def run3c(fill, kpts, shls_slice=None):
intor = 'int3c2e_sph'
nao = cell.nao_nr()
nkpts = len(kpts)
if fill == 'PBCnr3c_fill_gs2':
out = numpy.empty((nao * (nao + 1) // 2, nao))
kptij_idx = numpy.arange(nkpts).astype(numpy.int32)
elif fill == 'PBCnr3c_fill_gs1':
out = numpy.empty((nao, nao, nao))
kptij_idx = numpy.arange(nkpts).astype(numpy.int32)
elif fill in ('PBCnr3c_fill_kks1', 'PBCnr3c_fill_kks2'):
kptij_idx = numpy.asarray(
[i * nkpts + j for i in range(nkpts) for j in range(i + 1)],
dtype=numpy.int32)
out = numpy.empty((len(kptij_idx), nao, nao, nao),
dtype=numpy.complex128)
elif fill == 'PBCnr3c_fill_ks1':
kptij_idx = numpy.arange(nkpts).astype(numpy.int32)
out = numpy.empty((nkpts, nao, nao, nao), dtype=numpy.complex128)
elif fill == 'PBCnr3c_fill_ks2':
out = numpy.empty((nkpts, nao * (nao + 1) // 2, nao),
dtype=numpy.complex128)
kptij_idx = numpy.arange(nkpts).astype(numpy.int32)
else:
raise RuntimeError
nkpts_ij = len(kptij_idx)
nimgs = len(Ls)
expkL = numpy.exp(1j * numpy.dot(kpts, Ls.T))
comp = 1
if shls_slice is None:
shls_slice = (0, cell.nbas, cell.nbas, cell.nbas * 2, cell.nbas * 2,
cell.nbas * 3)
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)
atm, bas, env = gto.conc_env(atm, bas, env, cell._atm, cell._bas,
cell._env)
ao_loc = gto.moleintor.make_loc(bas, 'int3c2e_sph')
cintopt = lib.c_null_ptr()
pbcopt = _pbcintor.PBCOpt(pcell).init_rcut_cond(pcell, 1e-9)
libpbc.PBCnr3c_drv(getattr(libpbc, intor), getattr(libpbc, fill),
out.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(nkpts_ij), ctypes.c_int(nkpts),
ctypes.c_int(comp), ctypes.c_int(len(Ls)),
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,
lib.c_null_ptr(), 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),
ctypes.c_int(env.size))
return out
def run3c(fill, kpts, shls_slice=None):
intor = 'int3c2e_sph'
nao = cell.nao_nr()
nkpts = len(kpts)
if fill == 'PBCnr3c_fill_gs2':
out = numpy.empty((nao*(nao+1)//2,nao))
kptij_idx = numpy.arange(nkpts).astype(numpy.int32)
elif fill == 'PBCnr3c_fill_gs1':
out = numpy.empty((nao,nao,nao))
kptij_idx = numpy.arange(nkpts).astype(numpy.int32)
elif fill in ('PBCnr3c_fill_kks1', 'PBCnr3c_fill_kks2'):
kptij_idx = numpy.asarray([i*nkpts+j for i in range(nkpts) for j in range(i+1)], dtype=numpy.int32)
out = numpy.empty((len(kptij_idx),nao,nao,nao), dtype=numpy.complex128)
elif fill == 'PBCnr3c_fill_ks1':
kptij_idx = numpy.arange(nkpts).astype(numpy.int32)
out = numpy.empty((nkpts,nao,nao,nao), dtype=numpy.complex128)
elif fill == 'PBCnr3c_fill_ks2':
out = numpy.empty((nkpts,nao*(nao+1)//2,nao), dtype=numpy.complex128)
kptij_idx = numpy.arange(nkpts).astype(numpy.int32)
else:
raise RuntimeError
nkpts_ij = len(kptij_idx)
nimgs = len(Ls)
expkL = numpy.exp(1j*numpy.dot(kpts, Ls.T))
comp = 1
if shls_slice is None:
shls_slice = (0, cell.nbas, cell.nbas, cell.nbas*2,
cell.nbas*2, cell.nbas*3)
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)
atm, bas, env = gto.conc_env(atm, bas, env,
cell._atm, cell._bas, cell._env)
ao_loc = gto.moleintor.make_loc(bas, 'int3c2e_sph')
cintopt = lib.c_null_ptr()
pbcopt = _pbcintor.PBCOpt(pcell).init_rcut_cond(pcell, 1e-9)
libpbc.PBCnr3c_drv(getattr(libpbc, intor), getattr(libpbc, fill),
out.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(nkpts_ij), ctypes.c_int(nkpts),
ctypes.c_int(comp), ctypes.c_int(len(Ls)),
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, pbcopt._this,
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))
return out
def run2c(intor, fill, kpts, shls_slice=None):
nkpts = len(kpts)
atm, bas, env = gto.conc_env(cell._atm, cell._bas, cell._env, cell._atm,
cell._bas, cell._env)
if shls_slice is None:
shls_slice = (0, cell.nbas, cell.nbas, cell.nbas * 2)
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]]
comp = 1
out = numpy.empty((nkpts, comp, ni, nj), dtype=numpy.complex128)
fintor = getattr(gto.moleintor.libcgto, intor)
fill = getattr(libpbc, fill)
intopt = lib.c_null_ptr()
Ls = cell.get_lattice_Ls()
expkL = numpy.asarray(numpy.exp(1j * numpy.dot(kpts, Ls.T)), order='C')
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(len(Ls)),
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,
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))
return out
def run2c(intor, fill, kpts, shls_slice=None):
nkpts = len(kpts)
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)
if shls_slice is None:
shls_slice = (0, cell.nbas, cell.nbas, cell.nbas*2)
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]]
comp = 1
out = numpy.empty((nkpts,comp,ni,nj), dtype=numpy.complex128)
fintor = getattr(gto.moleintor.libcgto, intor)
fill = getattr(libpbc, fill)
intopt = lib.c_null_ptr()
pbcopt = _pbcintor.PBCOpt(pcell).init_rcut_cond(pcell, 1e-9)
expkL = numpy.asarray(numpy.exp(1j*numpy.dot(kpts, Ls.T)), order='C')
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(len(Ls)),
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, pbcopt._this,
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))
return out
def _int_nuc_vloc(mydf, nuccell, kpts, dm_kpts):
'''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)
v3c = df.incore.aux_e2(cell, fakenuc, 'int3c2e_ipip1', aosym='s1', comp=9,
kptij_lst=kptij_lst)
v3c += df.incore.aux_e2(cell, fakenuc, 'int3c2e_ipvip1', aosym='s1', comp=9,
kptij_lst=kptij_lst)
nao = cell.nao_nr()
natm = cell.natm
v3c = v3c.reshape(nkpts,3,3,nao,nao,natm*2)
efg_loc = 1./nkpts * numpy.einsum('kxypqz,kqp->zxy', v3c, dm_kpts)
efg_loc+= 1./nkpts * numpy.einsum('kyxqpz,kqp->zxy', v3c, dm_kpts)
v3c = None
# Fermi contact
fc = df.incore.aux_e2(cell, fakenuc, 'int3c1e', aosym='s1', kptij_lst=kptij_lst)
fc = fc.reshape(nkpts,nao,nao,natm*2)
vfc = 1./nkpts * numpy.einsum('kpqz,kqp->z', fc, dm_kpts)
for i in range(3):
efg_loc[:,i,i] += 4./3*numpy.pi * vfc
nuc_part = efg_loc[:natm]
modchg_part = efg_loc[natm:]
efg_loc = nuc_part - modchg_part
if cell.dimension == 3:
fac = numpy.pi/cell.vol
nucbar = numpy.array([fac/nuccell.bas_exp(i)[0] for i in range(natm)])
ipip = cell.pbc_intor('int1e_ipipovlp', 9, lib.HERMITIAN, kpts)
ipvip = cell.pbc_intor('int1e_ipovlpip', 9, lib.HERMITIAN, kpts)
d2rho_bar = 0
for k in range(nkpts):
v = (ipip[k] + ipvip[k]).reshape(3,3,nao,nao)
d2rho_bar += numpy.einsum('xypq,qp->xy', v, dm_kpts[k])
d2rho_bar += numpy.einsum('yxqp,qp->xy', v, dm_kpts[k])
d2rho_bar *= 1./nkpts
efg_loc -= numpy.einsum('z,xy->zxy', nucbar, d2rho_bar)
return efg_loc.real
def _int_nuc_vloc(mydf, nuccell, kpts, dm_kpts):
'''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)
v3c = df.incore.aux_e2(cell, fakenuc, 'int3c2e_ipip1', aosym='s1', comp=9,
kptij_lst=kptij_lst)
v3c += df.incore.aux_e2(cell, fakenuc, 'int3c2e_ipvip1', aosym='s1', comp=9,
kptij_lst=kptij_lst)
nao = cell.nao_nr()
natm = cell.natm
v3c = v3c.reshape(nkpts,3,3,nao,nao,natm*2)
efg_loc = 1./nkpts * numpy.einsum('kxypqz,kqp->zxy', v3c, dm_kpts)
efg_loc+= 1./nkpts * numpy.einsum('kyxqpz,kqp->zxy', v3c, dm_kpts)
v3c = None
# Fermi contact
fc = df.incore.aux_e2(cell, fakenuc, 'int3c1e', aosym='s1', kptij_lst=kptij_lst)
fc = fc.reshape(nkpts,nao,nao,natm*2)
vfc = 1./nkpts * numpy.einsum('kpqz,kqp->z', fc, dm_kpts)
for i in range(3):
efg_loc[:,i,i] += 4./3*numpy.pi * vfc
nuc_part = efg_loc[:natm]
modchg_part = efg_loc[natm:]
efg_loc = nuc_part - modchg_part
if cell.dimension == 3:
fac = numpy.pi/cell.vol
nucbar = numpy.array([fac/nuccell.bas_exp(i)[0] for i in range(natm)])
ipip = cell.pbc_intor('int1e_ipipovlp', 9, lib.HERMITIAN, kpts)
ipvip = cell.pbc_intor('int1e_ipovlpip', 9, lib.HERMITIAN, kpts)
d2rho_bar = 0
for k in range(nkpts):
v = (ipip[k] + ipvip[k]).reshape(3,3,nao,nao)
d2rho_bar += numpy.einsum('xypq,qp->xy', v, dm_kpts[k])
d2rho_bar += numpy.einsum('yxqp,qp->xy', v, dm_kpts[k])
d2rho_bar *= 1./nkpts
efg_loc -= numpy.einsum('z,xy->zxy', nucbar, d2rho_bar)
return efg_loc.real