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, 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
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