def get_full_t3p2(mycc, t1, t2, eris):
'''Build the entire T3[2] array in memory.
'''
nkpts = mycc.nkpts
nocc = mycc.nocc
nmo = mycc.nmo
nvir = nmo - nocc
kconserv = mycc.khelper.kconserv
def get_wijkabc(ki, kj, kk, ka, kb, kc):
'''Build T3[2] for `ijkabc` at a given set of k-points'''
km = kconserv[kc, kk, kb]
kf = kconserv[kk, kc, kj]
ret = einsum('kjcf,ifab->ijkabc', t2[kk, kj, kc], eris.ovvv[ki, kf,
ka].conj())
ret = ret - einsum('jima,mkbc->ijkabc', eris.ooov[kj, ki, km].conj(),
t2[km, kk, kb])
return ret
#fock = eris.fock
#fov = fock[:, :nocc, nocc:]
#foo = numpy.array([fock[ikpt, :nocc, :nocc].diagonal() for ikpt in range(nkpts)])
#fvv = numpy.array([fock[ikpt, nocc:, nocc:].diagonal() for ikpt in range(nkpts)])
mo_energy_occ = numpy.array(
[eris.mo_energy[ki][:nocc] for ki in range(nkpts)])
mo_energy_vir = numpy.array(
[eris.mo_energy[ki][nocc:] for ki in range(nkpts)])
mo_e_o = mo_energy_occ
mo_e_v = mo_energy_vir
# Get location of padded elements in occupied and virtual space
nonzero_opadding, nonzero_vpadding = padding_k_idx(mycc, kind="split")
t3 = numpy.empty((nkpts, nkpts, nkpts, nkpts, nkpts, nocc, nocc, nocc,
nvir, nvir, nvir),
dtype=t2.dtype)
for ki, kj, kk, ka, kb in product(range(nkpts), repeat=5):
kc = kpts_helper.get_kconserv3(mycc._scf.cell, mycc.kpts,
[ki, kj, kk, ka, kb])
# Perform P(abc)
t3[ki, kj, kk, ka, kb] = get_wijkabc(ki, kj, kk, ka, kb, kc)
t3[ki, kj, kk, ka, kb] += get_wijkabc(ki, kj, kk, kb, kc,
ka).transpose(0, 1, 2, 5, 3, 4)
t3[ki, kj, kk, ka, kb] += get_wijkabc(ki, kj, kk, kc, ka,
kb).transpose(0, 1, 2, 4, 5, 3)
# Perform P(ijk)
t3 = (t3.transpose(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10) +
t3.transpose(1, 2, 0, 3, 4, 6, 7, 5, 8, 9, 10) +
t3.transpose(2, 0, 1, 3, 4, 7, 5, 6, 8, 9, 10))
for ki, kj, kk in product(range(nkpts), repeat=3):
eijk = _get_epqr([0, nocc, ki, mo_e_o, nonzero_opadding],
[0, nocc, kj, mo_e_o, nonzero_opadding],
[0, nocc, kk, mo_e_o, nonzero_opadding])
for ka, kb in product(range(nkpts), repeat=2):
kc = kpts_helper.get_kconserv3(mycc._scf.cell, mycc.kpts,
[ki, kj, kk, ka, kb])
eabc = _get_epqr([0, nvir, ka, mo_e_v, nonzero_vpadding],
[0, nvir, kb, mo_e_v, nonzero_vpadding],
[0, nvir, kc, mo_e_v, nonzero_vpadding],
fac=[-1., -1., -1.])
eijkabc = eijk[:, :, :, None, None, None] + eabc[None, None,
None, :, :, :]
t3[ki, kj, kk, ka, kb] /= eijkabc
return t3
def get_t3p2_imds(mycc, t1, t2, eris=None, t3p2_ip_out=None, t3p2_ea_out=None):
"""For a description of arguments, see `get_t3p2_imds_slow` in
the corresponding `kintermediates.py`.
"""
from pyscf.pbc.cc.kccsd_t_rhf import _get_epqr
cpu1 = cpu0 = (logger.process_clock(), logger.perf_counter())
if eris is None:
eris = mycc.ao2mo()
fock = eris.fock
nkpts, nocc, nvir = t1.shape
cell = mycc._scf.cell
kpts = mycc.kpts
kconserv = mycc.khelper.kconserv
dtype = np.result_type(t1, t2)
fov = fock[:, :nocc, nocc:]
#foo = np.asarray([fock[ikpt, :nocc, :nocc].diagonal() for ikpt in range(nkpts)])
#fvv = np.asarray([fock[ikpt, nocc:, nocc:].diagonal() for ikpt in range(nkpts)])
mo_energy_occ = np.array(
[eris.mo_energy[ki][:nocc] for ki in range(nkpts)])
mo_energy_vir = np.array(
[eris.mo_energy[ki][nocc:] for ki in range(nkpts)])
mo_e_o = mo_energy_occ
mo_e_v = mo_energy_vir
ccsd_energy = mycc.energy(t1, t2, eris)
if t3p2_ip_out is None:
t3p2_ip_out = np.zeros((nkpts, nkpts, nkpts, nocc, nvir, nocc, nocc),
dtype=dtype)
Wmcik = t3p2_ip_out
if t3p2_ea_out is None:
t3p2_ea_out = np.zeros((nkpts, nkpts, nkpts, nvir, nvir, nvir, nocc),
dtype=dtype)
Wacek = t3p2_ea_out
# Create necessary temporary eris for fast read
from pyscf.pbc.cc.kccsd_t_rhf import create_t3_eris, get_data_slices
feri_tmp, t2T, eris_vvop, eris_vooo_C = create_t3_eris(
mycc, kconserv, [eris.vovv, eris.oovv, eris.ooov, t2])
#t1T = np.array([x.T for x in t1], dtype=np.complex, order='C')
#fvo = np.array([x.T for x in fov], dtype=np.complex, order='C')
cpu1 = logger.timer_debug1(mycc, 'CCSD(T) tmp eri creation', *cpu1)
def get_w(ki, kj, kk, ka, kb, kc, a0, a1, b0, b1, c0, c1):
'''Wijkabc intermediate as described in Scuseria paper before Pijkabc acts
Function copied for `kccsd_t_rhf.py`'''
km = kconserv[kc, kk, kb]
kf = kconserv[kk, kc, kj]
out = einsum('cfjk,abif->abcijk', t2T[kc, kf, kj, c0:c1, :, :, :],
eris_vvop[ka, kb, ki, a0:a1, b0:b1, :, nocc:])
out = out - einsum('cbmk,aijm->abcijk', t2T[kc, kb, km, c0:c1,
b0:b1, :, :],
eris_vooo_C[ka, ki, kj, a0:a1, :, :, :])
return out
def get_permuted_w(ki, kj, kk, ka, kb, kc, orb_indices):
'''Pijkabc operating on Wijkabc intermediate as described in Scuseria paper
Function copied for `kccsd_t_rhf.py`'''
a0, a1, b0, b1, c0, c1 = orb_indices
out = get_w(ki, kj, kk, ka, kb, kc, a0, a1, b0, b1, c0, c1)
out = out + get_w(kj, kk, ki, kb, kc, ka, b0, b1, c0, c1, a0,
a1).transpose(2, 0, 1, 5, 3, 4)
out = out + get_w(kk, ki, kj, kc, ka, kb, c0, c1, a0, a1, b0,
b1).transpose(1, 2, 0, 4, 5, 3)
out = out + get_w(ki, kk, kj, ka, kc, kb, a0, a1, c0, c1, b0,
b1).transpose(0, 2, 1, 3, 5, 4)
out = out + get_w(kk, kj, ki, kc, kb, ka, c0, c1, b0, b1, a0,
a1).transpose(2, 1, 0, 5, 4, 3)
out = out + get_w(kj, ki, kk, kb, ka, kc, b0, b1, a0, a1, c0,
c1).transpose(1, 0, 2, 4, 3, 5)
return out
def get_data(kpt_indices):
idx_args = get_data_slices(kpt_indices, task, kconserv)
vvop_indices, vooo_indices, t2T_vvop_indices, t2T_vooo_indices = idx_args
vvop_data = [eris_vvop[tuple(x)] for x in vvop_indices]
vooo_data = [eris_vooo_C[tuple(x)] for x in vooo_indices]
t2T_vvop_data = [t2T[tuple(x)] for x in t2T_vvop_indices]
t2T_vooo_data = [t2T[tuple(x)] for x in t2T_vooo_indices]
data = [vvop_data, vooo_data, t2T_vvop_data, t2T_vooo_data]
return data
def add_and_permute(kpt_indices, orb_indices, data):
'''Performs permutation and addition of t3 temporary arrays.'''
ki, kj, kk, ka, kb, kc = kpt_indices
a0, a1, b0, b1, c0, c1 = orb_indices
tmp_t3Tv_ijk = np.asarray(data[0], dtype=dtype, order='C')
tmp_t3Tv_jik = np.asarray(data[1], dtype=dtype, order='C')
tmp_t3Tv_kji = np.asarray(data[2], dtype=dtype, order='C')
#out_ijk = np.empty(data[0].shape, dtype=dtype, order='C')
#drv = _ccsd.libcc.MPICCadd_and_permute_t3T
#drv(ctypes.c_int(nocc), ctypes.c_int(nvir),
# ctypes.c_int(0),
# out_ijk.ctypes.data_as(ctypes.c_void_p),
# tmp_t3Tv_ijk.ctypes.data_as(ctypes.c_void_p),
# tmp_t3Tv_jik.ctypes.data_as(ctypes.c_void_p),
# tmp_t3Tv_kji.ctypes.data_as(ctypes.c_void_p),
# mo_offset.ctypes.data_as(ctypes.c_void_p),
# slices.ctypes.data_as(ctypes.c_void_p))
return (2. * tmp_t3Tv_ijk - tmp_t3Tv_jik.transpose(0, 1, 2, 4, 3, 5) -
tmp_t3Tv_kji.transpose(0, 1, 2, 5, 4, 3))
#return out_ijk
# Get location of padded elements in occupied and virtual space
nonzero_opadding, nonzero_vpadding = padding_k_idx(mycc, kind="split")
mem_now = lib.current_memory()[0]
max_memory = max(0, mycc.max_memory - mem_now)
blkmin = 4
# temporary t3 array is size: nkpts**3 * blksize**3 * nocc**3 * 16
vir_blksize = min(
nvir,
max(blkmin, int(
(max_memory * .9e6 / 16 / nocc**3 / nkpts**3)**(1. / 3))))
tasks = []
logger.debug(mycc, 'max_memory %d MB (%d MB in use)', max_memory, mem_now)
logger.debug(mycc, 'virtual blksize = %d (nvir = %d)', vir_blksize, nvir)
for a0, a1 in lib.prange(0, nvir, vir_blksize):
for b0, b1 in lib.prange(0, nvir, vir_blksize):
for c0, c1 in lib.prange(0, nvir, vir_blksize):
tasks.append((a0, a1, b0, b1, c0, c1))
eaa = []
for ka in range(nkpts):
eaa.append(mo_e_o[ka][:, None] - mo_e_v[ka][None, :])
pt1 = np.zeros((nkpts, nocc, nvir), dtype=dtype)
pt2 = np.zeros((nkpts, nkpts, nkpts, nocc, nocc, nvir, nvir), dtype=dtype)
for ka, kb in product(range(nkpts), repeat=2):
for task_id, task in enumerate(tasks):
cput2 = (logger.process_clock(), logger.perf_counter())
a0, a1, b0, b1, c0, c1 = task
my_permuted_w = np.zeros(
(nkpts, ) * 3 + (a1 - a0, b1 - b0, c1 - c0) + (nocc, ) * 3,
dtype=dtype)
for ki, kj, kk in product(range(nkpts), repeat=3):
# Find momentum conservation condition for triples
# amplitude t3ijkabc
kc = kpts_helper.get_kconserv3(cell, kpts,
[ki, kj, kk, ka, kb])
kpt_indices = [ki, kj, kk, ka, kb, kc]
#data = get_data(kpt_indices)
my_permuted_w[ki, kj,
kk] = get_permuted_w(ki, kj, kk, ka, kb, kc,
task)
for ki, kj, kk in product(range(nkpts), repeat=3):
# eigenvalue denominator: e(i) + e(j) + e(k)
eijk = _get_epqr([0, nocc, ki, mo_e_o, nonzero_opadding],
[0, nocc, kj, mo_e_o, nonzero_opadding],
[0, nocc, kk, mo_e_o, nonzero_opadding])
# Find momentum conservation condition for triples
# amplitude t3ijkabc
kc = kpts_helper.get_kconserv3(cell, kpts,
[ki, kj, kk, ka, kb])
eabc = _get_epqr([a0, a1, ka, mo_e_v, nonzero_vpadding],
[b0, b1, kb, mo_e_v, nonzero_vpadding],
[c0, c1, kc, mo_e_v, nonzero_vpadding],
fac=[-1., -1., -1.])
kpt_indices = [ki, kj, kk, ka, kb, kc]
eabcijk = (eijk[None, None, None, :, :, :] +
eabc[:, :, :, None, None, None])
tmp_t3Tv_ijk = my_permuted_w[ki, kj, kk]
tmp_t3Tv_jik = my_permuted_w[kj, ki, kk]
tmp_t3Tv_kji = my_permuted_w[kk, kj, ki]
Ptmp_t3Tv = add_and_permute(
kpt_indices, task,
(tmp_t3Tv_ijk, tmp_t3Tv_jik, tmp_t3Tv_kji))
Ptmp_t3Tv /= eabcijk
# Contribution to T1 amplitudes
if ki == ka and kc == kconserv[kj, kb, kk]:
eris_Soovv = (
2. * eris.oovv[kj, kk, kb, :, :, b0:b1, c0:c1] -
eris.oovv[kj, kk, kc, :, :, c0:c1, b0:b1].transpose(
0, 1, 3, 2))
pt1[ka, :, a0:a1] += 0.5 * einsum('abcijk,jkbc->ia',
Ptmp_t3Tv, eris_Soovv)
# Contribution to T2 amplitudes
if ki == ka and kc == kconserv[kj, kb, kk]:
tmp = einsum('abcijk,ia->jkbc', Ptmp_t3Tv,
0.5 * fov[ki, :, a0:a1])
_add_pt2(pt2, nkpts, kconserv, [kj, kk, kb],
[None, None, (b0, b1), (c0, c1)], tmp)
kd = kconserv[ka, ki, kb]
eris_vovv = eris.vovv[kd, ki, kb, :, :, b0:b1, a0:a1]
tmp = einsum('abcijk,diba->jkdc', Ptmp_t3Tv, eris_vovv)
_add_pt2(pt2, nkpts, kconserv, [kj, kk, kd],
[None, None, None, (c0, c1)], tmp)
km = kconserv[kc, kk, kb]
eris_ooov = eris.ooov[kj, ki, km, :, :, :, a0:a1]
tmp = einsum('abcijk,jima->mkbc', Ptmp_t3Tv, eris_ooov)
_add_pt2(pt2, nkpts, kconserv, [km, kk, kb],
[None, None, (b0, b1), (c0, c1)], -1. * tmp)
# Contribution to Wovoo array
km = kconserv[ka, ki, kc]
eris_oovv = eris.oovv[km, ki, kc, :, :, c0:c1, a0:a1]
tmp = einsum('abcijk,mica->mbkj', Ptmp_t3Tv, eris_oovv)
Wmcik[km, kb, kk, :, b0:b1, :, :] += tmp
# Contribution to Wvvoo array
ke = kconserv[ki, ka, kk]
eris_oovv = eris.oovv[ki, kk, ka, :, :, a0:a1, :]
tmp = einsum('abcijk,ikae->cbej', Ptmp_t3Tv, eris_oovv)
Wacek[kc, kb, ke, c0:c1, b0:b1, :, :] -= tmp
logger.timer_debug1(
mycc, 'EOM-CCSD T3[2] ka,kb,vir=(%d,%d,%d/%d) [total=%d]' %
(ka, kb, task_id, len(tasks), nkpts**5), *cput2)
for ki in range(nkpts):
ka = ki
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]
pt1[ki] /= eia
for ki, ka in product(range(nkpts), repeat=2):
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]
for kj in range(nkpts):
kb = kconserv[ki, ka, kj]
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, :]
pt2[ki, kj, ka] /= eijab
pt1 += t1
pt2 += t2
logger.timer(mycc, 'EOM-CCSD(T) imds', *cpu0)
delta_ccsd_energy = mycc.energy(pt1, pt2, eris) - ccsd_energy
logger.info(mycc, 'CCSD energy T3[2] correction : %16.12e',
delta_ccsd_energy)
return delta_ccsd_energy, pt1, pt2, Wmcik, Wacek
def kernel(mycc, eris, t1=None, t2=None, max_memory=2000, verbose=logger.INFO):
'''Returns the CCSD(T) for general spin-orbital integrals with k-points.
Note:
Returns real part of the CCSD(T) energy, raises warning if there is
a complex part.
Args:
mycc (:class:`GCCSD`): Coupled-cluster object storing results of
a coupled-cluster calculation.
eris (:class:`_ERIS`): Integral object holding the relevant electron-
repulsion integrals and Fock matrix elements
t1 (:obj:`ndarray`): t1 coupled-cluster amplitudes
t2 (:obj:`ndarray`): t2 coupled-cluster amplitudes
max_memory (float): Maximum memory used in calculation (NOT USED)
verbose (int, :class:`Logger`): verbosity of calculation
Returns:
energy_t (float): The real-part of the k-point CCSD(T) energy.
'''
assert isinstance(mycc, pyscf.pbc.cc.kccsd.GCCSD)
if isinstance(verbose, logger.Logger):
log = verbose
else:
log = logger.Logger(mycc.stdout, verbose)
if t1 is None: t1 = mycc.t1
if t2 is None: t2 = mycc.t2
if t1 is None or t2 is None:
raise TypeError(
'Must pass in t1/t2 amplitudes to k-point CCSD(T)! (Maybe '
'need to run `.ccsd()` on the ccsd object?)')
cell = mycc._scf.cell
kpts = mycc.kpts
# The dtype of any local arrays that will be created
dtype = t1.dtype
nkpts, nocc, nvir = t1.shape
mo_energy_occ = [eris.mo_energy[ki][:nocc] for ki in range(nkpts)]
mo_energy_vir = [eris.mo_energy[ki][nocc:] for ki in range(nkpts)]
fov = eris.fock[:, :nocc, nocc:]
mo_e_o = mo_energy_occ
mo_e_v = mo_energy_vir
# Set up class for k-point conservation
kconserv = kpts_helper.get_kconserv(cell, kpts)
# Get location of padded elements in occupied and virtual space
nonzero_opadding, nonzero_vpadding = padding_k_idx(mycc, kind="split")
energy_t = 0.0
for ki in range(nkpts):
for kj in range(ki + 1):
for kk in range(kj + 1):
# eigenvalue denominator: e(i) + e(j) + e(k)
eijk = _get_epqr([0, nocc, ki, mo_e_o, nonzero_opadding],
[0, nocc, kj, mo_e_o, nonzero_opadding],
[0, nocc, kk, mo_e_o, nonzero_opadding])
# Factors to include for permutational symmetry among k-points for occupied space
if ki == kj and kj == kk:
symm_ijk_kpt = 1. # only one degeneracy
elif ki == kj or kj == kk:
symm_ijk_kpt = 3. # 3 degeneracies when only one k-point is unique
else:
symm_ijk_kpt = 6. # 3! combinations of arranging 3 distinct k-points
for ka in range(nkpts):
for kb in range(ka + 1):
# Find momentum conservation condition for triples
# amplitude t3ijkabc
kc = kpts_helper.get_kconserv3(cell, kpts,
[ki, kj, kk, ka, kb])
if kc not in range(kb + 1):
continue
# -1.0 so the LARGE_DENOM does not cancel with the one from eijk
eabc = _get_epqr(
[0, nvir, ka, mo_e_v, nonzero_vpadding],
[0, nvir, kb, mo_e_v, nonzero_vpadding],
[0, nvir, kc, mo_e_v, nonzero_vpadding],
fac=[-1., -1., -1.])
# Factors to include for permutational symmetry among k-points for virtual space
if ka == kb and kb == kc:
symm_abc_kpt = 1. # one unique combination of (ka, kb, kc)
elif ka == kb or kb == kc:
symm_abc_kpt = 3. # 3 unique combinations of (ka, kb, kc)
else:
symm_abc_kpt = 6. # 6 unique combinations of (ka, kb, kc)
# Determine the a, b, c indices we will loop over as
# determined by the k-point symmetry.
abc_indices = cartesian_prod([range(nvir)] * 3)
symm_3d = symm_2d_ab = symm_2d_bc = False
if ka == kc: # == kb from lower triangular summation
abc_indices = tril_product(
range(nvir), repeat=3,
tril_idx=[0, 1, 2]) # loop a >= b >= c
symm_3d = True
elif ka == kb:
abc_indices = tril_product(
range(nvir), repeat=3,
tril_idx=[0, 1]) # loop a >= b
symm_2d_ab = True
elif kb == kc:
abc_indices = tril_product(
range(nvir), repeat=3,
tril_idx=[1, 2]) # loop b >= c
symm_2d_bc = True
for a, b, c in abc_indices:
# See symm_3d and abc_indices above for description of factors
symm_abc = 1.
if symm_3d:
if a == b == c:
symm_abc = 1.
elif a == b or b == c:
symm_abc = 3.
else:
symm_abc = 6.
elif symm_2d_ab:
if a == b:
symm_abc = 1.
else:
symm_abc = 2.
elif symm_2d_bc:
if b == c:
symm_abc = 1.
else:
symm_abc = 2.
# Form energy denominator
eijkabc = (eijk[:, :, :] + eabc[a, b, c])
# Form connected triple excitation amplitude
t3c = np.zeros((nocc, nocc, nocc), dtype=dtype)
# First term: 1 - p(ij) - p(ik)
ke = kconserv[kj, ka, kk]
t3c = t3c + einsum(
'jke,ie->ijk', t2[kj, kk, ka, :, :, a, :],
-eris.ovvv[ki, ke, kc, :, :, c, b].conj())
ke = kconserv[ki, ka, kk]
t3c = t3c - einsum(
'ike,je->ijk', t2[ki, kk, ka, :, :, a, :],
-eris.ovvv[kj, ke, kc, :, :, c, b].conj())
ke = kconserv[kj, ka, ki]
t3c = t3c - einsum(
'jie,ke->ijk', t2[kj, ki, ka, :, :, a, :],
-eris.ovvv[kk, ke, kc, :, :, c, b].conj())
km = kconserv[kb, ki, kc]
t3c = t3c - einsum(
'mi,jkm->ijk', t2[km, ki, kb, :, :, b, c],
eris.ooov[kj, kk, km, :, :, :, a].conj())
km = kconserv[kb, kj, kc]
t3c = t3c + einsum(
'mj,ikm->ijk', t2[km, kj, kb, :, :, b, c],
eris.ooov[ki, kk, km, :, :, :, a].conj())
km = kconserv[kb, kk, kc]
t3c = t3c + einsum(
'mk,jim->ijk', t2[km, kk, kb, :, :, b, c],
eris.ooov[kj, ki, km, :, :, :, a].conj())
# Second term: - p(ab) + p(ab) p(ij) + p(ab) p(ik)
ke = kconserv[kj, kb, kk]
t3c = t3c - einsum(
'jke,ie->ijk', t2[kj, kk, kb, :, :, b, :],
-eris.ovvv[ki, ke, kc, :, :, c, a].conj())
ke = kconserv[ki, kb, kk]
t3c = t3c + einsum(
'ike,je->ijk', t2[ki, kk, kb, :, :, b, :],
-eris.ovvv[kj, ke, kc, :, :, c, a].conj())
ke = kconserv[kj, kb, ki]
t3c = t3c + einsum(
'jie,ke->ijk', t2[kj, ki, kb, :, :, b, :],
-eris.ovvv[kk, ke, kc, :, :, c, a].conj())
km = kconserv[ka, ki, kc]
t3c = t3c + einsum(
'mi,jkm->ijk', t2[km, ki, ka, :, :, a, c],
eris.ooov[kj, kk, km, :, :, :, b].conj())
km = kconserv[ka, kj, kc]
t3c = t3c - einsum(
'mj,ikm->ijk', t2[km, kj, ka, :, :, a, c],
eris.ooov[ki, kk, km, :, :, :, b].conj())
km = kconserv[ka, kk, kc]
t3c = t3c - einsum(
'mk,jim->ijk', t2[km, kk, ka, :, :, a, c],
eris.ooov[kj, ki, km, :, :, :, b].conj())
# Third term: - p(ac) + p(ac) p(ij) + p(ac) p(ik)
ke = kconserv[kj, kc, kk]
t3c = t3c - einsum(
'jke,ie->ijk', t2[kj, kk, kc, :, :, c, :],
-eris.ovvv[ki, ke, ka, :, :, a, b].conj())
ke = kconserv[ki, kc, kk]
t3c = t3c + einsum(
'ike,je->ijk', t2[ki, kk, kc, :, :, c, :],
-eris.ovvv[kj, ke, ka, :, :, a, b].conj())
ke = kconserv[kj, kc, ki]
t3c = t3c + einsum(
'jie,ke->ijk', t2[kj, ki, kc, :, :, c, :],
-eris.ovvv[kk, ke, ka, :, :, a, b].conj())
km = kconserv[kb, ki, ka]
t3c = t3c + einsum(
'mi,jkm->ijk', t2[km, ki, kb, :, :, b, a],
eris.ooov[kj, kk, km, :, :, :, c].conj())
km = kconserv[kb, kj, ka]
t3c = t3c - einsum(
'mj,ikm->ijk', t2[km, kj, kb, :, :, b, a],
eris.ooov[ki, kk, km, :, :, :, c].conj())
km = kconserv[kb, kk, ka]
t3c = t3c - einsum(
'mk,jim->ijk', t2[km, kk, kb, :, :, b, a],
eris.ooov[kj, ki, km, :, :, :, c].conj())
# Form disconnected triple excitation amplitude contribution
t3d = np.zeros((nocc, nocc, nocc), dtype=dtype)
# First term: 1 - p(ij) - p(ik)
if ki == ka:
t3d = t3d + einsum(
'i,jk->ijk', t1[ki, :, a],
-eris.oovv[kj, kk, kb, :, :, b, c].conj())
t3d = t3d + einsum('i,jk->ijk', -fov[ki, :, a],
t2[kj, kk, kb, :, :, b, c])
if kj == ka:
t3d = t3d - einsum(
'j,ik->ijk', t1[kj, :, a],
-eris.oovv[ki, kk, kb, :, :, b, c].conj())
t3d = t3d - einsum('j,ik->ijk', -fov[kj, :, a],
t2[ki, kk, kb, :, :, b, c])
if kk == ka:
t3d = t3d - einsum(
'k,ji->ijk', t1[kk, :, a],
-eris.oovv[kj, ki, kb, :, :, b, c].conj())
t3d = t3d - einsum('k,ji->ijk', -fov[kk, :, a],
t2[kj, ki, kb, :, :, b, c])
# Second term: - p(ab) + p(ab) p(ij) + p(ab) p(ik)
if ki == kb:
t3d = t3d - einsum(
'i,jk->ijk', t1[ki, :, b],
-eris.oovv[kj, kk, ka, :, :, a, c].conj())
t3d = t3d - einsum('i,jk->ijk', -fov[ki, :, b],
t2[kj, kk, ka, :, :, a, c])
if kj == kb:
t3d = t3d + einsum(
'j,ik->ijk', t1[kj, :, b],
-eris.oovv[ki, kk, ka, :, :, a, c].conj())
t3d = t3d + einsum('j,ik->ijk', -fov[kj, :, b],
t2[ki, kk, ka, :, :, a, c])
if kk == kb:
t3d = t3d + einsum(
'k,ji->ijk', t1[kk, :, b],
-eris.oovv[kj, ki, ka, :, :, a, c].conj())
t3d = t3d + einsum('k,ji->ijk', -fov[kk, :, b],
t2[kj, ki, ka, :, :, a, c])
# Third term: - p(ac) + p(ac) p(ij) + p(ac) p(ik)
if ki == kc:
t3d = t3d - einsum(
'i,jk->ijk', t1[ki, :, c],
-eris.oovv[kj, kk, kb, :, :, b, a].conj())
t3d = t3d - einsum('i,jk->ijk', -fov[ki, :, c],
t2[kj, kk, kb, :, :, b, a])
if kj == kc:
t3d = t3d + einsum(
'j,ik->ijk', t1[kj, :, c],
-eris.oovv[ki, kk, kb, :, :, b, a].conj())
t3d = t3d + einsum('j,ik->ijk', -fov[kj, :, c],
t2[ki, kk, kb, :, :, b, a])
if kk == kc:
t3d = t3d + einsum(
'k,ji->ijk', t1[kk, :, c],
-eris.oovv[kj, ki, kb, :, :, b, a].conj())
t3d = t3d + einsum('k,ji->ijk', -fov[kk, :, c],
t2[kj, ki, kb, :, :, b, a])
t3c_plus_d = t3c + t3d
t3c_plus_d /= eijkabc
energy_t += symm_abc_kpt * symm_ijk_kpt * symm_abc * einsum(
'ijk,ijk', t3c, t3c_plus_d.conj())
energy_t = (1. / 36) * energy_t / nkpts
if abs(energy_t.imag) > 1e-4:
log.warn('Non-zero imaginary part of CCSD(T) energy was found %s',
energy_t.imag)
log.note('CCSD(T) correction per cell = %.15g', energy_t.real)
return energy_t.real
def get_t3p2_imds_slow(cc,
t1,
t2,
eris=None,
t3p2_ip_out=None,
t3p2_ea_out=None):
"""For a description of arguments, see `get_t3p2_imds_slow` in
the corresponding `kintermediates.py`.
"""
from pyscf.pbc.cc.kccsd_t_rhf import _get_epqr
if eris is None:
eris = cc.ao2mo()
fock = eris.fock
nkpts, nocc, nvir = t1.shape
kconserv = cc.khelper.kconserv
dtype = np.result_type(t1, t2)
fov = fock[:, :nocc, nocc:]
#foo = [fock[ikpt, :nocc, :nocc].diagonal() for ikpt in range(nkpts)]
#fvv = [fock[ikpt, nocc:, nocc:].diagonal() for ikpt in range(nkpts)]
mo_energy_occ = np.array(
[eris.mo_energy[ki][:nocc] for ki in range(nkpts)])
mo_energy_vir = np.array(
[eris.mo_energy[ki][nocc:] for ki in range(nkpts)])
mo_e_o = mo_energy_occ
mo_e_v = mo_energy_vir
# Get location of padded elements in occupied and virtual space
nonzero_opadding, nonzero_vpadding = padding_k_idx(cc, kind="split")
ccsd_energy = cc.energy(t1, t2, eris)
if t3p2_ip_out is None:
t3p2_ip_out = np.zeros((nkpts, nkpts, nkpts, nocc, nvir, nocc, nocc),
dtype=dtype)
Wmcik = t3p2_ip_out
if t3p2_ea_out is None:
t3p2_ea_out = np.zeros((nkpts, nkpts, nkpts, nvir, nvir, nvir, nocc),
dtype=dtype)
Wacek = t3p2_ea_out
from itertools import product
tmp_t3 = np.empty((nkpts, nkpts, nkpts, nkpts, nkpts, nocc, nocc, nocc,
nvir, nvir, nvir),
dtype=t2.dtype)
def get_w(ki, kj, kk, ka, kb, kc):
kf = kconserv[ka, ki, kb]
ret = lib.einsum('fiba,kjcf->ijkabc', eris.vovv[kf, ki, kb].conj(),
t2[kk, kj, kc])
km = kconserv[kc, kk, kb]
ret -= lib.einsum('jima,mkbc->ijkabc', eris.ooov[kj, ki, km].conj(),
t2[km, kk, kb])
return ret
for ki, kj, kk, ka, kb in product(range(nkpts), repeat=5):
kc = kpts_helper.get_kconserv3(cc._scf.cell, cc.kpts,
[ki, kj, kk, ka, kb])
tmp_t3[ki, kj, kk, ka, kb] = get_w(ki, kj, kk, ka, kb, kc)
tmp_t3[ki, kj, kk, ka, kb] += get_w(ki, kk, kj, ka, kc,
kb).transpose(0, 2, 1, 3, 5, 4)
tmp_t3[ki, kj, kk, ka, kb] += get_w(kj, ki, kk, kb, ka,
kc).transpose(1, 0, 2, 4, 3, 5)
tmp_t3[ki, kj, kk, ka, kb] += get_w(kj, kk, ki, kb, kc,
ka).transpose(2, 0, 1, 5, 3, 4)
tmp_t3[ki, kj, kk, ka, kb] += get_w(kk, ki, kj, kc, ka,
kb).transpose(1, 2, 0, 4, 5, 3)
tmp_t3[ki, kj, kk, ka, kb] += get_w(kk, kj, ki, kc, kb,
ka).transpose(2, 1, 0, 5, 4, 3)
eijk = _get_epqr([0, nocc, ki, mo_e_o, nonzero_opadding],
[0, nocc, kj, mo_e_o, nonzero_opadding],
[0, nocc, kk, mo_e_o, nonzero_opadding])
eabc = _get_epqr([0, nvir, ka, mo_e_v, nonzero_vpadding],
[0, nvir, kb, mo_e_v, nonzero_vpadding],
[0, nvir, kc, mo_e_v, nonzero_vpadding],
fac=[-1., -1., -1.])
eijkabc = eijk[:, :, :, None, None, None] + eabc[None, None,
None, :, :, :]
tmp_t3[ki, kj, kk, ka, kb] /= eijkabc
pt1 = np.zeros((nkpts, nocc, nvir), dtype=t2.dtype)
for ki in range(nkpts):
for km, kn, ke in product(range(nkpts), repeat=3):
kf = kconserv[km, ke, kn]
Soovv = 2. * eris.oovv[km, kn, ke] - eris.oovv[km, kn,
kf].transpose(
0, 1, 3, 2)
St3 = (tmp_t3[ki, km, kn, ki, ke] -
tmp_t3[ki, km, kn, ke, ki].transpose(0, 1, 2, 4, 3, 5))
pt1[ki] += lib.einsum('mnef,imnaef->ia', Soovv, St3)
pt2 = np.zeros((nkpts, nkpts, nkpts, nocc, nocc, nvir, nvir),
dtype=t2.dtype)
for ki, kj, ka in product(range(nkpts), repeat=3):
kb = kconserv[ki, ka, kj]
for km in range(nkpts):
for kn in range(nkpts):
# (ia,jb) -> (ia,jb)
ke = kconserv[km, kj, kn]
pt2[ki, kj, ka] += -2. * lib.einsum(
'imnabe,mnje->ijab', tmp_t3[ki, km, kn, ka,
kb], eris.ooov[km, kn, kj])
pt2[ki, kj, ka] += lib.einsum('imnabe,nmje->ijab',
tmp_t3[ki, km, kn, ka, kb],
eris.ooov[kn, km, kj])
pt2[ki, kj, ka] += lib.einsum('inmeab,mnje->ijab',
tmp_t3[ki, kn, km, ke, ka],
eris.ooov[km, kn, kj])
# (ia,jb) -> (jb,ia)
ke = kconserv[km, ki, kn]
pt2[ki, kj, ka] += -2. * lib.einsum(
'jmnbae,mnie->ijab', tmp_t3[kj, km, kn, kb,
ka], eris.ooov[km, kn, ki])
pt2[ki, kj, ka] += lib.einsum('jmnbae,nmie->ijab',
tmp_t3[kj, km, kn, kb, ka],
eris.ooov[kn, km, ki])
pt2[ki, kj, ka] += lib.einsum('jnmeba,mnie->ijab',
tmp_t3[kj, kn, km, ke, kb],
eris.ooov[km, kn, ki])
# (ia,jb) -> (ia,jb)
pt2[ki, kj, ka] += lib.einsum('ijmabe,me->ijab',
tmp_t3[ki, kj, km, ka, kb], fov[km])
pt2[ki, kj, ka] -= lib.einsum('ijmaeb,me->ijab',
tmp_t3[ki, kj, km, ka, km], fov[km])
# (ia,jb) -> (jb,ia)
pt2[ki, kj, ka] += lib.einsum('jimbae,me->ijab',
tmp_t3[kj, ki, km, kb, ka], fov[km])
pt2[ki, kj, ka] -= lib.einsum('jimbea,me->ijab',
tmp_t3[kj, ki, km, kb, km], fov[km])
for ke in range(nkpts):
# (ia,jb) -> (ia,jb)
kf = kconserv[km, ke, kb]
pt2[ki, kj, ka] += 2. * lib.einsum(
'ijmaef,bmef->ijab', tmp_t3[ki, kj, km, ka,
ke], eris.vovv[kb, km, ke])
pt2[ki, kj, ka] -= lib.einsum('ijmaef,bmfe->ijab',
tmp_t3[ki, kj, km, ka, ke],
eris.vovv[kb, km, kf])
pt2[ki, kj, ka] -= lib.einsum('imjfae,bmef->ijab',
tmp_t3[ki, km, kj, kf, ka],
eris.vovv[kb, km, ke])
# (ia,jb) -> (jb,ia)
kf = kconserv[km, ke, ka]
pt2[ki, kj, ka] += 2. * lib.einsum(
'jimbef,amef->ijab', tmp_t3[kj, ki, km, kb,
ke], eris.vovv[ka, km, ke])
pt2[ki, kj, ka] -= lib.einsum('jimbef,amfe->ijab',
tmp_t3[kj, ki, km, kb, ke],
eris.vovv[ka, km, kf])
pt2[ki, kj, ka] -= lib.einsum('jmifbe,amef->ijab',
tmp_t3[kj, km, ki, kf, kb],
eris.vovv[ka, km, ke])
for ki in range(nkpts):
ka = ki
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]
pt1[ki] /= eia
for ki, ka in product(range(nkpts), repeat=2):
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]
for kj in range(nkpts):
kb = kconserv[ki, ka, kj]
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, :]
pt2[ki, kj, ka] /= eijab
pt1 += t1
pt2 += t2
for ki, kj, kk, ka, kb in product(range(nkpts), repeat=5):
kc = kpts_helper.get_kconserv3(cc._scf.cell, cc.kpts,
[ki, kj, kk, ka, kb])
km = kconserv[kc, ki, ka]
_oovv = eris.oovv[km, ki, kc]
Wmcik[km, kb, kk] += 2. * lib.einsum('ijkabc,mica->mbkj',
tmp_t3[ki, kj, kk, ka, kb], _oovv)
Wmcik[km, kb, kk] -= lib.einsum('jikabc,mica->mbkj',
tmp_t3[kj, ki, kk, ka, kb], _oovv)
Wmcik[km, kb, kk] -= lib.einsum('kjiabc,mica->mbkj',
tmp_t3[kk, kj, ki, ka, kb], _oovv)
for ki, kj, kk, ka, kb in product(range(nkpts), repeat=5):
kc = kpts_helper.get_kconserv3(cc._scf.cell, cc.kpts,
[ki, kj, kk, ka, kb])
ke = kconserv[ki, ka, kk]
_oovv = eris.oovv[ki, kk, ka]
Wacek[kc, kb, ke] -= 2. * lib.einsum('ijkabc,ikae->cbej',
tmp_t3[ki, kj, kk, ka, kb], _oovv)
Wacek[kc, kb, ke] += lib.einsum('jikabc,ikae->cbej',
tmp_t3[kj, ki, kk, ka, kb], _oovv)
Wacek[kc, kb, ke] += lib.einsum('kjiabc,ikae->cbej',
tmp_t3[kk, kj, ki, ka, kb], _oovv)
delta_ccsd_energy = cc.energy(pt1, pt2, eris) - ccsd_energy
lib.logger.info(cc, 'CCSD energy T3[2] correction : %16.12e',
delta_ccsd_energy)
return delta_ccsd_energy, pt1, pt2, Wmcik, Wacek