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 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 IX_intermediates(cc, t1, t2, l1, l2, eris=None, d1=None, d2=None):
if eris is None:
# Note eris are in Chemist's notation
eris = ccsd._ERIS(cc)
if d1 is None:
doo, dvv = ccsd_rdm.gamma1_intermediates(cc, t1, t2, l1, l2)
else:
doo, dvv = d1
if d2 is None:
# Note gamma2 are in Chemist's notation
d2 = ccsd_rdm.gamma2_intermediates(cc, t1, t2, l1, l2)
dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov = d2
dvvov = dovvv.transpose(2,3,0,1)
nocc, nvir = t1.shape
dvvvv = pyscf.ao2mo.restore(1, dvvvv, nvir).reshape((nvir,)*4)
# Note Ioo is not hermitian
Ioo =(numpy.einsum('jakb,iakb->ij', dovov, eris.ovov)
+ numpy.einsum('kbja,iakb->ij', dovov, eris.ovov))
Ioo +=(numpy.einsum('jabk,iakb->ij', dovvo, eris.ovov)
+ numpy.einsum('kbaj,iakb->ij', dovvo, eris.ovov)
+ numpy.einsum('jkab,ikab->ij', doovv, eris.oovv)
+ numpy.einsum('kjba,ikab->ij', doovv, eris.oovv))
Ioo +=(numpy.einsum('jmlk,imlk->ij', doooo, eris.oooo) * 2
+ numpy.einsum('mjkl,imlk->ij', doooo, eris.oooo) * 2)
Ioo +=(numpy.einsum('jlka,ilka->ij', dooov, eris.ooov)
+ numpy.einsum('klja,klia->ij', dooov, eris.ooov))
Ioo += numpy.einsum('abjc,icab->ij', dvvov, eris.ovvv)
Ioo += numpy.einsum('ljka,lika->ij', dooov, eris.ooov)
Ioo *= -1
# Note Ivv is not hermitian
Ivv =(numpy.einsum('ibjc,iajc->ab', dovov, eris.ovov)
+ numpy.einsum('jcib,iajc->ab', dovov, eris.ovov))
Ivv +=(numpy.einsum('jcbi,iajc->ab', dovvo, eris.ovov)
+ numpy.einsum('ibcj,iajc->ab', dovvo, eris.ovov)
+ numpy.einsum('jibc,jiac->ab', doovv, eris.oovv)
+ numpy.einsum('ijcb,jiac->ab', doovv, eris.oovv))
Ivv +=(numpy.einsum('bced,aced->ab', dvvvv, eris.vvvv) * 2
+ numpy.einsum('cbde,aced->ab', dvvvv, eris.vvvv) * 2)
Ivv +=(numpy.einsum('dbic,icda->ab', dvvov, eris.ovvv)
+ numpy.einsum('dcib,iadc->ab', dvvov, eris.ovvv))
Ivv += numpy.einsum('bcid,idac->ab', dvvov, eris.ovvv)
Ivv += numpy.einsum('jikb,jika->ab', dooov, eris.ooov)
Ivv *= -1
Ivo =(numpy.einsum('kajb,kijb->ai', dovov, eris.ooov)
+ numpy.einsum('kbja,jikb->ai', dovov, eris.ooov))
Ivo +=(numpy.einsum('acbd,icbd->ai', dvvvv, eris.ovvv) * 2
+ numpy.einsum('cadb,icbd->ai', dvvvv, eris.ovvv) * 2)
Ivo +=(numpy.einsum('jbak,jbik->ai', dovvo, eris.ovoo)
+ numpy.einsum('kabj,jbik->ai', dovvo, eris.ovoo)
+ numpy.einsum('jkab,jkib->ai', doovv, eris.ooov)
+ numpy.einsum('kjba,jkib->ai', doovv, eris.ooov))
Ivo +=(numpy.einsum('dajc,idjc->ai', dvvov, eris.ovov)
+ numpy.einsum('dcja,jidc->ai', dvvov, eris.oovv))
Ivo += numpy.einsum('abjc,ibjc->ai', dvvov, eris.ovov)
Ivo += numpy.einsum('jlka,jlki->ai', dooov, eris.oooo)
Ivo *= -1
Xvo =(numpy.einsum('kj,kjia->ai', doo, eris.ooov) * 2
+ numpy.einsum('kj,kjia->ai', doo, eris.ooov) * 2
- numpy.einsum('kj,kija->ai', doo, eris.ooov)
- numpy.einsum('kj,ijka->ai', doo, eris.ooov))
Xvo +=(numpy.einsum('cb,iacb->ai', dvv, eris.ovvv) * 2
+ numpy.einsum('cb,iacb->ai', dvv, eris.ovvv) * 2
- numpy.einsum('cb,icab->ai', dvv, eris.ovvv)
- numpy.einsum('cb,ibca->ai', dvv, eris.ovvv))
Xvo +=(numpy.einsum('icjb,jbac->ai', dovov, eris.ovvv)
+ numpy.einsum('jcib,jcab->ai', dovov, eris.ovvv))
Xvo +=(numpy.einsum('iklj,ljka->ai', doooo, eris.ooov) * 2
+ numpy.einsum('kijl,ljka->ai', doooo, eris.ooov) * 2)
Xvo +=(numpy.einsum('ibcj,jcab->ai', dovvo, eris.ovvv)
+ numpy.einsum('jcbi,jcab->ai', dovvo, eris.ovvv)
+ numpy.einsum('ijcb,jacb->ai', doovv, eris.ovvv)
+ numpy.einsum('jibc,jacb->ai', doovv, eris.ovvv))
Xvo +=(numpy.einsum('ijkb,jakb->ai', dooov, eris.ovov)
+ numpy.einsum('kjib,kjab->ai', dooov, eris.oovv))
Xvo += numpy.einsum('dbic,dbac->ai', dvvov, eris.vvvv)
Xvo += numpy.einsum('jikb,jakb->ai', dooov, eris.ovov)
Xvo += Ivo
return Ioo, Ivv, Ivo, Xvo
def kernel(cc, t1=None, t2=None, l1=None, l2=None, eris=None, atmlst=None):
if t1 is None: t1 = cc.t1
if t2 is None: t2 = cc.t2
if l1 is None: l1 = cc.l1
if l2 is None: l2 = cc.l2
if eris is None: eris = ccsd._ERIS(cc)
mol = cc.mol
mo_coeff = cc.mo_coeff #FIXME: ensure cc.mo_coeff is canonical orbital
mo_energy = cc.mo_energy
nocc, nvir = t1.shape
nao, nmo = mo_coeff.shape
doo, dvv = ccsd_rdm.gamma1_intermediates(cc, t1, t2, l1, l2)
d2 = ccsd_rdm.gamma2_intermediates(cc, t1, t2, l1, l2)
Ioo, Ivv, Ivo, Xvo = IX_intermediates(cc, t1, t2, l1, l2, eris, (doo,dvv), d2)
dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov = d2
dvvov = dovvv.transpose(2,3,0,1)
dvvvv = pyscf.ao2mo.restore(1, dvvvv, nvir).reshape((nvir,)*4)
dm1mo = response_dm1(cc, 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(dm1ao)
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))
h1 =-(mol.intor('cint1e_ipkin_sph', comp=3)
+mol.intor('cint1e_ipnuc_sph', comp=3))
s1 =-mol.intor('cint1e_ipovlp_sph', comp=3)
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))
eri0 = mol.intor('cint2e_ip1_sph', 3).reshape(3,nao,nao,nao,nao)
dm2 = numpy.zeros((nmo,)*4)
dm2[:nocc,nocc:,:nocc,nocc:] = dovov
dm2[nocc:,nocc:,nocc:,nocc:] = dvvvv
dm2[:nocc,:nocc,:nocc,:nocc] = doooo
dm2[:nocc,nocc:,nocc:,:nocc] = dovvo
dm2[:nocc,:nocc,nocc:,nocc:] = doovv
dm2[nocc:,nocc:,:nocc,nocc:] = dvvov
dm2[:nocc,:nocc,:nocc,nocc:] = dooov
for i in range(nocc):
dm2[i,i,:,:] += dm1mo
dm2[:,i,i,:] -= dm1mo * .5
dm2 = numpy.einsum('pjkl,ip->ijkl', dm2, mo_coeff)
dm2 = numpy.einsum('ipkl,jp->ijkl', dm2, mo_coeff)
dm2 = numpy.einsum('ijpl,kp->ijkl', dm2, mo_coeff)
dm2 = numpy.einsum('ijkp,lp->ijkl', dm2, mo_coeff)
if atmlst is None:
atmlst = range(mol.natm)
offsetdic = aorange_by_atom(mol)
de = numpy.empty((mol.natm,3))
for k,ia in enumerate(atmlst):
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
mol.set_rinv_origin_(mol.atom_coord(k))
vrinv = -mol.atom_charge(k) * mol.intor('cint1e_iprinv_sph', comp=3)
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]))
s1ij = []
for i in range(3):
mocc = mo_coeff[:,:nocc]
s1mo = reduce(numpy.dot, (mocc[p0:p1].T, s1[i,p0:p1], mocc))
s1mo = s1mo + s1mo.T
s1ij.append(reduce(numpy.dot, (mocc, s1mo, mocc.T)))
# -vhf[s_ij[1]], contribute to f1, *2 because get_veff returns J-.5K
de[k] -= numpy.einsum('xij,ij->x', cc._scf.get_veff(mol, s1ij), dm1ao)*2
# 2e AO integrals dot 2pdm
de[k] -= numpy.einsum('xijkl,ijkl->x', eri0[:,p0:p1], dm2[p0:p1]) * 2
de[k] -= numpy.einsum('xjikl,ijkl->x', eri0[:,p0:p1], dm2[:,p0:p1]) * 2
de[k] -= numpy.einsum('xklij,ijkl->x', eri0[:,p0:p1], dm2[:,:,p0:p1]) * 2
de[k] -= numpy.einsum('xlkij,ijkl->x', eri0[:,p0:p1], dm2[:,:,:,p0:p1]) * 2
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(cc, t1, t2, l1, l2, eris=None, d1=None, d2=None):
if eris is None:
# Note eris are in Chemist's notation
eris = ccsd._ERIS(cc)
if d1 is None:
doo, dov, dvo, dvv = ccsd_rdm.gamma1_intermediates(cc, t1, t2, l1, l2)
else:
doo, dov, dvo, dvv = d1
if d2 is None:
# Note gamma2 are in Chemist's notation
d2 = ccsd_rdm.gamma2_intermediates(cc, t1, t2, l1, l2)
dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov = d2
dvvov = dovvv.transpose(2,3,0,1)
nocc, nvir = t1.shape
dvvvv = pyscf.ao2mo.restore(1, dvvvv, nvir).reshape((nvir,)*4)
# Note Ioo is not hermitian
Ioo =(numpy.einsum('jakb,iakb->ij', dovov, eris.ovov)
+ numpy.einsum('kbja,iakb->ij', dovov, eris.ovov))
Ioo +=(numpy.einsum('jabk,iakb->ij', dovvo, eris.ovov)
+ numpy.einsum('kbaj,iakb->ij', dovvo, eris.ovov)
+ numpy.einsum('jkab,ikab->ij', doovv, eris.oovv)
+ numpy.einsum('kjba,ikab->ij', doovv, eris.oovv))
Ioo +=(numpy.einsum('jmlk,imlk->ij', doooo, eris.oooo) * 2
+ numpy.einsum('mjkl,imlk->ij', doooo, eris.oooo) * 2)
Ioo +=(numpy.einsum('jlka,ilka->ij', dooov, eris.ooov)
+ numpy.einsum('klja,klia->ij', dooov, eris.ooov))
Ioo += numpy.einsum('abjc,icab->ij', dvvov, eris.ovvv)
Ioo += numpy.einsum('ljka,lika->ij', dooov, eris.ooov)
Ioo *= -1
# Note Ivv is not hermitian
Ivv =(numpy.einsum('ibjc,iajc->ab', dovov, eris.ovov)
+ numpy.einsum('jcib,iajc->ab', dovov, eris.ovov))
Ivv +=(numpy.einsum('jcbi,iajc->ab', dovvo, eris.ovov)
+ numpy.einsum('ibcj,iajc->ab', dovvo, eris.ovov)
+ numpy.einsum('jibc,jiac->ab', doovv, eris.oovv)
+ numpy.einsum('ijcb,jiac->ab', doovv, eris.oovv))
Ivv +=(numpy.einsum('bced,aced->ab', dvvvv, eris.vvvv) * 2
+ numpy.einsum('cbde,aced->ab', dvvvv, eris.vvvv) * 2)
Ivv +=(numpy.einsum('dbic,icda->ab', dvvov, eris.ovvv)
+ numpy.einsum('dcib,iadc->ab', dvvov, eris.ovvv))
Ivv += numpy.einsum('bcid,idac->ab', dvvov, eris.ovvv)
Ivv += numpy.einsum('jikb,jika->ab', dooov, eris.ooov)
Ivv *= -1
Ivo =(numpy.einsum('kajb,kijb->ai', dovov, eris.ooov)
+ numpy.einsum('kbja,jikb->ai', dovov, eris.ooov))
Ivo +=(numpy.einsum('acbd,icbd->ai', dvvvv, eris.ovvv) * 2
+ numpy.einsum('cadb,icbd->ai', dvvvv, eris.ovvv) * 2)
Ivo +=(numpy.einsum('jbak,jbik->ai', dovvo, eris.ovoo)
+ numpy.einsum('kabj,jbik->ai', dovvo, eris.ovoo)
+ numpy.einsum('jkab,jkib->ai', doovv, eris.ooov)
+ numpy.einsum('kjba,jkib->ai', doovv, eris.ooov))
Ivo +=(numpy.einsum('dajc,idjc->ai', dvvov, eris.ovov)
+ numpy.einsum('dcja,jidc->ai', dvvov, eris.oovv))
Ivo += numpy.einsum('abjc,ibjc->ai', dvvov, eris.ovov)
Ivo += numpy.einsum('jlka,jlki->ai', dooov, eris.oooo)
Ivo *= -1
Xvo =(numpy.einsum('kj,kjia->ai', doo, eris.ooov) * 2
+ numpy.einsum('kj,kjia->ai', doo, eris.ooov) * 2
- numpy.einsum('kj,kija->ai', doo, eris.ooov)
- numpy.einsum('kj,ijka->ai', doo, eris.ooov))
Xvo +=(numpy.einsum('cb,iacb->ai', dvv, eris.ovvv) * 2
+ numpy.einsum('cb,iacb->ai', dvv, eris.ovvv) * 2
- numpy.einsum('cb,icab->ai', dvv, eris.ovvv)
- numpy.einsum('cb,ibca->ai', dvv, eris.ovvv))
Xvo +=(numpy.einsum('icjb,jbac->ai', dovov, eris.ovvv)
+ numpy.einsum('jcib,jcab->ai', dovov, eris.ovvv))
Xvo +=(numpy.einsum('iklj,ljka->ai', doooo, eris.ooov) * 2
+ numpy.einsum('kijl,ljka->ai', doooo, eris.ooov) * 2)
Xvo +=(numpy.einsum('ibcj,jcab->ai', dovvo, eris.ovvv)
+ numpy.einsum('jcbi,jcab->ai', dovvo, eris.ovvv)
+ numpy.einsum('ijcb,jacb->ai', doovv, eris.ovvv)
+ numpy.einsum('jibc,jacb->ai', doovv, eris.ovvv))
Xvo +=(numpy.einsum('ijkb,jakb->ai', dooov, eris.ovov)
+ numpy.einsum('kjib,kjab->ai', dooov, eris.oovv))
Xvo += numpy.einsum('dbic,dbac->ai', dvvov, eris.vvvv)
Xvo += numpy.einsum('jikb,jakb->ai', dooov, eris.ovov)
Xvo += Ivo
return Ioo, Ivv, Ivo, Xvo
def kernel(cc, t1=None, t2=None, l1=None, l2=None, eris=None, atmlst=None):
if t1 is None: t1 = cc.t1
if t2 is None: t2 = cc.t2
if l1 is None: l1 = cc.l1
if l2 is None: l2 = cc.l2
if eris is None: eris = ccsd._ERIS(cc)
mol = cc.mol
mo_coeff = cc.mo_coeff #FIXME: ensure cc.mo_coeff is canonical orbital
mo_energy = cc.mo_energy
nocc, nvir = t1.shape
nao, nmo = mo_coeff.shape
d1 = ccsd_rdm.gamma1_intermediates(cc, t1, t2, l1, l2)
d2 = ccsd_rdm.gamma2_intermediates(cc, t1, t2, l1, l2)
Ioo, Ivv, Ivo, Xvo = IX_intermediates(cc, t1, t2, l1, l2, eris, d1, d2)
doo, dov, dvo, dvv = d1
dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov = d2
dvvov = dovvv.transpose(2,3,0,1)
dvvvv = pyscf.ao2mo.restore(1, dvvvv, nvir).reshape((nvir,)*4)
dm1mo = response_dm1(cc, 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))
dm0 = numpy.dot(mo_coeff[:,:nocc], mo_coeff[:,:nocc].T)*2
im1 = numpy.zeros_like(dm1ao)
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))
dme0 = grad.rhf.make_rdm1e(cc._scf.mo_energy, mo_coeff, cc._scf.mo_occ)
h1 =-(mol.intor('cint1e_ipkin_sph', comp=3)
+mol.intor('cint1e_ipnuc_sph', comp=3))
s1 =-mol.intor('cint1e_ipovlp_sph', comp=3)
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))
eri0 = mol.intor('cint2e_ip1_sph', 3).reshape(3,nao,nao,nao,nao)
dm2 = numpy.zeros((nmo,)*4)
dm2[:nocc,nocc:,:nocc,nocc:] = dovov
dm2[nocc:,nocc:,nocc:,nocc:] = dvvvv
dm2[:nocc,:nocc,:nocc,:nocc] = doooo
dm2[:nocc,nocc:,nocc:,:nocc] = dovvo
dm2[:nocc,:nocc,nocc:,nocc:] = doovv
dm2[nocc:,nocc:,:nocc,nocc:] = dvvov
dm2[:nocc,:nocc,:nocc,nocc:] = dooov
for i in range(nocc):
dm2[i,i,:,:] += dm1mo
dm2[:,i,i,:] -= dm1mo * .5
for i in range(nocc): # for HF gradeint
for j in range(nocc):
dm2[i,i,j,j] += 1
dm2[i,j,j,i] -= .5
dm2 = numpy.einsum('pjkl,ip->ijkl', dm2, mo_coeff)
dm2 = numpy.einsum('ipkl,jp->ijkl', dm2, mo_coeff)
dm2 = numpy.einsum('ijpl,kp->ijkl', dm2, mo_coeff)
dm2 = numpy.einsum('ijkp,lp->ijkl', dm2, mo_coeff)
if atmlst is None:
atmlst = range(mol.natm)
offsetdic = aorange_by_atom(mol)
de = numpy.empty((mol.natm,3))
for k,ia in enumerate(atmlst):
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
mol.set_rinv_origin(mol.atom_coord(k))
vrinv = -mol.atom_charge(k) * mol.intor('cint1e_iprinv_sph', comp=3)
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]))
s1ij = []
for i in range(3):
mocc = mo_coeff[:,:nocc]
s1mo = reduce(numpy.dot, (mocc[p0:p1].T, s1[i,p0:p1], mocc))
s1mo = s1mo + s1mo.T
s1ij.append(reduce(numpy.dot, (mocc, s1mo, mocc.T)))
# -vhf[s_ij[1]], contribute to f1, *2 because get_veff returns J-.5K
de[k] -= numpy.einsum('xij,ij->x', cc._scf.get_veff(mol, s1ij), dm1ao)*2
# 2e AO integrals dot 2pdm
de[k] -= numpy.einsum('xijkl,ijkl->x', eri0[:,p0:p1], dm2[p0:p1]) * 2
de[k] -= numpy.einsum('xijkl,jikl->x', eri0[:,p0:p1], dm2[:,p0:p1]) * 2
de[k] -= numpy.einsum('xijkl,klij->x', eri0[:,p0:p1], dm2[:,:,p0:p1]) * 2
de[k] -= numpy.einsum('xijkl,klji->x', eri0[:,p0:p1], dm2[:,:,:,p0:p1]) * 2
# HF gradients, J1*2-K1 was merged into previous contraction to dm2
de[k] +=(numpy.einsum('xij,ij->x', h1[:,p0:p1], dm0[p0:p1])
+ numpy.einsum('xji,ij->x', h1[:,p0:p1], dm0[:,p0:p1]))
de[k] +=(numpy.einsum('xij,ij->x', vrinv, dm0)
+ numpy.einsum('xji,ij->x', vrinv, dm0))
de[k] -=(numpy.einsum('xij,ij->x', s1[:,p0:p1], dme0[p0:p1])
+ numpy.einsum('xji,ij->x', s1[:,p0:p1], dme0[:,p0:p1]))
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_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 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 kernel(mycc, t1=None, t2=None, l1=None, l2=None, eris=None, atmlst=None,
grad_hf=None, max_memory=2000, 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 = pyscf.grad.hf.RHF(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, max_memory)
time1 = log.timer('rdm1 intermediates', *time0)
log.debug('Build ccsd rdm2 intermediates')
_d2tmpfile = tempfile.NamedTemporaryFile()
fd2intermediate = h5py.File(_d2tmpfile.name, 'w')
d2 = ccsd_rdm.gamma2_outcore(mycc, t1, t2, l1, l2, fd2intermediate, max_memory)
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, max_memory)
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')
_dm2file = tempfile.NamedTemporaryFile()
fdm2 = h5py.File(_dm2file.name, 'w')
_rdm2_mo2ao(mycc, d2, dm1mo, mo_coeff, fdm2, max_memory)
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 = grad_hf.get_hcore(mol)
s1 = grad_hf.get_ovlp(mol)
zeta = numpy.empty((nmo,nmo))
zeta[:nocc,:nocc] = (mo_energy[:nocc].reshape(-1,1) + mo_energy[:nocc]) * .5
zeta[nocc:,nocc:] = (mo_energy[nocc:].reshape(-1,1) + mo_energy[nocc:]) * .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()
max_memory1 = max_memory - lib.current_memory()[0]
blksize = max(1, int(max_memory1*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
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
ip0 = p0
for b0, b1, nf in shell_prange(mol, shl0, shl1, blksize):
eri1 = gto.moleintor.getints('cint2e_ip1_sph', mol._atm, mol._bas,
mol._env, numpy.arange(b0,b1), comp=3,
aosym='s2kl').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
for i in range(3):
#:tmp = _ccsd.unpack_tril(eri1[i].reshape(-1,nao_pair))
#:vj = numpy.einsum('ijkl,kl->ij', tmp, hf_dm1[ip0:ip0+nf])
#:vk = numpy.einsum('ijkl,jk->il', tmp, hf_dm1[ip0:ip0+nf])
vj, vk = hf_get_jk_incore(eri1[i], hf_dm1)
de[k,i] -=(numpy.einsum('ij,ij->', vj, hf_dm1[ip0:ip0+nf])
- numpy.einsum('ij,ij->', vk, hf_dm1[ip0:ip0+nf])*.5) * 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
