def kernel(cc, t1, t2, l1, l2, eris=None):
if eris is None:
eris = _ERIS(cc, cc.mo_coeff)
mol = cc.mol
mo_coeff = cc.mo_coeff
mo_energy = cc._scf.mo_energy
nao, nmo = mo_coeff.shape
nocc = numpy.count_nonzero(cc.mo_occ > 0)
nvir = nmo - nocc
mo_e_o = mo_energy[:nocc]
mo_e_v = mo_energy[nocc:]
with_frozen = not (cc.frozen is None or cc.frozen is 0)
d1 = _gamma1_intermediates(cc, t1, t2, l1, l2)
d2 = _gamma2_intermediates(cc, t1, t2, l1, l2)
dm2 = ccsd_rdm._make_rdm2(cc, d1, d2, with_dm1=False, with_frozen=False)
eri = ao2mo.restore(1, ao2mo.full(cc.mol, mo_coeff), nmo)
Imat = numpy.einsum('jqrs,iqrs->ij', dm2, eri) * -1
Ioo = Imat[:nocc, :nocc]
Ivv = Imat[nocc:, nocc:]
doo, dov, dvo, dvv = d1
if with_frozen:
OA, VA, OF, VF = index_frozen_active(cc)
doo[OF[:, None], OA] = Ioo[OF[:, None], OA] / lib.direct_sum(
'i-j->ij', mo_e_o[OF], mo_e_o[OA])
doo[OA[:, None], OF] = Ioo[OA[:, None], OF] / lib.direct_sum(
'i-j->ij', mo_e_o[OA], mo_e_o[OF])
dvv[VF[:, None], VA] = Ivv[VF[:, None], VA] / lib.direct_sum(
'a-b->ab', mo_e_v[VF], mo_e_v[VA])
dvv[VA[:, None], VF] = Ivv[VA[:, None], VF] / lib.direct_sum(
'a-b->ab', mo_e_v[VA], mo_e_v[VF])
dm1 = scipy.linalg.block_diag(doo + doo.T, dvv + dvv.T)
dm1ao = reduce(numpy.dot, (mo_coeff, dm1, mo_coeff.T))
vj, vk = cc._scf.get_jk(cc.mol, dm1ao)
Xvo = reduce(numpy.dot,
(mo_coeff[:, nocc:].T, vj * 2 - vk, mo_coeff[:, :nocc]))
Xvo += Imat[:nocc, nocc:].T - Imat[nocc:, :nocc]
dm1 += ccsd_grad._response_dm1(cc, Xvo, eris)
Imat[nocc:, :nocc] = Imat[:nocc, nocc:].T
h1 = -(mol.intor('int1e_ipkin', comp=3) + mol.intor('int1e_ipnuc', comp=3))
s1 = -mol.intor('int1e_ipovlp', comp=3)
zeta = lib.direct_sum('i-j->ij', mo_energy, mo_energy)
eri1 = mol.intor('int2e_ip1', comp=3).reshape(3, nao, nao, nao, nao)
eri1 = numpy.einsum('xipkl,pj->xijkl', eri1, mo_coeff)
eri1 = numpy.einsum('xijpl,pk->xijkl', eri1, mo_coeff)
eri1 = numpy.einsum('xijkp,pl->xijkl', eri1, mo_coeff)
g0 = ao2mo.restore(1, ao2mo.full(mol, mo_coeff), nmo)
de = numpy.empty((mol.natm, 3))
for k, (sh0, sh1, p0, p1) in enumerate(mol.offset_nr_by_atom()):
mol.set_rinv_origin(mol.atom_coord(k))
vrinv = -mol.atom_charge(k) * mol.intor('int1e_iprinv', comp=3)
# 2e AO integrals dot 2pdm
de2 = numpy.zeros(3)
for i in range(3):
g1 = numpy.einsum('pjkl,pi->ijkl', eri1[i, p0:p1], mo_coeff[p0:p1])
g1 = g1 + g1.transpose(1, 0, 2, 3)
g1 = g1 + g1.transpose(2, 3, 0, 1)
g1 *= -1
hx = (numpy.einsum('pq,pi,qj->ij', h1[i, p0:p1], mo_coeff[p0:p1],
mo_coeff) +
reduce(numpy.dot, (mo_coeff.T, vrinv[i], mo_coeff)))
hx = hx + hx.T
sx = numpy.einsum('pq,pi,qj->ij', s1[i, p0:p1], mo_coeff[p0:p1],
mo_coeff)
sx = sx + sx.T
fij = (hx[:nocc, :nocc] -
numpy.einsum('ij,j->ij', sx[:nocc, :nocc], mo_e_o) * .5 -
numpy.einsum('ij,i->ij', sx[:nocc, :nocc], mo_e_o) * .5 -
numpy.einsum('kl,ijlk->ij', sx[:nocc, :nocc],
g0[:nocc, :nocc, :nocc, :nocc]) * 2 +
numpy.einsum('kl,iklj->ij', sx[:nocc, :nocc],
g0[:nocc, :nocc, :nocc, :nocc]) +
numpy.einsum('ijkk->ij', g1[:nocc, :nocc, :nocc, :nocc]) * 2
- numpy.einsum('ikkj->ij', g1[:nocc, :nocc, :nocc, :nocc]))
fab = (hx[nocc:, nocc:] -
numpy.einsum('ij,j->ij', sx[nocc:, nocc:], mo_e_v) * .5 -
numpy.einsum('ij,i->ij', sx[nocc:, nocc:], mo_e_v) * .5 -
numpy.einsum('kl,ijlk->ij', sx[:nocc, :nocc],
g0[nocc:, nocc:, :nocc, :nocc]) * 2 +
numpy.einsum('kl,iklj->ij', sx[:nocc, :nocc],
g0[nocc:, :nocc, :nocc, nocc:]) +
numpy.einsum('ijkk->ij', g1[nocc:, nocc:, :nocc, :nocc]) * 2
- numpy.einsum('ikkj->ij', g1[nocc:, :nocc, :nocc, nocc:]))
if with_frozen:
fij[OA[:, None], OF] -= numpy.einsum(
'ij,j->ij', sx[OA[:, None], OF], mo_e_o[OF]) * .5
fij[OA[:, None], OF] += numpy.einsum(
'ij,i->ij', sx[OA[:, None], OF], mo_e_o[OA]) * .5
fij[OF[:, None], OA] -= numpy.einsum(
'ij,j->ij', sx[OF[:, None], OA], mo_e_o[OA]) * .5
fij[OF[:, None], OA] += numpy.einsum(
'ij,i->ij', sx[OF[:, None], OA], mo_e_o[OF]) * .5
fab[VA[:, None], VF] -= numpy.einsum(
'ij,j->ij', sx[VA[:, None], VF], mo_e_v[VF]) * .5
fab[VA[:, None], VF] += numpy.einsum(
'ij,i->ij', sx[VA[:, None], VF], mo_e_v[VA]) * .5
fab[VF[:, None], VA] -= numpy.einsum(
'ij,j->ij', sx[VF[:, None], VA], mo_e_v[VA]) * .5
fab[VF[:, None], VA] += numpy.einsum(
'ij,i->ij', sx[VF[:, None], VA], mo_e_v[VF]) * .5
fai = (
hx[nocc:, :nocc] -
numpy.einsum('ai,i->ai', sx[nocc:, :nocc], mo_e_o) -
numpy.einsum('kl,ijlk->ij', sx[:nocc, :nocc],
g0[nocc:, :nocc, :nocc, :nocc]) * 2 +
numpy.einsum('kl,iklj->ij', sx[:nocc, :nocc],
g0[nocc:, :nocc, :nocc, :nocc]) +
numpy.einsum('ijkk->ij', g1[nocc:, :nocc, :nocc, :nocc]) * 2 -
numpy.einsum('ikkj->ij', g1[nocc:, :nocc, :nocc, :nocc]))
f1 = numpy.zeros((nmo, nmo))
f1[:nocc, :nocc] = fij
f1[nocc:, nocc:] = fab
f1[nocc:, :nocc] = fai
f1[:nocc, nocc:] = fai.T
de2[i] += numpy.einsum('ij,ji', f1, dm1)
de2[i] += numpy.einsum('ij,ji', sx, Imat)
de2[i] += numpy.einsum('iajb,iajb', dm2, g1) * .5
de[k] = de2
return de
def kernel(cc, t1, t2, l1, l2, eris=None):
if eris is None:
eris = _ERIS(cc, cc.mo_coeff)
mol = cc.mol
mo_coeff = cc.mo_coeff
mo_energy = cc._scf.mo_energy
nao, nmo = mo_coeff.shape
nocc = numpy.count_nonzero(cc.mo_occ > 0)
nvir = nmo - nocc
mo_e_o = mo_energy[:nocc]
mo_e_v = mo_energy[nocc:]
with_frozen = not (cc.frozen is None or cc.frozen is 0)
d1 = _gamma1_intermediates(cc, t1, t2, l1, l2)
d2 = _gamma2_intermediates(cc, t1, t2, l1, l2)
dm2 = ccsd_rdm._make_rdm2(cc, d1, d2, with_dm1=False, with_frozen=False)
eri = ao2mo.restore(1, ao2mo.full(cc.mol, mo_coeff), nmo)
Imat = numpy.einsum('jqrs,iqrs->ij', dm2, eri) * -1
Ioo = Imat[:nocc,:nocc]
Ivv = Imat[nocc:,nocc:]
doo, dov, dvo, dvv = d1
if with_frozen:
OA, VA, OF, VF = index_frozen_active(cc)
doo[OF[:,None],OA] = Ioo[OF[:,None],OA] / lib.direct_sum('i-j->ij', mo_e_o[OF], mo_e_o[OA])
doo[OA[:,None],OF] = Ioo[OA[:,None],OF] / lib.direct_sum('i-j->ij', mo_e_o[OA], mo_e_o[OF])
dvv[VF[:,None],VA] = Ivv[VF[:,None],VA] / lib.direct_sum('a-b->ab', mo_e_v[VF], mo_e_v[VA])
dvv[VA[:,None],VF] = Ivv[VA[:,None],VF] / lib.direct_sum('a-b->ab', mo_e_v[VA], mo_e_v[VF])
dm1 = scipy.linalg.block_diag(doo+doo.T, dvv+dvv.T)
dm1ao = reduce(numpy.dot, (mo_coeff, dm1, mo_coeff.T))
vj, vk = cc._scf.get_jk(cc.mol, dm1ao)
Xvo = reduce(numpy.dot, (mo_coeff[:,nocc:].T, vj*2-vk, mo_coeff[:,:nocc]))
Xvo += Imat[:nocc,nocc:].T - Imat[nocc:,:nocc]
dm1 += ccsd_grad._response_dm1(cc, Xvo, eris)
Imat[nocc:,:nocc] = Imat[:nocc,nocc:].T
h1 =-(mol.intor('int1e_ipkin', comp=3)
+mol.intor('int1e_ipnuc', comp=3))
s1 =-mol.intor('int1e_ipovlp', comp=3)
zeta = lib.direct_sum('i-j->ij', mo_energy, mo_energy)
eri1 = mol.intor('int2e_ip1', comp=3).reshape(3,nao,nao,nao,nao)
eri1 = numpy.einsum('xipkl,pj->xijkl', eri1, mo_coeff)
eri1 = numpy.einsum('xijpl,pk->xijkl', eri1, mo_coeff)
eri1 = numpy.einsum('xijkp,pl->xijkl', eri1, mo_coeff)
g0 = ao2mo.restore(1, ao2mo.full(mol, mo_coeff), nmo)
de = numpy.empty((mol.natm,3))
for k,(sh0, sh1, p0, p1) in enumerate(mol.offset_nr_by_atom()):
mol.set_rinv_origin(mol.atom_coord(k))
vrinv = -mol.atom_charge(k) * mol.intor('int1e_iprinv', comp=3)
# 2e AO integrals dot 2pdm
de2 = numpy.zeros(3)
for i in range(3):
g1 = numpy.einsum('pjkl,pi->ijkl', eri1[i,p0:p1], mo_coeff[p0:p1])
g1 = g1 + g1.transpose(1,0,2,3)
g1 = g1 + g1.transpose(2,3,0,1)
g1 *= -1
hx =(numpy.einsum('pq,pi,qj->ij', h1[i,p0:p1], mo_coeff[p0:p1], mo_coeff)
+ reduce(numpy.dot, (mo_coeff.T, vrinv[i], mo_coeff)))
hx = hx + hx.T
sx = numpy.einsum('pq,pi,qj->ij', s1[i,p0:p1], mo_coeff[p0:p1], mo_coeff)
sx = sx + sx.T
fij =(hx[:nocc,:nocc]
- numpy.einsum('ij,j->ij', sx[:nocc,:nocc], mo_e_o) * .5
- numpy.einsum('ij,i->ij', sx[:nocc,:nocc], mo_e_o) * .5
- numpy.einsum('kl,ijlk->ij', sx[:nocc,:nocc],
g0[:nocc,:nocc,:nocc,:nocc]) * 2
+ numpy.einsum('kl,iklj->ij', sx[:nocc,:nocc],
g0[:nocc,:nocc,:nocc,:nocc])
+ numpy.einsum('ijkk->ij', g1[:nocc,:nocc,:nocc,:nocc]) * 2
- numpy.einsum('ikkj->ij', g1[:nocc,:nocc,:nocc,:nocc]))
fab =(hx[nocc:,nocc:]
- numpy.einsum('ij,j->ij', sx[nocc:,nocc:], mo_e_v) * .5
- numpy.einsum('ij,i->ij', sx[nocc:,nocc:], mo_e_v) * .5
- numpy.einsum('kl,ijlk->ij', sx[:nocc,:nocc],
g0[nocc:,nocc:,:nocc,:nocc]) * 2
+ numpy.einsum('kl,iklj->ij', sx[:nocc,:nocc],
g0[nocc:,:nocc,:nocc,nocc:])
+ numpy.einsum('ijkk->ij', g1[nocc:,nocc:,:nocc,:nocc]) * 2
- numpy.einsum('ikkj->ij', g1[nocc:,:nocc,:nocc,nocc:]))
if with_frozen:
fij[OA[:,None],OF] -= numpy.einsum('ij,j->ij', sx[OA[:,None],OF], mo_e_o[OF]) * .5
fij[OA[:,None],OF] += numpy.einsum('ij,i->ij', sx[OA[:,None],OF], mo_e_o[OA]) * .5
fij[OF[:,None],OA] -= numpy.einsum('ij,j->ij', sx[OF[:,None],OA], mo_e_o[OA]) * .5
fij[OF[:,None],OA] += numpy.einsum('ij,i->ij', sx[OF[:,None],OA], mo_e_o[OF]) * .5
fab[VA[:,None],VF] -= numpy.einsum('ij,j->ij', sx[VA[:,None],VF], mo_e_v[VF]) * .5
fab[VA[:,None],VF] += numpy.einsum('ij,i->ij', sx[VA[:,None],VF], mo_e_v[VA]) * .5
fab[VF[:,None],VA] -= numpy.einsum('ij,j->ij', sx[VF[:,None],VA], mo_e_v[VA]) * .5
fab[VF[:,None],VA] += numpy.einsum('ij,i->ij', sx[VF[:,None],VA], mo_e_v[VF]) * .5
fai =(hx[nocc:,:nocc]
- numpy.einsum('ai,i->ai', sx[nocc:,:nocc], mo_e_o)
- numpy.einsum('kl,ijlk->ij', sx[:nocc,:nocc],
g0[nocc:,:nocc,:nocc,:nocc]) * 2
+ numpy.einsum('kl,iklj->ij', sx[:nocc,:nocc],
g0[nocc:,:nocc,:nocc,:nocc])
+ numpy.einsum('ijkk->ij', g1[nocc:,:nocc,:nocc,:nocc]) * 2
- numpy.einsum('ikkj->ij', g1[nocc:,:nocc,:nocc,:nocc]))
f1 = numpy.zeros((nmo,nmo))
f1[:nocc,:nocc] = fij
f1[nocc:,nocc:] = fab
f1[nocc:,:nocc] = fai
f1[:nocc,nocc:] = fai.T
de2[i] += numpy.einsum('ij,ji', f1, dm1)
de2[i] += numpy.einsum('ij,ji', sx, Imat)
de2[i] += numpy.einsum('iajb,iajb', dm2, g1) * .5
de[k] = de2
return de