def __init__(self, mf):
from pyscf.pbc import scf
assert(isinstance(mf, scf.khf.KSCF))
self.cell = mf.cell
uhf.TDA.__init__(self, mf)
from pyscf.pbc.df.df_ao2mo import warn_pbc2d_eri
warn_pbc2d_eri(mf)
def __init__(self, mf):
from pyscf.pbc import scf
assert (isinstance(mf, scf.khf.KSCF))
self.cell = mf.cell
uhf.TDA.__init__(self, mf)
from pyscf.pbc.df.df_ao2mo import warn_pbc2d_eri
warn_pbc2d_eri(mf)
def ccsd(self, t1=None, t2=None, eris=None, mbpt2=False):
from pyscf.pbc.df.df_ao2mo import warn_pbc2d_eri
warn_pbc2d_eri(self._scf)
if mbpt2:
pt = mp.RMP2(self._scf, self.frozen, self.mo_coeff, self.mo_occ)
self.e_corr, self.t2 = pt.kernel(eris=eris)
nocc, nvir = self.t2.shape[1:3]
self.t1 = numpy.zeros((nocc, nvir))
return self.e_corr, self.t1, self.t2
return rccsd.RCCSD.ccsd(self, t1, t2, eris)
def ccsd(self, t1=None, t2=None, eris=None, mbpt2=False):
from pyscf.pbc.df.df_ao2mo import warn_pbc2d_eri
warn_pbc2d_eri(self._scf)
if mbpt2:
pt = mp.RMP2(self._scf, self.frozen, self.mo_coeff, self.mo_occ)
self.e_corr, self.t2 = pt.kernel(eris=eris)
nocc, nvir = self.t2.shape[1:3]
self.t1 = numpy.zeros((nocc,nvir))
return self.e_corr, self.t1, self.t2
return rccsd.RCCSD.ccsd(self, t1, t2, eris)
def ccsd(self, t1=None, t2=None, eris=None, mbpt2=False):
from pyscf.pbc.df.df_ao2mo import warn_pbc2d_eri
warn_pbc2d_eri(self._scf)
if mbpt2:
pt = mp.UMP2(self._scf, self.frozen, self.mo_coeff, self.mo_occ)
self.e_corr, self.t2 = pt.kernel(eris=eris)
nocca, noccb = self.nocc
nmoa, nmob = self.nmo
nvira, nvirb = nmoa-nocca, nmob-noccb
self.t1 = (numpy.zeros((nocca,nvira)), numpy.zeros((noccb,nvirb)))
return self.e_corr, self.t1, self.t2
return uccsd.UCCSD.ccsd(self, t1, t2, eris)
def ccsd(self, t1=None, t2=None, eris=None, mbpt2=False):
from pyscf.pbc.df.df_ao2mo import warn_pbc2d_eri
warn_pbc2d_eri(self._scf)
if mbpt2:
pt = mp.UMP2(self._scf, self.frozen, self.mo_coeff, self.mo_occ)
self.e_corr, self.t2 = pt.kernel(eris=eris)
nocca, nvira = self.nocc
nmoa, nmoa = self.nmo
nvira, nvirb = nmoa-nocca, nmob-noccb
self.t1 = (numpy.zeros((nocca,nvira)), numpy.zeros((noccb,nvirb)))
return self.e_corr, self.t1, self.t2
return uccsd.UCCSD.ccsd(self, t1, t2, eris)
def general(mydf, mo_coeffs, kpts=None,
compact=getattr(__config__, 'pbc_df_ao2mo_general_compact', True)):
'''General MO integral transformation'''
from pyscf.pbc.df.df_ao2mo import warn_pbc2d_eri
warn_pbc2d_eri(mydf)
cell = mydf.cell
kptijkl = _format_kpts(kpts)
kpti, kptj, kptk, kptl = kptijkl
if isinstance(mo_coeffs, numpy.ndarray) and mo_coeffs.ndim == 2:
mo_coeffs = (mo_coeffs,) * 4
mo_coeffs = [numpy.asarray(mo, order='F') for mo in mo_coeffs]
if not _iskconserv(cell, kptijkl):
lib.logger.warn(cell, 'fft_ao2mo: momentum conservation not found in '
'the given k-points %s', kptijkl)
return numpy.zeros([mo.shape[1] for mo in mo_coeffs])
allreal = not any(numpy.iscomplexobj(mo) for mo in mo_coeffs)
q = kptj - kpti
coulG = tools.get_coulG(cell, q, mesh=mydf.mesh)
coords = cell.gen_uniform_grids(mydf.mesh)
max_memory = mydf.max_memory - lib.current_memory()[0]
if gamma_point(kptijkl) and allreal:
ao = mydf._numint.eval_ao(cell, coords, kpti)[0]
if ((iden_coeffs(mo_coeffs[0], mo_coeffs[1]) and
iden_coeffs(mo_coeffs[0], mo_coeffs[2]) and
iden_coeffs(mo_coeffs[0], mo_coeffs[3]))):
moiT = mojT = numpy.asarray(lib.dot(mo_coeffs[0].T,ao.T), order='C')
ao = None
max_memory = max_memory - moiT.nbytes*1e-6
eri = _contract_compact(mydf, (moiT,mojT), coulG, max_memory=max_memory)
if not compact:
nmo = moiT.shape[0]
eri = ao2mo.restore(1, eri, nmo).reshape(nmo**2,nmo**2)
else:
mos = [numpy.asarray(lib.dot(c.T, ao.T), order='C') for c in mo_coeffs]
ao = None
fac = numpy.array(1.)
max_memory = max_memory - sum([x.nbytes for x in mos])*1e-6
eri = _contract_plain(mydf, mos, coulG, fac, max_memory=max_memory).real
return eri
else:
aos = mydf._numint.eval_ao(cell, coords, kptijkl)
mos = [numpy.asarray(lib.dot(c.T, aos[i].T), order='C')
for i,c in enumerate(mo_coeffs)]
aos = None
fac = numpy.exp(-1j * numpy.dot(coords, q))
max_memory = max_memory - sum([x.nbytes for x in mos])*1e-6
eri = _contract_plain(mydf, mos, coulG, fac, max_memory=max_memory)
return eri
def __init__(self, mf, frozen=0, mo_coeff=None, mo_occ=None):
from pyscf.pbc.df.df_ao2mo import warn_pbc2d_eri
warn_pbc2d_eri(mf)
gcisd.GCISD.__init__(self, mf, frozen, mo_coeff, mo_occ)
def __init__(self, mf, frozen=0, mo_coeff=None, mo_occ=None):
if abs(mf.kpt).max() > 1e-9:
raise NotImplementedError
from pyscf.pbc.df.df_ao2mo import warn_pbc2d_eri
warn_pbc2d_eri(mf)
ucisd.UCISD.__init__(self, mf, frozen, mo_coeff, mo_occ)
def __init__(self, mf, frozen=0, mo_coeff=None, mo_occ=None):
from pyscf.pbc.df.df_ao2mo import warn_pbc2d_eri
warn_pbc2d_eri(mf)
gmp2.GMP2.__init__(self, mf, frozen, mo_coeff, mo_occ)
def __init__(self, mf, frozen=0, mo_coeff=None, mo_occ=None):
if abs(mf.kpt).max() > 1e-9:
raise NotImplementedError
from pyscf.pbc.df.df_ao2mo import warn_pbc2d_eri
warn_pbc2d_eri(mf)
ump2.UMP2.__init__(self, mf, frozen, mo_coeff, mo_occ)
def general(mydf, mo_coeffs, kpts=None,
compact=getattr(__config__, 'pbc_df_ao2mo_general_compact', True)):
warn_pbc2d_eri(mydf)
cell = mydf.cell
kptijkl = _format_kpts(kpts)
kpti, kptj, kptk, kptl = kptijkl
if isinstance(mo_coeffs, numpy.ndarray) and mo_coeffs.ndim == 2:
mo_coeffs = (mo_coeffs,) * 4
if not _iskconserv(cell, kptijkl):
lib.logger.warn(cell, 'aft_ao2mo: momentum conservation not found in '
'the given k-points %s', kptijkl)
return numpy.zeros([mo.shape[1] for mo in mo_coeffs])
q = kptj - kpti
mesh = mydf.mesh
coulG = mydf.weighted_coulG(q, False, mesh)
all_real = not any(numpy.iscomplexobj(mo) for mo in mo_coeffs)
max_memory = max(2000, (mydf.max_memory - lib.current_memory()[0]) * .5)
####################
# gamma point, the integral is real and with s4 symmetry
if gamma_point(kptijkl) and all_real:
ijmosym, nij_pair, moij, ijslice = _conc_mos(mo_coeffs[0], mo_coeffs[1], compact)
klmosym, nkl_pair, mokl, klslice = _conc_mos(mo_coeffs[2], mo_coeffs[3], compact)
eri_mo = numpy.zeros((nij_pair,nkl_pair))
sym = (iden_coeffs(mo_coeffs[0], mo_coeffs[2]) and
iden_coeffs(mo_coeffs[1], mo_coeffs[3]))
ijR = ijI = klR = klI = buf = None
for pqkR, pqkI, p0, p1 \
in mydf.pw_loop(mesh, kptijkl[:2], q, max_memory=max_memory,
aosym='s2'):
buf = lib.transpose(pqkR, out=buf)
ijR, klR = _dtrans(buf, ijR, ijmosym, moij, ijslice,
buf, klR, klmosym, mokl, klslice, sym)
lib.ddot(ijR.T, klR*coulG[p0:p1,None], 1, eri_mo, 1)
buf = lib.transpose(pqkI, out=buf)
ijI, klI = _dtrans(buf, ijI, ijmosym, moij, ijslice,
buf, klI, klmosym, mokl, klslice, sym)
lib.ddot(ijI.T, klI*coulG[p0:p1,None], 1, eri_mo, 1)
pqkR = pqkI = None
return eri_mo
####################
# (kpt) i == j == k == l != 0
# (kpt) i == l && j == k && i != j && j != k =>
#
elif is_zero(kpti-kptl) and is_zero(kptj-kptk):
mo_coeffs = _mo_as_complex(mo_coeffs)
nij_pair, moij, ijslice = _conc_mos(mo_coeffs[0], mo_coeffs[1])[1:]
nlk_pair, molk, lkslice = _conc_mos(mo_coeffs[3], mo_coeffs[2])[1:]
eri_mo = numpy.zeros((nij_pair,nlk_pair), dtype=numpy.complex)
sym = (iden_coeffs(mo_coeffs[0], mo_coeffs[3]) and
iden_coeffs(mo_coeffs[1], mo_coeffs[2]))
zij = zlk = buf = None
for pqkR, pqkI, p0, p1 \
in mydf.pw_loop(mesh, kptijkl[:2], q, max_memory=max_memory):
buf = lib.transpose(pqkR+pqkI*1j, out=buf)
zij, zlk = _ztrans(buf, zij, moij, ijslice,
buf, zlk, molk, lkslice, sym)
lib.dot(zij.T, zlk.conj()*coulG[p0:p1,None], 1, eri_mo, 1)
pqkR = pqkI = None
nmok = mo_coeffs[2].shape[1]
nmol = mo_coeffs[3].shape[1]
eri_mo = lib.transpose(eri_mo.reshape(-1,nmol,nmok), axes=(0,2,1))
return eri_mo.reshape(nij_pair,nlk_pair)
####################
# aosym = s1, complex integrals
#
# If kpti == kptj, (kptl-kptk)*a has to be multiples of 2pi because of the wave
# vector symmetry. k is a fraction of reciprocal basis, 0 < k/b < 1, by definition.
# So kptl/b - kptk/b must be -1 < k/b < 1. => kptl == kptk
#
else:
mo_coeffs = _mo_as_complex(mo_coeffs)
nij_pair, moij, ijslice = _conc_mos(mo_coeffs[0], mo_coeffs[1])[1:]
nkl_pair, mokl, klslice = _conc_mos(mo_coeffs[2], mo_coeffs[3])[1:]
eri_mo = numpy.zeros((nij_pair,nkl_pair), dtype=numpy.complex)
tao = []
ao_loc = None
zij = zkl = buf = None
for (pqkR, pqkI, p0, p1), (rskR, rskI, q0, q1) in \
lib.izip(mydf.pw_loop(mesh, kptijkl[:2], q, max_memory=max_memory*.5),
mydf.pw_loop(mesh,-kptijkl[2:], q, max_memory=max_memory*.5)):
buf = lib.transpose(pqkR+pqkI*1j, out=buf)
zij = _ao2mo.r_e2(buf, moij, ijslice, tao, ao_loc, out=zij)
buf = lib.transpose(rskR-rskI*1j, out=buf)
zkl = _ao2mo.r_e2(buf, mokl, klslice, tao, ao_loc, out=zkl)
zij *= coulG[p0:p1,None]
lib.dot(zij.T, zkl, 1, eri_mo, 1)
pqkR = pqkI = rskR = rskI = None
return eri_mo
def __init__(self, mf, frozen=None, mo_coeff=None, mo_occ=None):
from pyscf.pbc.df.df_ao2mo import warn_pbc2d_eri
warn_pbc2d_eri(mf)
gcisd.GCISD.__init__(self, mf, frozen, mo_coeff, mo_occ)
def general(mydf, mo_coeffs, kpts=None,
compact=getattr(__config__, 'pbc_df_ao2mo_general_compact', True)):
warn_pbc2d_eri(mydf)
cell = mydf.cell
kptijkl = _format_kpts(kpts)
kpti, kptj, kptk, kptl = kptijkl
if isinstance(mo_coeffs, numpy.ndarray) and mo_coeffs.ndim == 2:
mo_coeffs = (mo_coeffs,) * 4
if not _iskconserv(cell, kptijkl):
lib.logger.warn(cell, 'aft_ao2mo: momentum conservation not found in '
'the given k-points %s', kptijkl)
return numpy.zeros([mo.shape[1] for mo in mo_coeffs])
q = kptj - kpti
mesh = mydf.mesh
coulG = mydf.weighted_coulG(q, False, mesh)
all_real = not any(numpy.iscomplexobj(mo) for mo in mo_coeffs)
max_memory = max(2000, (mydf.max_memory - lib.current_memory()[0]) * .5)
####################
# gamma point, the integral is real and with s4 symmetry
if gamma_point(kptijkl) and all_real:
ijmosym, nij_pair, moij, ijslice = _conc_mos(mo_coeffs[0], mo_coeffs[1], compact)
klmosym, nkl_pair, mokl, klslice = _conc_mos(mo_coeffs[2], mo_coeffs[3], compact)
eri_mo = numpy.zeros((nij_pair,nkl_pair))
sym = (iden_coeffs(mo_coeffs[0], mo_coeffs[2]) and
iden_coeffs(mo_coeffs[1], mo_coeffs[3]))
ijR = ijI = klR = klI = buf = None
for pqkR, pqkI, p0, p1 \
in mydf.pw_loop(mesh, kptijkl[:2], q, max_memory=max_memory,
aosym='s2'):
buf = lib.transpose(pqkR, out=buf)
ijR, klR = _dtrans(buf, ijR, ijmosym, moij, ijslice,
buf, klR, klmosym, mokl, klslice, sym)
lib.ddot(ijR.T, klR*coulG[p0:p1,None], 1, eri_mo, 1)
buf = lib.transpose(pqkI, out=buf)
ijI, klI = _dtrans(buf, ijI, ijmosym, moij, ijslice,
buf, klI, klmosym, mokl, klslice, sym)
lib.ddot(ijI.T, klI*coulG[p0:p1,None], 1, eri_mo, 1)
pqkR = pqkI = None
return eri_mo
####################
# (kpt) i == j == k == l != 0
# (kpt) i == l && j == k && i != j && j != k =>
#
elif is_zero(kpti-kptl) and is_zero(kptj-kptk):
mo_coeffs = _mo_as_complex(mo_coeffs)
nij_pair, moij, ijslice = _conc_mos(mo_coeffs[0], mo_coeffs[1])[1:]
nlk_pair, molk, lkslice = _conc_mos(mo_coeffs[3], mo_coeffs[2])[1:]
eri_mo = numpy.zeros((nij_pair,nlk_pair), dtype=numpy.complex)
sym = (iden_coeffs(mo_coeffs[0], mo_coeffs[3]) and
iden_coeffs(mo_coeffs[1], mo_coeffs[2]))
zij = zlk = buf = None
for pqkR, pqkI, p0, p1 \
in mydf.pw_loop(mesh, kptijkl[:2], q, max_memory=max_memory):
buf = lib.transpose(pqkR+pqkI*1j, out=buf)
zij, zlk = _ztrans(buf, zij, moij, ijslice,
buf, zlk, molk, lkslice, sym)
lib.dot(zij.T, zlk.conj()*coulG[p0:p1,None], 1, eri_mo, 1)
pqkR = pqkI = None
nmok = mo_coeffs[2].shape[1]
nmol = mo_coeffs[3].shape[1]
eri_mo = lib.transpose(eri_mo.reshape(-1,nmol,nmok), axes=(0,2,1))
return eri_mo.reshape(nij_pair,nlk_pair)
####################
# aosym = s1, complex integrals
#
# If kpti == kptj, (kptl-kptk)*a has to be multiples of 2pi because of the wave
# vector symmetry. k is a fraction of reciprocal basis, 0 < k/b < 1, by definition.
# So kptl/b - kptk/b must be -1 < k/b < 1. => kptl == kptk
#
else:
mo_coeffs = _mo_as_complex(mo_coeffs)
nij_pair, moij, ijslice = _conc_mos(mo_coeffs[0], mo_coeffs[1])[1:]
nkl_pair, mokl, klslice = _conc_mos(mo_coeffs[2], mo_coeffs[3])[1:]
eri_mo = numpy.zeros((nij_pair,nkl_pair), dtype=numpy.complex)
tao = []
ao_loc = None
zij = zkl = buf = None
for (pqkR, pqkI, p0, p1), (rskR, rskI, q0, q1) in \
lib.izip(mydf.pw_loop(mesh, kptijkl[:2], q, max_memory=max_memory*.5),
mydf.pw_loop(mesh,-kptijkl[2:], q, max_memory=max_memory*.5)):
buf = lib.transpose(pqkR+pqkI*1j, out=buf)
zij = _ao2mo.r_e2(buf, moij, ijslice, tao, ao_loc, out=zij)
buf = lib.transpose(rskR-rskI*1j, out=buf)
zkl = _ao2mo.r_e2(buf, mokl, klslice, tao, ao_loc, out=zkl)
zij *= coulG[p0:p1,None]
lib.dot(zij.T, zkl, 1, eri_mo, 1)
pqkR = pqkI = rskR = rskI = None
return eri_mo
def get_eri(mydf, kpts=None,
compact=getattr(__config__, 'pbc_df_ao2mo_get_eri_compact', True)):
warn_pbc2d_eri(mydf)
cell = mydf.cell
nao = cell.nao_nr()
kptijkl = _format_kpts(kpts)
if not _iskconserv(cell, kptijkl):
lib.logger.warn(cell, 'aft_ao2mo: momentum conservation not found in '
'the given k-points %s', kptijkl)
return numpy.zeros((nao,nao,nao,nao))
kpti, kptj, kptk, kptl = kptijkl
q = kptj - kpti
mesh = mydf.mesh
coulG = mydf.weighted_coulG(q, False, mesh)
nao_pair = nao * (nao+1) // 2
max_memory = max(2000, (mydf.max_memory - lib.current_memory()[0]) * .8)
####################
# gamma point, the integral is real and with s4 symmetry
if gamma_point(kptijkl):
eriR = numpy.zeros((nao_pair,nao_pair))
for pqkR, pqkI, p0, p1 \
in mydf.pw_loop(mesh, kptijkl[:2], q, max_memory=max_memory,
aosym='s2'):
vG = numpy.sqrt(coulG[p0:p1])
pqkR *= vG
pqkI *= vG
lib.ddot(pqkR, pqkR.T, 1, eriR, 1)
lib.ddot(pqkI, pqkI.T, 1, eriR, 1)
pqkR = pqkI = None
if not compact:
eriR = ao2mo.restore(1, eriR, nao).reshape(nao**2,-1)
return eriR
####################
# (kpt) i == j == k == l != 0
# (kpt) i == l && j == k && i != j && j != k =>
#
# complex integrals, N^4 elements
elif is_zero(kpti-kptl) and is_zero(kptj-kptk):
eriR = numpy.zeros((nao**2,nao**2))
eriI = numpy.zeros((nao**2,nao**2))
for pqkR, pqkI, p0, p1 \
in mydf.pw_loop(mesh, kptijkl[:2], q, max_memory=max_memory):
vG = numpy.sqrt(coulG[p0:p1])
pqkR *= vG
pqkI *= vG
# rho_pq(G+k_pq) * conj(rho_rs(G-k_rs))
zdotNC(pqkR, pqkI, pqkR.T, pqkI.T, 1, eriR, eriI, 1)
pqkR = pqkI = None
pqkR = pqkI = coulG = None
# transpose(0,1,3,2) because
# j == k && i == l =>
# (L|ij).transpose(0,2,1).conj() = (L^*|ji) = (L^*|kl) => (M|kl)
# rho_rs(-G+k_rs) = conj(transpose(rho_sr(G+k_sr), (0,2,1)))
eri = lib.transpose((eriR+eriI*1j).reshape(-1,nao,nao), axes=(0,2,1))
return eri.reshape(nao**2,-1)
####################
# aosym = s1, complex integrals
#
# If kpti == kptj, (kptl-kptk)*a has to be multiples of 2pi because of the wave
# vector symmetry. k is a fraction of reciprocal basis, 0 < k/b < 1, by definition.
# So kptl/b - kptk/b must be -1 < k/b < 1. => kptl == kptk
#
else:
eriR = numpy.zeros((nao**2,nao**2))
eriI = numpy.zeros((nao**2,nao**2))
#
# (pq|rs) = \sum_G 4\pi rho_pq rho_rs / |G+k_{pq}|^2
# rho_pq = 1/N \sum_{Tp,Tq} \int exp(-i(G+k_{pq})*r) p(r-Tp) q(r-Tq) dr
# = \sum_{Tq} exp(i k_q*Tq) \int exp(-i(G+k_{pq})*r) p(r) q(r-Tq) dr
# Note the k-point wrap-around for rho_rs, which leads to G+k_{pq} in FT
# rho_rs = 1/N \sum_{Tr,Ts} \int exp( i(G+k_{pq})*r) r(r-Tr) s(r-Ts) dr
# = \sum_{Ts} exp(i k_s*Ts) \int exp( i(G+k_{pq})*r) r(r) s(r-Ts) dr
# rho_pq can be directly evaluated by AFT (function pw_loop)
# rho_pq = pw_loop(k_q, G+k_{pq})
# Assuming r(r) and s(r) are real functions, rho_rs is evaluated
# rho_rs = 1/N \sum_{Tr,Ts} \int exp( i(G+k_{pq})*r) r(r-Tr) s(r-Ts) dr
# = conj(\sum_{Ts} exp(-i k_s*Ts) \int exp(-i(G+k_{pq})*r) r(r) s(r-Ts) dr)
# = conj( pw_loop(-k_s, G+k_{pq}) )
#
# TODO: For complex AO function r(r) and s(r), pw_loop function needs to be
# extended to include Gv vector in the arguments
for (pqkR, pqkI, p0, p1), (rskR, rskI, q0, q1) in \
lib.izip(mydf.pw_loop(mesh, kptijkl[:2], q, max_memory=max_memory*.5),
mydf.pw_loop(mesh,-kptijkl[2:], q, max_memory=max_memory*.5)):
pqkR *= coulG[p0:p1]
pqkI *= coulG[p0:p1]
zdotNC(pqkR, pqkI, rskR.T, rskI.T, 1, eriR, eriI, 1)
pqkR = pqkI = rskR = rskI = None
return (eriR+eriI*1j)
