def _partial_hess_ejk(hessobj,
mo_energy=None,
mo_coeff=None,
mo_occ=None,
atmlst=None,
max_memory=4000,
verbose=None,
with_k=True):
log = logger.new_logger(hessobj, verbose)
time0 = t1 = (time.clock(), time.time())
mol = hessobj.mol
mf = hessobj.base
if mo_energy is None: mo_energy = mf.mo_energy
if mo_occ is None: mo_occ = mf.mo_occ
if mo_coeff is None: mo_coeff = mf.mo_coeff
if atmlst is None: atmlst = range(mol.natm)
nao, nmo = mo_coeff[0].shape
mocca = mo_coeff[0][:, mo_occ[0] > 0]
moccb = mo_coeff[1][:, mo_occ[1] > 0]
nocca = mocca.shape[1]
noccb = moccb.shape[1]
dm0a = numpy.dot(mocca, mocca.T)
dm0b = numpy.dot(moccb, moccb.T)
dm0 = dm0a + dm0b
# Energy weighted density matrix
mo_ea = mo_energy[0][mo_occ[0] > 0]
mo_eb = mo_energy[1][mo_occ[1] > 0]
dme0 = numpy.einsum('pi,qi,i->pq', mocca, mocca, mo_ea)
dme0 += numpy.einsum('pi,qi,i->pq', moccb, moccb, mo_eb)
auxmol = hessobj.base.with_df.auxmol
naux = auxmol.nao
nbas = mol.nbas
auxslices = auxmol.aoslice_by_atom()
aoslices = mol.aoslice_by_atom()
aux_loc = auxmol.ao_loc
blksize = min(480, hessobj.max_memory * .3e6 / 8 / nao**2)
aux_ranges = ao2mo.outcore.balance_partition(auxmol.ao_loc, blksize)
hcore_deriv = hessobj.hcore_generator(mol)
s1aa, s1ab, s1a = rhf_hess.get_ovlp(mol)
ftmp = lib.H5TmpFile()
get_int3c = _int3c_wrapper(mol, auxmol, 'int3c2e', 's1')
# Without RI basis response
# (20|0)(0|00)
# (11|0)(0|00)
# (10|0)(0|10)
int2c = auxmol.intor('int2c2e', aosym='s1')
int2c_low = scipy.linalg.cho_factor(int2c, lower=True)
int2c_ip1 = auxmol.intor('int2c2e_ip1', aosym='s1')
rhoj0_P = 0
if with_k:
if hessobj.max_memory * .4e6 / 8 < naux * nocca * (nocca + nao):
raise RuntimeError(
'Memory not enough. You need to increase mol.max_memory')
rhok0a_Pl_ = np.empty((naux, nao, nocca))
rhok0b_Pl_ = np.empty((naux, nao, noccb))
for i, (shl0, shl1, p0, p1) in enumerate(aoslices):
int3c = get_int3c((shl0, shl1, 0, nbas, 0, auxmol.nbas))
rhoj0_P += np.einsum('klp,kl->p', int3c, dm0[p0:p1])
if with_k:
tmp = lib.einsum('ijp,jk->pik', int3c, mocca)
tmp = scipy.linalg.cho_solve(int2c_low,
tmp.reshape(naux, -1),
overwrite_b=True)
rhok0a_Pl_[:, p0:p1] = tmp.reshape(naux, p1 - p0, nocca)
tmp = lib.einsum('ijp,jk->pik', int3c, moccb)
tmp = scipy.linalg.cho_solve(int2c_low,
tmp.reshape(naux, -1),
overwrite_b=True)
rhok0b_Pl_[:, p0:p1] = tmp.reshape(naux, p1 - p0, noccb)
int3c = tmp = None
rhoj0_P = scipy.linalg.cho_solve(int2c_low, rhoj0_P)
get_int3c_ipip1 = _int3c_wrapper(mol, auxmol, 'int3c2e_ipip1', 's1')
vj1_diag = 0
vk1a_diag = 0
vk1b_diag = 0
for shl0, shl1, nL in aux_ranges:
shls_slice = (0, nbas, 0, nbas, shl0, shl1)
p0, p1 = aux_loc[shl0], aux_loc[shl1]
int3c_ipip1 = get_int3c_ipip1(shls_slice)
vj1_diag += np.einsum('xijp,p->xij', int3c_ipip1,
rhoj0_P[p0:p1]).reshape(3, 3, nao, nao)
if with_k:
tmp = lib.einsum('Plj,Jj->PlJ', rhok0a_Pl_[p0:p1], mocca)
vk1a_diag += lib.einsum('xijp,plj->xil', int3c_ipip1,
tmp).reshape(3, 3, nao, nao)
tmp = lib.einsum('Plj,Jj->PlJ', rhok0b_Pl_[p0:p1], moccb)
vk1b_diag += lib.einsum('xijp,plj->xil', int3c_ipip1,
tmp).reshape(3, 3, nao, nao)
vhfa_diag = vj1_diag - vk1a_diag
vhfb_diag = vj1_diag - vk1b_diag
t1 = log.timer_debug1('contracting int2e_ipip1', *t1)
int3c_ipip1 = get_int3c_ipip1 = tmp = None
get_int3c_ip1 = _int3c_wrapper(mol, auxmol, 'int3c2e_ip1', 's1')
rho_ip1 = ftmp.create_dataset('rho_ip1', (nao, nao, naux, 3), 'f8')
rhoka_ip1_IkP = ftmp.create_group('rhoka_ip1_IkP')
rhokb_ip1_IkP = ftmp.create_group('rhokb_ip1_IkP')
rhoka_ip1_PkI = ftmp.create_group('rhoka_ip1_PkI')
rhokb_ip1_PkI = ftmp.create_group('rhokb_ip1_PkI')
rhoj1 = np.empty((mol.natm, naux, 3))
wj1 = np.empty((mol.natm, naux, 3))
for i0, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = aoslices[ia]
shls_slice = (shl0, shl1, 0, nbas, 0, auxmol.nbas)
int3c_ip1 = get_int3c_ip1(shls_slice)
tmp_ip1 = scipy.linalg.cho_solve(int2c_low,
int3c_ip1.reshape(-1, naux).T,
overwrite_b=True).reshape(
naux, 3, p1 - p0, nao)
rhoj1[i0] = np.einsum('pxij,ji->px', tmp_ip1, dm0[:, p0:p1])
wj1[i0] = np.einsum('xijp,ji->px', int3c_ip1, dm0[:, p0:p1])
rho_ip1[p0:p1] = tmp_ip1.transpose(2, 3, 0, 1)
if with_k:
tmp = lib.einsum('pykl,li->ikpy', tmp_ip1, dm0a)
rhoka_ip1_IkP['%.4d' % ia] = tmp
rhoka_ip1_PkI['%.4d' % ia] = tmp.transpose(2, 1, 0, 3)
tmp = None
tmp = lib.einsum('pykl,li->ikpy', tmp_ip1, dm0b)
rhokb_ip1_IkP['%.4d' % ia] = tmp
rhokb_ip1_PkI['%.4d' % ia] = tmp.transpose(2, 1, 0, 3)
tmp = None
ej = lib.einsum('ipx,jpy->ijxy', rhoj1, wj1) * 4
ek = np.zeros_like(ej)
e1 = np.zeros_like(ej)
rhoj1 = wj1 = None
if with_k:
vk2a_buf = 0
vk2b_buf = 0
for shl0, shl1, nL in aux_ranges:
shls_slice = (0, nbas, 0, nbas, shl0, shl1)
p0, p1 = aux_loc[shl0], aux_loc[shl1]
int3c_ip1 = get_int3c_ip1(shls_slice)
vk2a_buf += lib.einsum('xijp,pkjy->xyki', int3c_ip1,
_load_dim0(rhoka_ip1_PkI, p0, p1))
vk2b_buf += lib.einsum('xijp,pkjy->xyki', int3c_ip1,
_load_dim0(rhokb_ip1_PkI, p0, p1))
get_int3c_ip2 = _int3c_wrapper(mol, auxmol, 'int3c2e_ip2', 's1')
wj_ip2 = np.empty((naux, 3))
wka_ip2_Ipk = ftmp.create_dataset('wka_ip2', (nao, naux, 3, nao), 'f8')
wkb_ip2_Ipk = ftmp.create_dataset('wkb_ip2', (nao, naux, 3, nao), 'f8')
if hessobj.auxbasis_response > 1:
wka_ip2_P__ = np.empty((naux, 3, nocca, nocca))
wkb_ip2_P__ = np.empty((naux, 3, noccb, noccb))
for shl0, shl1, nL in aux_ranges:
shls_slice = (0, nbas, 0, nbas, shl0, shl1)
p0, p1 = aux_loc[shl0], aux_loc[shl1]
int3c_ip2 = get_int3c_ip2(shls_slice)
wj_ip2[p0:p1] = np.einsum('yklp,lk->py', int3c_ip2, dm0)
if with_k:
wka_ip2_Ipk[:, p0:p1] = lib.einsum('yklp,il->ipyk', int3c_ip2,
dm0a)
wkb_ip2_Ipk[:, p0:p1] = lib.einsum('yklp,il->ipyk', int3c_ip2,
dm0b)
if hessobj.auxbasis_response > 1:
wka_ip2_P__[p0:p1] = lib.einsum('xuvp,ui,vj->pxij', int3c_ip2,
mocca, mocca)
wkb_ip2_P__[p0:p1] = lib.einsum('xuvp,ui,vj->pxij', int3c_ip2,
moccb, moccb)
int3c_ip2 = None
if hessobj.auxbasis_response > 1:
get_int3c_ipip2 = _int3c_wrapper(mol, auxmol, 'int3c2e_ipip2', 's1')
rhok0a_P__ = lib.einsum('plj,li->pij', rhok0a_Pl_, mocca)
rhok0b_P__ = lib.einsum('plj,li->pij', rhok0b_Pl_, moccb)
rho2c_0 = lib.einsum('pij,qij->pq', rhok0a_P__, rhok0a_P__)
rho2c_0 += lib.einsum('pij,qij->pq', rhok0b_P__, rhok0b_P__)
int2c_inv = np.linalg.inv(int2c)
int2c_ipip1 = auxmol.intor('int2c2e_ipip1', aosym='s1')
int2c_ip_ip = lib.einsum('xpq,qr,ysr->xyps', int2c_ip1, int2c_inv,
int2c_ip1)
int2c_ip_ip -= auxmol.intor('int2c2e_ip1ip2',
aosym='s1').reshape(3, 3, naux, naux)
int2c = int2c_low = None
get_int3c_ipvip1 = _int3c_wrapper(mol, auxmol, 'int3c2e_ipvip1', 's1')
get_int3c_ip1ip2 = _int3c_wrapper(mol, auxmol, 'int3c2e_ip1ip2', 's1')
for i0, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = aoslices[ia]
shls_slice = (shl0, shl1, 0, nbas, 0, auxmol.nbas)
# (10|0)(0|10) without response of RI basis
if with_k:
int3c_ip1 = get_int3c_ip1(shls_slice)
vk1a = lib.einsum('xijp,ikpy->xykj', int3c_ip1,
_load_dim0(rhoka_ip1_IkP, p0, p1))
vk1b = lib.einsum('xijp,ikpy->xykj', int3c_ip1,
_load_dim0(rhokb_ip1_IkP, p0, p1))
vk1a[:, :, :, p0:p1] += vk2a_buf[:, :, :, p0:p1]
vk1b[:, :, :, p0:p1] += vk2b_buf[:, :, :, p0:p1]
t1 = log.timer_debug1('contracting int2e_ip1ip2 for atom %d' % ia, *t1)
int3c_ip1 = None
# (11|0)(0|00) without response of RI basis
int3c_ipvip1 = get_int3c_ipvip1(shls_slice)
vj1 = np.einsum('xijp,p->xji', int3c_ipvip1,
rhoj0_P).reshape(3, 3, nao, p1 - p0)
if with_k:
tmp = lib.einsum('pki,ji->pkj', rhok0a_Pl_, mocca[p0:p1])
vk1a += lib.einsum('xijp,pki->xjk', int3c_ipvip1,
tmp).reshape(3, 3, nao, nao)
tmp = lib.einsum('pki,ji->pkj', rhok0b_Pl_, moccb[p0:p1])
vk1b += lib.einsum('xijp,pki->xjk', int3c_ipvip1,
tmp).reshape(3, 3, nao, nao)
t1 = log.timer_debug1('contracting int2e_ipvip1 for atom %d' % ia, *t1)
int3c_ipvip1 = tmp = None
s1ao = numpy.zeros((3, nao, nao))
s1ao[:, p0:p1] += s1a[:, p0:p1]
s1ao[:, :, p0:p1] += s1a[:, p0:p1].transpose(0, 2, 1)
s1ooa = numpy.einsum('xpq,pi,qj->xij', s1ao, mocca, mocca)
s1oob = numpy.einsum('xpq,pi,qj->xij', s1ao, moccb, moccb)
e1[i0, i0] -= numpy.einsum('xypq,pq->xy', s1aa[:, :, p0:p1],
dme0[p0:p1]) * 2
ej[i0, i0] += numpy.einsum('xypq,pq->xy', vj1_diag[:, :, p0:p1],
dm0[p0:p1]) * 2
if with_k:
ek[i0, i0] += numpy.einsum('xypq,pq->xy', vk1a_diag[:, :, p0:p1],
dm0a[p0:p1]) * 2
ek[i0, i0] += numpy.einsum('xypq,pq->xy', vk1b_diag[:, :, p0:p1],
dm0b[p0:p1]) * 2
for j0, ja in enumerate(atmlst[:i0 + 1]):
q0, q1 = aoslices[ja][2:]
ej[i0, j0] += numpy.einsum('xypq,pq->xy', vj1[:, :, q0:q1],
dm0[q0:q1, p0:p1]) * 2
e1[i0, j0] -= numpy.einsum('xypq,pq->xy', s1ab[:, :, p0:p1, q0:q1],
dme0[p0:p1, q0:q1]) * 2
if with_k:
ek[i0, j0] += numpy.einsum('xypq,pq->xy', vk1a[:, :, q0:q1],
dm0a[q0:q1]) * 2
ek[i0, j0] += numpy.einsum('xypq,pq->xy', vk1b[:, :, q0:q1],
dm0b[q0:q1]) * 2
h1ao = hcore_deriv(ia, ja)
e1[i0, j0] += numpy.einsum('xypq,pq->xy', h1ao, dm0)
# The first order RI basis response
# (10|1)(0|00)
# (10|0)(1|0)(0|00)
# (10|0)(0|1)(0|00)
# (10|0)(1|00)
if hessobj.auxbasis_response:
wk1_Pij = rho_ip1[p0:p1].transpose(2, 3, 0, 1)
rhoj1_P = np.einsum('pxij,ji->px', wk1_Pij, dm0[:, p0:p1])
# (10|1)(0|0)(0|00)
int3c_ip1ip2 = get_int3c_ip1ip2(shls_slice)
wj11_p = np.einsum('xijp,ji->xp', int3c_ip1ip2, dm0[:, p0:p1])
# (10|0)(1|0)(0|00)
wj0_01 = np.einsum('ypq,q->yp', int2c_ip1, rhoj0_P)
if with_k:
rhok0_P_I = lib.einsum('plj,il->pji', rhok0a_Pl_, dm0a[p0:p1])
rhok0_PJI = lib.einsum('pji,Jj->pJi', rhok0_P_I, mocca)
rhok0_P_I = lib.einsum('plj,il->pji', rhok0b_Pl_, dm0b[p0:p1])
rhok0_PJI += lib.einsum('pji,Jj->pJi', rhok0_P_I, moccb)
wk1_pJI = lib.einsum('ypq,qji->ypji', int2c_ip1, rhok0_PJI)
wk1_IpJ = lib.einsum('ipyk,kj->ipyj', wka_ip2_Ipk[p0:p1], dm0a)
wk1_IpJ += lib.einsum('ipyk,kj->ipyj', wkb_ip2_Ipk[p0:p1],
dm0b)
rho2c_PQ = lib.einsum('pxij,qji->xqp', wk1_Pij, rhok0_PJI)
for j0, (q0, q1) in enumerate(auxslices[:, 2:]):
# (10|1)(0|00)
_ej = np.einsum('xp,p->x', wj11_p[:, q0:q1],
rhoj0_P[q0:q1]).reshape(3, 3)
# (10|0)(0|1)(0|00)
_ej -= lib.einsum('yqp,q,px->xy', int2c_ip1[:, q0:q1],
rhoj0_P[q0:q1], rhoj1_P)
# (10|0)(1|0)(0|00)
_ej -= lib.einsum('px,yp->xy', rhoj1_P[q0:q1], wj0_01[:,
q0:q1])
# (10|0)(1|00)
_ej += lib.einsum('px,py->xy', rhoj1_P[q0:q1], wj_ip2[q0:q1])
if hessobj.auxbasis_response > 1:
ej[i0, j0] += _ej * 2
ej[j0, i0] += _ej.T * 2
else:
ej[i0, j0] += _ej
ej[j0, i0] += _ej.T
if with_k:
_ek = lib.einsum('xijp,pji->x', int3c_ip1ip2[:, :, :,
q0:q1],
rhok0_PJI[q0:q1]).reshape(3, 3)
_ek -= lib.einsum('pxij,ypji->xy', wk1_Pij[q0:q1],
wk1_pJI[:, q0:q1])
_ek -= lib.einsum('xqp,yqp->xy', rho2c_PQ[:, q0:q1],
int2c_ip1[:, q0:q1])
_ek += lib.einsum('pxij,ipyj->xy', wk1_Pij[q0:q1],
wk1_IpJ[:, q0:q1])
if hessobj.auxbasis_response > 1:
ek[i0, j0] += _ek * 2
ek[j0, i0] += _ek.T * 2
else:
ek[i0, j0] += _ek
ek[j0, i0] += _ek.T
int3c_ip1ip2 = None
# The second order RI basis response
if hessobj.auxbasis_response > 1:
# (00|2)(0|00)
# (00|0)(2|0)(0|00)
shl0, shl1, p0, p1 = auxslices[ia]
shls_slice = (0, nbas, 0, nbas, shl0, shl1)
int3c_ipip2 = get_int3c_ipip2(shls_slice)
ej[i0, i0] += np.einsum('xijp,ji,p->x', int3c_ipip2, dm0,
rhoj0_P[p0:p1]).reshape(3, 3)
ej[i0, i0] -= np.einsum('p,xpq,q->x', rhoj0_P[p0:p1],
int2c_ipip1[:,
p0:p1], rhoj0_P).reshape(3, 3)
if with_k:
rhok0_PJI = lib.einsum('Pij,Jj,Ii->PJI', rhok0a_P__[p0:p1],
mocca, mocca)
rhok0_PJI += lib.einsum('Pij,Jj,Ii->PJI', rhok0b_P__[p0:p1],
moccb, moccb)
ek[i0, i0] += np.einsum('xijp,pij->x', int3c_ipip2,
rhok0_PJI).reshape(3, 3)
ek[i0, i0] -= np.einsum('pq,xpq->x', rho2c_0[p0:p1],
int2c_ipip1[:, p0:p1]).reshape(3, 3)
rhok0_PJI = None
# (00|0)(1|1)(0|00)
# (00|1)(1|0)(0|00)
# (00|1)(0|1)(0|00)
# (00|1)(1|00)
rhoj1 = lib.einsum('px,pq->xq', wj_ip2[p0:p1], int2c_inv[p0:p1])
# (00|0)(0|1)(1|0)(0|00)
rhoj0_01 = lib.einsum('xp,pq->xq', wj0_01[:, p0:p1],
int2c_inv[p0:p1])
# (00|0)(1|0)(1|0)(0|00)
ip1_2c_2c = lib.einsum('xpq,qr->xpr', int2c_ip1[:, p0:p1],
int2c_inv)
rhoj0_10 = lib.einsum('p,xpq->xq', rhoj0_P[p0:p1], ip1_2c_2c)
if with_k:
# (00|0)(0|1)(1|0)(0|00)
ip1_rho2c = .5 * lib.einsum('xpq,qr->xpr', int2c_ip1[:, p0:p1],
rho2c_0)
rho2c_1 = lib.einsum('xrq,rp->xpq', ip1_rho2c,
int2c_inv[p0:p1])
# (00|0)(1|0)(1|0)(0|00)
rho2c_1 += lib.einsum('xrp,rq->xpq', ip1_2c_2c, rho2c_0[p0:p1])
# (00|1)(0|1)(0|00)
# (00|1)(1|0)(0|00)
int3c_ip2 = get_int3c_ip2(shls_slice)
tmp = lib.einsum('xuvr,vj,ui,qij,rp->xpq', int3c_ip2, mocca,
mocca, rhok0a_P__, int2c_inv[p0:p1])
tmp += lib.einsum('xuvr,vj,ui,qij,rp->xpq', int3c_ip2, moccb,
moccb, rhok0b_P__, int2c_inv[p0:p1])
rho2c_1 -= tmp
rho2c_1 -= tmp.transpose(0, 2, 1)
int3c_ip2 = tmp = None
for j0, (q0, q1) in enumerate(auxslices[:, 2:]):
_ej = 0
# (00|0)(1|1)(0|00)
# (00|0)(1|0)(0|1)(0|00)
_ej += .5 * np.einsum('p,xypq,q->xy', rhoj0_P[p0:p1],
int2c_ip_ip[:, :, p0:p1,
q0:q1], rhoj0_P[q0:q1])
# (00|1)(1|0)(0|00)
_ej -= lib.einsum('xp,yp->xy', rhoj1[:, q0:q1], wj0_01[:,
q0:q1])
# (00|1)(1|00)
_ej += .5 * lib.einsum('xp,py->xy', rhoj1[:, q0:q1],
wj_ip2[q0:q1])
# (00|0)(0|1)(1|0)(0|00)
_ej += .5 * np.einsum('xp,yp->xy', rhoj0_01[:, q0:q1],
wj0_01[:, q0:q1])
# (00|1)(0|1)(0|00)
_ej -= lib.einsum('yqp,q,xp->xy', int2c_ip1[:, q0:q1],
rhoj0_P[q0:q1], rhoj1)
# (00|0)(1|0)(1|0)(0|00)
_ej += np.einsum('xp,yp->xy', rhoj0_10[:, q0:q1],
wj0_01[:, q0:q1])
ej[i0, j0] += _ej
ej[j0, i0] += _ej.T
if with_k:
# (00|0)(1|1)(0|00)
# (00|0)(1|0)(0|1)(0|00)
_ek = .5 * np.einsum('pq,xypq->xy', rho2c_0[p0:p1, q0:q1],
int2c_ip_ip[:, :, p0:p1, q0:q1])
# (00|1)(0|1)(0|00)
# (00|1)(1|0)(0|00)
# (00|0)(0|1)(1|0)(0|00)
# (00|0)(1|0)(1|0)(0|00)
_ek += np.einsum('xpq,ypq->xy', rho2c_1[:, q0:q1],
int2c_ip1[:, q0:q1])
# (00|1)(1|00)
_ek += .5 * lib.einsum(
'pxij,pq,qyij->xy', wka_ip2_P__[p0:p1],
int2c_inv[p0:p1, q0:q1], wka_ip2_P__[q0:q1])
_ek += .5 * lib.einsum(
'pxij,pq,qyij->xy', wkb_ip2_P__[p0:p1],
int2c_inv[p0:p1, q0:q1], wkb_ip2_P__[q0:q1])
ek[i0, j0] += _ek
ek[j0, i0] += _ek.T
for i0, ia in enumerate(atmlst):
for j0 in range(i0):
e1[j0, i0] = e1[i0, j0].T
ej[j0, i0] = ej[i0, j0].T
ek[j0, i0] = ek[i0, j0].T
log.timer('UHF partial hessian', *time0)
return e1, ej, ek
def _gen_jk(hessobj,
mo_coeff,
mo_occ,
chkfile=None,
atmlst=None,
verbose=None,
with_k=True):
time0 = t1 = (time.clock(), time.time())
mol = hessobj.mol
if atmlst is None:
atmlst = range(mol.natm)
auxmol = hessobj.base.with_df.auxmol
nbas = mol.nbas
auxslices = auxmol.aoslice_by_atom()
aux_loc = auxmol.ao_loc
nao, nmo = mo_coeff[0].shape
mocca = mo_coeff[0][:, mo_occ[0] > 0]
moccb = mo_coeff[1][:, mo_occ[1] > 0]
nocca = mocca.shape[1]
noccb = moccb.shape[1]
dm0a = numpy.dot(mocca, mocca.T)
dm0b = numpy.dot(moccb, moccb.T)
dm0 = dm0a + dm0b
hcore_deriv = hessobj.base.nuc_grad_method().hcore_generator(mol)
get_int3c = _int3c_wrapper(mol, auxmol, 'int3c2e', 's1')
aoslices = mol.aoslice_by_atom()
naux = auxmol.nao
ftmp = lib.H5TmpFile()
rho0_Pij = ftmp.create_group('rho0_Pij')
wj_Pij = ftmp.create_group('wj_Pij')
int2c = auxmol.intor('int2c2e', aosym='s1')
int2c_low = scipy.linalg.cho_factor(int2c, lower=True)
int2c_ip1 = auxmol.intor('int2c2e_ip1', aosym='s1')
rhoj0_P = 0
if with_k:
rhok0a_Pl_ = np.empty((naux, nao, nocca))
rhok0b_Pl_ = np.empty((naux, nao, noccb))
for i, (shl0, shl1, p0, p1) in enumerate(aoslices):
int3c = get_int3c((shl0, shl1, 0, nbas, 0, auxmol.nbas))
coef3c = scipy.linalg.cho_solve(int2c_low,
int3c.reshape(-1, naux).T,
overwrite_b=True)
rho0_Pij['%.4d' % i] = coef3c = coef3c.reshape(naux, p1 - p0, nao)
rhoj0_P += np.einsum('pkl,kl->p', coef3c, dm0[p0:p1])
if with_k:
rhok0a_Pl_[:, p0:p1] = lib.einsum('pij,jk->pik', coef3c, mocca)
rhok0b_Pl_[:, p0:p1] = lib.einsum('pij,jk->pik', coef3c, moccb)
if hessobj.auxbasis_response:
wj_Pij['%.4d' % i] = lib.einsum('xqp,pij->qixj', int2c_ip1, coef3c)
int3c = coef3c = None
get_int3c_ip1 = _int3c_wrapper(mol, auxmol, 'int3c2e_ip1', 's1')
get_int3c_ip2 = _int3c_wrapper(mol, auxmol, 'int3c2e_ip2', 's1')
aux_ranges = ao2mo.outcore.balance_partition(auxmol.ao_loc, 480)
vk1a_buf = np.zeros((3, nao, nao))
vk1b_buf = np.zeros((3, nao, nao))
vj1_buf = np.zeros((mol.natm, 3, nao, nao))
for shl0, shl1, nL in aux_ranges:
shls_slice = (0, nbas, 0, nbas, shl0, shl1)
p0, p1 = aux_loc[shl0], aux_loc[shl1]
int3c_ip1 = get_int3c_ip1(shls_slice)
coef3c = _load_dim0(rho0_Pij, p0, p1)
for i, (shl0, shl1, q0, q1) in enumerate(aoslices):
wj1 = np.einsum('xijp,ji->xp', int3c_ip1[:, q0:q1], dm0[:, q0:q1])
vj1_buf[i] += np.einsum('xp,pij->xij', wj1, coef3c)
rhok0_PlJ = lib.einsum('plj,Jj->plJ', rhok0a_Pl_[p0:p1], mocca)
vk1a_buf += lib.einsum('xijp,plj->xil', int3c_ip1, rhok0_PlJ[p0:p1])
rhok0_PlJ = lib.einsum('plj,Jj->plJ', rhok0b_Pl_[p0:p1], moccb)
vk1b_buf += lib.einsum('xijp,plj->xil', int3c_ip1, rhok0_PlJ[p0:p1])
int3c_ip1 = None
vj1_buf = ftmp['vj1_buf'] = vj1_buf
for i0, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = aoslices[ia]
shls_slice = (shl0, shl1, 0, nbas, 0, auxmol.nbas)
int3c_ip1 = get_int3c_ip1(shls_slice)
vj1 = -np.asarray(vj1_buf[ia])
rhok0_PlJ = lib.einsum('plj,Jj->plJ', rhok0a_Pl_, mocca[p0:p1])
vk1a = -lib.einsum('xijp,pki->xkj', int3c_ip1, rhok0_PlJ)
rhok0_PlJ = lib.einsum('plj,Jj->plJ', rhok0b_Pl_, moccb[p0:p1])
vk1b = -lib.einsum('xijp,pki->xkj', int3c_ip1, rhok0_PlJ)
vj1[:, p0:p1] -= np.einsum('xijp,p->xij', int3c_ip1, rhoj0_P)
vk1a[:, p0:p1] -= vk1a_buf[:, p0:p1]
vk1b[:, p0:p1] -= vk1b_buf[:, p0:p1]
if hessobj.auxbasis_response:
shl0, shl1, q0, q1 = auxslices[ia]
shls_slice = (0, nbas, 0, nbas, shl0, shl1)
int3c_ip2 = get_int3c_ip2(shls_slice)
rhoj1 = np.einsum('xijp,ji->xp', int3c_ip2, dm0)
coef3c = _load_dim0(rho0_Pij, q0, q1)
Pij = _load_dim0(wj_Pij, q0, q1)
vj1 += .5 * np.einsum('pij,xp->xij', coef3c, -rhoj1)
vj1 += .5 * np.einsum('xijp,p->xij', int3c_ip2, -rhoj0_P[q0:q1])
vj1 -= .5 * lib.einsum('xpq,q,pij->xij', int2c_ip1[:, q0:q1],
-rhoj0_P, coef3c)
vj1 -= .5 * lib.einsum('pixj,p->xij', Pij, -rhoj0_P[q0:q1])
rhok0_PlJ = lib.einsum('plj,Jj->plJ', rhok0a_Pl_[q0:q1], mocca)
vk1a -= lib.einsum('plj,xijp->xil', rhok0_PlJ, int3c_ip2)
vk1a += lib.einsum('pjxi,plj->xil', Pij, rhok0_PlJ)
rhok0_PlJ = lib.einsum('plj,Jj->plJ', rhok0b_Pl_[q0:q1], moccb)
vk1b -= lib.einsum('plj,xijp->xil', rhok0_PlJ, int3c_ip2)
vk1b += lib.einsum('pjxi,plj->xil', Pij, rhok0_PlJ)
vj1 = vj1 + vj1.transpose(0, 2, 1)
vk1a = vk1a + vk1a.transpose(0, 2, 1)
vk1b = vk1b + vk1b.transpose(0, 2, 1)
h1 = hcore_deriv(ia)
yield ia, h1, vj1, vk1a, vk1b