])
with h5py.File(tmpfile.name, 'r') as f:
self.assertTrue(numpy.allclose(refk0, f['eri_mo/0'].value.T))
self.assertTrue(numpy.allclose(refk1, f['eri_mo/1'].value.T))
self.assertTrue(numpy.allclose(refk2, f['eri_mo/2'].value.T))
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_aux_e2(self):
cell = pgto.Cell()
cell.unit = 'B'
cell.a = numpy.eye(3) * 3.
cell.mesh = numpy.array([41] * 3)
cell.atom = 'He 0 1 1; He 1 1 0'
cell.basis = {'He': [[0, (0.8, 1.0)], [0, (1.2, 1.0)]]}
cell.verbose = 0
cell.build(0, 0)
auxcell = incore.format_aux_basis(cell)
a1 = incore.aux_e2(cell, auxcell, 'int3c1e_sph')
self.assertAlmostEqual(lib.fp(a1), 0.1208944790152819, 9)
a2 = incore.aux_e2(cell, auxcell, 'int3c1e_sph', aosym='s2ij')
self.assertTrue(
numpy.allclose(a1,
lib.unpack_tril(a2, axis=0).reshape(a1.shape)))
numpy.random.seed(3)
kpt = numpy.random.random(3)
kptij_lst = numpy.array([[kpt, kpt]])
a1 = incore.aux_e2(cell, auxcell, 'int3c1e_sph', kptij_lst=kptij_lst)
self.assertAlmostEqual(lib.fp(a1),
-0.073719031689332651 - 0.054002639392614758j,
9)
a2 = incore.aux_e2(cell,
auxcell,
'int3c1e_sph',
aosym='s2',
kptij_lst=kptij_lst)
self.assertTrue(
numpy.allclose(a1,
lib.unpack_tril(a2, 1, axis=0).reshape(a1.shape)))
numpy.random.seed(1)
kptij_lst = numpy.random.random((1, 2, 3))
a1 = incore.aux_e2(cell, auxcell, 'int3c1e_sph', kptij_lst=kptij_lst)
self.assertAlmostEqual(lib.fp(a1),
0.039329191948685879 - 0.039836453846241987j, 9)
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_aux_e2(self):
tmpfile = tempfile.NamedTemporaryFile(dir=lib.param.TMPDIR)
numpy.random.seed(1)
kptij_lst = numpy.random.random((3,2,3))
kptij_lst[0] = 0
outcore.aux_e2(cell, cell, tmpfile.name, aosym='s2', comp=1,
kptij_lst=kptij_lst, verbose=0)
refk = incore.aux_e2(cell, cell, aosym='s2', kptij_lst=kptij_lst)
with h5py.File(tmpfile.name, 'r') as f:
nao = cell.nao_nr()
idx = numpy.tril_indices(nao)
idx = idx[0] * nao + idx[1]
self.assertTrue(numpy.allclose(refk[0,idx], f['eri_mo/0'].value.T))
self.assertTrue(numpy.allclose(refk[1], f['eri_mo/1'].value.T))
self.assertTrue(numpy.allclose(refk[2], f['eri_mo/2'].value.T))
def test_aux_e1(self):
tmpfile = tempfile.NamedTemporaryFile(dir=lib.param.TMPDIR)
numpy.random.seed(1)
kptij_lst = numpy.random.random((3,2,3))
kptij_lst[0] = 0
outcore.aux_e1(cell, cell, tmpfile.name, aosym='s2', comp=1,
kptij_lst=kptij_lst, verbose=0)
refk = incore.aux_e2(cell, cell, aosym='s2', kptij_lst=kptij_lst)
with h5py.File(tmpfile.name, 'r') as f:
nao = cell.nao_nr()
idx = numpy.tril_indices(nao)
idx = idx[0] * nao + idx[1]
self.assertTrue(numpy.allclose(refk[0,idx], f['eri_mo/0'].value.T))
self.assertTrue(numpy.allclose(refk[1], f['eri_mo/1'].value.T))
self.assertTrue(numpy.allclose(refk[2], f['eri_mo/2'].value.T))
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 get_pp_loc_part2(cell, kpts=None):
'''PRB, 58, 3641 Eq (1), integrals associated to C1, C2, C3, C4
'''
from pyscf.pbc.df import incore
if kpts is None:
kpts_lst = numpy.zeros((1, 3))
else:
kpts_lst = numpy.reshape(kpts, (-1, 3))
nkpts = len(kpts_lst)
intors = ('int3c2e', 'int3c1e', 'int3c1e_r2_origk', 'int3c1e_r4_origk',
'int3c1e_r6_origk')
kptij_lst = numpy.hstack((kpts_lst, kpts_lst)).reshape(-1, 2, 3)
buf = 0
for cn in range(1, 5):
fakecell = fake_cell_vloc(cell, cn)
if fakecell.nbas > 0:
v = incore.aux_e2(cell,
fakecell,
intors[cn],
aosym='s2',
comp=1,
kptij_lst=kptij_lst)
buf += numpy.einsum('...i->...', v)
if isinstance(buf, int):
if any(
cell.atom_symbol(ia) in cell._pseudo
for ia in range(cell.natm)):
pass
else:
lib.logger.warn(
cell, 'cell.pseudo was specified but its elements %s '
'were not found in the system.', cell._pseudo.keys())
vpploc = [0] * nkpts
else:
buf = buf.reshape(nkpts, -1)
vpploc = []
for k, kpt in enumerate(kpts_lst):
v = lib.unpack_tril(buf[k])
if abs(kpt).sum() < 1e-9: # gamma_point:
v = v.real
vpploc.append(v)
if kpts is None or numpy.shape(kpts) == (3, ):
vpploc = vpploc[0]
return vpploc
def ecp_int(cell, kpts=None):
from pyscf.pbc.df import incore
if kpts is None:
kpts_lst = numpy.zeros((1, 3))
else:
kpts_lst = numpy.reshape(kpts, (-1, 3))
cell, contr_coeff = gto.cell._split_basis(cell)
lib.logger.debug1(cell, 'nao %d -> nao %d', *(contr_coeff.shape))
ecpcell = gto.Cell()
ecpcell._atm = cell._atm
# append a fictitious s function to mimic the auxiliary index in pbc.incore.
# ptr2last_env_idx to force PBCnr3c_fill_* function to copy the entire "env"
ptr2last_env_idx = len(cell._env) - 1
ecpbas = numpy.vstack([[0, 0, 1, 1, 0, ptr2last_env_idx, 0, 0],
cell._ecpbas]).astype(numpy.int32)
ecpcell._bas = ecpbas
ecpcell._env = cell._env
# In pbc.incore _ecpbas is appended to two sets of cell._bas and the
# fictitious s function.
cell._env[AS_ECPBAS_OFFSET] = cell.nbas * 2 + 1
cell._env[AS_NECPBAS] = len(cell._ecpbas)
# shls_slice of auxiliary index (0,1) corresponds to the fictitious s function
shls_slice = (0, cell.nbas, 0, cell.nbas, 0, 1)
kptij_lst = numpy.hstack((kpts_lst, kpts_lst)).reshape(-1, 2, 3)
buf = incore.aux_e2(cell,
ecpcell,
'ECPscalar',
aosym='s2',
kptij_lst=kptij_lst,
shls_slice=shls_slice)
buf = buf.reshape(len(kpts_lst), -1)
mat = []
for k, kpt in enumerate(kpts_lst):
v = lib.unpack_tril(buf[k], lib.HERMITIAN)
if abs(kpt).sum() < 1e-9: # gamma_point:
v = v.real
mat.append(reduce(numpy.dot, (contr_coeff.T, v, contr_coeff)))
if kpts is None or numpy.shape(kpts) == (3, ):
mat = mat[0]
return mat
def get_pp_loc_part2(cell, kpts=None):
'''PRB, 58, 3641 Eq (1), integrals associated to C1, C2, C3, C4
'''
from pyscf.pbc.df import incore
if kpts is None:
kpts_lst = numpy.zeros((1,3))
else:
kpts_lst = numpy.reshape(kpts, (-1,3))
nkpts = len(kpts_lst)
intors = ('int3c2e', 'int3c1e', 'int3c1e_r2_origk',
'int3c1e_r4_origk', 'int3c1e_r6_origk')
kptij_lst = numpy.hstack((kpts_lst,kpts_lst)).reshape(-1,2,3)
buf = 0
for cn in range(1, 5):
fakecell = fake_cell_vloc(cell, cn)
if fakecell.nbas > 0:
v = incore.aux_e2(cell, fakecell, intors[cn], aosym='s2', comp=1,
kptij_lst=kptij_lst)
buf += numpy.einsum('...i->...', v)
if isinstance(buf, int):
if any(cell.atom_symbol(ia) in cell._pseudo for ia in range(cell.natm)):
pass
else:
lib.logger.warn(cell, 'cell.pseudo was specified but its elements %s '
'were not found in the system.', cell._pseudo.keys())
vpploc = [0] * nkpts
else:
buf = buf.reshape(nkpts,-1)
vpploc = []
for k, kpt in enumerate(kpts_lst):
v = lib.unpack_tril(buf[k])
if abs(kpt).sum() < 1e-9: # gamma_point:
v = v.real
vpploc.append(v)
if kpts is None or numpy.shape(kpts) == (3,):
vpploc = vpploc[0]
return vpploc
def ecp_int(cell, kpts=None):
from pyscf.pbc.df import incore
if kpts is None:
kpts_lst = numpy.zeros((1,3))
else:
kpts_lst = numpy.reshape(kpts, (-1,3))
cell, contr_coeff = gto.cell._split_basis(cell)
lib.logger.debug1(cell, 'nao %d -> nao %d', *(contr_coeff.shape))
ecpcell = gto.Cell()
ecpcell._atm = cell._atm
# append a fictitious s function to mimic the auxiliary index in pbc.incore.
# ptr2last_env_idx to force PBCnr3c_fill_* function to copy the entire "env"
ptr2last_env_idx = len(cell._env) - 1
ecpbas = numpy.vstack([[0, 0, 1, 1, 0, ptr2last_env_idx, 0, 0],
cell._ecpbas]).astype(numpy.int32)
ecpcell._bas = ecpbas
ecpcell._env = cell._env
# In pbc.incore _ecpbas is appended to two sets of cell._bas and the
# fictitious s function.
cell._env[AS_ECPBAS_OFFSET] = cell.nbas * 2 + 1
cell._env[AS_NECPBAS] = len(cell._ecpbas)
# shls_slice of auxiliary index (0,1) corresponds to the fictitious s function
shls_slice = (0, cell.nbas, 0, cell.nbas, 0, 1)
kptij_lst = numpy.hstack((kpts_lst,kpts_lst)).reshape(-1,2,3)
buf = incore.aux_e2(cell, ecpcell, 'ECPscalar', aosym='s2',
kptij_lst=kptij_lst, shls_slice=shls_slice)
buf = buf.reshape(len(kpts_lst),-1)
mat = []
for k, kpt in enumerate(kpts_lst):
v = lib.unpack_tril(buf[k], lib.HERMITIAN)
if abs(kpt).sum() < 1e-9: # gamma_point:
v = v.real
mat.append(reduce(numpy.dot, (contr_coeff.T, v, contr_coeff)))
if kpts is None or numpy.shape(kpts) == (3,):
mat = mat[0]
return mat
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)
if cell.dimension != 0 and intor in ('int3c2e', 'int3c2e_sph',
'int3c2e_cart'):
assert (comp == 1)
charge = -cell.atom_charges()
if cell.dimension == 1 or cell.dimension == 2:
Gv, Gvbase, kws = cell.get_Gv_weights(mydf.mesh)
G0idx, SI_on_z = pbcgto.cell._SI_for_uniform_model_charge(cell, Gv)
ZSI = numpy.einsum("i,ix->x", charge, cell.get_SI(Gv[G0idx]))
ZSI -= numpy.einsum('i,xi->x', charge,
ft_ao.ft_ao(nuccell, Gv[G0idx]))
coulG = 4 * numpy.pi / numpy.linalg.norm(Gv[G0idx], axis=1)**2
nucbar = numpy.einsum('i,i,i,i', ZSI.conj(), coulG, kws[G0idx],
SI_on_z)
if abs(kpts).sum() < 1e-9:
nucbar = nucbar.real
else: # cell.dimension == 3
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
