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 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 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 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
