def Wovoo(cc,t1,t2,eris,kconserv):
nkpts, nocc, nvir = t1.shape
Wmbij = eris.ovoo.copy()
for km, kb, ki in kpts_helper.loop_kkk(nkpts):
kj = kconserv[km, ki, kb]
for kn in range(nkpts):
Wmbij[km, kb, ki] += einsum('mnie,jnbe->mbij', eris.ooov[km, kn, ki], t2[kj, kn, kb])
Wmbij[km, kb, ki] += einsum('ie,mbej->mbij', t1[ki], -eris.ovov[km, kb, kj].transpose(0, 1, 3, 2))
for kf in range(nkpts):
kn = kconserv[kb, kj, kf]
Wmbij[km, kb, ki] -= einsum('ie,njbf,mnef->mbij', t1[ki], t2[kn, kj, kb], eris.oovv[km, kn, ki])
# P(ij)
for kn in range(nkpts):
Wmbij[km, kb, ki] -= einsum('mnje,inbe->mbij', eris.ooov[km, kn, kj], t2[ki, kn, kb])
Wmbij[km, kb, ki] -= einsum('je,mbei->mbij', t1[kj], -eris.ovov[km, kb, ki].transpose(0, 1, 3, 2))
for kf in range(nkpts):
kn = kconserv[kb, ki, kf]
Wmbij[km, kb, ki] += einsum('je,nibf,mnef->mbij', t1[kj], t2[kn, ki, kb], eris.oovv[km, kn, kj])
FFov = Fov(cc,t1,t2,eris,kconserv)
WWoooo = Woooo(cc,t1,t2,eris,kconserv)
tau = make_tau(cc,t2,t1,t1,kconserv)
for km, kb, ki in kpts_helper.loop_kkk(nkpts):
kj = kconserv[km, ki, kb]
Wmbij[km, kb, ki] -= einsum('me,ijbe->mbij', FFov[km], t2[ki, kj, kb])
Wmbij[km, kb, ki] -= einsum('nb,mnij->mbij', t1[kb], WWoooo[km, kb, ki])
for km, kb, ki in kpts_helper.loop_kkk(nkpts):
kj = kconserv[km, ki, kb]
Wmbij[km, kb, ki] += 0.5 * einsum('xmbef,xijef->mbij', eris.ovvv[km, kb, :], tau[ki, kj, :])
return Wmbij
def test_ao2mo_7d(self):
L = 3.
n = 6
cell = pgto.Cell()
cell.a = numpy.diag([L,L,L])
cell.mesh = [n,n,n]
cell.atom = '''He 2. 2.2 2.
He 1.2 1. 1.'''
cell.basis = {'He': [[0, (1.2, 1)], [1, (0.6, 1)]]}
cell.verbose = 0
cell.build(0,0)
kpts = cell.make_kpts([1,3,1])
nkpts = len(kpts)
nao = cell.nao_nr()
numpy.random.seed(1)
mo =(numpy.random.random((nkpts,nao,nao)) +
numpy.random.random((nkpts,nao,nao))*1j)
with_df = df.GDF(cell, kpts)
out = with_df.ao2mo_7d(mo, kpts)
ref = numpy.empty_like(out)
kconserv = kpts_helper.get_kconserv(cell, kpts)
for ki, kj, kk in kpts_helper.loop_kkk(nkpts):
kl = kconserv[ki, kj, kk]
tmp = with_df.ao2mo((mo[ki], mo[kj], mo[kk], mo[kl]), kpts[[ki,kj,kk,kl]])
ref[ki,kj,kk] = tmp.reshape([nao]*4)
self.assertAlmostEqual(abs(out-ref).max(), 0, 12)
def Wooov(cc,t1,t2,eris,kconserv):
nkpts, nocc, nvir = t1.shape
Wmnie = eris.ooov.copy()
for km, kn, ki in kpts_helper.loop_kkk(nkpts):
kf = ki
Wmnie[km, kn, ki] += einsum('if,mnfe->mnie',t1[ki], eris.oovv[km, kn, kf])
return Wmnie
def Wvovv(cc,t1,t2,eris,kconserv):
nkpts, nocc, nvir = t1.shape
Wamef = numpy.empty((nkpts, nkpts, nkpts, nvir, nocc, nvir, nvir), dtype=eris.ovvv.dtype)
for ka, km, ke in kpts_helper.loop_kkk(nkpts):
kn = ka
Wamef[ka, km, ke] = -eris.ovvv[km, ka, ke].transpose(1, 0, 2, 3)
Wamef[ka, km, ke] -= einsum('na,nmef->amef',t1[kn],eris.oovv[kn, km, ke])
return Wamef
def Wovvo(cc,t1,t2,eris,kconserv):
nkpts, nocc, nvir = t1.shape
Wmbej = cc_Wovvo(cc,t1,t2,eris,kconserv)
for km, kb, ke in kpts_helper.loop_kkk(nkpts):
kj = kconserv[km, ke, kb]
for kn in range(nkpts):
kf = kconserv[km, ke, kn]
Wmbej[km, kb, ke] -= 0.5*einsum('jnfb,mnef->mbej',t2[kj, kn, kf],
eris.oovv[km, kn, ke])
return Wmbej
def Wvvvv(cc,t1,t2,eris,kconserv):
nkpts, nocc, nvir = t1.shape
tau = make_tau(cc,t2,t1,t1,kconserv)
Wabef = cc_Wvvvv(cc,t1,t2,eris,kconserv)
for ka, kb, ke in kpts_helper.loop_kkk(nkpts):
kf = kconserv[ka, ke, kb]
for km in range(nkpts):
kn = kconserv[ka, km, kb]
Wabef[ka, kb, ke] += 0.25*einsum('mnab,mnef->abef',tau[km, kn, ka],
eris.oovv[km, kn, ke])
return Wabef
def Wvvvo(cc,t1,t2,eris,kconserv,WWvvvv=None):
nkpts, nocc, nvir = t1.shape
FFov = Fov(cc,t1,t2,eris,kconserv)
if WWvvvv is None:
WWvvvv = Wvvvv(cc,t1,t2,eris,kconserv)
eris_ovvo = numpy.zeros(shape=(nkpts,nkpts,nkpts,nocc,nvir,nvir,nocc),dtype=t2.dtype)
for km in range(nkpts):
for kb in range(nkpts):
for ke in range(nkpts):
kj = kconserv[km,ke,kb]
eris_ovvo[km,kb,ke] = -eris.ovov[km,kb,kj].transpose(0,1,3,2)
tmp1 = numpy.zeros((nkpts, nkpts, nkpts, nvir, nvir, nvir, nocc),dtype=t2.dtype)
tmp2 = numpy.zeros((nkpts, nkpts, nkpts, nvir, nvir, nvir, nocc),dtype=t2.dtype)
for ka, kb, ke in kpts_helper.loop_kkk(nkpts):
ki = kconserv[ka,ke,kb]
tmp2[ka,kb,ke] += einsum('ma,mbei->abei',t1[ka],eris_ovvo[ka,kb,ke])
for kn in range(nkpts):
tmp2[ka,kb,ke] -= einsum('ma,nibf,mnef->abei',t1[ka],t2[kn,ki,kb],eris.oovv[ka,kn,ke])
for km in range(nkpts):
tmp1[ka,kb,ke] += einsum('mbef,miaf->abei',eris.ovvv[km,kb,ke],t2[km,ki,ka])
tau = make_tau(cc,t2,t1,t1,kconserv)
Wabei = -tmp1 + tmp1.transpose(1,0,2,4,3,5,6)
Wabei -= tmp2 - tmp2.transpose(1,0,2,4,3,5,6)
for ka, kb, ke in kpts_helper.loop_kkk(nkpts):
ki = kconserv[ka, ke, kb]
Wabei[ka, kb, ke] += eris.ovvv[ki, ke, kb].conj().transpose(3, 2, 1, 0)
Wabei[ka, kb, ke] += einsum('if,abef->abei',t1[ki],WWvvvv[ka, kb, ke])
Wabei[ka, kb, ke] -= einsum('me,miab->abei',FFov[ke],t2[ke, ki, ka])
for km in range(nkpts):
kn = kconserv[ka, km, kb]
Wabei[ka, kb, ke] += 0.5 * einsum('nmie,mnab->abei',
eris.ooov[kn, km, ki],
tau[km, kn, ka])
return Wabei
def check_antisymm_34(cc, kpts, integrals):
kconserv = kpts_helper.get_kconserv(cc._scf.cell, cc.kpts)
nkpts = len(kpts)
diff = 0.0
for kp, kq, kr in kpts_helper.loop_kkk(nkpts):
ks = kconserv[kp, kr, kq]
for p in range(integrals.shape[3]):
for q in range(integrals.shape[4]):
for r in range(integrals.shape[5]):
for s in range(integrals.shape[6]):
pqrs = integrals[kp, kq, kr, p, q, r, s]
pqsr = integrals[kp, kq, ks, p, q, s, r]
cdiff = numpy.linalg.norm(pqrs + pqsr).real
if diff > 1e-5:
print("AS diff = %.15g" % cdiff, pqrs, pqsr, kp, kq, kr, ks, p, q, r, s)
diff = max(diff, cdiff)
print("antisymmetrization : max diff = %.15g" % diff)
if diff > 1e-5:
print("Energy cutoff (or cell.mesh) is not enough to converge AO integrals.")
def spin2spatial(tx, orbspin, kconserv):
if tx.ndim == 3: # t1
nocc, nvir = tx.shape[1:]
else:
nocc, nvir = tx.shape[4:6]
nkpts = len(tx)
idxoa = [numpy.where(orbspin[k][:nocc] == 0)[0] for k in range(nkpts)]
idxob = [numpy.where(orbspin[k][:nocc] == 1)[0] for k in range(nkpts)]
idxva = [numpy.where(orbspin[k][nocc:] == 0)[0] for k in range(nkpts)]
idxvb = [numpy.where(orbspin[k][nocc:] == 1)[0] for k in range(nkpts)]
nocc_a = len(idxoa[0])
nocc_b = len(idxob[0])
nvir_a = len(idxva[0])
nvir_b = len(idxvb[0])
if tx.ndim == 3: # t1
t1a = numpy.zeros((nkpts,nocc_a,nvir_a), dtype=tx.dtype)
t1b = numpy.zeros((nkpts,nocc_b,nvir_b), dtype=tx.dtype)
for k in range(nkpts):
lib.take_2d(tx[k], idxoa[k], idxva[k], out=t1a[k])
lib.take_2d(tx[k], idxob[k], idxvb[k], out=t1b[k])
return t1a, t1b
else:
t2aa = numpy.zeros((nkpts,nkpts,nkpts,nocc_a,nocc_a,nvir_a,nvir_a), dtype=tx.dtype)
t2ab = numpy.zeros((nkpts,nkpts,nkpts,nocc_a,nocc_b,nvir_a,nvir_b), dtype=tx.dtype)
t2bb = numpy.zeros((nkpts,nkpts,nkpts,nocc_b,nocc_b,nvir_b,nvir_b), dtype=tx.dtype)
t2 = tx.reshape(nkpts,nkpts,nkpts,nocc**2,nvir**2)
for ki, kj, ka in kpts_helper.loop_kkk(nkpts):
kb = kconserv[ki,ka,kj]
idxoaa = idxoa[ki][:,None] * nocc + idxoa[kj]
idxoab = idxoa[ki][:,None] * nocc + idxob[kj]
idxobb = idxob[ki][:,None] * nocc + idxob[kj]
idxvaa = idxva[ka][:,None] * nvir + idxva[kb]
idxvab = idxva[ka][:,None] * nvir + idxvb[kb]
idxvbb = idxvb[ka][:,None] * nvir + idxvb[kb]
lib.take_2d(t2[ki,kj,ka], idxoaa.ravel(), idxvaa.ravel(), out=t2aa[ki,kj,ka])
lib.take_2d(t2[ki,kj,ka], idxobb.ravel(), idxvbb.ravel(), out=t2bb[ki,kj,ka])
lib.take_2d(t2[ki,kj,ka], idxoab.ravel(), idxvab.ravel(), out=t2ab[ki,kj,ka])
return t2aa, t2ab, t2bb
def init_amps(self, eris):
time0 = time.clock(), time.time()
nocc = self.nocc
nvir = self.nmo - nocc
nkpts = self.nkpts
mo_e_o = [eris.mo_energy[k][:nocc] for k in range(nkpts)]
mo_e_v = [eris.mo_energy[k][nocc:] for k in range(nkpts)]
t1 = numpy.zeros((nkpts, nocc, nvir), dtype=numpy.complex128)
t2 = numpy.zeros((nkpts, nkpts, nkpts, nocc, nocc, nvir, nvir), dtype=numpy.complex128)
self.emp2 = 0
foo = eris.fock[:, :nocc, :nocc].copy()
fvv = eris.fock[:, nocc:, nocc:].copy()
fov = eris.fock[:, :nocc, nocc:].copy()
eris_oovv = eris.oovv.copy()
# Get location of padded elements in occupied and virtual space
nonzero_opadding, nonzero_vpadding = padding_k_idx(self, kind="split")
kconserv = kpts_helper.get_kconserv(self._scf.cell, self.kpts)
for ki, kj, ka in kpts_helper.loop_kkk(nkpts):
kb = kconserv[ki, ka, kj]
# For LARGE_DENOM, see t1new update above
eia = LARGE_DENOM * numpy.ones((nocc, nvir), dtype=eris.mo_energy[0].dtype)
n0_ovp_ia = numpy.ix_(nonzero_opadding[ki], nonzero_vpadding[ka])
eia[n0_ovp_ia] = (mo_e_o[ki][:,None] - mo_e_v[ka])[n0_ovp_ia]
ejb = LARGE_DENOM * numpy.ones((nocc, nvir), dtype=eris.mo_energy[0].dtype)
n0_ovp_jb = numpy.ix_(nonzero_opadding[kj], nonzero_vpadding[kb])
ejb[n0_ovp_jb] = (mo_e_o[kj][:,None] - mo_e_v[kb])[n0_ovp_jb]
eijab = eia[:, None, :, None] + ejb[:, None, :]
t2[ki, kj, ka] = eris_oovv[ki, kj, ka] / eijab
t2 = numpy.conj(t2)
self.emp2 = 0.25 * numpy.einsum('pqrijab,pqrijab', t2, eris_oovv).real
self.emp2 /= nkpts
logger.info(self, 'Init t2, MP2 energy = %.15g', self.emp2.real)
logger.timer(self, 'init mp2', *time0)
return self.emp2, t1, t2
def check_antisymm_3412(cc, kpts, integrals):
kconserv = kpts_helper.get_kconserv(cc._scf.cell, cc.kpts)
nkpts = len(kpts)
diff = 0.0
for kp, kq, kr in kpts_helper.loop_kkk(nkpts):
ks = kconserv[kp, kr, kq]
for p in range(integrals.shape[3]):
for q in range(integrals.shape[4]):
for r in range(integrals.shape[5]):
for s in range(integrals.shape[6]):
pqrs = integrals[kp, kq, kr, p, q, r, s]
rspq = integrals[kq, kp, kr, q, p, r, s]
cdiff = numpy.linalg.norm(pqrs - rspq).real
if diff > 1e-5:
print("AS diff = %.15g" % cdiff, pqrs, rspq, kp,
kq, kr, ks, p, q, r, s)
diff = max(diff, cdiff)
print("antisymmetrization : max diff = %.15g" % diff)
if diff > 1e-5:
print(
"Energy cutoff (or cell.mesh) is not enough to converge AO integrals."
)
return diff
def init_amps(self, eris):
time0 = logger.process_clock(), logger.perf_counter()
nocc = self.nocc
nvir = self.nmo - nocc
nkpts = self.nkpts
mo_e_o = [eris.mo_energy[k][:nocc] for k in range(nkpts)]
mo_e_v = [eris.mo_energy[k][nocc:] for k in range(nkpts)]
t1 = numpy.zeros((nkpts, nocc, nvir), dtype=numpy.complex128)
t2 = numpy.zeros((nkpts, nkpts, nkpts, nocc, nocc, nvir, nvir), dtype=numpy.complex128)
self.emp2 = 0
eris_oovv = eris.oovv.copy()
# Get location of padded elements in occupied and virtual space
nonzero_opadding, nonzero_vpadding = padding_k_idx(self, kind="split")
kconserv = kpts_helper.get_kconserv(self._scf.cell, self.kpts)
for ki, kj, ka in kpts_helper.loop_kkk(nkpts):
kb = kconserv[ki, ka, kj]
# For LARGE_DENOM, see t1new update above
eia = LARGE_DENOM * numpy.ones((nocc, nvir), dtype=eris.mo_energy[0].dtype)
n0_ovp_ia = numpy.ix_(nonzero_opadding[ki], nonzero_vpadding[ka])
eia[n0_ovp_ia] = (mo_e_o[ki][:,None] - mo_e_v[ka])[n0_ovp_ia]
ejb = LARGE_DENOM * numpy.ones((nocc, nvir), dtype=eris.mo_energy[0].dtype)
n0_ovp_jb = numpy.ix_(nonzero_opadding[kj], nonzero_vpadding[kb])
ejb[n0_ovp_jb] = (mo_e_o[kj][:,None] - mo_e_v[kb])[n0_ovp_jb]
eijab = eia[:, None, :, None] + ejb[:, None, :]
t2[ki, kj, ka] = eris_oovv[ki, kj, ka] / eijab
t2 = numpy.conj(t2)
self.emp2 = 0.25 * numpy.einsum('pqrijab,pqrijab', t2, eris_oovv).real
self.emp2 /= nkpts
logger.info(self, 'Init t2, MP2 energy = %.15g', self.emp2.real)
logger.timer(self, 'init mp2', *time0)
return self.emp2, t1, t2
def init_amps(self, eris):
time0 = time.clock(), time.time()
nocc = self.nocc
nvir = self.nmo - nocc
nkpts = self.nkpts
t1 = numpy.zeros((nkpts, nocc, nvir), dtype=numpy.complex128)
t2 = numpy.zeros((nkpts, nkpts, nkpts, nocc, nocc, nvir, nvir),
dtype=numpy.complex128)
self.emp2 = 0
foo = eris.fock[:, :nocc, :nocc].copy()
fvv = eris.fock[:, nocc:, nocc:].copy()
fov = eris.fock[:, :nocc, nocc:].copy()
eris_oovv = eris.oovv.copy()
eia = numpy.zeros((nocc, nvir))
eijab = numpy.zeros((nocc, nocc, nvir, nvir))
kconserv = kpts_helper.get_kconserv(self._scf.cell, self.kpts)
for ki, kj, ka in kpts_helper.loop_kkk(nkpts):
kb = kconserv[ki, ka, kj]
eijab = (foo[ki].diagonal()[:, None, None, None] +
foo[kj].diagonal()[None, :, None, None] -
fvv[ka].diagonal()[None, None, :, None] -
fvv[kb].diagonal()[None, None, None, :])
# Due to padding; see above discussion concerning t1new in update_amps()
idx = numpy.where(abs(eijab) < LOOSE_ZERO_TOL)[0]
eijab[idx] = LARGE_DENOM
t2[ki, kj, ka] = eris_oovv[ki, kj, ka] / eijab
t2 = numpy.conj(t2)
self.emp2 = 0.25 * numpy.einsum('pqrijab,pqrijab', t2, eris_oovv).real
self.emp2 /= nkpts
logger.info(self, 'Init t2, MP2 energy = %.15g', self.emp2.real)
logger.timer(self, 'init mp2', *time0)
return self.emp2, t1, t2
def update_amps(cc, t1, t2, eris):
time0 = time.clock(), time.time()
log = logger.Logger(cc.stdout, cc.verbose)
nkpts, nocc, nvir = t1.shape
fock = eris.fock
mo_e_o = [e[:nocc] for e in eris.mo_energy]
mo_e_v = [e[nocc:] + cc.level_shift for e in eris.mo_energy]
# Get location of padded elements in occupied and virtual space
nonzero_opadding, nonzero_vpadding = padding_k_idx(cc, kind="split")
fov = fock[:, :nocc, nocc:].copy()
foo = fock[:, :nocc, :nocc].copy()
fvv = fock[:, nocc:, nocc:].copy()
# Get the momentum conservation array
# Note: chemist's notation for momentum conserving t2(ki,kj,ka,kb), even though
# integrals are in physics notation
kconserv = kpts_helper.get_kconserv(cc._scf.cell, cc.kpts)
tau = imdk.make_tau(cc, t2, t1, t1, kconserv)
Fvv = imdk.cc_Fvv(cc, t1, t2, eris, kconserv)
Foo = imdk.cc_Foo(cc, t1, t2, eris, kconserv)
Fov = imdk.cc_Fov(cc, t1, t2, eris, kconserv)
Woooo = imdk.cc_Woooo(cc, t1, t2, eris, kconserv)
Wvvvv = imdk.cc_Wvvvv(cc, t1, t2, eris, kconserv)
Wovvo = imdk.cc_Wovvo(cc, t1, t2, eris, kconserv)
# Move energy terms to the other side
for k in range(nkpts):
Foo[k][numpy.diag_indices(nocc)] -= mo_e_o[k]
Fvv[k][numpy.diag_indices(nvir)] -= mo_e_v[k]
eris_ovvo = numpy.zeros(shape=(nkpts, nkpts, nkpts, nocc, nvir, nvir,
nocc),
dtype=t2.dtype)
eris_oovo = numpy.zeros(shape=(nkpts, nkpts, nkpts, nocc, nocc, nvir,
nocc),
dtype=t2.dtype)
eris_vvvo = numpy.zeros(shape=(nkpts, nkpts, nkpts, nvir, nvir, nvir,
nocc),
dtype=t2.dtype)
for km, kb, ke in kpts_helper.loop_kkk(nkpts):
kj = kconserv[km, ke, kb]
# <mb||je> -> -<mb||ej>
eris_ovvo[km, kb, ke] = -eris.ovov[km, kb, kj].transpose(0, 1, 3, 2)
# <mn||je> -> -<mn||ej>
# let kb = kn as a dummy variable
eris_oovo[km, kb, ke] = -eris.ooov[km, kb, kj].transpose(0, 1, 3, 2)
# <ma||be> -> - <be||am>*
# let kj = ka as a dummy variable
kj = kconserv[km, ke, kb]
eris_vvvo[ke, kj,
kb] = -eris.ovvv[km, kb, ke].transpose(2, 3, 1, 0).conj()
# T1 equation
t1new = numpy.zeros(shape=t1.shape, dtype=t1.dtype)
for ka in range(nkpts):
ki = ka
t1new[ka] += numpy.array(fov[ka, :, :]).conj()
t1new[ka] += einsum('ie,ae->ia', t1[ka], Fvv[ka])
t1new[ka] += -einsum('ma,mi->ia', t1[ka], Foo[ka])
for km in range(nkpts):
t1new[ka] += einsum('imae,me->ia', t2[ka, km, ka], Fov[km])
t1new[ka] += -einsum('nf,naif->ia', t1[km], eris.ovov[km, ka, ki])
for kn in range(nkpts):
ke = kconserv[km, ki, kn]
t1new[ka] += -0.5 * einsum('imef,maef->ia', t2[ki, km, ke],
eris.ovvv[km, ka, ke])
t1new[ka] += -0.5 * einsum('mnae,nmei->ia', t2[km, kn, ka],
eris_oovo[kn, km, ke])
# T2 equation
t2new = numpy.array(eris.oovv).conj()
for ki, kj, ka in kpts_helper.loop_kkk(nkpts):
# Chemist's notation for momentum conserving t2(ki,kj,ka,kb)
kb = kconserv[ki, ka, kj]
Ftmp = Fvv[kb] - 0.5 * einsum('mb,me->be', t1[kb], Fov[kb])
tmp = einsum('ijae,be->ijab', t2[ki, kj, ka], Ftmp)
t2new[ki, kj, ka] += tmp
#t2new[ki,kj,kb] -= tmp.transpose(0,1,3,2)
Ftmp = Fvv[ka] - 0.5 * einsum('ma,me->ae', t1[ka], Fov[ka])
tmp = einsum('ijbe,ae->ijab', t2[ki, kj, kb], Ftmp)
t2new[ki, kj, ka] -= tmp
Ftmp = Foo[kj] + 0.5 * einsum('je,me->mj', t1[kj], Fov[kj])
tmp = einsum('imab,mj->ijab', t2[ki, kj, ka], Ftmp)
t2new[ki, kj, ka] -= tmp
#t2new[kj,ki,ka] += tmp.transpose(1,0,2,3)
Ftmp = Foo[ki] + 0.5 * einsum('ie,me->mi', t1[ki], Fov[ki])
tmp = einsum('jmab,mi->ijab', t2[kj, ki, ka], Ftmp)
t2new[ki, kj, ka] += tmp
for km in range(nkpts):
# Wminj
# - km - kn + ka + kb = 0
# => kn = ka - km + kb
kn = kconserv[ka, km, kb]
t2new[ki, kj, ka] += 0.5 * einsum(
'mnab,mnij->ijab', tau[km, kn, ka], Woooo[km, kn, ki])
ke = km
t2new[ki, kj, ka] += 0.5 * einsum(
'ijef,abef->ijab', tau[ki, kj, ke], Wvvvv[ka, kb, ke])
# Wmbej
# - km - kb + ke + kj = 0
# => ke = km - kj + kb
ke = kconserv[km, kj, kb]
tmp = einsum('imae,mbej->ijab', t2[ki, km, ka], Wovvo[km, kb, ke])
# - km - kb + ke + kj = 0
# => ke = km - kj + kb
#
# t[i,e] => ki = ke
# t[m,a] => km = ka
if km == ka and ke == ki:
tmp -= einsum('ie,ma,mbej->ijab', t1[ki], t1[km],
eris_ovvo[km, kb, ke])
t2new[ki, kj, ka] += tmp
t2new[ki, kj, kb] -= tmp.transpose(0, 1, 3, 2)
t2new[kj, ki, ka] -= tmp.transpose(1, 0, 2, 3)
t2new[kj, ki, kb] += tmp.transpose(1, 0, 3, 2)
ke = ki
tmp = einsum('ie,abej->ijab', t1[ki], eris_vvvo[ka, kb, ke])
t2new[ki, kj, ka] += tmp
# P(ij) term
ke = kj
tmp = einsum('je,abei->ijab', t1[kj], eris_vvvo[ka, kb, ke])
t2new[ki, kj, ka] -= tmp
km = ka
tmp = einsum('ma,mbij->ijab', t1[ka], eris.ovoo[km, kb, ki])
t2new[ki, kj, ka] -= tmp
# P(ab) term
km = kb
tmp = einsum('mb,maij->ijab', t1[kb], eris.ovoo[km, ka, ki])
t2new[ki, kj, ka] += tmp
for ki in range(nkpts):
ka = ki
# Remove zero/padded elements from denominator
eia = LARGE_DENOM * numpy.ones(
(nocc, nvir), dtype=eris.mo_energy[0].dtype)
n0_ovp_ia = numpy.ix_(nonzero_opadding[ki], nonzero_vpadding[ka])
eia[n0_ovp_ia] = (mo_e_o[ki][:, None] - mo_e_v[ka])[n0_ovp_ia]
t1new[ki] /= eia
kconserv = kpts_helper.get_kconserv(cc._scf.cell, cc.kpts)
for ki, kj, ka in kpts_helper.loop_kkk(nkpts):
kb = kconserv[ki, ka, kj]
# For LARGE_DENOM, see t1new update above
eia = LARGE_DENOM * numpy.ones(
(nocc, nvir), dtype=eris.mo_energy[0].dtype)
n0_ovp_ia = numpy.ix_(nonzero_opadding[ki], nonzero_vpadding[ka])
eia[n0_ovp_ia] = (mo_e_o[ki][:, None] - mo_e_v[ka])[n0_ovp_ia]
ejb = LARGE_DENOM * numpy.ones(
(nocc, nvir), dtype=eris.mo_energy[0].dtype)
n0_ovp_jb = numpy.ix_(nonzero_opadding[kj], nonzero_vpadding[kb])
ejb[n0_ovp_jb] = (mo_e_o[kj][:, None] - mo_e_v[kb])[n0_ovp_jb]
eijab = eia[:, None, :, None] + ejb[:, None, :]
t2new[ki, kj, ka] /= eijab
time0 = log.timer_debug1('update t1 t2', *time0)
return t1new, t2new
def _make_eris_incore(cc, mo_coeff=None):
from pyscf.pbc import tools
from pyscf.pbc.cc.ccsd import _adjust_occ
log = logger.Logger(cc.stdout, cc.verbose)
cput0 = (time.clock(), time.time())
eris = gccsd._PhysicistsERIs()
cell = cc._scf.cell
kpts = cc.kpts
nkpts = cc.nkpts
nocc = cc.nocc
nmo = cc.nmo
nvir = nmo - nocc
eris.nocc = nocc
#if any(nocc != numpy.count_nonzero(cc._scf.mo_occ[k] > 0) for k in range(nkpts)):
# raise NotImplementedError('Different occupancies found for different k-points')
if mo_coeff is None:
mo_coeff = cc.mo_coeff
nao = mo_coeff[0].shape[0]
dtype = mo_coeff[0].dtype
moidx = get_frozen_mask(cc)
nocc_per_kpt = numpy.asarray(get_nocc(cc, per_kpoint=True))
nmo_per_kpt = numpy.asarray(get_nmo(cc, per_kpoint=True))
padded_moidx = []
for k in range(nkpts):
kpt_nocc = nocc_per_kpt[k]
kpt_nvir = nmo_per_kpt[k] - kpt_nocc
kpt_padded_moidx = numpy.concatenate(
(numpy.ones(kpt_nocc, dtype=numpy.bool),
numpy.zeros(nmo - kpt_nocc - kpt_nvir, dtype=numpy.bool),
numpy.ones(kpt_nvir, dtype=numpy.bool)))
padded_moidx.append(kpt_padded_moidx)
eris.mo_coeff = []
eris.orbspin = []
# Generate the molecular orbital coefficients with the frozen orbitals masked.
# Each MO is tagged with orbspin, a list of 0's and 1's that give the overall
# spin of each MO.
#
# Here we will work with two index arrays; one is for our original (small) moidx
# array while the next is for our new (large) padded array.
for k in range(nkpts):
kpt_moidx = moidx[k]
kpt_padded_moidx = padded_moidx[k]
mo = numpy.zeros((nao, nmo), dtype=dtype)
mo[:, kpt_padded_moidx] = mo_coeff[k][:, kpt_moidx]
if getattr(mo_coeff[k], 'orbspin', None) is not None:
orbspin_dtype = mo_coeff[k].orbspin[kpt_moidx].dtype
orbspin = numpy.zeros(nmo, dtype=orbspin_dtype)
orbspin[kpt_padded_moidx] = mo_coeff[k].orbspin[kpt_moidx]
mo = lib.tag_array(mo, orbspin=orbspin)
eris.orbspin.append(orbspin)
# FIXME: What if the user freezes all up spin orbitals in
# an RHF calculation? The number of electrons will still be
# even.
else: # guess orbital spin - assumes an RHF calculation
assert (numpy.count_nonzero(kpt_moidx) % 2 == 0)
orbspin = numpy.zeros(mo.shape[1], dtype=int)
orbspin[1::2] = 1
mo = lib.tag_array(mo, orbspin=orbspin)
eris.orbspin.append(orbspin)
eris.mo_coeff.append(mo)
# Re-make our fock MO matrix elements from density and fock AO
dm = cc._scf.make_rdm1(cc.mo_coeff, cc.mo_occ)
with lib.temporary_env(cc._scf, exxdiv=None):
# _scf.exxdiv affects eris.fock. HF exchange correction should be
# excluded from the Fock matrix.
fockao = cc._scf.get_hcore() + cc._scf.get_veff(cell, dm)
eris.fock = numpy.asarray([
reduce(numpy.dot, (mo.T.conj(), fockao[k], mo))
for k, mo in enumerate(eris.mo_coeff)
])
eris.mo_energy = [eris.fock[k].diagonal().real for k in range(nkpts)]
# Add HFX correction in the eris.mo_energy to improve convergence in
# CCSD iteration. It is useful for the 2D systems since their occupied and
# the virtual orbital energies may overlap which may lead to numerical
# issue in the CCSD iterations.
# FIXME: Whether to add this correction for other exxdiv treatments?
# Without the correction, MP2 energy may be largely off the correct value.
madelung = tools.madelung(cell, kpts)
eris.mo_energy = [
_adjust_occ(mo_e, nocc, -madelung)
for k, mo_e in enumerate(eris.mo_energy)
]
# Get location of padded elements in occupied and virtual space.
nocc_per_kpt = get_nocc(cc, per_kpoint=True)
nonzero_padding = padding_k_idx(cc, kind="joint")
# Check direct and indirect gaps for possible issues with CCSD convergence.
mo_e = [eris.mo_energy[kp][nonzero_padding[kp]] for kp in range(nkpts)]
mo_e = numpy.sort([y for x in mo_e for y in x]) # Sort de-nested array
gap = mo_e[numpy.sum(nocc_per_kpt)] - mo_e[numpy.sum(nocc_per_kpt) - 1]
if gap < 1e-5:
logger.warn(
cc, 'H**O-LUMO gap %s too small for KCCSD. '
'May cause issues in convergence.', gap)
kconserv = kpts_helper.get_kconserv(cell, kpts)
if getattr(mo_coeff[0], 'orbspin', None) is None:
# The bottom nao//2 coefficients are down (up) spin while the top are up (down).
mo_a_coeff = [mo[:nao // 2] for mo in eris.mo_coeff]
mo_b_coeff = [mo[nao // 2:] for mo in eris.mo_coeff]
eri = numpy.empty((nkpts, nkpts, nkpts, nmo, nmo, nmo, nmo),
dtype=numpy.complex128)
fao2mo = cc._scf.with_df.ao2mo
for kp, kq, kr in kpts_helper.loop_kkk(nkpts):
ks = kconserv[kp, kq, kr]
eri_kpt = fao2mo((mo_a_coeff[kp], mo_a_coeff[kq], mo_a_coeff[kr],
mo_a_coeff[ks]),
(kpts[kp], kpts[kq], kpts[kr], kpts[ks]),
compact=False)
eri_kpt += fao2mo((mo_b_coeff[kp], mo_b_coeff[kq], mo_b_coeff[kr],
mo_b_coeff[ks]),
(kpts[kp], kpts[kq], kpts[kr], kpts[ks]),
compact=False)
eri_kpt += fao2mo((mo_a_coeff[kp], mo_a_coeff[kq], mo_b_coeff[kr],
mo_b_coeff[ks]),
(kpts[kp], kpts[kq], kpts[kr], kpts[ks]),
compact=False)
eri_kpt += fao2mo((mo_b_coeff[kp], mo_b_coeff[kq], mo_a_coeff[kr],
mo_a_coeff[ks]),
(kpts[kp], kpts[kq], kpts[kr], kpts[ks]),
compact=False)
eri_kpt = eri_kpt.reshape(nmo, nmo, nmo, nmo)
eri[kp, kq, kr] = eri_kpt
else:
mo_a_coeff = [mo[:nao // 2] + mo[nao // 2:] for mo in eris.mo_coeff]
eri = numpy.empty((nkpts, nkpts, nkpts, nmo, nmo, nmo, nmo),
dtype=numpy.complex128)
fao2mo = cc._scf.with_df.ao2mo
for kp, kq, kr in kpts_helper.loop_kkk(nkpts):
ks = kconserv[kp, kq, kr]
eri_kpt = fao2mo((mo_a_coeff[kp], mo_a_coeff[kq], mo_a_coeff[kr],
mo_a_coeff[ks]),
(kpts[kp], kpts[kq], kpts[kr], kpts[ks]),
compact=False)
eri_kpt[(eris.orbspin[kp][:, None] !=
eris.orbspin[kq]).ravel()] = 0
eri_kpt[:,
(eris.orbspin[kr][:,
None] != eris.orbspin[ks]).ravel()] = 0
eri_kpt = eri_kpt.reshape(nmo, nmo, nmo, nmo)
eri[kp, kq, kr] = eri_kpt
# Check some antisymmetrized properties of the integrals
if DEBUG:
check_antisymm_3412(cc, cc.kpts, eri)
# Antisymmetrizing (pq|rs)-(ps|rq), where the latter integral is equal to
# (rq|ps); done since we aren't tracking the kpoint of orbital 's'
eri = eri - eri.transpose(2, 1, 0, 5, 4, 3, 6)
# Chemist -> physics notation
eri = eri.transpose(0, 2, 1, 3, 5, 4, 6)
# Set the various integrals
eris.dtype = eri.dtype
eris.oooo = eri[:, :, :, :nocc, :nocc, :nocc, :nocc].copy() / nkpts
eris.ooov = eri[:, :, :, :nocc, :nocc, :nocc, nocc:].copy() / nkpts
eris.ovoo = eri[:, :, :, :nocc, nocc:, :nocc, :nocc].copy() / nkpts
eris.oovv = eri[:, :, :, :nocc, :nocc, nocc:, nocc:].copy() / nkpts
eris.ovov = eri[:, :, :, :nocc, nocc:, :nocc, nocc:].copy() / nkpts
eris.ovvv = eri[:, :, :, :nocc, nocc:, nocc:, nocc:].copy() / nkpts
eris.vvvv = eri[:, :, :, nocc:, nocc:, nocc:, nocc:].copy() / nkpts
log.timer('CCSD integral transformation', *cput0)
return eris
def spatial2spin(tx, orbspin, kconserv):
'''Convert T1/T2 of spatial orbital representation to T1/T2 of
spin-orbital representation
'''
if isinstance(tx, numpy.ndarray) and tx.ndim == 3:
# KRCCSD t1 amplitudes
return spatial2spin((tx, tx), orbspin, kconserv)
elif isinstance(tx, numpy.ndarray) and tx.ndim == 7:
# KRCCSD t2 amplitudes
t2aa = tx - tx.transpose(0, 1, 2, 4, 3, 5, 6)
return spatial2spin((t2aa, tx, t2aa), orbspin, kconserv)
elif len(tx) == 2: # KUCCSD t1
t1a, t1b = tx
nocc_a, nvir_a = t1a.shape[1:]
nocc_b, nvir_b = t1b.shape[1:]
else: # KUCCSD t2
t2aa, t2ab, t2bb = tx
nocc_a, nocc_b, nvir_a, nvir_b = t2ab.shape[3:]
nkpts = len(orbspin)
nocc = nocc_a + nocc_b
nvir = nvir_a + nvir_b
idxoa = [numpy.where(orbspin[k][:nocc] == 0)[0] for k in range(nkpts)]
idxob = [numpy.where(orbspin[k][:nocc] == 1)[0] for k in range(nkpts)]
idxva = [numpy.where(orbspin[k][nocc:] == 0)[0] for k in range(nkpts)]
idxvb = [numpy.where(orbspin[k][nocc:] == 1)[0] for k in range(nkpts)]
if len(tx) == 2: # t1
t1 = numpy.zeros((nkpts, nocc, nvir), dtype=t1a.dtype)
for k in range(nkpts):
lib.takebak_2d(t1[k], t1a[k], idxoa[k], idxva[k])
lib.takebak_2d(t1[k], t1b[k], idxob[k], idxvb[k])
t1 = lib.tag_array(t1, orbspin=orbspin)
return t1
else:
t2 = numpy.zeros((nkpts, nkpts, nkpts, nocc**2, nvir**2),
dtype=t2aa.dtype)
for ki, kj, ka in kpts_helper.loop_kkk(nkpts):
kb = kconserv[ki, ka, kj]
idxoaa = idxoa[ki][:, None] * nocc + idxoa[kj]
idxoab = idxoa[ki][:, None] * nocc + idxob[kj]
idxoba = idxob[kj][:, None] * nocc + idxoa[ki]
idxobb = idxob[ki][:, None] * nocc + idxob[kj]
idxvaa = idxva[ka][:, None] * nvir + idxva[kb]
idxvab = idxva[ka][:, None] * nvir + idxvb[kb]
idxvba = idxvb[kb][:, None] * nvir + idxva[ka]
idxvbb = idxvb[ka][:, None] * nvir + idxvb[kb]
tmp2aa = t2aa[ki, kj, ka].reshape(nocc_a * nocc_a, nvir_a * nvir_a)
tmp2bb = t2bb[ki, kj, ka].reshape(nocc_b * nocc_b, nvir_b * nvir_b)
tmp2ab = t2ab[ki, kj, ka].reshape(nocc_a * nocc_b, nvir_a * nvir_b)
lib.takebak_2d(t2[ki, kj, ka], tmp2aa, idxoaa.ravel(),
idxvaa.ravel())
lib.takebak_2d(t2[ki, kj, ka], tmp2bb, idxobb.ravel(),
idxvbb.ravel())
lib.takebak_2d(t2[ki, kj, ka], tmp2ab, idxoab.ravel(),
idxvab.ravel())
lib.takebak_2d(t2[kj, ki, kb], tmp2ab, idxoba.T.ravel(),
idxvba.T.ravel())
abba = -tmp2ab
lib.takebak_2d(t2[ki, kj, kb], abba, idxoab.ravel(),
idxvba.T.ravel())
lib.takebak_2d(t2[kj, ki, ka], abba, idxoba.T.ravel(),
idxvab.ravel())
t2 = t2.reshape(nkpts, nkpts, nkpts, nocc, nocc, nvir, nvir)
t2 = lib.tag_array(t2, orbspin=orbspin)
return t2
def update_amps(cc, t1, t2, eris):
time0 = time1 = time.clock(), time.time()
log = logger.Logger(cc.stdout, cc.verbose)
nkpts, nocc, nvir = t1.shape
fock = eris.fock
mo_e_o = [e[:nocc] for e in eris.mo_energy]
mo_e_v = [e[nocc:] + cc.level_shift for e in eris.mo_energy]
# Get location of padded elements in occupied and virtual space
nonzero_opadding, nonzero_vpadding = padding_k_idx(cc, kind="split")
fov = fock[:, :nocc, nocc:]
foo = fock[:, :nocc, :nocc]
fvv = fock[:, nocc:, nocc:]
kconserv = cc.khelper.kconserv
Foo = imdk.cc_Foo(t1, t2, eris, kconserv)
Fvv = imdk.cc_Fvv(t1, t2, eris, kconserv)
Fov = imdk.cc_Fov(t1, t2, eris, kconserv)
Loo = imdk.Loo(t1, t2, eris, kconserv)
Lvv = imdk.Lvv(t1, t2, eris, kconserv)
# Move energy terms to the other side
for k in range(nkpts):
Foo[k][np.diag_indices(nocc)] -= mo_e_o[k]
Fvv[k][np.diag_indices(nvir)] -= mo_e_v[k]
Loo[k][np.diag_indices(nocc)] -= mo_e_o[k]
Lvv[k][np.diag_indices(nvir)] -= mo_e_v[k]
time1 = log.timer_debug1('intermediates', *time1)
# T1 equation
t1new = np.array(fov).astype(t1.dtype).conj()
for ka in range(nkpts):
ki = ka
# kc == ki; kk == ka
t1new[ka] += -2. * einsum('kc,ka,ic->ia', fov[ki], t1[ka], t1[ki])
t1new[ka] += einsum('ac,ic->ia', Fvv[ka], t1[ki])
t1new[ka] += -einsum('ki,ka->ia', Foo[ki], t1[ka])
tau_term = np.empty((nkpts, nocc, nocc, nvir, nvir), dtype=t1.dtype)
for kk in range(nkpts):
tau_term[kk] = 2 * t2[kk, ki, kk] - t2[ki, kk, kk].transpose(1, 0, 2, 3)
tau_term[ka] += einsum('ic,ka->kica', t1[ki], t1[ka])
for kk in range(nkpts):
kc = kk
t1new[ka] += einsum('kc,kica->ia', Fov[kc], tau_term[kk])
t1new[ka] += einsum('akic,kc->ia', 2 * eris.voov[ka, kk, ki], t1[kc])
t1new[ka] += einsum('kaic,kc->ia', -eris.ovov[kk, ka, ki], t1[kc])
for kc in range(nkpts):
kd = kconserv[ka, kc, kk]
Svovv = 2 * eris.vovv[ka, kk, kc] - eris.vovv[ka, kk, kd].transpose(0, 1, 3, 2)
tau_term_1 = t2[ki, kk, kc].copy()
if ki == kc and kk == kd:
tau_term_1 += einsum('ic,kd->ikcd', t1[ki], t1[kk])
t1new[ka] += einsum('akcd,ikcd->ia', Svovv, tau_term_1)
# kk - ki + kl = kc
# => kl = ki - kk + kc
kl = kconserv[ki, kk, kc]
Sooov = 2 * eris.ooov[kk, kl, ki] - eris.ooov[kl, kk, ki].transpose(1, 0, 2, 3)
tau_term_1 = t2[kk, kl, ka].copy()
if kk == ka and kl == kc:
tau_term_1 += einsum('ka,lc->klac', t1[ka], t1[kc])
t1new[ka] += -einsum('klic,klac->ia', Sooov, tau_term_1)
time1 = log.timer_debug1('t1', *time1)
# T2 equation
t2new = np.empty_like(t2)
for ki, kj, ka in kpts_helper.loop_kkk(nkpts):
t2new[ki, kj, ka] = eris.oovv[ki, kj, ka].conj()
mem_now = lib.current_memory()[0]
if (nocc ** 4 * nkpts ** 3) * 16 / 1e6 + mem_now < cc.max_memory * .9:
Woooo = imdk.cc_Woooo(t1, t2, eris, kconserv)
else:
fimd = lib.H5TmpFile()
Woooo = fimd.create_dataset('oooo', (nkpts, nkpts, nkpts, nocc, nocc, nocc, nocc), t1.dtype.char)
Woooo = imdk.cc_Woooo(t1, t2, eris, kconserv, Woooo)
for ki, kj, ka in kpts_helper.loop_kkk(nkpts):
# Chemist's notation for momentum conserving t2(ki,kj,ka,kb)
kb = kconserv[ki, ka, kj]
t2new_tmp = np.zeros((nocc, nocc, nvir, nvir), dtype=t2.dtype)
for kl in range(nkpts):
kk = kconserv[kj, kl, ki]
tau_term = t2[kk, kl, ka].copy()
if kl == kb and kk == ka:
tau_term += einsum('ic,jd->ijcd', t1[ka], t1[kb])
t2new_tmp += 0.5 * einsum('klij,klab->ijab', Woooo[kk, kl, ki], tau_term)
t2new[ki, kj, ka] += t2new_tmp
t2new[kj, ki, kb] += t2new_tmp.transpose(1, 0, 3, 2)
Woooo = None
fimd = None
time1 = log.timer_debug1('t2 oooo', *time1)
# einsum('abcd,ijcd->ijab', Wvvvv, tau)
add_vvvv_(cc, t2new, t1, t2, eris)
time1 = log.timer_debug1('t2 vvvv', *time1)
for ki, kj, ka in kpts_helper.loop_kkk(nkpts):
kb = kconserv[ki, ka, kj]
t2new_tmp = einsum('ac,ijcb->ijab', Lvv[ka], t2[ki, kj, ka])
t2new_tmp += einsum('ki,kjab->ijab', -Loo[ki], t2[ki, kj, ka])
kc = kconserv[ka, ki, kb]
tmp2 = np.asarray(eris.vovv[kc, ki, kb]).transpose(3, 2, 1, 0).conj() \
- einsum('kbic,ka->abic', eris.ovov[ka, kb, ki], t1[ka])
t2new_tmp += einsum('abic,jc->ijab', tmp2, t1[kj])
kk = kconserv[ki, ka, kj]
tmp2 = np.asarray(eris.ooov[kj, ki, kk]).transpose(3, 2, 1, 0).conj() \
+ einsum('akic,jc->akij', eris.voov[ka, kk, ki], t1[kj])
t2new_tmp -= einsum('akij,kb->ijab', tmp2, t1[kb])
t2new[ki, kj, ka] += t2new_tmp
t2new[kj, ki, kb] += t2new_tmp.transpose(1, 0, 3, 2)
mem_now = lib.current_memory()[0]
if (nocc ** 2 * nvir ** 2 * nkpts ** 3) * 16 / 1e6 * 2 + mem_now < cc.max_memory * .9:
Wvoov = imdk.cc_Wvoov(t1, t2, eris, kconserv)
Wvovo = imdk.cc_Wvovo(t1, t2, eris, kconserv)
else:
fimd = lib.H5TmpFile()
Wvoov = fimd.create_dataset('voov', (nkpts, nkpts, nkpts, nvir, nocc, nocc, nvir), t1.dtype.char)
Wvovo = fimd.create_dataset('vovo', (nkpts, nkpts, nkpts, nvir, nocc, nvir, nocc), t1.dtype.char)
Wvoov = imdk.cc_Wvoov(t1, t2, eris, kconserv, Wvoov)
Wvovo = imdk.cc_Wvovo(t1, t2, eris, kconserv, Wvovo)
for ki, kj, ka in kpts_helper.loop_kkk(nkpts):
kb = kconserv[ki, ka, kj]
t2new_tmp = np.zeros((nocc, nocc, nvir, nvir), dtype=t2.dtype)
for kk in range(nkpts):
kc = kconserv[ka, ki, kk]
tmp_voov = 2. * Wvoov[ka, kk, ki] - Wvovo[ka, kk, kc].transpose(0, 1, 3, 2)
t2new_tmp += einsum('akic,kjcb->ijab', tmp_voov, t2[kk, kj, kc])
kc = kconserv[ka, ki, kk]
t2new_tmp -= einsum('akic,kjbc->ijab', Wvoov[ka, kk, ki], t2[kk, kj, kb])
kc = kconserv[kk, ka, kj]
t2new_tmp -= einsum('bkci,kjac->ijab', Wvovo[kb, kk, kc], t2[kk, kj, ka])
t2new[ki, kj, ka] += t2new_tmp
t2new[kj, ki, kb] += t2new_tmp.transpose(1, 0, 3, 2)
Wvoov = Wvovo = None
fimd = None
time1 = log.timer_debug1('t2 voov', *time1)
for ki in range(nkpts):
ka = ki
# Remove zero/padded elements from denominator
eia = LARGE_DENOM * np.ones((nocc, nvir), dtype=eris.mo_energy[0].dtype)
n0_ovp_ia = np.ix_(nonzero_opadding[ki], nonzero_vpadding[ka])
eia[n0_ovp_ia] = (mo_e_o[ki][:,None] - mo_e_v[ka])[n0_ovp_ia]
t1new[ki] /= eia
for ki, kj, ka in kpts_helper.loop_kkk(nkpts):
kb = kconserv[ki, ka, kj]
# For LARGE_DENOM, see t1new update above
eia = LARGE_DENOM * np.ones((nocc, nvir), dtype=eris.mo_energy[0].dtype)
n0_ovp_ia = np.ix_(nonzero_opadding[ki], nonzero_vpadding[ka])
eia[n0_ovp_ia] = (mo_e_o[ki][:,None] - mo_e_v[ka])[n0_ovp_ia]
ejb = LARGE_DENOM * np.ones((nocc, nvir), dtype=eris.mo_energy[0].dtype)
n0_ovp_jb = np.ix_(nonzero_opadding[kj], nonzero_vpadding[kb])
ejb[n0_ovp_jb] = (mo_e_o[kj][:,None] - mo_e_v[kb])[n0_ovp_jb]
eijab = eia[:, None, :, None] + ejb[:, None, :]
t2new[ki, kj, ka] /= eijab
time0 = log.timer_debug1('update t1 t2', *time0)
return t1new, t2new
def add_vvvv_(cc, Ht2, t1, t2, eris):
nocc = cc.nocc
nmo = cc.nmo
nvir = nmo - nocc
nkpts = cc.nkpts
kconserv = cc.khelper.kconserv
mem_now = lib.current_memory()[0]
if cc.direct and getattr(eris, 'Lpv', None) is not None:
#: If memory is not enough to hold eris.Lpv
#:def get_Wvvvv(ka, kb, kc):
#: kd = kconserv[ka,kc,kb]
#: v = cc._scf.with_df.ao2mo([eris.mo_coeff[k] for k in [ka,kc,kb,kd]],
#: cc.kpts[[ka,kc,kb,kd]]).reshape([nmo]*4)
#: Wvvvv = lib.einsum('kcbd,ka->abcd', v[:nocc,nocc:,nocc:,nocc:], -t1[ka])
#: Wvvvv += lib.einsum('ackd,kb->abcd', v[nocc:,nocc:,:nocc,nocc:], -t1[kb])
#: Wvvvv += v[nocc:,nocc:,nocc:,nocc:].transpose(0,2,1,3)
#: Wvvvv *= (1./nkpts)
#: return Wvvvv
def get_Wvvvv(ka, kb, kc):
Lpv = eris.Lpv
kd = kconserv[ka, kc, kb]
Lbd = (Lpv[kb,kd][:,nocc:] -
lib.einsum('Lkd,kb->Lbd', Lpv[kb,kd][:,:nocc], t1[kb]))
Wvvvv = lib.einsum('Lac,Lbd->abcd', Lpv[ka,kc][:,nocc:], Lbd)
Lbd = None
kcbd = lib.einsum('Lkc,Lbd->kcbd', Lpv[ka,kc][:,:nocc],
Lpv[kb,kd][:,nocc:])
Wvvvv -= lib.einsum('kcbd,ka->abcd', kcbd, t1[ka])
Wvvvv *= (1. / nkpts)
return Wvvvv
elif (nvir ** 4 * nkpts ** 3) * 16 / 1e6 + mem_now < cc.max_memory * .9:
_Wvvvv = imdk.cc_Wvvvv(t1, t2, eris, kconserv)
def get_Wvvvv(ka, kb, kc):
return _Wvvvv[ka, kb, kc]
else:
fimd = lib.H5TmpFile()
_Wvvvv = fimd.create_dataset('vvvv', (nkpts, nkpts, nkpts, nvir, nvir, nvir, nvir), t1.dtype.char)
_Wvvvv = imdk.cc_Wvvvv(t1, t2, eris, kconserv, _Wvvvv)
def get_Wvvvv(ka, kb, kc):
return _Wvvvv[ka, kb, kc]
#:Ps = kconserve_pmatrix(cc.nkpts, cc.khelper.kconserv)
#:Wvvvv = einsum('xyzakcd,ykb->xyzabcd', eris.vovv, -t1)
#:Wvvvv = Wvvvv + einsum('xyzabcd,xyzw->yxwbadc', Wvvvv, Ps)
#:Wvvvv += eris.vvvv
#:
#:tau = t2.copy()
#:idx = np.arange(nkpts)
#:tau[idx,:,idx] += einsum('xic,yjd->xyijcd', t1, t1)
#:Ht2 += einsum('xyuijcd,zwuabcd,xyuv,zwuv->xyzijab', tau, Wvvvv, Ps, Ps)
for ka, kb, kc in kpts_helper.loop_kkk(nkpts):
kd = kconserv[ka, kc, kb]
Wvvvv = get_Wvvvv(ka, kb, kc)
for ki in range(nkpts):
kj = kconserv[ka, ki, kb]
tau = t2[ki, kj, kc].copy()
if ki == kc and kj == kd:
tau += np.einsum('ic,jd->ijcd', t1[ki], t1[kj])
Ht2[ki, kj, ka] += lib.einsum('abcd,ijcd->ijab', Wvvvv, tau)
fimd = None
return Ht2
def _make_eris_incore(cc, mo_coeff=None):
log = logger.Logger(cc.stdout, cc.verbose)
cput0 = (time.clock(), time.time())
eris = gccsd._PhysicistsERIs()
kpts = cc.kpts
nkpts = cc.nkpts
nocc = cc.nocc
nmo = cc.nmo
nvir = nmo - nocc
eris.nocc = nocc
#if any(nocc != numpy.count_nonzero(cc._scf.mo_occ[k] > 0) for k in range(nkpts)):
# raise NotImplementedError('Different occupancies found for different k-points')
if mo_coeff is None:
mo_coeff = cc.mo_coeff
#else:
# # If mo_coeff is not canonical orbital
# # TODO does this work for k-points? changed to conjugate.
# raise NotImplementedError
nao = mo_coeff[0].shape[0]
dtype = mo_coeff[0].dtype
moidx = get_frozen_mask(cc)
nocc_per_kpt = numpy.asarray(get_nocc(cc, per_kpoint=True))
nmo_per_kpt = numpy.asarray(get_nmo(cc, per_kpoint=True))
padded_moidx = []
for k in range(nkpts):
kpt_nocc = nocc_per_kpt[k]
kpt_nvir = nmo_per_kpt[k] - kpt_nocc
kpt_padded_moidx = numpy.concatenate(
(numpy.ones(kpt_nocc, dtype=numpy.bool),
numpy.zeros(nmo - kpt_nocc - kpt_nvir, dtype=numpy.bool),
numpy.ones(kpt_nvir, dtype=numpy.bool)))
padded_moidx.append(kpt_padded_moidx)
eris.mo_coeff = []
eris.orbspin = []
# Generate the molecular orbital coefficients with the frozen orbitals masked.
# Each MO is tagged with orbspin, a list of 0's and 1's that give the overall
# spin of each MO.
#
# Here we will work with two index arrays; one is for our original (small) moidx
# array while the next is for our new (large) padded array.
for k in range(nkpts):
kpt_moidx = moidx[k]
kpt_padded_moidx = padded_moidx[k]
mo = numpy.zeros((nao, nmo), dtype=dtype)
mo[:, kpt_padded_moidx] = mo_coeff[k][:, kpt_moidx]
if hasattr(mo_coeff[k], 'orbspin'):
orbspin_dtype = mo_coeff[k].orbspin[kpt_moidx].dtype
orbspin = numpy.zeros(nmo, dtype=orbspin_dtype)
orbspin[kpt_padded_moidx] = mo_coeff[k].orbspin[kpt_moidx]
mo = lib.tag_array(mo, orbspin=orbspin)
eris.orbspin.append(orbspin)
# FIXME: What if the user freezes all up spin orbitals in
# an RHF calculation? The number of electrons will still be
# even.
else: # guess orbital spin - assumes an RHF calculation
assert (numpy.count_nonzero(kpt_moidx) % 2 == 0)
orbspin = numpy.zeros(mo.shape[1], dtype=int)
orbspin[1::2] = 1
mo = lib.tag_array(mo, orbspin=orbspin)
eris.orbspin.append(orbspin)
eris.mo_coeff.append(mo)
# Re-make our fock MO matrix elements from density and fock AO
dm = cc._scf.make_rdm1(cc.mo_coeff, cc.mo_occ)
fockao = cc._scf.get_hcore() + cc._scf.get_veff(cc._scf.cell, dm)
eris.fock = numpy.asarray([
reduce(numpy.dot, (mo.T.conj(), fockao[k], mo))
for k, mo in enumerate(eris.mo_coeff)
])
kconserv = kpts_helper.get_kconserv(cc._scf.cell, cc.kpts)
# The bottom nao//2 coefficients are down (up) spin while the top are up (down).
# These are 'spin-less' quantities; spin-conservation will be added manually.
so_coeff = [mo[:nao // 2] + mo[nao // 2:] for mo in eris.mo_coeff]
eri = numpy.empty((nkpts, nkpts, nkpts, nmo, nmo, nmo, nmo),
dtype=numpy.complex128)
fao2mo = cc._scf.with_df.ao2mo
for kp, kq, kr in kpts_helper.loop_kkk(nkpts):
ks = kconserv[kp, kq, kr]
eri_kpt = fao2mo(
(so_coeff[kp], so_coeff[kq], so_coeff[kr], so_coeff[ks]),
(kpts[kp], kpts[kq], kpts[kr], kpts[ks]),
compact=False)
eri_kpt[(eris.orbspin[kp][:, None] != eris.orbspin[kq]).ravel()] = 0
eri_kpt[:, (eris.orbspin[kr][:, None] != eris.orbspin[ks]).ravel()] = 0
eri_kpt = eri_kpt.reshape(nmo, nmo, nmo, nmo)
eri[kp, kq, kr] = eri_kpt
# Check some antisymmetrized properties of the integrals
if DEBUG:
check_antisymm_3412(cc, cc.kpts, eri)
# Antisymmetrizing (pq|rs)-(ps|rq), where the latter integral is equal to
# (rq|ps); done since we aren't tracking the kpoint of orbital 's'
eri = eri - eri.transpose(2, 1, 0, 5, 4, 3, 6)
# Chemist -> physics notation
eri = eri.transpose(0, 2, 1, 3, 5, 4, 6)
# Set the various integrals
eris.dtype = eri.dtype
eris.oooo = eri[:, :, :, :nocc, :nocc, :nocc, :nocc].copy() / nkpts
eris.ooov = eri[:, :, :, :nocc, :nocc, :nocc, nocc:].copy() / nkpts
eris.ovoo = eri[:, :, :, :nocc, nocc:, :nocc, :nocc].copy() / nkpts
eris.oovv = eri[:, :, :, :nocc, :nocc, nocc:, nocc:].copy() / nkpts
eris.ovov = eri[:, :, :, :nocc, nocc:, :nocc, nocc:].copy() / nkpts
eris.ovvv = eri[:, :, :, :nocc, nocc:, nocc:, nocc:].copy() / nkpts
eris.vvvv = eri[:, :, :, nocc:, nocc:, nocc:, nocc:].copy() / nkpts
log.timer('CCSD integral transformation', *cput0)
return eris
def update_amps(cc, t1, t2, eris):
time0 = time.clock(), time.time()
log = logger.Logger(cc.stdout, cc.verbose)
nkpts, nocc, nvir = t1.shape
fock = eris.fock
mo_e_o = [e[:nocc] for e in eris.mo_energy]
mo_e_v = [e[nocc:] + cc.level_shift for e in eris.mo_energy]
# Get location of padded elements in occupied and virtual space
nonzero_opadding, nonzero_vpadding = padding_k_idx(cc, kind="split")
fov = fock[:, :nocc, nocc:].copy()
foo = fock[:, :nocc, :nocc].copy()
fvv = fock[:, nocc:, nocc:].copy()
# Get the momentum conservation array
# Note: chemist's notation for momentum conserving t2(ki,kj,ka,kb), even though
# integrals are in physics notation
kconserv = kpts_helper.get_kconserv(cc._scf.cell, cc.kpts)
tau = imdk.make_tau(cc, t2, t1, t1, kconserv)
Fvv = imdk.cc_Fvv(cc, t1, t2, eris, kconserv)
Foo = imdk.cc_Foo(cc, t1, t2, eris, kconserv)
Fov = imdk.cc_Fov(cc, t1, t2, eris, kconserv)
Woooo = imdk.cc_Woooo(cc, t1, t2, eris, kconserv)
Wvvvv = imdk.cc_Wvvvv(cc, t1, t2, eris, kconserv)
Wovvo = imdk.cc_Wovvo(cc, t1, t2, eris, kconserv)
# Move energy terms to the other side
for k in range(nkpts):
Foo[k][numpy.diag_indices(nocc)] -= mo_e_o[k]
Fvv[k][numpy.diag_indices(nvir)] -= mo_e_v[k]
eris_ovvo = numpy.zeros(shape=(nkpts, nkpts, nkpts, nocc, nvir, nvir, nocc), dtype=t2.dtype)
eris_oovo = numpy.zeros(shape=(nkpts, nkpts, nkpts, nocc, nocc, nvir, nocc), dtype=t2.dtype)
eris_vvvo = numpy.zeros(shape=(nkpts, nkpts, nkpts, nvir, nvir, nvir, nocc), dtype=t2.dtype)
for km, kb, ke in kpts_helper.loop_kkk(nkpts):
kj = kconserv[km, ke, kb]
# <mb||je> -> -<mb||ej>
eris_ovvo[km, kb, ke] = -eris.ovov[km, kb, kj].transpose(0, 1, 3, 2)
# <mn||je> -> -<mn||ej>
# let kb = kn as a dummy variable
eris_oovo[km, kb, ke] = -eris.ooov[km, kb, kj].transpose(0, 1, 3, 2)
# <ma||be> -> - <be||am>*
# let kj = ka as a dummy variable
kj = kconserv[km, ke, kb]
eris_vvvo[ke, kj, kb] = -eris.ovvv[km, kb, ke].transpose(2, 3, 1, 0).conj()
# T1 equation
t1new = numpy.zeros(shape=t1.shape, dtype=t1.dtype)
for ka in range(nkpts):
ki = ka
t1new[ka] += numpy.array(fov[ka, :, :]).conj()
t1new[ka] += einsum('ie,ae->ia', t1[ka], Fvv[ka])
t1new[ka] += -einsum('ma,mi->ia', t1[ka], Foo[ka])
for km in range(nkpts):
t1new[ka] += einsum('imae,me->ia', t2[ka, km, ka], Fov[km])
t1new[ka] += -einsum('nf,naif->ia', t1[km], eris.ovov[km, ka, ki])
for kn in range(nkpts):
ke = kconserv[km, ki, kn]
t1new[ka] += -0.5 * einsum('imef,maef->ia', t2[ki, km, ke], eris.ovvv[km, ka, ke])
t1new[ka] += -0.5 * einsum('mnae,nmei->ia', t2[km, kn, ka], eris_oovo[kn, km, ke])
# T2 equation
t2new = numpy.array(eris.oovv).conj()
for ki, kj, ka in kpts_helper.loop_kkk(nkpts):
# Chemist's notation for momentum conserving t2(ki,kj,ka,kb)
kb = kconserv[ki, ka, kj]
Ftmp = Fvv[kb] - 0.5 * einsum('mb,me->be', t1[kb], Fov[kb])
tmp = einsum('ijae,be->ijab', t2[ki, kj, ka], Ftmp)
t2new[ki, kj, ka] += tmp
#t2new[ki,kj,kb] -= tmp.transpose(0,1,3,2)
Ftmp = Fvv[ka] - 0.5 * einsum('ma,me->ae', t1[ka], Fov[ka])
tmp = einsum('ijbe,ae->ijab', t2[ki, kj, kb], Ftmp)
t2new[ki, kj, ka] -= tmp
Ftmp = Foo[kj] + 0.5 * einsum('je,me->mj', t1[kj], Fov[kj])
tmp = einsum('imab,mj->ijab', t2[ki, kj, ka], Ftmp)
t2new[ki, kj, ka] -= tmp
#t2new[kj,ki,ka] += tmp.transpose(1,0,2,3)
Ftmp = Foo[ki] + 0.5 * einsum('ie,me->mi', t1[ki], Fov[ki])
tmp = einsum('jmab,mi->ijab', t2[kj, ki, ka], Ftmp)
t2new[ki, kj, ka] += tmp
for km in range(nkpts):
# Wminj
# - km - kn + ka + kb = 0
# => kn = ka - km + kb
kn = kconserv[ka, km, kb]
t2new[ki, kj, ka] += 0.5 * einsum('mnab,mnij->ijab', tau[km, kn, ka], Woooo[km, kn, ki])
ke = km
t2new[ki, kj, ka] += 0.5 * einsum('ijef,abef->ijab', tau[ki, kj, ke], Wvvvv[ka, kb, ke])
# Wmbej
# - km - kb + ke + kj = 0
# => ke = km - kj + kb
ke = kconserv[km, kj, kb]
tmp = einsum('imae,mbej->ijab', t2[ki, km, ka], Wovvo[km, kb, ke])
# - km - kb + ke + kj = 0
# => ke = km - kj + kb
#
# t[i,e] => ki = ke
# t[m,a] => km = ka
if km == ka and ke == ki:
tmp -= einsum('ie,ma,mbej->ijab', t1[ki], t1[km], eris_ovvo[km, kb, ke])
t2new[ki, kj, ka] += tmp
t2new[ki, kj, kb] -= tmp.transpose(0, 1, 3, 2)
t2new[kj, ki, ka] -= tmp.transpose(1, 0, 2, 3)
t2new[kj, ki, kb] += tmp.transpose(1, 0, 3, 2)
ke = ki
tmp = einsum('ie,abej->ijab', t1[ki], eris_vvvo[ka, kb, ke])
t2new[ki, kj, ka] += tmp
# P(ij) term
ke = kj
tmp = einsum('je,abei->ijab', t1[kj], eris_vvvo[ka, kb, ke])
t2new[ki, kj, ka] -= tmp
km = ka
tmp = einsum('ma,mbij->ijab', t1[ka], eris.ovoo[km, kb, ki])
t2new[ki, kj, ka] -= tmp
# P(ab) term
km = kb
tmp = einsum('mb,maij->ijab', t1[kb], eris.ovoo[km, ka, ki])
t2new[ki, kj, ka] += tmp
for ki in range(nkpts):
ka = ki
# Remove zero/padded elements from denominator
eia = LARGE_DENOM * numpy.ones((nocc, nvir), dtype=eris.mo_energy[0].dtype)
n0_ovp_ia = numpy.ix_(nonzero_opadding[ki], nonzero_vpadding[ka])
eia[n0_ovp_ia] = (mo_e_o[ki][:,None] - mo_e_v[ka])[n0_ovp_ia]
t1new[ki] /= eia
kconserv = kpts_helper.get_kconserv(cc._scf.cell, cc.kpts)
for ki, kj, ka in kpts_helper.loop_kkk(nkpts):
kb = kconserv[ki, ka, kj]
# For LARGE_DENOM, see t1new update above
eia = LARGE_DENOM * numpy.ones((nocc, nvir), dtype=eris.mo_energy[0].dtype)
n0_ovp_ia = numpy.ix_(nonzero_opadding[ki], nonzero_vpadding[ka])
eia[n0_ovp_ia] = (mo_e_o[ki][:,None] - mo_e_v[ka])[n0_ovp_ia]
ejb = LARGE_DENOM * numpy.ones((nocc, nvir), dtype=eris.mo_energy[0].dtype)
n0_ovp_jb = numpy.ix_(nonzero_opadding[kj], nonzero_vpadding[kb])
ejb[n0_ovp_jb] = (mo_e_o[kj][:,None] - mo_e_v[kb])[n0_ovp_jb]
eijab = eia[:, None, :, None] + ejb[:, None, :]
t2new[ki, kj, ka] /= eijab
time0 = log.timer_debug1('update t1 t2', *time0)
return t1new, t2new
def _make_eris_incore(cc, mo_coeff=None):
from pyscf.pbc import tools
from pyscf.pbc.cc.ccsd import _adjust_occ
log = logger.Logger(cc.stdout, cc.verbose)
cput0 = (time.clock(), time.time())
eris = gccsd._PhysicistsERIs()
cell = cc._scf.cell
kpts = cc.kpts
nkpts = cc.nkpts
nocc = cc.nocc
nmo = cc.nmo
nvir = nmo - nocc
eris.nocc = nocc
#if any(nocc != numpy.count_nonzero(cc._scf.mo_occ[k] > 0) for k in range(nkpts)):
# raise NotImplementedError('Different occupancies found for different k-points')
if mo_coeff is None:
mo_coeff = cc.mo_coeff
nao = mo_coeff[0].shape[0]
dtype = mo_coeff[0].dtype
moidx = get_frozen_mask(cc)
nocc_per_kpt = numpy.asarray(get_nocc(cc, per_kpoint=True))
nmo_per_kpt = numpy.asarray(get_nmo(cc, per_kpoint=True))
padded_moidx = []
for k in range(nkpts):
kpt_nocc = nocc_per_kpt[k]
kpt_nvir = nmo_per_kpt[k] - kpt_nocc
kpt_padded_moidx = numpy.concatenate((numpy.ones(kpt_nocc, dtype=numpy.bool),
numpy.zeros(nmo - kpt_nocc - kpt_nvir, dtype=numpy.bool),
numpy.ones(kpt_nvir, dtype=numpy.bool)))
padded_moidx.append(kpt_padded_moidx)
eris.mo_coeff = []
eris.orbspin = []
# Generate the molecular orbital coefficients with the frozen orbitals masked.
# Each MO is tagged with orbspin, a list of 0's and 1's that give the overall
# spin of each MO.
#
# Here we will work with two index arrays; one is for our original (small) moidx
# array while the next is for our new (large) padded array.
for k in range(nkpts):
kpt_moidx = moidx[k]
kpt_padded_moidx = padded_moidx[k]
mo = numpy.zeros((nao, nmo), dtype=dtype)
mo[:, kpt_padded_moidx] = mo_coeff[k][:, kpt_moidx]
if getattr(mo_coeff[k], 'orbspin', None) is not None:
orbspin_dtype = mo_coeff[k].orbspin[kpt_moidx].dtype
orbspin = numpy.zeros(nmo, dtype=orbspin_dtype)
orbspin[kpt_padded_moidx] = mo_coeff[k].orbspin[kpt_moidx]
mo = lib.tag_array(mo, orbspin=orbspin)
eris.orbspin.append(orbspin)
# FIXME: What if the user freezes all up spin orbitals in
# an RHF calculation? The number of electrons will still be
# even.
else: # guess orbital spin - assumes an RHF calculation
assert (numpy.count_nonzero(kpt_moidx) % 2 == 0)
orbspin = numpy.zeros(mo.shape[1], dtype=int)
orbspin[1::2] = 1
mo = lib.tag_array(mo, orbspin=orbspin)
eris.orbspin.append(orbspin)
eris.mo_coeff.append(mo)
# Re-make our fock MO matrix elements from density and fock AO
dm = cc._scf.make_rdm1(cc.mo_coeff, cc.mo_occ)
with lib.temporary_env(cc._scf, exxdiv=None):
# _scf.exxdiv affects eris.fock. HF exchange correction should be
# excluded from the Fock matrix.
fockao = cc._scf.get_hcore() + cc._scf.get_veff(cell, dm)
eris.fock = numpy.asarray([reduce(numpy.dot, (mo.T.conj(), fockao[k], mo))
for k, mo in enumerate(eris.mo_coeff)])
eris.mo_energy = [eris.fock[k].diagonal().real for k in range(nkpts)]
# Add HFX correction in the eris.mo_energy to improve convergence in
# CCSD iteration. It is useful for the 2D systems since their occupied and
# the virtual orbital energies may overlap which may lead to numerical
# issue in the CCSD iterations.
# FIXME: Whether to add this correction for other exxdiv treatments?
# Without the correction, MP2 energy may be largely off the correct value.
madelung = tools.madelung(cell, kpts)
eris.mo_energy = [_adjust_occ(mo_e, nocc, -madelung)
for k, mo_e in enumerate(eris.mo_energy)]
# Get location of padded elements in occupied and virtual space.
nocc_per_kpt = get_nocc(cc, per_kpoint=True)
nonzero_padding = padding_k_idx(cc, kind="joint")
# Check direct and indirect gaps for possible issues with CCSD convergence.
mo_e = [eris.mo_energy[kp][nonzero_padding[kp]] for kp in range(nkpts)]
mo_e = numpy.sort([y for x in mo_e for y in x]) # Sort de-nested array
gap = mo_e[numpy.sum(nocc_per_kpt)] - mo_e[numpy.sum(nocc_per_kpt)-1]
if gap < 1e-5:
logger.warn(cc, 'H**O-LUMO gap %s too small for KCCSD. '
'May cause issues in convergence.', gap)
kconserv = kpts_helper.get_kconserv(cell, kpts)
if getattr(mo_coeff[0], 'orbspin', None) is None:
# The bottom nao//2 coefficients are down (up) spin while the top are up (down).
mo_a_coeff = [mo[:nao // 2] for mo in eris.mo_coeff]
mo_b_coeff = [mo[nao // 2:] for mo in eris.mo_coeff]
eri = numpy.empty((nkpts, nkpts, nkpts, nmo, nmo, nmo, nmo), dtype=numpy.complex128)
fao2mo = cc._scf.with_df.ao2mo
for kp, kq, kr in kpts_helper.loop_kkk(nkpts):
ks = kconserv[kp, kq, kr]
eri_kpt = fao2mo(
(mo_a_coeff[kp], mo_a_coeff[kq], mo_a_coeff[kr], mo_a_coeff[ks]), (kpts[kp], kpts[kq], kpts[kr], kpts[ks]),
compact=False)
eri_kpt += fao2mo(
(mo_b_coeff[kp], mo_b_coeff[kq], mo_b_coeff[kr], mo_b_coeff[ks]), (kpts[kp], kpts[kq], kpts[kr], kpts[ks]),
compact=False)
eri_kpt += fao2mo(
(mo_a_coeff[kp], mo_a_coeff[kq], mo_b_coeff[kr], mo_b_coeff[ks]), (kpts[kp], kpts[kq], kpts[kr], kpts[ks]),
compact=False)
eri_kpt += fao2mo(
(mo_b_coeff[kp], mo_b_coeff[kq], mo_a_coeff[kr], mo_a_coeff[ks]), (kpts[kp], kpts[kq], kpts[kr], kpts[ks]),
compact=False)
eri_kpt = eri_kpt.reshape(nmo, nmo, nmo, nmo)
eri[kp, kq, kr] = eri_kpt
else:
mo_a_coeff = [mo[:nao // 2] + mo[nao // 2:] for mo in eris.mo_coeff]
eri = numpy.empty((nkpts, nkpts, nkpts, nmo, nmo, nmo, nmo), dtype=numpy.complex128)
fao2mo = cc._scf.with_df.ao2mo
for kp, kq, kr in kpts_helper.loop_kkk(nkpts):
ks = kconserv[kp, kq, kr]
eri_kpt = fao2mo(
(mo_a_coeff[kp], mo_a_coeff[kq], mo_a_coeff[kr], mo_a_coeff[ks]), (kpts[kp], kpts[kq], kpts[kr], kpts[ks]),
compact=False)
eri_kpt[(eris.orbspin[kp][:, None] != eris.orbspin[kq]).ravel()] = 0
eri_kpt[:, (eris.orbspin[kr][:, None] != eris.orbspin[ks]).ravel()] = 0
eri_kpt = eri_kpt.reshape(nmo, nmo, nmo, nmo)
eri[kp, kq, kr] = eri_kpt
# Check some antisymmetrized properties of the integrals
if DEBUG:
check_antisymm_3412(cc, cc.kpts, eri)
# Antisymmetrizing (pq|rs)-(ps|rq), where the latter integral is equal to
# (rq|ps); done since we aren't tracking the kpoint of orbital 's'
eri = eri - eri.transpose(2, 1, 0, 5, 4, 3, 6)
# Chemist -> physics notation
eri = eri.transpose(0, 2, 1, 3, 5, 4, 6)
# Set the various integrals
eris.dtype = eri.dtype
eris.oooo = eri[:, :, :, :nocc, :nocc, :nocc, :nocc].copy() / nkpts
eris.ooov = eri[:, :, :, :nocc, :nocc, :nocc, nocc:].copy() / nkpts
eris.ovoo = eri[:, :, :, :nocc, nocc:, :nocc, :nocc].copy() / nkpts
eris.oovv = eri[:, :, :, :nocc, :nocc, nocc:, nocc:].copy() / nkpts
eris.ovov = eri[:, :, :, :nocc, nocc:, :nocc, nocc:].copy() / nkpts
eris.ovvv = eri[:, :, :, :nocc, nocc:, nocc:, nocc:].copy() / nkpts
eris.vvvv = eri[:, :, :, nocc:, nocc:, nocc:, nocc:].copy() / nkpts
log.timer('CCSD integral transformation', *cput0)
return eris
def spatial2spin(tx, orbspin, kconserv):
'''Convert T1/T2 of spatial orbital representation to T1/T2 of
spin-orbital representation
'''
if isinstance(tx, numpy.ndarray) and tx.ndim == 3:
# KRCCSD t1 amplitudes
return spatial2spin((tx,tx), orbspin, kconserv)
elif isinstance(tx, numpy.ndarray) and tx.ndim == 7:
# KRCCSD t2 amplitudes
t2aa = tx - tx.transpose(0,1,2,4,3,5,6)
return spatial2spin((t2aa,tx,t2aa), orbspin, kconserv)
elif len(tx) == 2: # KUCCSD t1
t1a, t1b = tx
nocc_a, nvir_a = t1a.shape[1:]
nocc_b, nvir_b = t1b.shape[1:]
else: # KUCCSD t2
t2aa, t2ab, t2bb = tx
nocc_a, nocc_b, nvir_a, nvir_b = t2ab.shape[3:]
nkpts = len(orbspin)
nocc = nocc_a + nocc_b
nvir = nvir_a + nvir_b
idxoa = [numpy.where(orbspin[k][:nocc] == 0)[0] for k in range(nkpts)]
idxob = [numpy.where(orbspin[k][:nocc] == 1)[0] for k in range(nkpts)]
idxva = [numpy.where(orbspin[k][nocc:] == 0)[0] for k in range(nkpts)]
idxvb = [numpy.where(orbspin[k][nocc:] == 1)[0] for k in range(nkpts)]
if len(tx) == 2: # t1
t1 = numpy.zeros((nkpts,nocc,nvir), dtype=t1a.dtype)
for k in range(nkpts):
lib.takebak_2d(t1[k], t1a[k], idxoa[k], idxva[k])
lib.takebak_2d(t1[k], t1b[k], idxob[k], idxvb[k])
t1 = lib.tag_array(t1, orbspin=orbspin)
return t1
else:
t2 = numpy.zeros((nkpts,nkpts,nkpts,nocc**2,nvir**2), dtype=t2aa.dtype)
for ki, kj, ka in kpts_helper.loop_kkk(nkpts):
kb = kconserv[ki,ka,kj]
idxoaa = idxoa[ki][:,None] * nocc + idxoa[kj]
idxoab = idxoa[ki][:,None] * nocc + idxob[kj]
idxoba = idxob[kj][:,None] * nocc + idxoa[ki]
idxobb = idxob[ki][:,None] * nocc + idxob[kj]
idxvaa = idxva[ka][:,None] * nvir + idxva[kb]
idxvab = idxva[ka][:,None] * nvir + idxvb[kb]
idxvba = idxvb[kb][:,None] * nvir + idxva[ka]
idxvbb = idxvb[ka][:,None] * nvir + idxvb[kb]
tmp2aa = t2aa[ki,kj,ka].reshape(nocc_a*nocc_a,nvir_a*nvir_a)
tmp2bb = t2bb[ki,kj,ka].reshape(nocc_b*nocc_b,nvir_b*nvir_b)
tmp2ab = t2ab[ki,kj,ka].reshape(nocc_a*nocc_b,nvir_a*nvir_b)
lib.takebak_2d(t2[ki,kj,ka], tmp2aa, idxoaa.ravel() , idxvaa.ravel() )
lib.takebak_2d(t2[ki,kj,ka], tmp2bb, idxobb.ravel() , idxvbb.ravel() )
lib.takebak_2d(t2[ki,kj,ka], tmp2ab, idxoab.ravel() , idxvab.ravel() )
lib.takebak_2d(t2[kj,ki,kb], tmp2ab, idxoba.T.ravel(), idxvba.T.ravel())
abba = -tmp2ab
lib.takebak_2d(t2[ki,kj,kb], abba, idxoab.ravel() , idxvba.T.ravel())
lib.takebak_2d(t2[kj,ki,ka], abba, idxoba.T.ravel(), idxvab.ravel() )
t2 = t2.reshape(nkpts,nkpts,nkpts,nocc,nocc,nvir,nvir)
t2 = lib.tag_array(t2, orbspin=orbspin)
return t2
def update_amps(cc, t1, t2, eris, max_memory=2000):
time0 = time.clock(), time.time()
log = logger.Logger(cc.stdout, cc.verbose)
nkpts, nocc, nvir = t1.shape
fock = eris.fock
fov = fock[:, :nocc, nocc:].copy()
foo = fock[:, :nocc, :nocc].copy()
fvv = fock[:, nocc:, nocc:].copy()
tau = imdk.make_tau(cc, t2, t1, t1)
Fvv = imdk.cc_Fvv(cc, t1, t2, eris)
Foo = imdk.cc_Foo(cc, t1, t2, eris)
Fov = imdk.cc_Fov(cc, t1, t2, eris)
Woooo = imdk.cc_Woooo(cc, t1, t2, eris)
Wvvvv = imdk.cc_Wvvvv(cc, t1, t2, eris)
Wovvo = imdk.cc_Wovvo(cc, t1, t2, eris)
# Move energy terms to the other side
for k in range(nkpts):
Fvv[k] -= numpy.diag(numpy.diag(fvv[k]))
Foo[k] -= numpy.diag(numpy.diag(foo[k]))
# Get the momentum conservation array
# Note: chemist's notation for momentum conserving t2(ki,kj,ka,kb), even though
# integrals are in physics notation
kconserv = kpts_helper.get_kconserv(cc._scf.cell, cc.kpts)
eris_ovvo = numpy.zeros(shape=(nkpts, nkpts, nkpts, nocc, nvir, nvir,
nocc),
dtype=t2.dtype)
eris_oovo = numpy.zeros(shape=(nkpts, nkpts, nkpts, nocc, nocc, nvir,
nocc),
dtype=t2.dtype)
eris_vvvo = numpy.zeros(shape=(nkpts, nkpts, nkpts, nvir, nvir, nvir,
nocc),
dtype=t2.dtype)
for km, kb, ke in kpts_helper.loop_kkk(nkpts):
kj = kconserv[km, ke, kb]
# <mb||je> -> -<mb||ej>
eris_ovvo[km, kb, ke] = -eris.ovov[km, kb, kj].transpose(0, 1, 3, 2)
# <mn||je> -> -<mn||ej>
# let kb = kn as a dummy variable
eris_oovo[km, kb, ke] = -eris.ooov[km, kb, kj].transpose(0, 1, 3, 2)
# <ma||be> -> - <be||am>*
# let kj = ka as a dummy variable
kj = kconserv[km, ke, kb]
eris_vvvo[ke, kj,
kb] = -eris.ovvv[km, kb, ke].transpose(2, 3, 1, 0).conj()
# T1 equation
t1new = numpy.zeros(shape=t1.shape, dtype=t1.dtype)
for ka in range(nkpts):
ki = ka
t1new[ka] += numpy.array(fov[ka, :, :]).conj()
t1new[ka] += einsum('ie,ae->ia', t1[ka], Fvv[ka])
t1new[ka] += -einsum('ma,mi->ia', t1[ka], Foo[ka])
for km in range(nkpts):
t1new[ka] += einsum('imae,me->ia', t2[ka, km, ka], Fov[km])
t1new[ka] += -einsum('nf,naif->ia', t1[km], eris.ovov[km, ka, ki])
for kn in range(nkpts):
ke = kconserv[km, ki, kn]
t1new[ka] += -0.5 * einsum('imef,maef->ia', t2[ki, km, ke],
eris.ovvv[km, ka, ke])
t1new[ka] += -0.5 * einsum('mnae,nmei->ia', t2[km, kn, ka],
eris_oovo[kn, km, ke])
# T2 equation
t2new = numpy.array(eris.oovv).conj()
for ki, kj, ka in kpts_helper.loop_kkk(nkpts):
# Chemist's notation for momentum conserving t2(ki,kj,ka,kb)
kb = kconserv[ki, ka, kj]
Ftmp = Fvv[kb] - 0.5 * einsum('mb,me->be', t1[kb], Fov[kb])
tmp = einsum('ijae,be->ijab', t2[ki, kj, ka], Ftmp)
t2new[ki, kj, ka] += tmp
#t2new[ki,kj,kb] -= tmp.transpose(0,1,3,2)
Ftmp = Fvv[ka] - 0.5 * einsum('ma,me->ae', t1[ka], Fov[ka])
tmp = einsum('ijbe,ae->ijab', t2[ki, kj, kb], Ftmp)
t2new[ki, kj, ka] -= tmp
Ftmp = Foo[kj] + 0.5 * einsum('je,me->mj', t1[kj], Fov[kj])
tmp = einsum('imab,mj->ijab', t2[ki, kj, ka], Ftmp)
t2new[ki, kj, ka] -= tmp
#t2new[kj,ki,ka] += tmp.transpose(1,0,2,3)
Ftmp = Foo[ki] + 0.5 * einsum('ie,me->mi', t1[ki], Fov[ki])
tmp = einsum('jmab,mi->ijab', t2[kj, ki, ka], Ftmp)
t2new[ki, kj, ka] += tmp
for km in range(nkpts):
# Wminj
# - km - kn + ka + kb = 0
# => kn = ka - km + kb
kn = kconserv[ka, km, kb]
t2new[ki, kj, ka] += 0.5 * einsum(
'mnab,mnij->ijab', tau[km, kn, ka], Woooo[km, kn, ki])
ke = km
t2new[ki, kj, ka] += 0.5 * einsum(
'ijef,abef->ijab', tau[ki, kj, ke], Wvvvv[ka, kb, ke])
# Wmbej
# - km - kb + ke + kj = 0
# => ke = km - kj + kb
ke = kconserv[km, kj, kb]
tmp = einsum('imae,mbej->ijab', t2[ki, km, ka], Wovvo[km, kb, ke])
# - km - kb + ke + kj = 0
# => ke = km - kj + kb
#
# t[i,e] => ki = ke
# t[m,a] => km = ka
if km == ka and ke == ki:
tmp -= einsum('ie,ma,mbej->ijab', t1[ki], t1[km],
eris_ovvo[km, kb, ke])
t2new[ki, kj, ka] += tmp
t2new[ki, kj, kb] -= tmp.transpose(0, 1, 3, 2)
t2new[kj, ki, ka] -= tmp.transpose(1, 0, 2, 3)
t2new[kj, ki, kb] += tmp.transpose(1, 0, 3, 2)
ke = ki
tmp = einsum('ie,abej->ijab', t1[ki], eris_vvvo[ka, kb, ke])
t2new[ki, kj, ka] += tmp
# P(ij) term
ke = kj
tmp = einsum('je,abei->ijab', t1[kj], eris_vvvo[ka, kb, ke])
t2new[ki, kj, ka] -= tmp
km = ka
tmp = einsum('ma,mbij->ijab', t1[ka], eris.ovoo[km, kb, ki])
t2new[ki, kj, ka] -= tmp
# P(ab) term
km = kb
tmp = einsum('mb,maij->ijab', t1[kb], eris.ovoo[km, ka, ki])
t2new[ki, kj, ka] += tmp
eia = numpy.zeros(shape=(nocc, nvir), dtype=t1new.dtype)
for ki in range(nkpts):
eia = foo[ki].diagonal()[:, None] - fvv[ki].diagonal()[None, :]
# When padding the occupied/virtual arrays, some fock elements will be zero
idx = numpy.where(abs(eia) < LOOSE_ZERO_TOL)[0]
eia[idx] = LARGE_DENOM
t1new[ki] /= eia
eijab = numpy.zeros(shape=(nocc, nocc, nvir, nvir), dtype=t2new.dtype)
kconserv = kpts_helper.get_kconserv(cc._scf.cell, cc.kpts)
for ki, kj, ka in kpts_helper.loop_kkk(nkpts):
kb = kconserv[ki, ka, kj]
eijab = (foo[ki].diagonal()[:, None, None, None] +
foo[kj].diagonal()[None, :, None, None] -
fvv[ka].diagonal()[None, None, :, None] -
fvv[kb].diagonal()[None, None, None, :])
# Due to padding; see above discussion concerning t1new in update_amps()
idx = numpy.where(abs(eijab) < LOOSE_ZERO_TOL)[0]
eijab[idx] = LARGE_DENOM
t2new[ki, kj, ka] /= eijab
time0 = log.timer_debug1('update t1 t2', *time0)
return t1new, t2new
