def response_dm1(mycc, t1, t2, l1, l2, eris=None, IX=None):
if eris is None:
# Note eris are in Chemist's notation
eris = ccsd._ERIS(mycc)
if IX is None:
Ioo, Ivv, Ivo, Xvo = IX_intermediates(mycc, t1, t2, l1, l2, eris)
else:
Ioo, Ivv, Ivo, Xvo = IX
nocc, nvir = t1.shape
nmo = nocc + nvir
def fvind(x):
x = x.reshape(Xvo.shape)
if eris is None:
mo_coeff = mycc.mo_coeff
dm = reduce(numpy.dot, (mo_coeff[:,nocc:], x, mo_coeff[:,:nocc].T))
dm = (dm + dm.T) * 2
v = reduce(numpy.dot, (mo_coeff[:,nocc:].T, mycc._scf.get_veff(mol, dm),
mo_coeff[:,:nocc]))
else:
eris_ovov = _cp(eris.ovov)
v = numpy.einsum('iajb,bj->ia', eris_ovov, x) * 4
v -= numpy.einsum('ibja,bj->ia', eris_ovov, x)
eris_ovov = None
v -= numpy.einsum('jiab,bj->ia', _cp(eris.oovv), x)
return v.T
mo_energy = eris.fock.diagonal()
mo_occ = numpy.zeros_like(mo_energy)
mo_occ[:nocc] = 2
dvo = cphf.solve(fvind, mo_energy, mo_occ, Xvo, max_cycle=30)[0]
dm1 = numpy.zeros((nmo,nmo))
dm1[nocc:,:nocc] = dvo
dm1[:nocc,nocc:] = dvo.T
return dm1
def gamma1_intermediates(mycc, t1, t2, l1, l2, eris=None):
doo, dov, dvo, dvv = ccsd_rdm.gamma1_intermediates(mycc, t1, t2, l1, l2)
if eris is None: eris = ccsd._ERIS(mycc)
nocc, nvir = t1.shape
eris_ovvv = _cp(eris.ovvv)
eris_ovvv = lib.unpack_tril(eris_ovvv.reshape(nocc * nvir, -1))
eris_ovvv = eris_ovvv.reshape(nocc, nvir, nvir, nvir)
mo_e = mycc._scf.mo_energy
eia = lib.direct_sum('i-a->ia', mo_e[:nocc], mo_e[nocc:])
d3 = lib.direct_sum('ia,jb,kc->ijkabc', eia, eia, eia)
eris_ovoo = eris.ovoo
w = (numpy.einsum('iabf,kjcf->ijkabc', eris_ovvv, t2) -
numpy.einsum('iajm,mkbc->ijkabc', eris_ovoo, t2)) / d3
v = numpy.einsum('iajb,kc->ijkabc', eris.ovov, t1) / d3 * .5
w = p6_(w)
v = p6_(v)
wv = w + v
rw = r6_(w)
goo = -numpy.einsum('iklabc,jklabc->ij', wv, rw) * .5
gvv = numpy.einsum('ijkacd,ijkbcd->ab', wv, rw) * .5
doo += goo
dvv += gvv
return doo, dov, dvo, dvv
def gamma2_intermediates(mycc, t1, t2, l1, l2, eris=None):
dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov = \
ccsd_rdm.gamma2_intermediates(mycc, t1, t2, l1, l2)
if eris is None: eris = ccsd._ERIS(mycc)
nocc, nvir = t1.shape
eris_ovvv = _cp(eris.ovvv)
eris_ovvv = _ccsd.unpack_tril(eris_ovvv.reshape(nocc*nvir,-1))
eris_ovvv = eris_ovvv.reshape(nocc,nvir,nvir,nvir)
mo_e = mycc._scf.mo_energy
eia = lib.direct_sum('i-a->ia',mo_e[:nocc], mo_e[nocc:])
d3 = lib.direct_sum('ia,jb,kc->ijkabc', eia, eia, eia)
eris_ovoo = eris.ovoo
w =(numpy.einsum('iabf,kjcf->ijkabc', eris_ovvv, t2)
- numpy.einsum('iajm,mkbc->ijkabc', eris_ovoo, t2)) / d3
v = numpy.einsum('iajb,kc->ijkabc', eris.ovov, t1) / d3 * .5
w = p6_(w)
v = p6_(v)
rw = r6_(w)
rwv = r6_(w*2+v)
dovov += numpy.einsum('kc,ijkabc->iajb', t1, rw) * .5
dooov -= numpy.einsum('mkbc,ijkabc->jmia', t2, rwv)
# Note "dovvv +=" also changes the value of dvvov
dovvv += numpy.einsum('kjcf,ijkabc->iabf', t2, rwv)
dvvov = dovvv.transpose(2,3,0,1)
return dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov
def gamma1_intermediates(mycc, t1, t2, l1, l2, eris=None):
doo, dov, dvo, dvv = ccsd_rdm.gamma1_intermediates(mycc, t1, t2, l1, l2)
if eris is None: eris = ccsd._ERIS(mycc)
nocc, nvir = t1.shape
eris_ovvv = _cp(eris.ovvv)
eris_ovvv = _ccsd.unpack_tril(eris_ovvv.reshape(nocc*nvir,-1))
eris_ovvv = eris_ovvv.reshape(nocc,nvir,nvir,nvir)
mo_e = mycc._scf.mo_energy
eia = lib.direct_sum('i-a->ia',mo_e[:nocc], mo_e[nocc:])
d3 = lib.direct_sum('ia,jb,kc->ijkabc', eia, eia, eia)
eris_ovoo = eris.ovoo
w =(numpy.einsum('iabf,kjcf->ijkabc', eris_ovvv, t2)
- numpy.einsum('iajm,mkbc->ijkabc', eris_ovoo, t2)) / d3
v = numpy.einsum('iajb,kc->ijkabc', eris.ovov, t1) / d3 * .5
w = p6_(w)
v = p6_(v)
wv = w+v
rw = r6_(w)
goo =-numpy.einsum('iklabc,jklabc->ij', wv, rw) * .5
gvv = numpy.einsum('ijkacd,ijkbcd->ab', wv, rw) * .5
doo += goo
dvv += gvv
return doo, dov, dvo, dvv
def response_dm1(mycc, t1, t2, l1, l2, eris=None, IX=None):
if eris is None:
# Note eris are in Chemist's notation
eris = ccsd._ERIS(mycc)
if IX is None:
Ioo, Ivv, Ivo, Xvo = IX_intermediates(mycc, t1, t2, l1, l2, eris)
else:
Ioo, Ivv, Ivo, Xvo = IX
nocc, nvir = t1.shape
nmo = nocc + nvir
def fvind(x):
x = x.reshape(Xvo.shape)
if eris is None:
mo_coeff = mycc.mo_coeff
dm = reduce(numpy.dot, (mo_coeff[:,nocc:], x, mo_coeff[:,:nocc].T))
dm = (dm + dm.T) * 2
v = reduce(numpy.dot, (mo_coeff[:,nocc:].T, mycc._scf.get_veff(mol, dm),
mo_coeff[:,:nocc]))
else:
eris_ovov = _cp(eris.ovov)
v = numpy.einsum('iajb,bj->ia', eris_ovov, x) * 4
v -= numpy.einsum('ibja,bj->ia', eris_ovov, x)
eris_ovov = None
v -= numpy.einsum('jiab,bj->ia', _cp(eris.oovv), x)
return v.T
mo_energy = eris.fock.diagonal()
mo_occ = numpy.zeros_like(mo_energy)
mo_occ[:nocc] = 2
dvo = cphf.solve(fvind, mo_energy, mo_occ, Xvo, max_cycle=30)[0]
dm1 = numpy.zeros((nmo,nmo))
dm1[nocc:,:nocc] = dvo
dm1[:nocc,nocc:] = dvo.T
return dm1
def gamma2_intermediates(mycc, t1, t2, l1, l2, eris=None):
dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov = \
ccsd_rdm.gamma2_intermediates(mycc, t1, t2, l1, l2)
if eris is None: eris = ccsd._ERIS(mycc)
nocc, nvir = t1.shape
eris_ovvv = _cp(eris.ovvv)
eris_ovvv = lib.unpack_tril(eris_ovvv.reshape(nocc * nvir, -1))
eris_ovvv = eris_ovvv.reshape(nocc, nvir, nvir, nvir)
mo_e = mycc._scf.mo_energy
eia = lib.direct_sum('i-a->ia', mo_e[:nocc], mo_e[nocc:])
d3 = lib.direct_sum('ia,jb,kc->ijkabc', eia, eia, eia)
eris_ovoo = eris.ovoo
w = (numpy.einsum('iabf,kjcf->ijkabc', eris_ovvv, t2) -
numpy.einsum('iajm,mkbc->ijkabc', eris_ovoo, t2)) / d3
v = numpy.einsum('iajb,kc->ijkabc', eris.ovov, t1) / d3 * .5
w = p6_(w)
v = p6_(v)
rw = r6_(w)
rwv = r6_(w * 2 + v)
dovov += numpy.einsum('kc,ijkabc->iajb', t1, rw) * .5
dooov -= numpy.einsum('mkbc,ijkabc->jmia', t2, rwv)
# Note "dovvv +=" also changes the value of dvvov
dovvv += numpy.einsum('kjcf,ijkabc->iabf', t2, rwv)
dvvov = dovvv.transpose(2, 3, 0, 1)
return dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov
def update_amps(mycc, t1, t2, l1, l2, eris=None, saved=None):
if eris is None: eris = ccsd._ERIS(mycc)
if saved is None: saved = make_intermediates(mycc, t1, t2, eris)
nocc, nvir = t1.shape
l1, l2 = ccsd_lambda.update_amps(mycc, t1, t2, l1, l2, eris, saved)
mo_e = eris.fock.diagonal()
eia = lib.direct_sum('i-a->ia', mo_e[:nocc], mo_e[nocc:])
l1 += saved.jov/eia * .5
eijab = lib.direct_sum('ia+jb->ijab', eia, eia)
l2 += (saved.joovv*(2./3)+saved.joovv.transpose(1,0,2,3)*(1./3)) / eijab
return l1, l2
def response_dm1(mycc, t1, t2, l1, l2, eris=None, IX=None, max_memory=2000):
if eris is None:
# Note eris are in Chemist's notation
eris = ccsd._ERIS(mycc)
if IX is None:
Ioo, Ivv, Ivo, Xvo = IX_intermediates(mycc,
t1,
t2,
l1,
l2,
eris,
max_memory=2000)
else:
Ioo, Ivv, Ivo, Xvo = IX
nocc, nvir = t1.shape
nmo = nocc + nvir
max_memory = max_memory - lib.current_memory()[0]
blksize = max(ccsd.BLKMIN, int(max_memory * 1e6 / 8 / (nocc * nvir**2)))
def fvind(x):
x = x.reshape(Xvo.shape)
if eris is None:
mo_coeff = mycc.mo_coeff
dm = reduce(numpy.dot,
(mo_coeff[:, nocc:], x, mo_coeff[:, :nocc].T))
dm = (dm + dm.T) * 2
v = reduce(numpy.dot,
(mo_coeff[:, nocc:].T, mycc._scf.get_veff(
mol, dm), mo_coeff[:, :nocc]))
else:
v = numpy.zeros((nocc, nvir))
for p0, p1 in prange(0, nocc, blksize):
eris_ovov = _cp(eris.ovov[p0:p1])
v[p0:p1] += numpy.einsum('iajb,bj->ia', eris_ovov, x) * 4
v[p0:p1] -= numpy.einsum('ibja,bj->ia', eris_ovov, x)
eris_ovov = None
v[p0:p1] -= numpy.einsum('ijba,bj->ia', _cp(eris.oovv[p0:p1]),
x[:, p0:p1])
return v.T
mo_energy = eris.fock.diagonal()
mo_occ = numpy.zeros_like(mo_energy)
mo_occ[:nocc] = 2
dvo = cphf.solve(fvind, mo_energy, mo_occ, Xvo, max_cycle=30)[0]
dm1 = numpy.zeros((nmo, nmo))
dm1[nocc:, :nocc] = dvo
dm1[:nocc, nocc:] = dvo.T
return dm1
def kernel(mycc,
eris=None,
t1=None,
t2=None,
l1=None,
l2=None,
max_cycle=50,
tol=1e-8,
max_memory=2000,
verbose=logger.INFO):
cput0 = (time.clock(), time.time())
if isinstance(verbose, logger.Logger):
log = verbose
else:
log = logger.Logger(mycc.stdout, verbose)
if eris is None: eris = ccsd._ERIS(mycc)
if t1 is None: t1 = mycc.t1
if t2 is None: t2 = mycc.t2
if l1 is None: l1 = t1
if l2 is None: l2 = t2
nocc, nvir = t1.shape
saved = make_intermediates(mycc, t1, t2, eris)
if mycc.diis:
adiis = lib.diis.DIIS(mycc, mycc.diis_file)
adiis.space = mycc.diis_space
else:
adiis = lambda l1, l2, *args: (l1, l2)
cput0 = log.timer('CCSD lambda initialization', *cput0)
conv = False
for istep in range(max_cycle):
l1new, l2new = update_amps(mycc, t1, t2, l1, l2, eris, saved)
normt = numpy.linalg.norm(l1new - l1) + numpy.linalg.norm(l2new - l2)
l1, l2 = l1new, l2new
l1new = l2new = None
if mycc.diis:
l1, l2 = mycc.diis(l1, l2, istep, normt, 0, adiis)
log.info('istep = %d norm(lambda1,lambda2) = %.6g', istep, normt)
cput0 = log.timer('CCSD iter', *cput0)
if normt < tol:
conv = True
break
return conv, l1, l2
def response_dm1(mycc, t1, t2, l1, l2, eris=None, IX=None):
if eris is None:
# Note eris are in Chemist's notation
eris = ccsd._ERIS(mycc)
if IX is None:
Ioo, Ivv, Ivo, Xvo = IX_intermediates(mycc, t1, t2, l1, l2, eris)
else:
Ioo, Ivv, Ivo, Xvo = IX
nocc, nvir = t1.shape
nmo = nocc + nvir
max_memory = mycc.max_memory - lib.current_memory()[0]
blksize = max(ccsd.BLKMIN, int(max_memory * 1e6 / 8 / (nocc * nvir**2)))
def fvind(x):
x = x.reshape(Xvo.shape)
if eris is None:
mo_coeff = mycc.mo_coeff
dm = reduce(numpy.dot,
(mo_coeff[:, nocc:], x, mo_coeff[:, :nocc].T))
dm = (dm + dm.T) * 2
v = reduce(numpy.dot,
(mo_coeff[:, nocc:].T, mycc._scf.get_veff(mol, dm),
mo_coeff[:, :nocc]))
else:
v = numpy.zeros((nocc, nvir))
for p0, p1 in prange(0, nocc, blksize):
eris_ovov = _cp(eris.ovov[p0:p1])
v[p0:p1] += numpy.einsum('iajb,bj->ia', eris_ovov, x) * 4
v[p0:p1] -= numpy.einsum('ibja,bj->ia', eris_ovov, x)
eris_ovov = None
v[p0:p1] -= numpy.einsum('ijba,bj->ia', _cp(eris.oovv[p0:p1]),
x[:, p0:p1])
return v.T
mo_energy = eris.fock.diagonal()
mo_occ = numpy.zeros_like(mo_energy)
mo_occ[:nocc] = 2
dvo = cphf.solve(fvind, mo_energy, mo_occ, Xvo, max_cycle=30)[0]
dm1 = numpy.zeros((nmo, nmo))
dm1[nocc:, :nocc] = dvo
dm1[:nocc, nocc:] = dvo.T
return dm1
def kernel(mycc, eris=None, t1=None, t2=None, l1=None, l2=None,
max_cycle=50, tol=1e-8,
max_memory=2000, verbose=logger.INFO):
cput0 = (time.clock(), time.time())
if isinstance(verbose, logger.Logger):
log = verbose
else:
log = logger.Logger(mycc.stdout, verbose)
if eris is None: eris = ccsd._ERIS(mycc)
if t1 is None: t1 = mycc.t1
if t2 is None: t2 = mycc.t2
if l1 is None: l1 = t1
if l2 is None: l2 = t2
nocc, nvir = t1.shape
saved = make_intermediates(mycc, t1, t2, eris)
if mycc.diis:
adiis = lib.diis.DIIS(mycc, mycc.diis_file)
adiis.space = mycc.diis_space
else:
adiis = lambda l1,l2,*args: (l1,l2)
cput0 = log.timer('CCSD lambda initialization', *cput0)
conv = False
for istep in range(max_cycle):
l1new, l2new = update_amps(mycc, t1, t2, l1, l2, eris, saved)
normt = numpy.linalg.norm(l1new-l1) + numpy.linalg.norm(l2new-l2)
l1, l2 = l1new, l2new
l1new = l2new = None
if mycc.diis:
l1, l2 = mycc.diis(l1, l2, istep, normt, 0, adiis)
log.info('istep = %d norm(lambda1,lambda2) = %.6g', istep, normt)
cput0 = log.timer('CCSD iter', *cput0)
if normt < tol:
conv = True
break
return conv, l1, l2
def kernel(mycc, t1=None, t2=None, l1=None, l2=None, eris=None, atmlst=None, mf_grad=None, verbose=logger.INFO):
if t1 is None:
t1 = mycc.t1
if t2 is None:
t2 = mycc.t2
if l1 is None:
l1 = mycc.l1
if l2 is None:
l2 = mycc.l2
if eris is None:
eris = ccsd._ERIS(mycc)
if mf_grad is None:
mf_grad = rhf_grad.Gradients(mycc._scf)
log = logger.Logger(mycc.stdout, mycc.verbose)
time0 = time.clock(), time.time()
mol = mycc.mol
moidx = numpy.ones(mycc.mo_energy.size, dtype=numpy.bool)
if isinstance(mycc.frozen, (int, numpy.integer)):
raise NotImplementedError("frozen orbital ccsd_grad")
moidx[: mycc.frozen] = False
else:
moidx[mycc.frozen] = False
mo_coeff = mycc.mo_coeff[:, moidx] # FIXME: ensure mycc.mo_coeff is canonical orbital
mo_energy = mycc.mo_energy[moidx]
nocc, nvir = t1.shape
nao, nmo = mo_coeff.shape
nao_pair = nao * (nao + 1) // 2
log.debug("Build ccsd rdm1 intermediates")
d1 = ccsd_rdm.gamma1_intermediates(mycc, t1, t2, l1, l2)
doo, dov, dvo, dvv = d1
time1 = log.timer("rdm1 intermediates", *time0)
log.debug("Build ccsd rdm2 intermediates")
d2 = ccsd_rdm.gamma2_incore(mycc, t1, t2, l1, l2)
time1 = log.timer("rdm2 intermediates", *time1)
log.debug("Build ccsd response_rdm1")
Ioo, Ivv, Ivo, Xvo = IX_intermediates(mycc, t1, t2, l1, l2, eris, d1, d2)
time1 = log.timer("response_rdm1 intermediates", *time1)
dm1mo = response_dm1(mycc, t1, t2, l1, l2, eris, (Ioo, Ivv, Ivo, Xvo))
dm1mo[:nocc, :nocc] = doo * 2
dm1mo[nocc:, nocc:] = dvv * 2
dm1ao = reduce(numpy.dot, (mo_coeff, dm1mo, mo_coeff.T))
im1 = numpy.zeros_like(dm1mo)
im1[:nocc, :nocc] = Ioo
im1[nocc:, nocc:] = Ivv
im1[nocc:, :nocc] = Ivo
im1[:nocc, nocc:] = Ivo.T
im1 = reduce(numpy.dot, (mo_coeff, im1, mo_coeff.T))
time1 = log.timer("response_rdm1", *time1)
log.debug("symmetrized rdm2 and MO->AO transformation")
dm1_with_hf = dm1mo.copy()
for i in range(nocc):
dm1_with_hf[i, i] += 1
dm2ao = _rdm2_mo2ao(mycc, d2, dm1_with_hf, mo_coeff)
time1 = log.timer("MO->AO transformation", *time1)
log.debug("h1 and JK1")
h1 = mf_grad.get_hcore(mol)
s1 = mf_grad.get_ovlp(mol)
zeta = lib.direct_sum("i+j->ij", mo_energy, mo_energy) * 0.5
zeta[nocc:, :nocc] = mo_energy[:nocc]
zeta[:nocc, nocc:] = mo_energy[:nocc].reshape(-1, 1)
zeta = reduce(numpy.dot, (mo_coeff, zeta * dm1mo, mo_coeff.T))
p1 = numpy.dot(mo_coeff[:, :nocc], mo_coeff[:, :nocc].T)
vhf4sij = reduce(numpy.dot, (p1, mycc._scf.get_veff(mol, dm1ao + dm1ao.T), p1))
time1 = log.timer("h1 and JK1", *time1)
# Hartree-Fock part contribution
hf_dm1 = mycc._scf.make_rdm1(mycc.mo_coeff, mycc.mo_occ)
dm1ao += hf_dm1
zeta += mf_grad.make_rdm1e(mycc.mo_energy, mycc.mo_coeff, mycc.mo_occ)
if atmlst is None:
atmlst = range(mol.natm)
offsetdic = mol.offset_nr_by_atom()
de = numpy.zeros((len(atmlst), 3))
for k, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = offsetdic[ia]
# s[1] dot I, note matrix im1 is not hermitian
de[k] = numpy.einsum("xij,ij->x", s1[:, p0:p1], im1[p0:p1]) + numpy.einsum(
"xji,ij->x", s1[:, p0:p1], im1[:, p0:p1]
)
# h[1] \dot DM, *2 for +c.c., contribute to f1
h1ao = mf_grad._grad_rinv(mol, ia)
h1ao[:, p0:p1] += h1[:, p0:p1]
de[k] += numpy.einsum("xij,ij->x", h1ao, dm1ao) + numpy.einsum("xji,ij->x", h1ao, dm1ao)
# -s[1]*e \dot DM, contribute to f1
de[k] -= numpy.einsum("xij,ij->x", s1[:, p0:p1], zeta[p0:p1]) + numpy.einsum(
"xji,ij->x", s1[:, p0:p1], zeta[:, p0:p1]
)
# -vhf[s_ij[1]], contribute to f1, *2 for s1+s1.T
de[k] -= numpy.einsum("xij,ij->x", s1[:, p0:p1], vhf4sij[p0:p1]) * 2
# 2e AO integrals dot 2pdm
eri1 = gto.moleintor.getints(
"cint2e_ip1_sph", mol._atm, mol._bas, mol._env, numpy.arange(shl0, shl1), comp=3, aosym="s2kl"
).reshape(3, p1 - p0, nao, -1)
dm2buf = _load_block_tril(dm2ao, p0, p1)
de[k] -= numpy.einsum("xijk,ijk->x", eri1, dm2buf) * 2
eri1 = dm2buf = None
log.debug("grad of atom %d %s = %s", ia, mol.atom_symbol(ia), de[k])
time1 = log.timer("grad of atom %d" % ia, *time1)
log.note("CCSD gradinets")
log.note("==============")
log.note(" x y z")
for k, ia in enumerate(atmlst):
log.note("%d %s %15.9f %15.9f %15.9f", ia, mol.atom_symbol(ia), de[k, 0], de[k, 1], de[k, 2])
log.timer("CCSD gradients", *time0)
return de
def IX_intermediates(mycc, t1, t2, l1, l2, eris=None, d1=None, d2=None):
if eris is None:
# Note eris are in Chemist's notation
eris = ccsd._ERIS(mycc)
if d1 is None:
d1 = ccsd_rdm.gamma1_intermediates(mycc, t1, t2, l1, l2)
doo, dov, dvo, dvv = d1
if d2 is None:
_d2tmpfile = tempfile.NamedTemporaryFile(dir=lib.param.TMPDIR)
fd2intermediate = h5py.File(_d2tmpfile.name, 'w')
ccsd_rdm.gamma2_outcore(mycc, t1, t2, l1, l2, fd2intermediate)
dovov = fd2intermediate['dovov']
dvvvv = fd2intermediate['dvvvv']
doooo = fd2intermediate['doooo']
doovv = fd2intermediate['doovv']
dovvo = fd2intermediate['dovvo']
dovvv = fd2intermediate['dovvv']
dooov = fd2intermediate['dooov']
else:
dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov = d2
log = logger.Logger(mycc.stdout, mycc.verbose)
nocc, nvir = t1.shape
nov = nocc * nvir
nvir_pair = nvir * (nvir + 1) // 2
_tmpfile = tempfile.NamedTemporaryFile(dir=lib.param.TMPDIR)
fswap = h5py.File(_tmpfile.name, 'w')
fswap.create_group('e_vvov')
fswap.create_group('c_vvov')
# Note Ioo, Ivv are not hermitian
Ioo = numpy.zeros((nocc, nocc))
Ivv = numpy.zeros((nvir, nvir))
Ivo = numpy.zeros((nvir, nocc))
Xvo = numpy.zeros((nvir, nocc))
eris_oooo = _cp(eris.oooo)
eris_ooov = _cp(eris.ooov)
d_oooo = _cp(doooo)
d_oooo = _cp(d_oooo + d_oooo.transpose(1, 0, 2, 3))
#:Ioo += numpy.einsum('jmlk,imlk->ij', d_oooo, eris_oooo) * 2
Ioo += lib.dot(eris_oooo.reshape(nocc, -1), d_oooo.reshape(nocc, -1).T, 2)
d_oooo = _cp(d_oooo.transpose(0, 2, 3, 1))
#:Xvo += numpy.einsum('iljk,ljka->ai', d_oooo, eris_ooov) * 2
Xvo += lib.dot(
eris_ooov.reshape(-1, nvir).T,
d_oooo.reshape(nocc, -1).T, 2)
Xvo += (numpy.einsum('kj,kjia->ai', doo, eris_ooov) * 4 - numpy.einsum(
'kj,ikja->ai', doo + doo.T, eris_ooov))
eris_oooo = eris_ooov = d_oooo = None
d_ovov = numpy.empty((nocc, nvir, nocc, nvir))
blksize = 8
for p0, p1 in prange(0, nocc, blksize):
d_ovov[p0:p1] = _cp(dovov[p0:p1])
d_ovvo = _cp(dovvo[p0:p1])
for i in range(p0, p1):
d_ovov[i] += d_ovvo[i - p0].transpose(0, 2, 1)
d_ovvo = None
d_ovov = lib.transpose_sum(d_ovov.reshape(nov, nov)).reshape(
nocc, nvir, nocc, nvir)
#:Ivo += numpy.einsum('jbka,jbki->ai', d_ovov, eris.ovoo)
Ivo += lib.dot(
d_ovov.reshape(-1, nvir).T,
_cp(eris.ovoo).reshape(-1, nocc))
eris_ovov = _cp(eris.ovov)
#:Ioo += numpy.einsum('jakb,iakb->ij', d_ovov, eris.ovov)
#:Ivv += numpy.einsum('jcib,jcia->ab', d_ovov, eris.ovov)
Ioo += lib.dot(eris_ovov.reshape(nocc, -1), d_ovov.reshape(nocc, -1).T)
Ivv += lib.dot(eris_ovov.reshape(-1, nvir).T, d_ovov.reshape(-1, nvir))
eris_ovov = None
fswap['dovvo'] = d_ovov.transpose(0, 1, 3, 2)
d_ovov = None
max_memory = mycc.max_memory - lib.current_memory()[0]
unit = max(nvir**3 * 2.5, nvir**3 * 2 + nocc * nvir**2)
blksize = max(ccsd.BLKMIN, int(max_memory * 1e6 / 8 / unit))
iobuflen = int(256e6 / 8 / (blksize * nvir))
log.debug1(
'IX_intermediates pass 1: block size = %d, nocc = %d in %d blocks',
blksize, nocc, int((nocc + blksize - 1) / blksize))
for istep, (p0, p1) in enumerate(prange(0, nocc, blksize)):
d_ooov = _cp(dooov[p0:p1])
eris_oooo = _cp(eris.oooo[p0:p1])
eris_ooov = _cp(eris.ooov[p0:p1])
#:Ivv += numpy.einsum('ijkb,ijka->ab', d_ooov, eris_ooov)
#:Ivo += numpy.einsum('jlka,jlki->ai', d_ooov, eris_oooo)
Ivv += lib.dot(eris_ooov.reshape(-1, nvir).T, d_ooov.reshape(-1, nvir))
Ivo += lib.dot(d_ooov.reshape(-1, nvir).T, eris_oooo.reshape(-1, nocc))
#:Ioo += numpy.einsum('klja,klia->ij', d_ooov, eris_ooov)
#:Xvo += numpy.einsum('kjib,kjba->ai', d_ooov, eris.oovv)
eris_oovv = _cp(eris.oovv[p0:p1])
tmp = _cp(d_ooov.transpose(0, 1, 3, 2).reshape(-1, nocc))
Ioo += lib.dot(
_cp(eris_ooov.transpose(0, 1, 3, 2).reshape(-1, nocc)).T, tmp)
Xvo += lib.dot(eris_oovv.reshape(-1, nvir).T, tmp)
eris_oooo = tmp = None
d_ooov = d_ooov + dooov[:, p0:p1].transpose(1, 0, 2, 3)
eris_ovov = _cp(eris.ovov[p0:p1])
#:Ioo += numpy.einsum('ljka,lika->ij', d_ooov, eris_ooov)
#:Xvo += numpy.einsum('jikb,jakb->ai', d_ooov, eris_ovov)
for i in range(p1 - p0):
lib.dot(eris_ooov[i].reshape(nocc, -1), d_ooov[i].reshape(
nocc, -1).T, 1, Ioo, 1)
lib.dot(eris_ovov[i].reshape(nvir, -1), d_ooov[i].reshape(
nocc, -1).T, 1, Xvo, 1)
d_ooov = None
#:Ioo += numpy.einsum('kjba,kiba->ij', d_oovv, eris.oovv)
#:Ivv += numpy.einsum('ijcb,ijca->ab', d_oovv, eris.oovv)
#:Ivo += numpy.einsum('kjba,kjib->ai', d_oovv, eris.ooov)
d_oovv = _cp(doovv[p0:p1]) + doovv[:, p0:p1].transpose(1, 0, 3, 2)
for i in range(p1 - p0):
Ioo += lib.dot(eris_oovv[i].reshape(nocc, -1), d_oovv[i].reshape(
nocc, -1).T)
Ivv += lib.dot(eris_oovv.reshape(-1, nvir).T, d_oovv.reshape(-1, nvir))
Ivo += lib.dot(
d_oovv.reshape(-1, nvir).T,
_cp(eris_ooov.transpose(0, 1, 3, 2).reshape(-1, nocc)))
eris_ooov = None
d_oovv = _ccsd.precontract(d_oovv.reshape(-1, nvir, nvir)).reshape(
p1 - p0, nocc, -1)
d_ovvv = numpy.empty((p1 - p0, nvir, nvir, nvir))
ao2mo.outcore._load_from_h5g(dovvv, p0 * nvir, p1 * nvir,
d_ovvv.reshape(-1, nvir**2))
#:Ivo += numpy.einsum('jadc,jidc->ai', d_ovvv, eris_oovv)
for i in range(p1 - p0):
Ivo += lib.dot(d_ovvv[i].reshape(nvir, -1), eris_oovv[i].reshape(
nocc, -1).T)
eris_oovv = None
# tril part of (d_ovvv + d_ovvv.transpose(0,1,3,2))
c_ovvv = _ccsd.precontract(d_ovvv.reshape(-1, nvir, nvir))
ao2mo.outcore._transpose_to_h5g(fswap, 'c_vvov/%d' % istep, c_ovvv,
iobuflen)
c_ovvv = c_ovvv.reshape(-1, nvir, nvir_pair)
eris_ovx = _cp(eris.ovvv[p0:p1])
ao2mo.outcore._transpose_to_h5g(fswap, 'e_vvov/%d' % istep,
eris_ovx.reshape(-1, nvir_pair),
iobuflen)
#:Xvo += numpy.einsum('jibc,jabc->ai', d_oovv, eris_ovvv)
#:Ivv += numpy.einsum('ibdc,iadc->ab', d_ovvv, eris_ovvv)
for i in range(p1 - p0):
lib.dot(eris_ovx[i].reshape(nvir, -1),
d_oovv[i].reshape(nocc, -1).T, 1, Xvo, 1)
lib.dot(eris_ovx[i].reshape(nvir, -1),
c_ovvv[i].reshape(nvir, -1).T, 1, Ivv, 1)
c_ovvv = d_oovv = None
eris_ovvo = numpy.empty((p1 - p0, nvir, nvir, nocc))
for i in range(p1 - p0):
d_ovvv[i] = _ccsd.sum021(d_ovvv[i])
eris_ovvo[i] = eris_ovov[i].transpose(0, 2, 1)
#:Ivo += numpy.einsum('abjc,ibjc->ai', d_ovvv, eris_ovov)
Ivo += lib.dot(d_ovvv.reshape(-1, nvir).T, eris_ovvo.reshape(-1, nocc))
eris_ovvo = eris_ovov = None
eris_ovvv = lib.unpack_tril(eris_ovx.reshape(-1, nvir_pair))
eris_ovx = None
eris_ovvv = eris_ovvv.reshape(p1 - p0, nvir, nvir, nvir)
#:Ivv += numpy.einsum('icdb,icda->ab', d_ovvv, eris_ovvv)
#:Xvo += numpy.einsum('jibc,jabc->ai', d_oovv, eris_ovvv)
Ivv += lib.dot(eris_ovvv.reshape(-1, nvir).T, d_ovvv.reshape(-1, nvir))
Xvo[:, p0:p1] += (numpy.einsum('cb,iacb->ai', dvv, eris_ovvv) * 4 -
numpy.einsum('cb,icba->ai', dvv + dvv.T, eris_ovvv))
d_ovvo = _cp(fswap['dovvo'][p0:p1])
#:Xvo += numpy.einsum('jbic,jbca->ai', d_ovov, eris_ovvv)
lib.dot(
eris_ovvv.reshape(-1, nvir).T, d_ovvo.reshape(-1, nocc), 1, Xvo, 1)
d_ovvv = d_ovvo = eris_ovvv = None
max_memory = mycc.max_memory - lib.current_memory()[0]
unit = nocc * nvir**2 + nvir**3 * 2.5
blksize = max(ccsd.BLKMIN, int(max_memory * 1e6 / 8 / unit))
log.debug1(
'IX_intermediates pass 2: block size = %d, nocc = %d in %d blocks',
blksize, nocc, int((nocc + blksize - 1) / blksize))
for p0, p1 in prange(0, nvir, blksize):
off0 = p0 * (p0 + 1) // 2
off1 = p1 * (p1 + 1) // 2
d_vvvv = _cp(dvvvv[off0:off1]) * 4
for i in range(p0, p1):
d_vvvv[i * (i + 1) // 2 + i - off0] *= .5
d_vvvv = lib.unpack_tril(d_vvvv)
eris_vvvv = lib.unpack_tril(_cp(eris.vvvv[off0:off1]))
#:Ivv += numpy.einsum('decb,deca->ab', d_vvvv, eris_vvvv) * 2
#:Xvo += numpy.einsum('dbic,dbca->ai', d_vvov, eris_vvvv)
lib.dot(
eris_vvvv.reshape(-1, nvir).T, d_vvvv.reshape(-1, nvir), 2, Ivv, 1)
#:d_vvvv = _cp(d_vvvv + d_vvvv.transpose(0,1,3,2))
d_vvov = numpy.empty((off1 - off0, nocc, nvir))
ao2mo.outcore._load_from_h5g(fswap['c_vvov'], off0, off1,
d_vvov.reshape(-1, nov))
d_vvvo = _cp(d_vvov.transpose(0, 2, 1))
lib.dot(
eris_vvvv.reshape(-1, nvir).T, d_vvvo.reshape(-1, nocc), 1, Xvo, 1)
d_vvov = eris_vvvv = None
eris_vvov = numpy.empty((off1 - off0, nocc, nvir))
ao2mo.outcore._load_from_h5g(fswap['e_vvov'], off0, off1,
eris_vvov.reshape(-1, nov))
eris_vvvo = _cp(eris_vvov.transpose(0, 2, 1))
#:Ioo += numpy.einsum('abjc,abci->ij', d_vvov, eris_vvvo)
#:Ivo += numpy.einsum('dbca,dbci->ai', d_vvvv, eris_vvvo) * 2
lib.dot(
d_vvvv.reshape(-1, nvir).T, eris_vvvo.reshape(-1, nocc), 2, Ivo, 1)
lib.dot(
eris_vvvo.reshape(-1, nocc).T, d_vvvo.reshape(-1, nocc), 1, Ioo, 1)
eris_vvov = eris_vovv = d_vvvv = None
del (fswap['e_vvov'])
del (fswap['c_vvov'])
del (fswap['dovvo'])
fswap.close()
_tmpfile = None
if d2 is None:
for key in fd2intermediate.keys():
del (fd2intermediate[key])
fd2intermediate.close()
_d2tmpfile = None
Ioo *= -1
Ivv *= -1
Ivo *= -1
Xvo += Ivo
return Ioo, Ivv, Ivo, Xvo
def IX_intermediates(mycc, t1, t2, l1, l2, eris=None, d1=None, d2=None):
if eris is None:
# Note eris are in Chemist's notation
eris = ccsd._ERIS(mycc)
if d1 is None:
d1 = ccsd_rdm.gamma1_intermediates(mycc, t1, t2, l1, l2)
if d2 is None:
d2 = ccsd_rdm.gamma2_incore(mycc, t1, t2, l1, l2)
doo, dov, dvo, dvv = d1
dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov = d2
log = logger.Logger(mycc.stdout, mycc.verbose)
nocc, nvir = t1.shape
nov = nocc * nvir
# Note Ioo, Ivv are not hermitian
Ioo = numpy.zeros((nocc, nocc))
Ivv = numpy.zeros((nvir, nvir))
Ivo = numpy.zeros((nvir, nocc))
Xvo = numpy.zeros((nvir, nocc))
eris_oooo = _cp(eris.oooo)
eris_ooov = _cp(eris.ooov)
d_oooo = _cp(doooo)
d_oooo = _cp(d_oooo + d_oooo.transpose(1, 0, 2, 3))
#:Ioo += numpy.einsum('jmlk,imlk->ij', d_oooo, eris_oooo) * 2
Ioo += lib.dot(eris_oooo.reshape(nocc, -1), d_oooo.reshape(nocc, -1).T, 2)
d_oooo = _cp(d_oooo.transpose(0, 2, 3, 1))
#:Xvo += numpy.einsum('iljk,ljka->ai', d_oooo, eris_ooov) * 2
Xvo += lib.dot(
eris_ooov.reshape(-1, nvir).T,
d_oooo.reshape(nocc, -1).T, 2)
Xvo += (numpy.einsum('kj,kjia->ai', doo, eris_ooov) * 4 -
numpy.einsum('kj,ikja->ai', doo + doo.T, eris_ooov))
eris_oooo = eris_ooov = d_oooo = None
d_ooov = _cp(dooov)
eris_oooo = _cp(eris.oooo)
eris_ooov = _cp(eris.ooov)
#:Ivv += numpy.einsum('ijkb,ijka->ab', d_ooov, eris_ooov)
#:Ivo += numpy.einsum('jlka,jlki->ai', d_ooov, eris_oooo)
Ivv += lib.dot(eris_ooov.reshape(-1, nvir).T, d_ooov.reshape(-1, nvir))
Ivo += lib.dot(d_ooov.reshape(-1, nvir).T, eris_oooo.reshape(-1, nocc))
#:Ioo += numpy.einsum('klja,klia->ij', d_ooov, eris_ooov)
#:Xvo += numpy.einsum('kjib,kjba->ai', d_ooov, eris.oovv)
eris_oovv = _cp(eris.oovv)
tmp = _cp(d_ooov.transpose(0, 1, 3, 2).reshape(-1, nocc))
tmpooov = _cp(eris_ooov.transpose(0, 1, 3, 2))
Ioo += lib.dot(tmpooov.reshape(-1, nocc).T, tmp)
Xvo += lib.dot(eris_oovv.reshape(-1, nvir).T, tmp)
eris_oooo = tmp = None
d_ooov = d_ooov + d_ooov.transpose(1, 0, 2, 3)
eris_ovov = _cp(eris.ovov)
#:Ioo += numpy.einsum('jlka,ilka->ij', d_ooov, eris_ooov)
#:Xvo += numpy.einsum('ijkb,kbja->ai', d_ooov, eris.ovov)
Ioo += lib.dot(eris_ooov.reshape(nocc, -1), d_ooov.reshape(nocc, -1).T)
Xvo += lib.dot(
eris_ovov.reshape(-1, nvir).T,
_cp(d_ooov.transpose(0, 2, 3, 1).reshape(nocc, -1)).T)
d_ooov = None
#:Ioo += numpy.einsum('kjba,kiba->ij', d_oovv, eris.oovv)
#:Ivv += numpy.einsum('ijcb,ijca->ab', d_oovv, eris.oovv)
#:Ivo += numpy.einsum('kjba,kjib->ai', d_oovv, eris.ooov)
d_oovv = _cp(doovv + doovv.transpose(1, 0, 3, 2))
for i in range(nocc):
Ioo += lib.dot(eris_oovv[i].reshape(nocc, -1),
d_oovv[i].reshape(nocc, -1).T)
Ivv += lib.dot(eris_oovv.reshape(-1, nvir).T, d_oovv.reshape(-1, nvir))
Ivo += lib.dot(d_oovv.reshape(-1, nvir).T, tmpooov.reshape(-1, nocc))
d_oovv = _ccsd.precontract(d_oovv.reshape(-1, nvir,
nvir)).reshape(nocc, nocc, -1)
eris_ooov = tmpooov = None
blksize = 4
d_ovov = numpy.empty((nocc, nvir, nocc, nvir))
for p0, p1 in prange(0, nocc, blksize):
d_ovov[p0:p1] = _cp(dovov[p0:p1])
d_ovvo = _cp(dovvo[p0:p1])
for i in range(p0, p1):
d_ovov[i] += d_ovvo[i - p0].transpose(0, 2, 1)
d_ovvo = None
#:d_ovov = d_ovov + d_ovov.transpose(2,3,0,1)
lib.transpose_sum(d_ovov.reshape(nov, nov), inplace=True)
#:Ivo += numpy.einsum('jbka,jbki->ai', d_ovov, eris.ovoo)
Ivo += lib.dot(
d_ovov.reshape(-1, nvir).T,
_cp(eris.ovoo).reshape(-1, nocc))
#:Ioo += numpy.einsum('jakb,iakb->ij', d_ovov, eris.ovov)
#:Ivv += numpy.einsum('jcib,jcia->ab', d_ovov, eris.ovov)
Ioo += lib.dot(eris_ovov.reshape(nocc, -1), d_ovov.reshape(nocc, -1).T)
Ivv += lib.dot(eris_ovov.reshape(-1, nvir).T, d_ovov.reshape(-1, nvir))
nvir_pair = nvir * (nvir + 1) // 2
bufe_ovvv = numpy.empty((blksize, nvir, nvir, nvir))
bufc_ovvv = numpy.empty((blksize, nvir, nvir_pair))
bufc_ovvv.data = bufe_ovvv.data
c_vvvo = numpy.empty((nvir_pair, nvir, nocc))
for p0, p1 in prange(0, nocc, blksize):
d_ovvv = numpy.empty((p1 - p0, nvir, nvir, nvir))
#:Ivo += numpy.einsum('jadc,jidc->ai', d_ovvv, eris_oovv)
for i in range(p1 - p0):
lib.dot(dovvv[p0 + i].reshape(nvir, -1),
eris_oovv[p0 + i].reshape(nocc, -1).T, 1, Ivo, 1)
c_ovvv = bufc_ovvv[:p1 - p0]
# tril part of (d_ovvv + d_ovvv.transpose(0,1,3,2))
_ccsd.precontract(dovvv[p0:p1].reshape(-1, nvir, nvir), out=c_ovvv)
for i0, i1, in prange(0, nvir_pair, BLKSIZE):
for j0, j1 in prange(0, nvir, BLKSIZE // (p1 - p0) + 1):
c_vvvo[i0:i1, j0:j1, p0:p1] = c_ovvv[:, j0:j1,
i0:i1].transpose(2, 1, 0)
eris_ovx = _cp(eris.ovvv[p0:p1])
#:Xvo += numpy.einsum('jibc,jabc->ai', d_oovv, eris_ovvv)
#:Ivv += numpy.einsum('ibdc,iadc->ab', d_ovvv, eris_ovvv)
for i in range(p1 - p0):
lib.dot(eris_ovx[i].reshape(nvir, -1),
d_oovv[p0 + i].reshape(nocc, -1).T, 1, Xvo, 1)
lib.dot(eris_ovx[i].reshape(nvir, -1),
c_ovvv[i].reshape(nvir, -1).T, 1, Ivv, 1)
eris_ovvv = bufe_ovvv[:p1 - p0]
lib.unpack_tril(eris_ovx.reshape(-1, nvir_pair),
out=eris_ovvv.reshape(-1, nvir**2))
eris_ovx = None
#:Xvo += numpy.einsum('icjb,acjb->ai', d_ovov, eris_vvov)
d_ovvo = _cp(d_ovov[p0:p1].transpose(0, 1, 3, 2))
lib.dot(
eris_ovvv.reshape(-1, nvir).T, d_ovvo.reshape(-1, nocc), 1, Xvo, 1)
e_ovvo, d_ovvo = d_ovvo, None
for i in range(p1 - p0):
d_ovvv[i] = _ccsd.sum021(dovvv[p0 + i])
e_ovvo[i] = eris_ovov[p0 + i].transpose(0, 2, 1)
#:Ivo += numpy.einsum('jcab,jcib->ai', d_ovvv, eris_ovov)
#:Ivv += numpy.einsum('icdb,icda->ab', d_ovvv, eris_ovvv)
lib.dot(
d_ovvv.reshape(-1, nvir).T, e_ovvo[:p1 - p0].reshape(-1, nocc), 1,
Ivo, 1)
lib.dot(
eris_ovvv.reshape(-1, nvir).T, d_ovvv.reshape(-1, nvir), 1, Ivv, 1)
Xvo[:, p0:p1] += (numpy.einsum('cb,iacb->ai', dvv, eris_ovvv) * 4 -
numpy.einsum('cb,icba->ai', dvv + dvv.T, eris_ovvv))
d_oovv = d_ovvv = bufc_ovvv = bufe_ovvv = None
eris_ovov = eris_ovvv = eris_oovv = e_ovvo = None
eris_ovvv = _cp(eris.ovvv)
bufe_vvvo = numpy.empty((blksize * nvir, nvir, nocc))
bufe_vvvv = numpy.empty((blksize * nvir, nvir, nvir))
bufd_vvvv = numpy.empty((blksize * nvir, nvir, nvir))
for p0, p1 in prange(0, nvir, blksize):
off0 = p0 * (p0 + 1) // 2
off1 = p1 * (p1 + 1) // 2
d_vvvv = _cp(dvvvv[off0:off1]) * 4
for i in range(p0, p1):
d_vvvv[i * (i + 1) // 2 + i - off0] *= .5
d_vvvv = lib.unpack_tril(d_vvvv, out=bufd_vvvv[:off1 - off0])
eris_vvvv = lib.unpack_tril(eris.vvvv[off0:off1],
out=bufe_vvvv[:off1 - off0])
#:Ivv += numpy.einsum('decb,deca->ab', d_vvvv, eris_vvvv) * 2
#:Xvo += numpy.einsum('icdb,acdb->ai', d_ovvv, eris_vvvv)
lib.dot(
eris_vvvv.reshape(-1, nvir).T, d_vvvv.reshape(-1, nvir), 2, Ivv, 1)
d_vvvo = _cp(c_vvvo[off0:off1])
lib.dot(
eris_vvvv.reshape(-1, nvir).T, d_vvvo.reshape(-1, nocc), 1, Xvo, 1)
#:Ioo += numpy.einsum('abjc,abci->ij', d_vvov, eris_vvvo)
#:Ivo += numpy.einsum('dbca,dbci->ai', d_vvvv, eris_vvvo) * 2
eris_vvvo = bufe_vvvo[:off1 - off0]
for i0, i1 in prange(off0, off1, BLKSIZE):
for j0, j1, in prange(0, nvir, BLKSIZE // nocc + 1):
eris_vvvo[i0 - off0:i1 - off0,
j0:j1, :] = eris_ovvv[:, j0:j1,
i0:i1].transpose(2, 1, 0)
lib.dot(
eris_vvvo.reshape(-1, nocc).T, d_vvvo.reshape(-1, nocc), 1, Ioo, 1)
lib.dot(
d_vvvv.reshape(-1, nvir).T, eris_vvvo.reshape(-1, nocc), 2, Ivo, 1)
Ioo *= -1
Ivv *= -1
Ivo *= -1
Xvo += Ivo
return Ioo, Ivv, Ivo, Xvo
def kernel(mycc,
t1=None,
t2=None,
l1=None,
l2=None,
eris=None,
atmlst=None,
mf_grad=None,
verbose=logger.INFO):
if t1 is None: t1 = mycc.t1
if t2 is None: t2 = mycc.t2
if l1 is None: l1 = mycc.l1
if l2 is None: l2 = mycc.l2
if eris is None: eris = ccsd._ERIS(mycc)
if mf_grad is None:
mf_grad = rhf_grad.Gradients(mycc._scf)
log = logger.Logger(mycc.stdout, mycc.verbose)
time0 = time.clock(), time.time()
mol = mycc.mol
if mycc.frozen is not 0:
raise NotImplementedError('frozen orbital ccsd_grad')
moidx = ccsd.get_moidx(mycc)
mo_coeff = mycc.mo_coeff[:,
moidx] #FIXME: ensure mycc.mo_coeff is canonical orbital
mo_energy = eris.fock.diagonal()
nocc, nvir = t1.shape
nao, nmo = mo_coeff.shape
nao_pair = nao * (nao + 1) // 2
log.debug('Build ccsd rdm1 intermediates')
d1 = ccsd_rdm.gamma1_intermediates(mycc, t1, t2, l1, l2)
doo, dov, dvo, dvv = d1
time1 = log.timer('rdm1 intermediates', *time0)
log.debug('Build ccsd rdm2 intermediates')
d2 = ccsd_rdm.gamma2_incore(mycc, t1, t2, l1, l2)
time1 = log.timer('rdm2 intermediates', *time1)
log.debug('Build ccsd response_rdm1')
Ioo, Ivv, Ivo, Xvo = IX_intermediates(mycc, t1, t2, l1, l2, eris, d1, d2)
time1 = log.timer('response_rdm1 intermediates', *time1)
dm1mo = response_dm1(mycc, t1, t2, l1, l2, eris, (Ioo, Ivv, Ivo, Xvo))
dm1mo[:nocc, :nocc] = doo * 2
dm1mo[nocc:, nocc:] = dvv * 2
dm1ao = reduce(numpy.dot, (mo_coeff, dm1mo, mo_coeff.T))
im1 = numpy.zeros_like(dm1mo)
im1[:nocc, :nocc] = Ioo
im1[nocc:, nocc:] = Ivv
im1[nocc:, :nocc] = Ivo
im1[:nocc, nocc:] = Ivo.T
im1 = reduce(numpy.dot, (mo_coeff, im1, mo_coeff.T))
time1 = log.timer('response_rdm1', *time1)
log.debug('symmetrized rdm2 and MO->AO transformation')
dm1_with_hf = dm1mo.copy()
for i in range(nocc):
dm1_with_hf[i, i] += 1
dm2ao = _rdm2_mo2ao(mycc, d2, dm1_with_hf, mo_coeff)
time1 = log.timer('MO->AO transformation', *time1)
log.debug('h1 and JK1')
h1 = mf_grad.get_hcore(mol)
s1 = mf_grad.get_ovlp(mol)
zeta = lib.direct_sum('i+j->ij', mo_energy, mo_energy) * .5
zeta[nocc:, :nocc] = mo_energy[:nocc]
zeta[:nocc, nocc:] = mo_energy[:nocc].reshape(-1, 1)
zeta = reduce(numpy.dot, (mo_coeff, zeta * dm1mo, mo_coeff.T))
p1 = numpy.dot(mo_coeff[:, :nocc], mo_coeff[:, :nocc].T)
vhf4sij = reduce(numpy.dot,
(p1, mycc._scf.get_veff(mol, dm1ao + dm1ao.T), p1))
time1 = log.timer('h1 and JK1', *time1)
# Hartree-Fock part contribution
hf_dm1 = mycc._scf.make_rdm1(mycc.mo_coeff, mycc.mo_occ)
dm1ao += hf_dm1
zeta += mf_grad.make_rdm1e(mycc.mo_energy, mycc.mo_coeff, mycc.mo_occ)
if atmlst is None:
atmlst = range(mol.natm)
offsetdic = mol.offset_nr_by_atom()
de = numpy.zeros((len(atmlst), 3))
for k, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = offsetdic[ia]
# s[1] dot I, note matrix im1 is not hermitian
de[k] = (numpy.einsum('xij,ij->x', s1[:, p0:p1], im1[p0:p1]) +
numpy.einsum('xji,ij->x', s1[:, p0:p1], im1[:, p0:p1]))
# h[1] \dot DM, *2 for +c.c., contribute to f1
h1ao = mf_grad._grad_rinv(mol, ia)
h1ao[:, p0:p1] += h1[:, p0:p1]
de[k] += (numpy.einsum('xij,ij->x', h1ao, dm1ao) +
numpy.einsum('xji,ij->x', h1ao, dm1ao))
# -s[1]*e \dot DM, contribute to f1
de[k] -= (numpy.einsum('xij,ij->x', s1[:, p0:p1], zeta[p0:p1]) +
numpy.einsum('xji,ij->x', s1[:, p0:p1], zeta[:, p0:p1]))
# -vhf[s_ij[1]], contribute to f1, *2 for s1+s1.T
de[k] -= numpy.einsum('xij,ij->x', s1[:, p0:p1], vhf4sij[p0:p1]) * 2
# 2e AO integrals dot 2pdm
eri1 = mol.intor('int2e_ip1',
comp=3,
aosym='s2kl',
shls_slice=(shl0, shl1, 0, mol.nbas, 0, mol.nbas, 0,
mol.nbas))
eri1 = eri1.reshape(3, p1 - p0, nao, -1)
dm2buf = _load_block_tril(dm2ao, p0, p1)
de[k] -= numpy.einsum('xijk,ijk->x', eri1, dm2buf) * 2
eri1 = dm2buf = None
log.debug('grad of atom %d %s = %s', ia, mol.atom_symbol(ia), de[k])
time1 = log.timer('grad of atom %d' % ia, *time1)
de += rhf_grad.grad_nuc(mol)
log.note('CCSD gradinets')
log.note('==============')
log.note(' x y z')
for k, ia in enumerate(atmlst):
log.note('%d %s %15.9f %15.9f %15.9f', ia, mol.atom_symbol(ia),
*de[k])
log.timer('CCSD gradients', *time0)
return de
def kernel(mycc,
t1=None,
t2=None,
l1=None,
l2=None,
eris=None,
atmlst=None,
mf_grad=None,
verbose=logger.INFO):
if t1 is None: t1 = mycc.t1
if t2 is None: t2 = mycc.t2
if l1 is None: l1 = mycc.l1
if l2 is None: l2 = mycc.l2
if eris is None: eris = ccsd._ERIS(mycc)
if mf_grad is None:
mf_grad = rhf_grad.Gradients(mycc._scf)
log = logger.Logger(mycc.stdout, mycc.verbose)
time0 = time.clock(), time.time()
mol = mycc.mol
moidx = numpy.ones(mycc.mo_coeff.shape[1], dtype=numpy.bool)
if isinstance(mycc.frozen, (int, numpy.integer)):
raise NotImplementedError('frozen orbital ccsd_grad')
moidx[:mycc.frozen] = False
else:
moidx[mycc.frozen] = False
mo_coeff = mycc.mo_coeff[:,
moidx] #FIXME: ensure mycc.mo_coeff is canonical orbital
mo_energy = eris.fock.diagonal()
nocc, nvir = t1.shape
nao, nmo = mo_coeff.shape
nao_pair = nao * (nao + 1) // 2
log.debug('Build ccsd rdm1 intermediates')
d1 = ccsd_rdm.gamma1_intermediates(mycc, t1, t2, l1, l2)
doo, dov, dvo, dvv = d1
time1 = log.timer('rdm1 intermediates', *time0)
log.debug('Build ccsd rdm2 intermediates')
_d2tmpfile = tempfile.NamedTemporaryFile(dir=lib.param.TMPDIR)
fd2intermediate = h5py.File(_d2tmpfile.name, 'w')
d2 = ccsd_rdm.gamma2_outcore(mycc, t1, t2, l1, l2, fd2intermediate)
time1 = log.timer('rdm2 intermediates', *time1)
log.debug('Build ccsd response_rdm1')
Ioo, Ivv, Ivo, Xvo = IX_intermediates(mycc, t1, t2, l1, l2, eris, d1, d2)
time1 = log.timer('response_rdm1 intermediates', *time1)
dm1mo = response_dm1(mycc, t1, t2, l1, l2, eris, (Ioo, Ivv, Ivo, Xvo))
dm1mo[:nocc, :nocc] = doo + doo.T
dm1mo[nocc:, nocc:] = dvv + dvv.T
dm1ao = reduce(numpy.dot, (mo_coeff, dm1mo, mo_coeff.T))
im1 = numpy.zeros_like(dm1mo)
im1[:nocc, :nocc] = Ioo
im1[nocc:, nocc:] = Ivv
im1[nocc:, :nocc] = Ivo
im1[:nocc, nocc:] = Ivo.T
im1 = reduce(numpy.dot, (mo_coeff, im1, mo_coeff.T))
time1 = log.timer('response_rdm1', *time1)
log.debug('symmetrized rdm2 and MO->AO transformation')
_dm2file = tempfile.NamedTemporaryFile(dir=lib.param.TMPDIR)
# Basically, 4 times of dm2 is computed. *2 in _rdm2_mo2ao, *2 in _load_block_tril
fdm2 = h5py.File(_dm2file.name, 'w')
dm1_with_hf = dm1mo.copy()
for i in range(
nocc
): # HF 2pdm ~ 4(ij)(kl)-2(il)(jk), diagonal+1 because of 4*dm2
dm1_with_hf[i, i] += 1
_rdm2_mo2ao(mycc, d2, dm1_with_hf, mo_coeff, fdm2)
time1 = log.timer('MO->AO transformation', *time1)
for key in fd2intermediate.keys():
del (fd2intermediate[key])
fd2intermediate.close()
#TODO: pass hf_grad object to compute h1 and s1
log.debug('h1 and JK1')
h1 = mf_grad.get_hcore(mol)
s1 = mf_grad.get_ovlp(mol)
zeta = lib.direct_sum('i+j->ij', mo_energy, mo_energy) * .5
zeta[nocc:, :nocc] = mo_energy[:nocc]
zeta[:nocc, nocc:] = mo_energy[:nocc].reshape(-1, 1)
zeta = reduce(numpy.dot, (mo_coeff, zeta * dm1mo, mo_coeff.T))
p1 = numpy.dot(mo_coeff[:, :nocc], mo_coeff[:, :nocc].T)
vhf4sij = reduce(numpy.dot,
(p1, mycc._scf.get_veff(mol, dm1ao + dm1ao.T), p1))
time1 = log.timer('h1 and JK1', *time1)
# Hartree-Fock part contribution
hf_dm1 = mycc._scf.make_rdm1(mycc._scf.mo_coeff, mycc._scf.mo_occ)
dm1ao += hf_dm1
zeta += mf_grad.make_rdm1e(mycc._scf.mo_energy, mycc._scf.mo_coeff,
mycc._scf.mo_occ)
if atmlst is None:
atmlst = range(mol.natm)
offsetdic = mol.offset_nr_by_atom()
max_memory = mycc.max_memory - lib.current_memory()[0]
blksize = max(1, int(max_memory * 1e6 / 8 / (nao**3 * 2.5)))
ioblksize = fdm2['dm2/0'].shape[-1]
de = numpy.zeros((len(atmlst), 3))
for k, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = offsetdic[ia]
# s[1] dot I, note matrix im1 is not hermitian
de[k] = (numpy.einsum('xij,ij->x', s1[:, p0:p1], im1[p0:p1]) +
numpy.einsum('xji,ij->x', s1[:, p0:p1], im1[:, p0:p1]))
# h[1] \dot DM, *2 for +c.c., contribute to f1
h1ao = mf_grad._grad_rinv(mol, ia)
h1ao[:, p0:p1] += h1[:, p0:p1]
de[k] += (numpy.einsum('xij,ij->x', h1ao, dm1ao) +
numpy.einsum('xji,ij->x', h1ao, dm1ao))
# -s[1]*e \dot DM, contribute to f1
de[k] -= (numpy.einsum('xij,ij->x', s1[:, p0:p1], zeta[p0:p1]) +
numpy.einsum('xji,ij->x', s1[:, p0:p1], zeta[:, p0:p1]))
# -vhf[s_ij[1]], contribute to f1, *2 for s1+s1.T
de[k] -= numpy.einsum('xij,ij->x', s1[:, p0:p1], vhf4sij[p0:p1]) * 2
# 2e AO integrals dot 2pdm
ip0 = p0
for b0, b1, nf in shell_prange(mol, shl0, shl1, blksize):
eri1 = mol.intor('cint2e_ip1_sph',
comp=3,
aosym='s2kl',
shls_slice=(b0, b1, 0, mol.nbas, 0, mol.nbas, 0,
mol.nbas))
eri1 = eri1.reshape(3, nf, nao, -1)
dm2buf = numpy.empty((nf, nao, nao_pair))
for ic, (i0, i1) in enumerate(prange(0, nao_pair, ioblksize)):
_load_block_tril(fdm2['dm2/%d' % ic], ip0, ip0 + nf,
dm2buf[:, :, i0:i1])
de[k] -= numpy.einsum('xijk,ijk->x', eri1, dm2buf) * 2
eri1 = dm2buf = None
ip0 += nf
log.debug('grad of atom %d %s = %s', ia, mol.atom_symbol(ia), de[k])
time1 = log.timer('grad of atom %d' % ia, *time1)
log.note('CCSD gradinets')
log.note('==============')
log.note(' x y z')
for k, ia in enumerate(atmlst):
log.note('%d %s %15.9f %15.9f %15.9f', ia, mol.atom_symbol(ia),
de[k, 0], de[k, 1], de[k, 2])
log.timer('CCSD gradients', *time0)
for key in fdm2.keys():
del (fdm2[key])
fdm2.close()
_d2tmpfile = _dm2file = None
return de
def IX_intermediates(mycc, t1, t2, l1, l2, eris=None, d1=None, d2=None):
if eris is None:
# Note eris are in Chemist's notation
eris = ccsd._ERIS(mycc)
if d1 is None:
d1 = ccsd_rdm.gamma1_intermediates(mycc, t1, t2, l1, l2)
doo, dov, dvo, dvv = d1
if d2 is None:
_d2tmpfile = tempfile.NamedTemporaryFile(dir=lib.param.TMPDIR)
fd2intermediate = h5py.File(_d2tmpfile.name, 'w')
ccsd_rdm.gamma2_outcore(mycc, t1, t2, l1, l2, fd2intermediate)
dovov = fd2intermediate['dovov']
dvvvv = fd2intermediate['dvvvv']
doooo = fd2intermediate['doooo']
doovv = fd2intermediate['doovv']
dovvo = fd2intermediate['dovvo']
dovvv = fd2intermediate['dovvv']
dooov = fd2intermediate['dooov']
else:
dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov = d2
log = logger.Logger(mycc.stdout, mycc.verbose)
nocc, nvir = t1.shape
nov = nocc * nvir
nvir_pair = nvir * (nvir + 1) // 2
_tmpfile = tempfile.NamedTemporaryFile(dir=lib.param.TMPDIR)
fswap = h5py.File(_tmpfile.name, 'w')
fswap.create_group('e_vvov')
fswap.create_group('c_vvov')
# Note Ioo, Ivv are not hermitian
Ioo = numpy.zeros((nocc, nocc))
Ivv = numpy.zeros((nvir, nvir))
Ivo = numpy.zeros((nvir, nocc))
Xvo = numpy.zeros((nvir, nocc))
eris_oooo = _cp(eris.oooo)
eris_ooov = _cp(eris.ooov)
d_oooo = _cp(doooo)
d_oooo = _cp(d_oooo + d_oooo.transpose(1, 0, 2, 3))
#:Ioo += numpy.einsum('jmlk,imlk->ij', d_oooo, eris_oooo) * 2
Ioo += lib.dot(eris_oooo.reshape(nocc, -1), d_oooo.reshape(nocc, -1).T, 2)
d_oooo = _cp(d_oooo.transpose(0, 2, 3, 1))
#:Xvo += numpy.einsum('iljk,ljka->ai', d_oooo, eris_ooov) * 2
Xvo += lib.dot(
eris_ooov.reshape(-1, nvir).T,
d_oooo.reshape(nocc, -1).T, 2)
Xvo += (numpy.einsum('kj,kjia->ai', doo, eris_ooov) * 4 -
numpy.einsum('kj,ikja->ai', doo + doo.T, eris_ooov))
eris_oooo = eris_ooov = d_oooo = None
d_ovov = numpy.empty((nocc, nvir, nocc, nvir))
blksize = 8
for p0, p1 in prange(0, nocc, blksize):
d_ovov[p0:p1] = _cp(dovov[p0:p1])
d_ovvo = _cp(dovvo[p0:p1])
for i in range(p0, p1):
d_ovov[i] += d_ovvo[i - p0].transpose(0, 2, 1)
d_ovvo = None
d_ovov = lib.transpose_sum(d_ovov.reshape(nov, nov)).reshape(
nocc, nvir, nocc, nvir)
#:Ivo += numpy.einsum('jbka,jbki->ai', d_ovov, eris.ovoo)
Ivo += lib.dot(
d_ovov.reshape(-1, nvir).T,
_cp(eris.ovoo).reshape(-1, nocc))
eris_ovov = _cp(eris.ovov)
#:Ioo += numpy.einsum('jakb,iakb->ij', d_ovov, eris.ovov)
#:Ivv += numpy.einsum('jcib,jcia->ab', d_ovov, eris.ovov)
Ioo += lib.dot(eris_ovov.reshape(nocc, -1), d_ovov.reshape(nocc, -1).T)
Ivv += lib.dot(eris_ovov.reshape(-1, nvir).T, d_ovov.reshape(-1, nvir))
eris_ovov = None
fswap['dovvo'] = d_ovov.transpose(0, 1, 3, 2)
d_ovov = None
max_memory = mycc.max_memory - lib.current_memory()[0]
unit = max(nvir**3 * 2.5, nvir**3 * 2 + nocc * nvir**2)
blksize = max(ccsd.BLKMIN, int(max_memory * 1e6 / 8 / unit))
iobuflen = int(256e6 / 8 / (blksize * nvir))
log.debug1(
'IX_intermediates pass 1: block size = %d, nocc = %d in %d blocks',
blksize, nocc, int((nocc + blksize - 1) / blksize))
for istep, (p0, p1) in enumerate(prange(0, nocc, blksize)):
d_ooov = _cp(dooov[p0:p1])
eris_oooo = _cp(eris.oooo[p0:p1])
eris_ooov = _cp(eris.ooov[p0:p1])
#:Ivv += numpy.einsum('ijkb,ijka->ab', d_ooov, eris_ooov)
#:Ivo += numpy.einsum('jlka,jlki->ai', d_ooov, eris_oooo)
Ivv += lib.dot(eris_ooov.reshape(-1, nvir).T, d_ooov.reshape(-1, nvir))
Ivo += lib.dot(d_ooov.reshape(-1, nvir).T, eris_oooo.reshape(-1, nocc))
#:Ioo += numpy.einsum('klja,klia->ij', d_ooov, eris_ooov)
#:Xvo += numpy.einsum('kjib,kjba->ai', d_ooov, eris.oovv)
eris_oovv = _cp(eris.oovv[p0:p1])
tmp = _cp(d_ooov.transpose(0, 1, 3, 2).reshape(-1, nocc))
Ioo += lib.dot(
_cp(eris_ooov.transpose(0, 1, 3, 2).reshape(-1, nocc)).T, tmp)
Xvo += lib.dot(eris_oovv.reshape(-1, nvir).T, tmp)
eris_oooo = tmp = None
d_ooov = d_ooov + dooov[:, p0:p1].transpose(1, 0, 2, 3)
eris_ovov = _cp(eris.ovov[p0:p1])
#:Ioo += numpy.einsum('ljka,lika->ij', d_ooov, eris_ooov)
#:Xvo += numpy.einsum('jikb,jakb->ai', d_ooov, eris_ovov)
for i in range(p1 - p0):
lib.dot(eris_ooov[i].reshape(nocc, -1),
d_ooov[i].reshape(nocc, -1).T, 1, Ioo, 1)
lib.dot(eris_ovov[i].reshape(nvir, -1),
d_ooov[i].reshape(nocc, -1).T, 1, Xvo, 1)
d_ooov = None
#:Ioo += numpy.einsum('kjba,kiba->ij', d_oovv, eris.oovv)
#:Ivv += numpy.einsum('ijcb,ijca->ab', d_oovv, eris.oovv)
#:Ivo += numpy.einsum('kjba,kjib->ai', d_oovv, eris.ooov)
d_oovv = _cp(doovv[p0:p1]) + doovv[:, p0:p1].transpose(1, 0, 3, 2)
for i in range(p1 - p0):
Ioo += lib.dot(eris_oovv[i].reshape(nocc, -1),
d_oovv[i].reshape(nocc, -1).T)
Ivv += lib.dot(eris_oovv.reshape(-1, nvir).T, d_oovv.reshape(-1, nvir))
Ivo += lib.dot(
d_oovv.reshape(-1, nvir).T,
_cp(eris_ooov.transpose(0, 1, 3, 2).reshape(-1, nocc)))
eris_ooov = None
d_oovv = _ccsd.precontract(d_oovv.reshape(-1, nvir, nvir)).reshape(
p1 - p0, nocc, -1)
d_ovvv = numpy.empty((p1 - p0, nvir, nvir, nvir))
ao2mo.outcore._load_from_h5g(dovvv, p0 * nvir, p1 * nvir,
d_ovvv.reshape(-1, nvir**2))
#:Ivo += numpy.einsum('jadc,jidc->ai', d_ovvv, eris_oovv)
for i in range(p1 - p0):
Ivo += lib.dot(d_ovvv[i].reshape(nvir, -1),
eris_oovv[i].reshape(nocc, -1).T)
eris_oovv = None
# tril part of (d_ovvv + d_ovvv.transpose(0,1,3,2))
c_ovvv = _ccsd.precontract(d_ovvv.reshape(-1, nvir, nvir))
ao2mo.outcore._transpose_to_h5g(fswap, 'c_vvov/%d' % istep, c_ovvv,
iobuflen)
c_ovvv = c_ovvv.reshape(-1, nvir, nvir_pair)
eris_ovx = _cp(eris.ovvv[p0:p1])
ao2mo.outcore._transpose_to_h5g(fswap, 'e_vvov/%d' % istep,
eris_ovx.reshape(-1, nvir_pair),
iobuflen)
#:Xvo += numpy.einsum('jibc,jabc->ai', d_oovv, eris_ovvv)
#:Ivv += numpy.einsum('ibdc,iadc->ab', d_ovvv, eris_ovvv)
for i in range(p1 - p0):
lib.dot(eris_ovx[i].reshape(nvir, -1),
d_oovv[i].reshape(nocc, -1).T, 1, Xvo, 1)
lib.dot(eris_ovx[i].reshape(nvir, -1),
c_ovvv[i].reshape(nvir, -1).T, 1, Ivv, 1)
c_ovvv = d_oovv = None
eris_ovvo = numpy.empty((p1 - p0, nvir, nvir, nocc))
for i in range(p1 - p0):
d_ovvv[i] = _ccsd.sum021(d_ovvv[i])
eris_ovvo[i] = eris_ovov[i].transpose(0, 2, 1)
#:Ivo += numpy.einsum('abjc,ibjc->ai', d_ovvv, eris_ovov)
Ivo += lib.dot(d_ovvv.reshape(-1, nvir).T, eris_ovvo.reshape(-1, nocc))
eris_ovvo = eris_ovov = None
eris_ovvv = lib.unpack_tril(eris_ovx.reshape(-1, nvir_pair))
eris_ovx = None
eris_ovvv = eris_ovvv.reshape(p1 - p0, nvir, nvir, nvir)
#:Ivv += numpy.einsum('icdb,icda->ab', d_ovvv, eris_ovvv)
#:Xvo += numpy.einsum('jibc,jabc->ai', d_oovv, eris_ovvv)
Ivv += lib.dot(eris_ovvv.reshape(-1, nvir).T, d_ovvv.reshape(-1, nvir))
Xvo[:, p0:p1] += (numpy.einsum('cb,iacb->ai', dvv, eris_ovvv) * 4 -
numpy.einsum('cb,icba->ai', dvv + dvv.T, eris_ovvv))
d_ovvo = _cp(fswap['dovvo'][p0:p1])
#:Xvo += numpy.einsum('jbic,jbca->ai', d_ovov, eris_ovvv)
lib.dot(
eris_ovvv.reshape(-1, nvir).T, d_ovvo.reshape(-1, nocc), 1, Xvo, 1)
d_ovvv = d_ovvo = eris_ovvv = None
max_memory = mycc.max_memory - lib.current_memory()[0]
unit = nocc * nvir**2 + nvir**3 * 2.5
blksize = max(ccsd.BLKMIN, int(max_memory * 1e6 / 8 / unit))
log.debug1(
'IX_intermediates pass 2: block size = %d, nocc = %d in %d blocks',
blksize, nocc, int((nocc + blksize - 1) / blksize))
for p0, p1 in prange(0, nvir, blksize):
off0 = p0 * (p0 + 1) // 2
off1 = p1 * (p1 + 1) // 2
d_vvvv = _cp(dvvvv[off0:off1]) * 4
for i in range(p0, p1):
d_vvvv[i * (i + 1) // 2 + i - off0] *= .5
d_vvvv = lib.unpack_tril(d_vvvv)
eris_vvvv = lib.unpack_tril(_cp(eris.vvvv[off0:off1]))
#:Ivv += numpy.einsum('decb,deca->ab', d_vvvv, eris_vvvv) * 2
#:Xvo += numpy.einsum('dbic,dbca->ai', d_vvov, eris_vvvv)
lib.dot(
eris_vvvv.reshape(-1, nvir).T, d_vvvv.reshape(-1, nvir), 2, Ivv, 1)
#:d_vvvv = _cp(d_vvvv + d_vvvv.transpose(0,1,3,2))
d_vvov = numpy.empty((off1 - off0, nocc, nvir))
ao2mo.outcore._load_from_h5g(fswap['c_vvov'], off0, off1,
d_vvov.reshape(-1, nov))
d_vvvo = _cp(d_vvov.transpose(0, 2, 1))
lib.dot(
eris_vvvv.reshape(-1, nvir).T, d_vvvo.reshape(-1, nocc), 1, Xvo, 1)
d_vvov = eris_vvvv = None
eris_vvov = numpy.empty((off1 - off0, nocc, nvir))
ao2mo.outcore._load_from_h5g(fswap['e_vvov'], off0, off1,
eris_vvov.reshape(-1, nov))
eris_vvvo = _cp(eris_vvov.transpose(0, 2, 1))
#:Ioo += numpy.einsum('abjc,abci->ij', d_vvov, eris_vvvo)
#:Ivo += numpy.einsum('dbca,dbci->ai', d_vvvv, eris_vvvo) * 2
lib.dot(
d_vvvv.reshape(-1, nvir).T, eris_vvvo.reshape(-1, nocc), 2, Ivo, 1)
lib.dot(
eris_vvvo.reshape(-1, nocc).T, d_vvvo.reshape(-1, nocc), 1, Ioo, 1)
eris_vvov = eris_vovv = d_vvvv = None
del (fswap['e_vvov'])
del (fswap['c_vvov'])
del (fswap['dovvo'])
fswap.close()
_tmpfile = None
if d2 is None:
for key in fd2intermediate.keys():
del (fd2intermediate[key])
fd2intermediate.close()
_d2tmpfile = None
Ioo *= -1
Ivv *= -1
Ivo *= -1
Xvo += Ivo
return Ioo, Ivv, Ivo, Xvo
def IX_intermediates(mycc, t1, t2, l1, l2, eris=None, d1=None, d2=None):
if eris is None:
# Note eris are in Chemist's notation
eris = ccsd._ERIS(mycc)
if d1 is None:
doo, dvv = ccsd_rdm.gamma1_intermediates(mycc, t1, t2, l1, l2)
else:
doo, dvv = d1
if d2 is None:
d2 = ccsd_rdm.gamma2_incore(mycc, t1, t2, l1, l2)
dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov = d2
log = logger.Logger(mycc.stdout, mycc.verbose)
nocc, nvir = t1.shape
nov = nocc * nvir
# Note Ioo, Ivv are not hermitian
Ioo = numpy.zeros((nocc,nocc))
Ivv = numpy.zeros((nvir,nvir))
Ivo = numpy.zeros((nvir,nocc))
Xvo = numpy.zeros((nvir,nocc))
eris_oooo = _cp(eris.oooo)
eris_ooov = _cp(eris.ooov)
d_oooo = _cp(doooo)
d_oooo = _cp(d_oooo + d_oooo.transpose(1,0,2,3))
#:Ioo += numpy.einsum('jmlk,imlk->ij', d_oooo, eris_oooo) * 2
Ioo += lib.dot(eris_oooo.reshape(nocc,-1), d_oooo.reshape(nocc,-1).T, 2)
d_oooo = _cp(d_oooo.transpose(0,2,3,1))
#:Xvo += numpy.einsum('iljk,ljka->ai', d_oooo, eris_ooov) * 2
Xvo += lib.dot(eris_ooov.reshape(-1,nvir).T, d_oooo.reshape(nocc,-1).T, 2)
Xvo +=(numpy.einsum('kj,kjia->ai', doo, eris_ooov) * 4
- numpy.einsum('kj,ikja->ai', doo+doo.T, eris_ooov))
eris_oooo = eris_ooov = d_oooo = None
d_ooov = _cp(dooov)
eris_oooo = _cp(eris.oooo)
eris_ooov = _cp(eris.ooov)
#:Ivv += numpy.einsum('ijkb,ijka->ab', d_ooov, eris_ooov)
#:Ivo += numpy.einsum('jlka,jlki->ai', d_ooov, eris_oooo)
Ivv += lib.dot(eris_ooov.reshape(-1,nvir).T, d_ooov.reshape(-1,nvir))
Ivo += lib.dot(d_ooov.reshape(-1,nvir).T, eris_oooo.reshape(-1,nocc))
#:Ioo += numpy.einsum('klja,klia->ij', d_ooov, eris_ooov)
#:Xvo += numpy.einsum('kjib,kjba->ai', d_ooov, eris.oovv)
eris_oovv = _cp(eris.oovv)
tmp = _cp(d_ooov.transpose(0,1,3,2).reshape(-1,nocc))
tmpooov = _cp(eris_ooov.transpose(0,1,3,2))
Ioo += lib.dot(tmpooov.reshape(-1,nocc).T, tmp)
Xvo += lib.dot(eris_oovv.reshape(-1,nvir).T, tmp)
eris_oooo = tmp = None
d_ooov = d_ooov + d_ooov.transpose(1,0,2,3)
eris_ovov = _cp(eris.ovov)
#:Ioo += numpy.einsum('jlka,ilka->ij', d_ooov, eris_ooov)
#:Xvo += numpy.einsum('ijkb,kbja->ai', d_ooov, eris.ovov)
Ioo += lib.dot(eris_ooov.reshape(nocc,-1), d_ooov.reshape(nocc,-1).T)
Xvo += lib.dot(eris_ovov.reshape(-1,nvir).T,
_cp(d_ooov.transpose(0,2,3,1).reshape(nocc,-1)).T)
d_ooov = None
#:Ioo += numpy.einsum('kjba,kiba->ij', d_oovv, eris.oovv)
#:Ivv += numpy.einsum('ijcb,ijca->ab', d_oovv, eris.oovv)
#:Ivo += numpy.einsum('kjba,kjib->ai', d_oovv, eris.ooov)
d_oovv = _cp(doovv + doovv.transpose(1,0,3,2))
for i in range(nocc):
Ioo += lib.dot(eris_oovv[i].reshape(nocc, -1), d_oovv[i].reshape(nocc,-1).T)
Ivv += lib.dot(eris_oovv.reshape(-1,nvir).T, d_oovv.reshape(-1,nvir))
Ivo += lib.dot(d_oovv.reshape(-1,nvir).T, tmpooov.reshape(-1,nocc))
d_oovv = _ccsd.precontract(d_oovv.reshape(-1,nvir,nvir)).reshape(nocc,nocc,-1)
eris_ooov = tmpooov = None
blksize = 4
d_ovov = numpy.empty((nocc,nvir,nocc,nvir))
for p0, p1 in prange(0, nocc, blksize):
d_ovov[p0:p1] = _cp(dovov[p0:p1])
d_ovvo = _cp(dovvo[p0:p1])
for i in range(p0,p1):
d_ovov[i] += d_ovvo[i-p0].transpose(0,2,1)
d_ovvo = None
#:d_ovov = d_ovov + d_ovov.transpose(2,3,0,1)
lib.transpose_sum(d_ovov.reshape(nov,nov), inplace=True)
#:Ivo += numpy.einsum('jbka,jbki->ai', d_ovov, eris.ovoo)
Ivo += lib.dot(d_ovov.reshape(-1,nvir).T, _cp(eris.ovoo).reshape(-1,nocc))
#:Ioo += numpy.einsum('jakb,iakb->ij', d_ovov, eris.ovov)
#:Ivv += numpy.einsum('jcib,jcia->ab', d_ovov, eris.ovov)
Ioo += lib.dot(eris_ovov.reshape(nocc,-1), d_ovov.reshape(nocc,-1).T)
Ivv += lib.dot(eris_ovov.reshape(-1,nvir).T, d_ovov.reshape(-1,nvir))
nvir_pair = nvir * (nvir+1) // 2
bufe_ovvv = numpy.empty((blksize,nvir,nvir,nvir))
bufc_ovvv = numpy.empty((blksize,nvir,nvir_pair))
bufc_ovvv.data = bufe_ovvv.data
c_vvvo = numpy.empty((nvir_pair,nvir,nocc))
for p0, p1 in prange(0, nocc, blksize):
d_ovvv = numpy.empty((p1-p0,nvir,nvir,nvir))
#:Ivo += numpy.einsum('jadc,jidc->ai', d_ovvv, eris_oovv)
for i in range(p1-p0):
lib.dot(dovvv[p0+i].reshape(nvir,-1),
eris_oovv[p0+i].reshape(nocc,-1).T, 1, Ivo, 1)
c_ovvv = bufc_ovvv[:p1-p0]
# tril part of (d_ovvv + d_ovvv.transpose(0,1,3,2))
_ccsd.precontract(dovvv[p0:p1].reshape(-1,nvir,nvir), out=c_ovvv)
for i0, i1, in prange(0, nvir_pair, BLKSIZE):
for j0, j1 in prange(0, nvir, BLKSIZE//(p1-p0)+1):
c_vvvo[i0:i1,j0:j1,p0:p1] = c_ovvv[:,j0:j1,i0:i1].transpose(2,1,0)
eris_ovx = _cp(eris.ovvv[p0:p1])
#:Xvo += numpy.einsum('jibc,jabc->ai', d_oovv, eris_ovvv)
#:Ivv += numpy.einsum('ibdc,iadc->ab', d_ovvv, eris_ovvv)
for i in range(p1-p0):
lib.dot(eris_ovx[i].reshape(nvir,-1),
d_oovv[p0+i].reshape(nocc,-1).T, 1, Xvo, 1)
lib.dot(eris_ovx[i].reshape(nvir,-1),
c_ovvv[i].reshape(nvir,-1).T, 1, Ivv, 1)
eris_ovvv = bufe_ovvv[:p1-p0]
_ccsd.unpack_tril(eris_ovx.reshape(-1,nvir_pair),
out=eris_ovvv.reshape(-1,nvir**2))
eris_ovx = None
#:Xvo += numpy.einsum('icjb,acjb->ai', d_ovov, eris_vvov)
d_ovvo = _cp(d_ovov[p0:p1].transpose(0,1,3,2))
lib.dot(eris_ovvv.reshape(-1,nvir).T, d_ovvo.reshape(-1,nocc), 1, Xvo, 1)
e_ovvo, d_ovvo = d_ovvo, None
for i in range(p1-p0):
d_ovvv[i] = _ccsd.sum021(dovvv[p0+i])
e_ovvo[i] = eris_ovov[p0+i].transpose(0,2,1)
#:Ivo += numpy.einsum('jcab,jcib->ai', d_ovvv, eris_ovov)
#:Ivv += numpy.einsum('icdb,icda->ab', d_ovvv, eris_ovvv)
lib.dot(d_ovvv.reshape(-1,nvir).T,
e_ovvo[:p1-p0].reshape(-1,nocc), 1, Ivo, 1)
lib.dot(eris_ovvv.reshape(-1,nvir).T, d_ovvv.reshape(-1,nvir), 1, Ivv, 1)
Xvo[:,p0:p1] +=(numpy.einsum('cb,iacb->ai', dvv, eris_ovvv) * 4
- numpy.einsum('cb,icba->ai', dvv+dvv.T, eris_ovvv))
d_oovv = d_ovvv = bufc_ovvv = bufe_ovvv = None
eris_ovov = eris_ovvv = eris_oovv = e_ovvo = None
eris_ovvv = _cp(eris.ovvv)
bufe_vvvo = numpy.empty((blksize*nvir,nvir,nocc))
bufe_vvvv = numpy.empty((blksize*nvir,nvir,nvir))
bufd_vvvv = numpy.empty((blksize*nvir,nvir,nvir))
for p0, p1 in prange(0, nvir, blksize):
off0 = p0*(p0+1)//2
off1 = p1*(p1+1)//2
d_vvvv = _cp(dvvvv[off0:off1]) * 4
for i in range(p0, p1):
d_vvvv[i*(i+1)//2+i-off0] *= .5
d_vvvv = _ccsd.unpack_tril(d_vvvv, out=bufd_vvvv[:off1-off0])
eris_vvvv = _ccsd.unpack_tril(eris.vvvv[off0:off1], out=bufe_vvvv[:off1-off0])
#:Ivv += numpy.einsum('decb,deca->ab', d_vvvv, eris_vvvv) * 2
#:Xvo += numpy.einsum('icdb,acdb->ai', d_ovvv, eris_vvvv)
lib.dot(eris_vvvv.reshape(-1,nvir).T, d_vvvv.reshape(-1,nvir), 2, Ivv, 1)
d_vvvo = _cp(c_vvvo[off0:off1])
lib.dot(eris_vvvv.reshape(-1,nvir).T, d_vvvo.reshape(-1,nocc), 1, Xvo, 1)
#:Ioo += numpy.einsum('abjc,abci->ij', d_vvov, eris_vvvo)
#:Ivo += numpy.einsum('dbca,dbci->ai', d_vvvv, eris_vvvo) * 2
eris_vvvo = bufe_vvvo[:off1-off0]
for i0, i1 in prange(off0, off1, BLKSIZE):
for j0, j1, in prange(0, nvir, BLKSIZE//nocc+1):
eris_vvvo[i0-off0:i1-off0,j0:j1,:] = eris_ovvv[:,j0:j1,i0:i1].transpose(2,1,0)
lib.dot(eris_vvvo.reshape(-1,nocc).T, d_vvvo.reshape(-1,nocc), 1, Ioo, 1)
lib.dot(d_vvvv.reshape(-1,nvir).T, eris_vvvo.reshape(-1,nocc), 2, Ivo, 1)
Ioo *= -1
Ivv *= -1
Ivo *= -1
Xvo += Ivo
return Ioo, Ivv, Ivo, Xvo
def kernel(mycc,
t1=None,
t2=None,
l1=None,
l2=None,
eris=None,
atmlst=None,
mf_grad=None,
verbose=logger.INFO):
if t1 is None: t1 = mycc.t1
if t2 is None: t2 = mycc.t2
if l1 is None: l1 = mycc.l1
if l2 is None: l2 = mycc.l2
if eris is None: eris = ccsd._ERIS(mycc)
if mf_grad is None:
mf_grad = rhf_grad.Gradients(mycc._scf)
log = logger.Logger(mycc.stdout, mycc.verbose)
time0 = time.clock(), time.time()
mol = mycc.mol
moidx = numpy.ones(mycc.mo_energy.size, dtype=numpy.bool)
if isinstance(mycc.frozen, (int, numpy.integer)):
raise NotImplementedError('frozen orbital ccsd_grad')
moidx[:mycc.frozen] = False
else:
moidx[mycc.frozen] = False
mo_coeff = mycc.mo_coeff[:,
moidx] #FIXME: ensure mycc.mo_coeff is canonical orbital
mo_energy = mycc.mo_energy[moidx]
nocc, nvir = t1.shape
nao, nmo = mo_coeff.shape
nao_pair = nao * (nao + 1) // 2
log.debug('Build ccsd rdm1 intermediates')
d1 = ccsd_rdm.gamma1_intermediates(mycc, t1, t2, l1, l2)
doo, dov, dvo, dvv = d1
time1 = log.timer('rdm1 intermediates', *time0)
log.debug('Build ccsd rdm2 intermediates')
_d2tmpfile = tempfile.NamedTemporaryFile(dir=lib.param.TMPDIR)
fd2intermediate = h5py.File(_d2tmpfile.name, 'w')
d2 = ccsd_rdm.gamma2_outcore(mycc, t1, t2, l1, l2, fd2intermediate)
time1 = log.timer('rdm2 intermediates', *time1)
log.debug('Build ccsd response_rdm1')
Ioo, Ivv, Ivo, Xvo = IX_intermediates(mycc, t1, t2, l1, l2, eris, d1, d2)
time1 = log.timer('response_rdm1 intermediates', *time1)
dm1mo = response_dm1(mycc, t1, t2, l1, l2, eris, (Ioo, Ivv, Ivo, Xvo))
dm1mo[:nocc, :nocc] = doo + doo.T
dm1mo[nocc:, nocc:] = dvv + dvv.T
dm1ao = reduce(numpy.dot, (mo_coeff, dm1mo, mo_coeff.T))
im1 = numpy.zeros_like(dm1mo)
im1[:nocc, :nocc] = Ioo
im1[nocc:, nocc:] = Ivv
im1[nocc:, :nocc] = Ivo
im1[:nocc, nocc:] = Ivo.T
im1 = reduce(numpy.dot, (mo_coeff, im1, mo_coeff.T))
time1 = log.timer('response_rdm1', *time1)
log.debug('symmetrized rdm2 and MO->AO transformation')
_dm2file = tempfile.NamedTemporaryFile(dir=lib.param.TMPDIR)
# Basically, 4 times of dm2 is computed. *2 in _rdm2_mo2ao, *2 in _load_block_tril
fdm2 = h5py.File(_dm2file.name, 'w')
dm1_with_hf = dm1mo.copy()
for i in range(
nocc
): # HF 2pdm ~ 4(ij)(kl)-2(il)(jk), diagonal+1 because of 4*dm2
dm1_with_hf[i, i] += 1
_rdm2_mo2ao(mycc, d2, dm1_with_hf, mo_coeff, fdm2)
time1 = log.timer('MO->AO transformation', *time1)
for key in fd2intermediate.keys():
del (fd2intermediate[key])
fd2intermediate.close()
#TODO: pass hf_grad object to compute h1 and s1
log.debug('h1 and JK1')
h1 = mf_grad.get_hcore(mol)
s1 = mf_grad.get_ovlp(mol)
zeta = lib.direct_sum('i+j->ij', mo_energy, mo_energy) * .5
zeta[nocc:, :nocc] = mo_energy[:nocc]
zeta[:nocc, nocc:] = mo_energy[:nocc].reshape(-1, 1)
zeta = reduce(numpy.dot, (mo_coeff, zeta * dm1mo, mo_coeff.T))
p1 = numpy.dot(mo_coeff[:, :nocc], mo_coeff[:, :nocc].T)
vhf4sij = reduce(numpy.dot,
(p1, mycc._scf.get_veff(mol, dm1ao + dm1ao.T), p1))
time1 = log.timer('h1 and JK1', *time1)
# Hartree-Fock part contribution
hf_dm1 = mycc._scf.make_rdm1(mycc.mo_coeff, mycc.mo_occ)
dm1ao += hf_dm1
zeta += mf_grad.make_rdm1e(mycc.mo_energy, mycc.mo_coeff, mycc.mo_occ)
if atmlst is None:
atmlst = range(mol.natm)
offsetdic = mol.offset_nr_by_atom()
max_memory = mycc.max_memory - lib.current_memory()[0]
blksize = max(1, int(max_memory * 1e6 / 8 / (nao**3 * 2.5)))
ioblksize = fdm2['dm2/0'].shape[-1]
de = numpy.zeros((len(atmlst), 3))
for k, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = offsetdic[ia]
# s[1] dot I, note matrix im1 is not hermitian
de[k] = (numpy.einsum('xij,ij->x', s1[:, p0:p1], im1[p0:p1]) +
numpy.einsum('xji,ij->x', s1[:, p0:p1], im1[:, p0:p1]))
# h[1] \dot DM, *2 for +c.c., contribute to f1
h1ao = mf_grad._grad_rinv(mol, ia)
h1ao[:, p0:p1] += h1[:, p0:p1]
de[k] += (numpy.einsum('xij,ij->x', h1ao, dm1ao) + numpy.einsum(
'xji,ij->x', h1ao, dm1ao))
# -s[1]*e \dot DM, contribute to f1
de[k] -= (numpy.einsum('xij,ij->x', s1[:, p0:p1], zeta[p0:p1]) +
numpy.einsum('xji,ij->x', s1[:, p0:p1], zeta[:, p0:p1]))
# -vhf[s_ij[1]], contribute to f1, *2 for s1+s1.T
de[k] -= numpy.einsum('xij,ij->x', s1[:, p0:p1], vhf4sij[p0:p1]) * 2
# 2e AO integrals dot 2pdm
ip0 = p0
for b0, b1, nf in shell_prange(mol, shl0, shl1, blksize):
eri1 = mol.intor(
'cint2e_ip1_sph',
comp=3,
aosym='s2kl',
shls_slice=(b0, b1, 0, mol.nbas, 0, mol.nbas, 0, mol.nbas))
eri1 = eri1.reshape(3, nf, nao, -1)
dm2buf = numpy.empty((nf, nao, nao_pair))
for ic, (i0, i1) in enumerate(prange(0, nao_pair, ioblksize)):
_load_block_tril(fdm2['dm2/%d' % ic], ip0, ip0 + nf,
dm2buf[:, :, i0:i1])
de[k] -= numpy.einsum('xijk,ijk->x', eri1, dm2buf) * 2
eri1 = dm2buf = None
ip0 += nf
log.debug('grad of atom %d %s = %s', ia, mol.atom_symbol(ia), de[k])
time1 = log.timer('grad of atom %d' % ia, *time1)
log.note('CCSD gradinets')
log.note('==============')
log.note(' x y z')
for k, ia in enumerate(atmlst):
log.note('%d %s %15.9f %15.9f %15.9f', ia, mol.atom_symbol(ia),
de[k, 0], de[k, 1], de[k, 2])
log.timer('CCSD gradients', *time0)
for key in fdm2.keys():
del (fdm2[key])
fdm2.close()
_d2tmpfile = _dm2file = None
return de
def kernel(mycc, t1=None, t2=None, l1=None, l2=None, eris=None, atmlst=None,
grad_hf=None, verbose=logger.INFO):
if t1 is None: t1 = mycc.t1
if t2 is None: t2 = mycc.t2
if l1 is None: l1 = mycc.l1
if l2 is None: l2 = mycc.l2
if eris is None: eris = ccsd._ERIS(mycc)
if grad_hf is None:
grad_hf = rhf_grad.Gradients(mycc._scf)
log = logger.Logger(mycc.stdout, mycc.verbose)
time0 = time.clock(), time.time()
mol = mycc.mol
moidx = numpy.ones(mycc.mo_energy.size, dtype=numpy.bool)
if isinstance(mycc.frozen, (int, numpy.integer)):
raise NotImplementedError('frozen orbital ccsd_grad')
moidx[:mycc.frozen] = False
else:
moidx[mycc.frozen] = False
mo_coeff = mycc.mo_coeff[:,moidx] #FIXME: ensure mycc.mo_coeff is canonical orbital
mo_energy = mycc.mo_energy[moidx]
nocc, nvir = t1.shape
nao, nmo = mo_coeff.shape
nao_pair = nao * (nao+1) // 2
log.debug('Build ccsd rdm1 intermediates')
doo, dvv = ccsd_rdm.gamma1_intermediates(mycc, t1, t2, l1, l2)
time1 = log.timer('rdm1 intermediates', *time0)
log.debug('Build ccsd rdm2 intermediates')
d2 = ccsd_rdm.gamma2_incore(mycc, t1, t2, l1, l2)
time1 = log.timer('rdm2 intermediates', *time1)
log.debug('Build ccsd response_rdm1')
Ioo, Ivv, Ivo, Xvo = IX_intermediates(mycc, t1, t2, l1, l2, eris, (doo,dvv), d2)
time1 = log.timer('response_rdm1 intermediates', *time1)
dm1mo = response_dm1(mycc, t1, t2, l1, l2, eris, (Ioo, Ivv, Ivo, Xvo))
dm1mo[:nocc,:nocc] = doo * 2
dm1mo[nocc:,nocc:] = dvv * 2
dm1ao = reduce(numpy.dot, (mo_coeff, dm1mo, mo_coeff.T))
im1 = numpy.zeros_like(dm1mo)
im1[:nocc,:nocc] = Ioo
im1[nocc:,nocc:] = Ivv
im1[nocc:,:nocc] = Ivo
im1[:nocc,nocc:] = Ivo.T
im1 = reduce(numpy.dot, (mo_coeff, im1, mo_coeff.T))
time1 = log.timer('response_rdm1', *time1)
log.debug('symmetrized rdm2 and MO->AO transformation')
dm2ao = _rdm2_mo2ao(mycc, d2, dm1mo, mo_coeff)
time1 = log.timer('MO->AO transformation', *time1)
#TODO: pass hf_grad object to compute h1 and s1
log.debug('h1 and JK1')
h1 = grad_hf.get_hcore(mol)
s1 = grad_hf.get_ovlp(mol)
zeta = lib.direct_sum('i+j->ij', mo_energy, mo_energy) * .5
zeta[nocc:,:nocc] = mo_energy[:nocc]
zeta[:nocc,nocc:] = mo_energy[:nocc].reshape(-1,1)
zeta = reduce(numpy.dot, (mo_coeff, zeta*dm1mo, mo_coeff.T))
p1 = numpy.dot(mo_coeff[:,:nocc], mo_coeff[:,:nocc].T)
vhf4sij = reduce(numpy.dot, (p1, mycc._scf.get_veff(mol, dm1ao+dm1ao.T), p1))
time1 = log.timer('h1 and JK1', *time1)
# Hartree-Fock part contribution
hf_dm1 = mycc._scf.make_rdm1(mycc.mo_coeff, mycc.mo_occ)
dm1ao += hf_dm1
zeta += grad_hf.make_rdm1e(mycc.mo_energy, mycc.mo_coeff, mycc.mo_occ)
if atmlst is None:
atmlst = range(mol.natm)
offsetdic = grad_hf.aorange_by_atom()
de = numpy.zeros((len(atmlst),3))
for k, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = offsetdic[ia]
# s[1] dot I, note matrix im1 is not hermitian
de[k] =(numpy.einsum('xij,ij->x', s1[:,p0:p1], im1[p0:p1])
+ numpy.einsum('xji,ij->x', s1[:,p0:p1], im1[:,p0:p1]))
# h[1] \dot DM, *2 for +c.c., contribute to f1
vrinv = grad_hf._grad_rinv(mol, ia)
de[k] +=(numpy.einsum('xij,ij->x', h1[:,p0:p1], dm1ao[p0:p1] )
+ numpy.einsum('xji,ij->x', h1[:,p0:p1], dm1ao[:,p0:p1]))
de[k] +=(numpy.einsum('xij,ij->x', vrinv, dm1ao)
+ numpy.einsum('xji,ij->x', vrinv, dm1ao))
# -s[1]*e \dot DM, contribute to f1
de[k] -=(numpy.einsum('xij,ij->x', s1[:,p0:p1], zeta[p0:p1] )
+ numpy.einsum('xji,ij->x', s1[:,p0:p1], zeta[:,p0:p1]))
# -vhf[s_ij[1]], contribute to f1, *2 for s1+s1.T
de[k] -= numpy.einsum('xij,ij->x', s1[:,p0:p1], vhf4sij[p0:p1]) * 2
# 2e AO integrals dot 2pdm
eri1 = gto.moleintor.getints('cint2e_ip1_sph', mol._atm, mol._bas,
mol._env, numpy.arange(shl0,shl1), comp=3,
aosym='s2kl').reshape(3,p1-p0,nao,-1)
dm2buf = _load_block_tril(dm2ao, p0, p1)
de[k] -= numpy.einsum('xijk,ijk->x', eri1, dm2buf) * 2
for i in range(3):
#:tmp = _ccsd.unpack_tril(eri1[i].reshape(-1,nao_pair))
#:vj = numpy.einsum('ijkl,kl->ij', tmp, hf_dm1)
#:vk = numpy.einsum('ijkl,jk->il', tmp, hf_dm1)
vj, vk = hf_get_jk_incore(eri1[i], hf_dm1)
de[k,i] -=(numpy.einsum('ij,ij->', vj, hf_dm1[p0:p1])
- numpy.einsum('ij,ij->', vk, hf_dm1[p0:p1])*.5) * 2
eri1 = dm2buf = None
log.debug('grad of atom %d %s = %s', ia, mol.atom_symbol(ia), de[k])
time1 = log.timer('grad of atom %d'%ia, *time1)
log.note('CCSD gradinets')
log.note('==============')
log.note(' x y z')
for k, ia in enumerate(atmlst):
log.note('%d %s %15.9f %15.9f %15.9f', ia, mol.atom_symbol(ia),
de[k,0], de[k,1], de[k,2])
log.timer('CCSD gradients', *time0)
return de
