def lazy_kernel(ot,
oneCDMs,
twoCDM_amo,
ao2amo,
max_memory=20000,
hermi=1,
veff2_mo=None):
''' Get the 1- and 2-body effective potential from MC-PDFT. Eventually I'll be able to specify
mo slices for the 2-body part
Args:
ot : an instance of otfnal class
oneCDMs : ndarray of shape (2, nao, nao)
containing spin-separated one-body density matrices
twoCDM_amo : ndarray of shape (ncas, ncas, ncas, ncas)
containing spin-summed two-body cumulant density matrix in an active space
ao2amo : ndarray of shape (nao, ncas)
containing molecular orbital coefficients for active-space orbitals
Kwargs:
max_memory : int or float
maximum cache size in MB
default is 20000
hermi : int
1 if 1CDMs are assumed hermitian, 0 otherwise
Returns : float
The MC-PDFT on-top exchange-correlation energy
'''
if veff2_mo is not None:
raise NotImplementedError(
'Molecular orbital slices for the two-body part')
ni, xctype, dens_deriv = ot._numint, ot.xctype, ot.dens_deriv
norbs_ao = ao2amo.shape[0]
npair = norbs_ao * (norbs_ao + 1) // 2
veff1 = np.zeros_like(oneCDMs[0])
veff2 = np.zeros((npair, npair), dtype=veff1.dtype)
t0 = (time.clock(), time.time())
make_rho = tuple(
ni._gen_rho_evaluator(ot.mol, oneCDMs[i, :, :], hermi)
for i in range(2))
for ao, mask, weight, coords in ni.block_loop(ot.mol, ot.grids, norbs_ao,
dens_deriv, max_memory):
rho = np.asarray([m[0](0, ao, mask, xctype) for m in make_rho])
t0 = logger.timer(ot, 'untransformed density', *t0)
Pi = get_ontop_pair_density(ot, rho, ao, oneCDMs, twoCDM_amo, ao2amo,
dens_deriv, mask)
t0 = logger.timer(ot, 'on-top pair density calculation', *t0)
eot, vrho, vPi = ot.eval_ot(rho, Pi, weights=weight)
t0 = logger.timer(ot, 'effective potential kernel calculation', *t0)
veff1 += ot.get_veff_1body(rho, Pi, ao, weight, kern=vrho)
t0 = logger.timer(ot, '1-body effective potential calculation', *t0)
veff2 += ot.get_veff_2body(rho, Pi, ao, weight, aosym='s4', kern=vPi)
t0 = logger.timer(ot, '2-body effective potential calculation', *t0)
return veff1, veff2
def get_E_ot(ot, oneCDMs, twoCDM_amo, ao2amo, max_memory=20000, hermi=1):
''' E_MCPDFT = h_pq l_pq + 1/2 v_pqrs l_pq l_rs + E_ot[rho,Pi]
or, in other terms,
E_MCPDFT = T_KS[rho] + E_ext[rho] + E_coul[rho] + E_ot[rho, Pi]
= E_DFT[1rdm] - E_xc[rho] + E_ot[rho, Pi]
Args:
ot : an instance of otfnal class
oneCDMs : ndarray of shape (2, nao, nao)
containing spin-separated one-body density matrices
twoCDM_amo : ndarray of shape (ncas, ncas, ncas, ncas)
containing spin-summed two-body cumulant density matrix in an active space
ao2amo : ndarray of shape (nao, ncas)
containing molecular orbital coefficients for active-space orbitals
Kwargs:
max_memory : int or float
maximum cache size in MB
default is 20000
hermi : int
1 if 1CDMs are assumed hermitian, 0 otherwise
Returns : float
The MC-PDFT on-top exchange-correlation energy
'''
ni, xctype, dens_deriv = ot._numint, ot.xctype, ot.dens_deriv
norbs_ao = ao2amo.shape[0]
E_ot = 0.0
t0 = (time.clock(), time.time())
make_rho = tuple(
ni._gen_rho_evaluator(ot.mol, oneCDMs[i, :, :], hermi)
for i in range(2))
for ao, mask, weight, coords in ni.block_loop(ot.mol, ot.grids, norbs_ao,
dens_deriv, max_memory):
rho = np.asarray([m[0](0, ao, mask, xctype) for m in make_rho])
if ot.verbose > logger.DEBUG and dens_deriv > 0:
for ideriv in range(1, 4):
rho_test = np.einsum('ijk,aj,ak->ia', oneCDMs, ao[ideriv],
ao[0])
rho_test += np.einsum('ijk,ak,aj->ia', oneCDMs, ao[ideriv],
ao[0])
logger.debug(ot,
"Spin-density derivatives, |PySCF-einsum| = %s",
linalg.norm(rho[:, ideriv, :] - rho_test))
t0 = logger.timer(ot, 'untransformed density', *t0)
Pi = get_ontop_pair_density(ot, rho, ao, oneCDMs, twoCDM_amo, ao2amo,
dens_deriv)
t0 = logger.timer(ot, 'on-top pair density calculation', *t0)
E_ot += ot.get_E_ot(rho, Pi, weight)
t0 = logger.timer(ot, 'on-top exchange-correlation energy calculation',
*t0)
return E_ot
def get_dens (d1, d2):
make_rho, nset, nao = ni._gen_rho_evaluator (ot.mol, d1, 1)
for ao, mask, weight, coords in ni.block_loop (ot.mol, ot.grids, nao, ot.dens_deriv, mc.max_memory, blksize=ngrids):
rho = np.asarray ([make_rho (i, ao, mask, ot.xctype) for i in range(2)])
Pi = get_ontop_pair_density (ot, rho, ao, d1, d2, mo_cas, ot.dens_deriv, mask)
return rho, Pi, weight
def mcpdft_HellmanFeynman_grad(mc,
ot,
veff1,
veff2,
mo_coeff=None,
ci=None,
atmlst=None,
mf_grad=None,
verbose=None):
''' Modification of pyscf.grad.casscf.kernel to compute instead the Hellman-Feynman gradient
terms of MC-PDFT. From the differentiated Hamiltonian matrix elements, only the core and
Coulomb energy parts remain. For the renormalization terms, the effective Fock matrix is as in
CASSCF, but with the same Hamiltonian substutition that is used for the energy response terms. '''
if mo_coeff is None: mo_coeff = mc.mo_coeff
if ci is None: ci = mc.ci
if mf_grad is None: mf_grad = mc._scf.nuc_grad_method()
if mc.frozen is not None:
raise NotImplementedError
t0 = (time.clock(), time.time())
mol = mc.mol
ncore = mc.ncore
ncas = mc.ncas
nocc = ncore + ncas
nelecas = mc.nelecas
nao, nmo = mo_coeff.shape
nao_pair = nao * (nao + 1) // 2
mo_occ = mo_coeff[:, :nocc]
mo_core = mo_coeff[:, :ncore]
mo_cas = mo_coeff[:, ncore:nocc]
casdm1, casdm2 = mc.fcisolver.make_rdm12(ci, ncas, nelecas)
# gfock = Generalized Fock, Adv. Chem. Phys., 69, 63
dm_core = np.dot(mo_core, mo_core.T) * 2
dm_cas = reduce(np.dot, (mo_cas, casdm1, mo_cas.T))
# MRH: I need to replace aapa with the equivalent array from veff2
# I'm not sure how the outcore file-paging system works, but hopefully I can do this
# I also need to generate vhf_c and vhf_a from veff2 rather than the molecule's actual integrals
# The true Coulomb repulsion should already be in veff1, but I need to generate the "fake"
# vj - vk/2 from veff2
h1e_mo = mo_coeff.T @ (mc.get_hcore() + veff1) @ mo_coeff + veff2.vhf_c
aapa = np.zeros((ncas, ncas, nmo, ncas), dtype=h1e_mo.dtype)
vhf_a = np.zeros((nmo, nmo), dtype=h1e_mo.dtype)
for i in range(nmo):
jbuf = veff2.ppaa[i]
kbuf = veff2.papa[i]
aapa[:, :, i, :] = jbuf[ncore:nocc, :, :]
vhf_a[i] = np.tensordot(jbuf, casdm1, axes=2)
vhf_a *= 0.5
# for this potential, vj = vk: vj - vk/2 = vj - vj/2 = vj/2
gfock = np.zeros((nmo, nmo))
gfock[:, :ncore] = (h1e_mo[:, :ncore] + vhf_a[:, :ncore]) * 2
gfock[:, ncore:nocc] = h1e_mo[:, ncore:nocc] @ casdm1
gfock[:, ncore:nocc] += np.einsum('uviw,vuwt->it', aapa, casdm2)
dme0 = reduce(np.dot, (mo_coeff, (gfock + gfock.T) * .5, mo_coeff.T))
aapa = vhf_a = h1e_mo = gfock = None
t0 = logger.timer(mc, 'PDFT HlFn gfock', *t0)
dm1 = dm_core + dm_cas
# MRH: vhf1c and vhf1a should be the TRUE vj_c and vj_a (no vk!)
vj = mf_grad.get_jk(dm=dm1)[0]
hcore_deriv = mf_grad.hcore_generator(mol)
s1 = mf_grad.get_ovlp(mol)
if atmlst is None:
atmlst = range(mol.natm)
aoslices = mol.aoslice_by_atom()
de_hcore = np.zeros((len(atmlst), 3))
de_renorm = np.zeros((len(atmlst), 3))
de_coul = np.zeros((len(atmlst), 3))
de_xc = np.zeros((len(atmlst), 3))
de_grid = np.zeros((len(atmlst), 3))
de_wgt = np.zeros((len(atmlst), 3))
de = np.zeros((len(atmlst), 3))
# MRH: Now I have to compute the gradient of the exchange-correlation energy
# This involves derivatives of the orbitals that construct rho and Pi and therefore another
# set of potentials. It also involves the derivatives of quadrature grid points which
# propagate through the densities and therefore yet another set of potentials.
# The orbital-derivative part includes all the grid points and some of the orbitals (- sign);
# the grid-derivative part includes all of the orbitals and some of the grid points (+ sign).
# I'll do a loop over grid sections and make arrays of type (3,nao, nao) and (3,nao, ncas, ncas, ncas).
# I'll contract them within the grid loop for the grid derivatives and in the following
# orbital loop for the xc derivatives
dm1s = mc.make_rdm1s()
casdm1s = np.stack(mc.fcisolver.make_rdm1s(ci, ncas, nelecas), axis=0)
twoCDM = get_2CDM_from_2RDM(casdm2, casdm1s)
casdm1s = None
make_rho = tuple(
ot._numint._gen_rho_evaluator(mol, dm1s[i], 1) for i in range(2))
make_rho_c = ot._numint._gen_rho_evaluator(mol, dm_core, 1)
make_rho_a = ot._numint._gen_rho_evaluator(mol, dm_cas, 1)
dv1 = np.zeros(
(3, nao,
nao)) # Term which should be contracted with the whole density matrix
dv1_a = np.zeros(
(3, nao, nao)
) # Term which should only be contracted with the core density matrix
dv2 = np.zeros((3, nao))
idx = np.array([[1, 4, 5, 6], [2, 5, 7, 8], [3, 6, 8, 9]],
dtype=np.int_) # For addressing particular ao derivatives
if ot.xctype == 'LDA': idx = idx[:, 0] # For LDAs no second derivatives
diag_idx = np.arange(ncas) # for puvx
diag_idx = diag_idx * (diag_idx + 1) // 2 + diag_idx
casdm2_pack = (casdm2 + casdm2.transpose(0, 1, 3, 2)).reshape(
ncas**2, ncas, ncas)
casdm2_pack = pack_tril(casdm2_pack).reshape(ncas, ncas, -1)
casdm2_pack[:, :, diag_idx] *= 0.5
diag_idx = np.arange(ncore, dtype=np.int_) * (ncore + 1) # for pqii
full_atmlst = -np.ones(mol.natm, dtype=np.int_)
t1 = logger.timer(mc, 'PDFT HlFn quadrature setup', *t0)
for k, ia in enumerate(atmlst):
full_atmlst[ia] = k
for ia, (coords, w0,
w1) in enumerate(rks_grad.grids_response_cc(ot.grids)):
# For the xc potential derivative, I need every grid point in the entire molecule regardless of atmlist. (Because that's about orbitals.)
# For the grid and weight derivatives, I only need the gridpoints that are in atmlst
mask = gen_grid.make_mask(mol, coords)
ao = ot._numint.eval_ao(
mol, coords, deriv=ot.dens_deriv + 1,
non0tab=mask) # Need 1st derivs for LDA, 2nd for GGA, etc.
if ot.xctype == 'LDA': # Might confuse the rho and Pi generators if I don't slice this down
aoval = ao[:1]
elif ot.xctype == 'GGA':
aoval = ao[:4]
rho = np.asarray([m[0](0, aoval, mask, ot.xctype) for m in make_rho])
Pi = get_ontop_pair_density(ot, rho, aoval, dm1s, twoCDM, mo_cas,
ot.dens_deriv)
t1 = logger.timer(
mc, 'PDFT HlFn quadrature atom {} rho/Pi calc'.format(ia), *t1)
moval_occ = np.tensordot(aoval, mo_occ, axes=1)
moval_core = moval_occ[..., :ncore]
moval_cas = moval_occ[..., ncore:]
t1 = logger.timer(mc,
'PDFT HlFn quadrature atom {} ao2mo grid'.format(ia),
*t1)
eot, vrho, vot = ot.eval_ot(rho, Pi, weights=w0)
ndpi = vot.shape[0]
# Weight response
de_wgt += np.tensordot(eot, w1[atmlst], axes=(0, 2))
t1 = logger.timer(
mc, 'PDFT HlFn quadrature atom {} weight response'.format(ia), *t1)
# Find the atoms that are a part of the atomlist - grid correction shouldn't be added if they aren't there
# The last stuff to vectorize is in get_veff_2body!
k = full_atmlst[ia]
# Vpq + Vpqii
vrho = _contract_vot_rho(vot,
make_rho_c[0](0, aoval, mask, ot.xctype),
add_vrho=vrho)
tmp_dv = np.stack([
ot.get_veff_1body(rho, Pi, [ao[ix], aoval], w0, kern=vrho)
for ix in idx
],
axis=0)
if k >= 0:
de_grid[k] += 2 * np.tensordot(tmp_dv, dm1.T,
axes=2) # Grid response
dv1 -= tmp_dv # XC response
t1 = logger.timer(
mc, 'PDFT HlFn quadrature atom {} Vpq + Vpqii'.format(ia), *t1)
# Viiuv * Duv
vrho_a = _contract_vot_rho(vot, make_rho_a[0](0, aoval, mask,
ot.xctype))
tmp_dv = np.stack([
ot.get_veff_1body(rho, Pi, [ao[ix], aoval], w0, kern=vrho_a)
for ix in idx
],
axis=0)
if k >= 0:
de_grid[k] += 2 * np.tensordot(tmp_dv, dm_core.T,
axes=2) # Grid response
dv1_a -= tmp_dv # XC response
t1 = logger.timer(mc, 'PDFT HlFn quadrature atom {} Viiuv'.format(ia),
*t1)
# Vpuvx
tmp_dv = ot.get_veff_2body_kl(rho,
Pi,
moval_cas,
moval_cas,
w0,
symm=True,
kern=vot) # ndpi,ngrids,ncas*(ncas+1)//2
tmp_dv = np.tensordot(tmp_dv, casdm2_pack,
axes=(-1, -1)) # ndpi, ngrids, ncas, ncas
tmp_dv[0] = (tmp_dv[:ndpi] * moval_cas[:ndpi, :, None, :]).sum(
0) # Chain and product rule
tmp_dv[1:ndpi] *= moval_cas[0, :, None, :] # Chain and product rule
tmp_dv = tmp_dv.sum(-1) # ndpi, ngrids, ncas
tmp_dv = np.tensordot(ao[idx[:, :ndpi]], tmp_dv,
axes=((1, 2),
(0, 1))) # comp, nao (orb), ncas (dm2)
tmp_dv = np.einsum('cpu,pu->cp', tmp_dv, mo_cas) # comp, ncas
if k >= 0: de_grid[k] += 2 * tmp_dv.sum(1)
dv2 -= tmp_dv # XC response
t1 = logger.timer(mc, 'PDFT HlFn quadrature atom {} Vpuvx'.format(ia),
*t1)
for k, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = aoslices[ia]
h1ao = hcore_deriv(ia) # MRH: this should be the TRUE hcore
de_hcore[k] += np.einsum('xij,ij->x', h1ao, dm1)
de_renorm[k] -= np.einsum('xij,ij->x', s1[:, p0:p1], dme0[p0:p1]) * 2
de_coul[k] += np.einsum('xij,ij->x', vj[:, p0:p1], dm1[p0:p1]) * 2
de_xc[k] += np.einsum(
'xij,ij->x', dv1[:, p0:p1],
dm1[p0:p1]) * 2 # Full quadrature, only some orbitals
de_xc[k] += np.einsum('xij,ij->x', dv1_a[:, p0:p1],
dm_core[p0:p1]) * 2 # Ditto
de_xc[k] += dv2[:, p0:p1].sum(1) * 2 # Ditto
de_nuc = mf_grad.grad_nuc(mol, atmlst)
logger.debug(mc, "MC-PDFT Hellmann-Feynman nuclear :\n{}".format(de_nuc))
logger.debug(
mc, "MC-PDFT Hellmann-Feynman hcore component:\n{}".format(de_hcore))
logger.debug(
mc, "MC-PDFT Hellmann-Feynman coulomb component:\n{}".format(de_coul))
logger.debug(mc,
"MC-PDFT Hellmann-Feynman xc component:\n{}".format(de_xc))
logger.debug(
mc, "MC-PDFT Hellmann-Feynman quadrature point component:\n{}".format(
de_grid))
logger.debug(
mc, "MC-PDFT Hellmann-Feynman quadrature weight component:\n{}".format(
de_wgt))
logger.debug(
mc, "MC-PDFT Hellmann-Feynman renorm component:\n{}".format(de_renorm))
de = de_nuc + de_hcore + de_coul + de_renorm + de_xc + de_grid + de_wgt
t1 = logger.timer(mc, 'PDFT HlFn total', *t0)
return de
def mcpdft_HellmanFeynman_grad(mc,
ot,
veff1,
veff2,
mo_coeff=None,
ci=None,
atmlst=None,
mf_grad=None,
verbose=None,
max_memory=None,
auxbasis_response=False):
''' Modification of pyscf.grad.casscf.kernel to compute instead the Hellman-Feynman gradient
terms of MC-PDFT. From the differentiated Hamiltonian matrix elements, only the core and
Coulomb energy parts remain. For the renormalization terms, the effective Fock matrix is as in
CASSCF, but with the same Hamiltonian substutition that is used for the energy response terms. '''
if mo_coeff is None: mo_coeff = mc.mo_coeff
if ci is None: ci = mc.ci
if mf_grad is None: mf_grad = mc._scf.nuc_grad_method()
if mc.frozen is not None:
raise NotImplementedError
if max_memory is None: max_memory = mc.max_memory
t0 = (time.process_time(), time.time())
mol = mc.mol
ncore = mc.ncore
ncas = mc.ncas
nocc = ncore + ncas
nelecas = mc.nelecas
nao, nmo = mo_coeff.shape
nao_pair = nao * (nao + 1) // 2
mo_occ = mo_coeff[:, :nocc]
mo_core = mo_coeff[:, :ncore]
mo_cas = mo_coeff[:, ncore:nocc]
casdm1, casdm2 = mc.fcisolver.make_rdm12(ci, ncas, nelecas)
# gfock = Generalized Fock, Adv. Chem. Phys., 69, 63
dm_core = np.dot(mo_core, mo_core.T) * 2
dm_cas = reduce(np.dot, (mo_cas, casdm1, mo_cas.T))
# MRH: I need to replace aapa with the equivalent array from veff2
# I'm not sure how the outcore file-paging system works, but hopefully I can do this
# I also need to generate vhf_c and vhf_a from veff2 rather than the molecule's actual integrals
# The true Coulomb repulsion should already be in veff1, but I need to generate the "fake"
# vj - vk/2 from veff2
h1e_mo = mo_coeff.T @ (mc.get_hcore() + veff1) @ mo_coeff + veff2.vhf_c
aapa = np.zeros((ncas, ncas, nmo, ncas), dtype=h1e_mo.dtype)
vhf_a = np.zeros((nmo, nmo), dtype=h1e_mo.dtype)
for i in range(nmo):
jbuf = veff2.ppaa[i]
kbuf = veff2.papa[i]
aapa[:, :, i, :] = jbuf[ncore:nocc, :, :]
vhf_a[i] = np.tensordot(jbuf, casdm1, axes=2)
vhf_a *= 0.5
# for this potential, vj = vk: vj - vk/2 = vj - vj/2 = vj/2
gfock = np.zeros((nmo, nmo))
gfock[:, :ncore] = (h1e_mo[:, :ncore] + vhf_a[:, :ncore]) * 2
gfock[:, ncore:nocc] = h1e_mo[:, ncore:nocc] @ casdm1
gfock[:, ncore:nocc] += np.einsum('uviw,vuwt->it', aapa, casdm2)
dme0 = reduce(np.dot, (mo_coeff, (gfock + gfock.T) * .5, mo_coeff.T))
aapa = vhf_a = h1e_mo = gfock = None
if atmlst is None:
atmlst = range(mol.natm)
aoslices = mol.aoslice_by_atom()
de_hcore = np.zeros((len(atmlst), 3))
de_renorm = np.zeros((len(atmlst), 3))
de_coul = np.zeros((len(atmlst), 3))
de_xc = np.zeros((len(atmlst), 3))
de_grid = np.zeros((len(atmlst), 3))
de_wgt = np.zeros((len(atmlst), 3))
de_aux = np.zeros((len(atmlst), 3))
de = np.zeros((len(atmlst), 3))
t0 = logger.timer(mc, 'PDFT HlFn gfock', *t0)
mo_coeff, ci, mo_occup = cas_natorb(mc, mo_coeff=mo_coeff, ci=ci)
mo_occ = mo_coeff[:, :nocc]
mo_core = mo_coeff[:, :ncore]
mo_cas = mo_coeff[:, ncore:nocc]
dm1 = dm_core + dm_cas
dm1 = tag_array(dm1, mo_coeff=mo_coeff, mo_occ=mo_occup)
# MRH: vhf1c and vhf1a should be the TRUE vj_c and vj_a (no vk!)
vj = mf_grad.get_jk(dm=dm1)[0]
hcore_deriv = mf_grad.hcore_generator(mol)
s1 = mf_grad.get_ovlp(mol)
if auxbasis_response:
de_aux += vj.aux
# MRH: Now I have to compute the gradient of the exchange-correlation energy
# This involves derivatives of the orbitals that construct rho and Pi and therefore another
# set of potentials. It also involves the derivatives of quadrature grid points which
# propagate through the densities and therefore yet another set of potentials.
# The orbital-derivative part includes all the grid points and some of the orbitals (- sign);
# the grid-derivative part includes all of the orbitals and some of the grid points (+ sign).
# I'll do a loop over grid sections and make arrays of type (3,nao, nao) and (3,nao, ncas, ncas, ncas).
# I'll contract them within the grid loop for the grid derivatives and in the following
# orbital loop for the xc derivatives
# MRH, 05/09/2020: This just in - the actual spin density doesn't matter at all in PDFT!
# I could probably save a fair amount of time by not screwing around with the actual spin density!
# Also, the cumulant decomposition can always be defined without the spin-density matrices and
# it's still valid! But one thing at a time.
mo_n = mo_occ * mo_occup[None, :nocc]
casdm1, casdm2 = mc.fcisolver.make_rdm12(ci, ncas, nelecas)
twoCDM = get_2CDM_from_2RDM(casdm2, casdm1)
dm1s = np.stack((dm1 / 2.0, ) * 2, axis=0)
dm1 = tag_array(dm1, mo_coeff=mo_occ, mo_occ=mo_occup[:nocc])
make_rho = ot._numint._gen_rho_evaluator(mol, dm1, 1)[0]
dvxc = np.zeros((3, nao))
idx = np.array([[1, 4, 5, 6], [2, 5, 7, 8], [3, 6, 8, 9]],
dtype=np.int_) # For addressing particular ao derivatives
if ot.xctype == 'LDA': idx = idx[:, 0:1] # For LDAs no second derivatives
diag_idx = np.arange(ncas) # for puvx
diag_idx = diag_idx * (diag_idx + 1) // 2 + diag_idx
casdm2_pack = (twoCDM + twoCDM.transpose(0, 1, 3, 2)).reshape(
ncas**2, ncas, ncas)
casdm2_pack = pack_tril(casdm2_pack).reshape(ncas, ncas, -1)
casdm2_pack[:, :, diag_idx] *= 0.5
diag_idx = np.arange(ncore, dtype=np.int_) * (ncore + 1) # for pqii
full_atmlst = -np.ones(mol.natm, dtype=np.int_)
t1 = logger.timer(mc, 'PDFT HlFn quadrature setup', *t0)
for k, ia in enumerate(atmlst):
full_atmlst[ia] = k
for ia, (coords, w0,
w1) in enumerate(rks_grad.grids_response_cc(ot.grids)):
mask = gen_grid.make_mask(mol, coords)
# For the xc potential derivative, I need every grid point in the entire molecule regardless of atmlist. (Because that's about orbitals.)
# For the grid and weight derivatives, I only need the gridpoints that are in atmlst
# It is conceivable that I can make this more efficient by only doing cross-combinations of grids and AOs, but I don't know how "mask"
# works yet or how else I could do this.
gc.collect()
ngrids = coords.shape[0]
ndao = (1, 4)[ot.dens_deriv]
ndpi = (1, 4)[ot.Pi_deriv]
ncols = 1.05 * 3 * (ndao *
(nao + nocc) + max(ndao * nao, ndpi * ncas * ncas))
remaining_floats = (max_memory - current_memory()[0]) * 1e6 / 8
blksize = int(remaining_floats / (ncols * BLKSIZE)) * BLKSIZE
blksize = max(BLKSIZE, min(blksize, ngrids, BLKSIZE * 1200))
t1 = logger.timer(
mc,
'PDFT HlFn quadrature atom {} mask and memory setup'.format(ia),
*t1)
for ip0 in range(0, ngrids, blksize):
ip1 = min(ngrids, ip0 + blksize)
logger.info(
mc, 'PDFT gradient atom {} slice {}-{} of {} total'.format(
ia, ip0, ip1, ngrids))
ao = ot._numint.eval_ao(
mol, coords[ip0:ip1], deriv=ot.dens_deriv + 1,
non0tab=mask) # Need 1st derivs for LDA, 2nd for GGA, etc.
t1 = logger.timer(
mc, 'PDFT HlFn quadrature atom {} ao grids'.format(ia), *t1)
if ot.xctype == 'LDA': # Might confuse the rho and Pi generators if I don't slice this down
aoval = ao[0]
if ot.xctype == 'GGA':
aoval = ao[:4]
rho = make_rho(0, aoval, mask, ot.xctype) / 2.0
rho = np.stack((rho, ) * 2, axis=0)
t1 = logger.timer(
mc, 'PDFT HlFn quadrature atom {} rho calc'.format(ia), *t1)
Pi = get_ontop_pair_density(ot, rho, aoval, dm1s, twoCDM, mo_cas,
ot.dens_deriv, mask)
t1 = logger.timer(
mc, 'PDFT HlFn quadrature atom {} Pi calc'.format(ia), *t1)
if ot.xctype == 'LDA': # TODO: consistent format requirements for shape of ao grid
aoval = ao[:1]
moval_occ = _grid_ao2mo(mol, aoval, mo_occ, mask)
t1 = logger.timer(
mc, 'PDFT HlFn quadrature atom {} ao2mo grid'.format(ia), *t1)
aoval = np.ascontiguousarray([
ao[ix].transpose(0, 2, 1) for ix in idx[:, :ndao]
]).transpose(0, 1, 3, 2)
ao = None
t1 = logger.timer(
mc, 'PDFT HlFn quadrature atom {} ao grid reshape'.format(ia),
*t1)
eot, vot = ot.eval_ot(rho, Pi, weights=w0[ip0:ip1])[:2]
vrho, vPi = vot
t1 = logger.timer(
mc, 'PDFT HlFn quadrature atom {} eval_ot'.format(ia), *t1)
puvx_mem = 2 * ndpi * (ip1 - ip0) * ncas * ncas * 8 / 1e6
remaining_mem = max_memory - current_memory()[0]
logger.info(
mc,
'PDFT gradient memory note: working on {} grid points; estimated puvx usage = {:.1f} of {:.1f} remaining MB'
.format((ip1 - ip0), puvx_mem, remaining_mem))
# Weight response
de_wgt += np.tensordot(eot, w1[atmlst, ..., ip0:ip1], axes=(0, 2))
t1 = logger.timer(
mc, 'PDFT HlFn quadrature atom {} weight response'.format(ia),
*t1)
# Find the atoms that are a part of the atomlist - grid correction shouldn't be added if they aren't there
# The last stuff to vectorize is in get_veff_2body!
k = full_atmlst[ia]
# Vpq + Vpqrs * Drs ; I'm not sure why the list comprehension down there doesn't break ao's stride order but I'm not complaining
vrho = _contract_vot_rho(vPi, rho.sum(0), add_vrho=vrho)
tmp_dv = np.stack([
ot.get_veff_1body(
rho, Pi, [ao_i, moval_occ], w0[ip0:ip1], kern=vrho)
for ao_i in aoval
],
axis=0)
tmp_dv = (tmp_dv * mo_occ[None, :, :] *
mo_occup[None, None, :nocc]).sum(2)
if k >= 0: de_grid[k] += 2 * tmp_dv.sum(1) # Grid response
dvxc -= tmp_dv # XC response
vrho = tmp_dv = None
t1 = logger.timer(
mc,
'PDFT HlFn quadrature atom {} Vpq + Vpqrs * Drs'.format(ia),
*t1)
# Vpuvx * Lpuvx ; remember the stupid slowest->fastest->medium stride order of the ao grid arrays
moval_cas = moval_occ = np.ascontiguousarray(
moval_occ[..., ncore:].transpose(0, 2, 1)).transpose(0, 2, 1)
tmp_dv = ot.get_veff_2body_kl(
rho,
Pi,
moval_cas,
moval_cas,
w0[ip0:ip1],
symm=True,
kern=vPi) # ndpi,ngrids,ncas*(ncas+1)//2
tmp_dv = np.tensordot(tmp_dv, casdm2_pack,
axes=(-1, -1)) # ndpi, ngrids, ncas, ncas
tmp_dv[0] = (tmp_dv[:ndpi] * moval_cas[:ndpi, :, None, :]).sum(
0) # Chain and product rule
tmp_dv[1:ndpi] *= moval_cas[0, :,
None, :] # Chain and product rule
tmp_dv = tmp_dv.sum(-1) # ndpi, ngrids, ncas
tmp_dv = np.tensordot(aoval[:, :ndpi],
tmp_dv,
axes=((1, 2),
(0, 1))) # comp, nao (orb), ncas (dm2)
tmp_dv = np.einsum(
'cpu,pu->cp', tmp_dv, mo_cas
) # comp, ncas (it's ok to not vectorize this b/c the quadrature grid is gone)
if k >= 0: de_grid[k] += 2 * tmp_dv.sum(1) # Grid response
dvxc -= tmp_dv # XC response
tmp_dv = None
t1 = logger.timer(
mc, 'PDFT HlFn quadrature atom {} Vpuvx * Lpuvx'.format(ia),
*t1)
rho = Pi = eot = vot = vPi = aoval = moval_occ = moval_cas = None
gc.collect()
for k, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = aoslices[ia]
h1ao = hcore_deriv(ia) # MRH: this should be the TRUE hcore
de_hcore[k] += np.einsum('xij,ij->x', h1ao, dm1)
de_renorm[k] -= np.einsum('xij,ij->x', s1[:, p0:p1], dme0[p0:p1]) * 2
de_coul[k] += np.einsum('xij,ij->x', vj[:, p0:p1], dm1[p0:p1]) * 2
de_xc[k] += dvxc[:, p0:p1].sum(
1) * 2 # Full quadrature, only some orbitals
de_nuc = mf_grad.grad_nuc(mol, atmlst)
logger.debug(mc, "MC-PDFT Hellmann-Feynman nuclear :\n{}".format(de_nuc))
logger.debug(
mc, "MC-PDFT Hellmann-Feynman hcore component:\n{}".format(de_hcore))
logger.debug(
mc, "MC-PDFT Hellmann-Feynman coulomb component:\n{}".format(de_coul))
logger.debug(mc,
"MC-PDFT Hellmann-Feynman xc component:\n{}".format(de_xc))
logger.debug(
mc, "MC-PDFT Hellmann-Feynman quadrature point component:\n{}".format(
de_grid))
logger.debug(
mc, "MC-PDFT Hellmann-Feynman quadrature weight component:\n{}".format(
de_wgt))
logger.debug(
mc, "MC-PDFT Hellmann-Feynman renorm component:\n{}".format(de_renorm))
de = de_nuc + de_hcore + de_coul + de_renorm + de_xc + de_grid + de_wgt
if auxbasis_response:
de += de_aux
logger.debug(
mc, "MC-PDFT Hellmann-Feynman aux component:\n{}".format(de_aux))
t1 = logger.timer(mc, 'PDFT HlFn total', *t0)
return de
def kernel(ot,
oneCDMs_amo,
twoCDM_amo,
mo_coeff,
ncore,
ncas,
max_memory=2000,
hermi=1,
paaa_only=False,
aaaa_only=False):
''' Get the 1- and 2-body effective potential from MC-PDFT.
Args:
ot : an instance of otfnal class
oneCDMs_amo : ndarray of shape (2, ncas, ncas)
containing spin-separated one-body density matrices
twoCDM_amo : ndarray of shape (ncas, ncas, ncas, ncas)
containing spin-summed two-body cumulant density matrix in an
active space
mo_coeff : ndarray of shape (nao, nmo)
containing molecular orbital coefficients
ncore : integer
number of inactive orbitals
ncas : integer
number of active orbitals
Kwargs:
max_memory : int or float
maximum cache size in MB
default is 2000
hermi : int
1 if 1CDMs are assumed hermitian, 0 otherwise
paaa_only : logical
If true, only compute the paaa range of papa and ppaa (all
other elements set to zero)
aaaa_only : logical
If true, only compute the aaaa range of papa and ppaa (all
other elements set to zero; overrides paaa_only)
Returns:
veff1 : ndarray of shape (nao, nao)
1-body effective potential
veff2 : object of class pdft_veff._ERIS
2-body effective potential and related quantities
'''
nocc = ncore + ncas
ni, xctype, dens_deriv = ot._numint, ot.xctype, ot.dens_deriv
nao = mo_coeff.shape[0]
mo_core = mo_coeff[:, :ncore]
ao2amo = mo_coeff[:, ncore:nocc]
npair = nao * (nao + 1) // 2
shls_slice = (0, ot.mol.nbas)
ao_loc = ot.mol.ao_loc_nr()
veff1 = np.zeros((nao, nao), dtype=oneCDMs_amo.dtype)
veff2 = _ERIS(ot.mol,
mo_coeff,
ncore,
ncas,
paaa_only=paaa_only,
aaaa_only=aaaa_only,
verbose=ot.verbose,
stdout=ot.stdout)
t0 = (time.process_time(), time.time())
# Make density matrices and TAG THEM with their own eigendecompositions
# because that speeds up the rho generators!
dm_core = mo_core @ mo_core.T
dm_cas = np.dot(ao2amo, np.dot(oneCDMs_amo, ao2amo.T)).transpose(1, 0, 2)
dm1s = dm_cas + dm_core[None, :, :]
dm_core *= 2
# tag dm_core
imo_occ = np.ones(ncore, dtype=dm_core.dtype) * 2.0
dm_core = tag_array(dm_core, mo_coeff=mo_core, mo_occ=imo_occ)
# tag dm_cas
amo_occ = np.zeros((2, ncas), dtype=dm_cas.dtype)
amo_coeff = np.stack([ao2amo.copy(), ao2amo.copy()], axis=0)
for i in range(2):
amo_occ[i], ua = linalg.eigh(oneCDMs_amo[i])
amo_coeff[i] = amo_coeff[i] @ ua
dm_cas = tag_array(dm_cas, mo_coeff=amo_coeff, mo_occ=amo_occ)
# tag dm1s
mo_occ = np.zeros((2, nocc), dtype=dm1s.dtype)
mo_occ[:, :ncore] = 1.0
mo_occ[:, ncore:nocc] = amo_occ
tag_coeff = np.stack(
(mo_coeff[:, :nocc].copy(), mo_coeff[:, :nocc].copy()), axis=0)
tag_coeff[:, :, ncore:nocc] = amo_coeff
dm1s = tag_array(dm1s, mo_coeff=tag_coeff, mo_occ=mo_occ)
# rho generators
make_rho_c, nset_c, nao_c = ni._gen_rho_evaluator(ot.mol, dm_core, hermi)
make_rho_a, nset_a, nao_a = ni._gen_rho_evaluator(ot.mol, dm_cas, hermi)
make_rho, nset, nao_ = ni._gen_rho_evaluator(ot.mol, dm1s, hermi)
# memory block size
gc.collect()
remaining_floats = (max_memory - current_memory()[0]) * 1e6 / 8
nderiv_rho = (1, 4, 10)[dens_deriv] # ?? for meta-GGA
nderiv_Pi = (1, 4)[ot.Pi_deriv]
ncols = 4 + nderiv_rho * nao # ao, weight, coords
ncols += nderiv_rho * 4 + nderiv_Pi # rho, rho_a, rho_c, Pi
ncols += 1 + nderiv_rho + nderiv_Pi # eot, vot
# Asynchronous part
nveff1 = nderiv_rho * (nao + 1) # footprint of get_veff_1body
nveff2 = veff2._accumulate_ftpt() * nderiv_Pi
ncols += np.amax([nveff1, nveff2]) # asynchronous fns
pdft_blksize = int(remaining_floats /
(ncols * BLKSIZE)) * BLKSIZE # round up
if ot.grids.coords is None:
ot.grids.build(with_non0tab=True)
ngrids = ot.grids.coords.shape[0]
pdft_blksize = max(BLKSIZE, min(pdft_blksize, ngrids, BLKSIZE * 1200))
logger.debug(
ot,
'{} MB used of {} available; block size of {} chosen for grid with {} points'
.format(current_memory()[0], max_memory, pdft_blksize, ngrids))
# The actual loop
for ao, mask, weight, coords in ni.block_loop(ot.mol,
ot.grids,
nao,
dens_deriv,
max_memory,
blksize=pdft_blksize):
rho = np.asarray([make_rho(i, ao, mask, xctype) for i in range(2)])
rho_a = sum([make_rho_a(i, ao, mask, xctype) for i in range(2)])
rho_c = make_rho_c(0, ao, mask, xctype)
t0 = logger.timer(ot, 'untransformed densities (core and total)', *t0)
Pi = get_ontop_pair_density(ot, rho, ao, dm1s, twoCDM_amo, ao2amo,
dens_deriv, mask)
t0 = logger.timer(ot, 'on-top pair density calculation', *t0)
eot, vot = ot.eval_ot(rho, Pi, weights=weight)[:2]
vrho, vPi = vot
t0 = logger.timer(ot, 'effective potential kernel calculation', *t0)
if ao.ndim == 2:
ao = ao[None, :, :] # TODO: consistent format req's ao LDA case
veff1 += ot.get_veff_1body(rho,
Pi,
ao,
weight,
non0tab=mask,
shls_slice=shls_slice,
ao_loc=ao_loc,
hermi=1,
kern=vrho)
t0 = logger.timer(ot, '1-body effective potential calculation', *t0)
veff2._accumulate(ot, rho, Pi, ao, weight, rho_c, rho_a, vPi, mask,
shls_slice, ao_loc)
t0 = logger.timer(ot, '2-body effective potential calculation', *t0)
veff2._finalize()
t0 = logger.timer(ot, 'Finalizing 2-body effective potential calculation',
*t0)
return veff1, veff2
def kernel(ot,
oneCDMs_amo,
twoCDM_amo,
mo_coeff,
ncore,
ncas,
max_memory=20000,
hermi=1,
veff2_mo=None,
paaa_only=False):
''' Get the 1- and 2-body effective potential from MC-PDFT. Eventually I'll be able to specify
mo slices for the 2-body part
Args:
ot : an instance of otfnal class
oneCDMs_amo : ndarray of shape (2, ncas, ncas)
containing spin-separated one-body density matrices
twoCDM_amo : ndarray of shape (ncas, ncas, ncas, ncas)
containing spin-summed two-body cumulant density matrix in an active space
ao2amo : ndarray of shape (nao, ncas)
containing molecular orbital coefficients for active-space orbitals
Kwargs:
max_memory : int or float
maximum cache size in MB
default is 20000
hermi : int
1 if 1CDMs are assumed hermitian, 0 otherwise
Returns : float
The MC-PDFT on-top exchange-correlation energy
'''
if veff2_mo is not None:
raise NotImplementedError(
'Molecular orbital slices for the two-body part')
nocc = ncore + ncas
ni, xctype, dens_deriv = ot._numint, ot.xctype, ot.dens_deriv
norbs_ao = mo_coeff.shape[0]
mo_core = mo_coeff[:, :ncore]
ao2amo = mo_coeff[:, ncore:nocc]
npair = norbs_ao * (norbs_ao + 1) // 2
veff1 = np.zeros((norbs_ao, norbs_ao), dtype=oneCDMs_amo.dtype)
veff2 = _ERIS(ot.mol,
mo_coeff,
ncore,
ncas,
paaa_only=paaa_only,
verbose=ot.verbose,
stdout=ot.stdout)
t0 = (time.clock(), time.time())
dm_core = mo_core @ mo_core.T
dm_cas = np.dot(ao2amo, np.dot(oneCDMs_amo, ao2amo.T)).transpose(1, 0, 2)
dm1s = dm_cas + dm_core[None, :, :]
dm_core *= 2
# Can't trust that NOs are the same for alpha and beta. Have to do this explicitly here
# Begin tag block: dm_core
imo_occ = np.ones(ncore, dtype=dm_core.dtype) * 2.0
dm_core = tag_array(dm_core, mo_coeff=mo_core, mo_occ=imo_occ)
# Begin tag block: dm_cas
amo_occ = np.zeros((2, ncas), dtype=dm_cas.dtype)
amo_coeff = np.stack([ao2amo.copy(), ao2amo.copy()], axis=0)
for i in range(2):
amo_occ[i], ua = linalg.eigh(oneCDMs_amo[i])
amo_coeff[i] = amo_coeff[i] @ ua
dm_cas = tag_array(dm_cas, mo_coeff=amo_coeff, mo_occ=amo_occ)
# Begin tag block: dm1s
mo_occ = np.zeros((2, nocc), dtype=dm1s.dtype)
mo_occ[:, :ncore] = 1.0
mo_occ[:, ncore:nocc] = amo_occ
tag_coeff = np.stack(
(mo_coeff[:, :nocc].copy(), mo_coeff[:, :nocc].copy()), axis=0)
tag_coeff[:, :, ncore:nocc] = amo_coeff
dm1s = tag_array(dm1s, mo_coeff=tag_coeff, mo_occ=mo_occ)
# End tag block
make_rho_c, nset_c, nao_c = ni._gen_rho_evaluator(ot.mol, dm_core, hermi)
make_rho_a, nset_a, nao_a = ni._gen_rho_evaluator(ot.mol, dm_cas, hermi)
make_rho, nset, nao = ni._gen_rho_evaluator(ot.mol, dm1s, hermi)
gc.collect()
remaining_floats = (max_memory - current_memory()[0]) * 1e6 / 8
nderiv_rho = (1, 4, 10)[dens_deriv] # ?? for meta-GGA
nderiv_Pi = (1, 4)[ot.Pi_deriv]
ncols_v2 = norbs_ao * ncas + ncas**2 if paaa_only else 2 * norbs_ao * ncas
ncols = 1 + nderiv_rho * (5 + norbs_ao * 2) + nderiv_Pi * (1 + ncols_v2)
pdft_blksize = int(
remaining_floats /
(ncols * BLKSIZE)) * BLKSIZE # something something indexing
if ot.grids.coords is None:
ot.grids.build(with_non0tab=True)
ngrids = ot.grids.coords.shape[0]
pdft_blksize = max(BLKSIZE, min(pdft_blksize, ngrids, BLKSIZE * 1200))
logger.debug(
ot,
'{} MB used of {} available; block size of {} chosen for grid with {} points'
.format(current_memory()[0], max_memory, pdft_blksize, ngrids))
shls_slice = (0, ot.mol.nbas)
ao_loc = ot.mol.ao_loc_nr()
for ao, mask, weight, coords in ni.block_loop(ot.mol,
ot.grids,
norbs_ao,
dens_deriv,
max_memory,
blksize=pdft_blksize):
rho = np.asarray([make_rho(i, ao, mask, xctype) for i in range(2)])
rho_a = np.asarray([make_rho_a(i, ao, mask, xctype) for i in range(2)])
rho_c = make_rho_c(0, ao, mask, xctype)
t0 = logger.timer(ot, 'untransformed densities (core and total)', *t0)
Pi = get_ontop_pair_density(ot, rho, ao, dm1s, twoCDM_amo, ao2amo,
dens_deriv, mask)
t0 = logger.timer(ot, 'on-top pair density calculation', *t0)
eot, vrho, vPi = ot.eval_ot(rho, Pi, weights=weight)
t0 = logger.timer(ot, 'effective potential kernel calculation', *t0)
veff1 += ot.get_veff_1body(rho,
Pi,
ao,
weight,
non0tab=mask,
shls_slice=shls_slice,
ao_loc=ao_loc,
hermi=1,
kern=vrho)
t0 = logger.timer(ot, '1-body effective potential calculation', *t0)
#ao[:,:,:] = np.tensordot (ao, mo_coeff, axes=1)
#t0 = logger.timer (ot, 'ao2mo grid points', *t0)
veff2._accumulate(ot, rho, Pi, ao, weight, rho_c, rho_a, vPi, mask,
shls_slice, ao_loc)
t0 = logger.timer(ot, '2-body effective potential calculation', *t0)
veff2._finalize()
t0 = logger.timer(ot, 'Finalizing 2-body effective potential calculation',
*t0)
return veff1, veff2