def uhf_internal(mf, with_symmetry=True, verbose=None):
log = logger.new_logger(mf, verbose)
g, hop, hdiag = newton_ah.gen_g_hop_uhf(mf, mf.mo_coeff, mf.mo_occ,
with_symmetry=with_symmetry)
hdiag *= 2
def precond(dx, e, x0):
hdiagd = hdiag - e
hdiagd[abs(hdiagd)<1e-8] = 1e-8
return dx/hdiagd
def hessian_x(x): # See comments in function rhf_internal
return hop(x).real * 2
x0 = numpy.zeros_like(g)
x0[g!=0] = 1. / hdiag[g!=0]
if not with_symmetry: # allow to break point group symmetry
x0[numpy.argmin(hdiag)] = 1
e, v = lib.davidson(hessian_x, x0, precond, tol=1e-4, verbose=log)
if e < -1e-5:
log.note('UHF/UKS wavefunction has an internal instablity.')
nocca = numpy.count_nonzero(mf.mo_occ[0]> 0)
nvira = numpy.count_nonzero(mf.mo_occ[0]==0)
mo = (_rotate_mo(mf.mo_coeff[0], mf.mo_occ[0], v[:nocca*nvira]),
_rotate_mo(mf.mo_coeff[1], mf.mo_occ[1], v[nocca*nvira:]))
else:
log.note('UHF/UKS wavefunction is stable in the intenral stability analysis')
mo = mf.mo_coeff
return mo
def casci(self, mo_coeff, ci0=None, eris=None, verbose=None, envs=None):
if eris is None:
fcasci = copy.copy(self)
fcasci.ao2mo = self.get_h2cas
else:
fcasci = _fake_h_for_fast_casci(self, mo_coeff, eris)
log = logger.new_logger(self, verbose)
e_tot, e_cas, fcivec = ucasci.kernel(fcasci, mo_coeff, ci0, log)
if envs is not None and log.verbose >= logger.INFO:
log.debug('CAS space CI energy = %.15g', e_cas)
if 'imicro' in envs: # Within CASSCF iteration
log.info('macro iter %d (%d JK %d micro), '
'UCASSCF E = %.15g dE = %.8g',
envs['imacro'], envs['njk'], envs['imicro'],
e_tot, e_tot-envs['elast'])
if 'norm_gci' in envs:
log.info(' |grad[o]|=%5.3g '
'|grad[c]|= %s |ddm|=%5.3g',
envs['norm_gorb0'],
envs['norm_gci'], envs['norm_ddm'])
else:
log.info(' |grad[o]|=%5.3g |ddm|=%5.3g',
envs['norm_gorb0'], envs['norm_ddm'])
else: # Initialization step
log.info('UCASCI E = %.15g', e_tot)
return e_tot, e_cas, fcivec
def rhf_external(mf, with_symmetry=True, verbose=None):
log = logger.new_logger(mf, verbose)
hop1, hdiag1, hop2, hdiag2 = _gen_hop_rhf_external(mf, with_symmetry)
def precond(dx, e, x0):
hdiagd = hdiag1 - e
hdiagd[abs(hdiagd)<1e-8] = 1e-8
return dx/hdiagd
x0 = numpy.zeros_like(hdiag1)
x0[hdiag1>1e-5] = 1. / hdiag1[hdiag1>1e-5]
if not with_symmetry: # allow to break point group symmetry
x0[numpy.argmin(hdiag1)] = 1
e1, v1 = lib.davidson(hop1, x0, precond, tol=1e-4, verbose=log)
if e1 < -1e-5:
log.note('RHF/RKS wavefunction has a real -> complex instablity')
else:
log.note('RHF/RKS wavefunction is stable in the real -> complex stability analysis')
def precond(dx, e, x0):
hdiagd = hdiag2 - e
hdiagd[abs(hdiagd)<1e-8] = 1e-8
return dx/hdiagd
x0 = v1
e3, v3 = lib.davidson(hop2, x0, precond, tol=1e-4, verbose=log)
if e3 < -1e-5:
log.note('RHF/RKS wavefunction has a RHF/RKS -> UHF/UKS instablity.')
mo = (_rotate_mo(mf.mo_coeff, mf.mo_occ, v3), mf.mo_coeff)
else:
log.note('RHF/RKS wavefunction is stable in the RHF/RKS -> UHF/UKS stability analysis')
mo = (mf.mo_coeff, mf.mo_coeff)
return mo
def kernel(self, h1, h2, norb, nelec, ci0=None, verbose=0, **kwargs):
# Note self.orbsym is initialized lazily in mc1step_symm.kernel function
log = logger.new_logger(self, verbose)
es = []
cs = []
for solver, c0 in loop_solver(fcisolvers, ci0):
e, c = solver.kernel(h1, h2, norb, get_nelec(solver, nelec), c0,
orbsym=self.orbsym, verbose=log, **kwargs)
if solver.nroots == 1:
es.append(e)
cs.append(c)
else:
es.extend(e)
cs.extend(c)
e_states[0] = es
if log.verbose >= logger.DEBUG:
if has_spin_square:
ss, multip = collect(solver.spin_square(c0, norb, get_nelec(solver, nelec))
for solver, c0 in loop_civecs(fcisolvers, cs))
for i, ei in enumerate(es):
log.debug('state %d E = %.15g S^2 = %.7f', i, ei, ss[i])
else:
for i, ei in enumerate(es):
log.debug('state %d E = %.15g', i, ei)
return numpy.einsum('i,i', numpy.array(es), weights), cs
def ghf_stability(mf, verbose=None):
log = logger.new_logger(mf, verbose)
with_symmetry = True
g, hop, hdiag = newton_ah.gen_g_hop_ghf(mf, mf.mo_coeff, mf.mo_occ,
with_symmetry=with_symmetry)
hdiag *= 2
def precond(dx, e, x0):
hdiagd = hdiag - e
hdiagd[abs(hdiagd)<1e-8] = 1e-8
return dx/hdiagd
def hessian_x(x): # See comments in function rhf_internal
return hop(x).real * 2
x0 = numpy.zeros_like(g)
x0[g!=0] = 1. / hdiag[g!=0]
if not with_symmetry: # allow to break point group symmetry
x0[numpy.argmin(hdiag)] = 1
e, v = lib.davidson(hessian_x, x0, precond, tol=1e-4, verbose=log)
if e < -1e-5:
log.note('GHF wavefunction has an internal instablity')
mo = _rotate_mo(mf.mo_coeff, mf.mo_occ, v)
else:
log.note('GHF wavefunction is stable in the intenral stability analysis')
mo = mf.mo_coeff
return mo
def gen_hop(hobj, mo_energy=None, mo_coeff=None, mo_occ=None, verbose=None):
log = logger.new_logger(hobj, verbose)
mol = hobj.mol
mf = hobj.base
if mo_energy is None: mo_energy = mf.mo_energy
if mo_occ is None: mo_occ = mf.mo_occ
if mo_coeff is None: mo_coeff = mf.mo_coeff
natm = mol.natm
nao, nmo = mo_coeff.shape
mocc = mo_coeff[:,mo_occ>0]
nocc = mocc.shape[1]
atmlst = range(natm)
max_memory = max(2000, hobj.max_memory - lib.current_memory()[0])
de2 = hobj.partial_hess_elec(mo_energy, mo_coeff, mo_occ, atmlst,
max_memory, log)
de2 += hobj.hess_nuc()
# Compute H1 integrals and store in hobj.chkfile
hobj.make_h1(mo_coeff, mo_occ, hobj.chkfile, atmlst, log)
aoslices = mol.aoslice_by_atom()
s1a = -mol.intor('int1e_ipovlp', comp=3)
fvind = gen_vind(mf, mo_coeff, mo_occ)
def h_op(x):
x = x.reshape(natm,3)
hx = numpy.einsum('abxy,ax->by', de2, x)
h1ao = 0
s1ao = 0
for ia in range(natm):
shl0, shl1, p0, p1 = aoslices[ia]
h1ao_i = lib.chkfile.load(hobj.chkfile, 'scf_f1ao/%d' % ia)
h1ao += numpy.einsum('x,xij->ij', x[ia], h1ao_i)
s1ao_i = numpy.zeros((3,nao,nao))
s1ao_i[:,p0:p1] += s1a[:,p0:p1]
s1ao_i[:,:,p0:p1] += s1a[:,p0:p1].transpose(0,2,1)
s1ao += numpy.einsum('x,xij->ij', x[ia], s1ao_i)
s1vo = reduce(numpy.dot, (mo_coeff.T, s1ao, mocc))
h1vo = reduce(numpy.dot, (mo_coeff.T, h1ao, mocc))
mo1, mo_e1 = cphf.solve(fvind, mo_energy, mo_occ, h1vo, s1vo)
mo1 = numpy.dot(mo_coeff, mo1)
mo_e1 = mo_e1.reshape(nocc,nocc)
dm1 = numpy.einsum('pi,qi->pq', mo1, mocc)
dme1 = numpy.einsum('pi,qi,i->pq', mo1, mocc, mo_energy[mo_occ>0])
dme1 = dme1 + dme1.T + reduce(numpy.dot, (mocc, mo_e1.T, mocc.T))
for ja in range(natm):
q0, q1 = aoslices[ja][2:]
h1ao = lib.chkfile.load(hobj.chkfile, 'scf_f1ao/%s'%ja)
hx[ja] += numpy.einsum('xpq,pq->x', h1ao, dm1) * 4
hx[ja] -= numpy.einsum('xpq,pq->x', s1a[:,q0:q1], dme1[q0:q1]) * 2
hx[ja] -= numpy.einsum('xpq,qp->x', s1a[:,q0:q1], dme1[:,q0:q1]) * 2
return hx.ravel()
hdiag = numpy.einsum('aaxx->ax', de2).ravel()
return h_op, hdiag
def dump_flags(self, verbose=None):
log = logger.new_logger(self, verbose)
log.info('')
log.info('******** CASCI flags ********')
ncore = self.ncore
ncas = self.ncas
nvir = self.mo_coeff.shape[1] - ncore - ncas
log.info('CAS (%de+%de, %do), ncore = %d, nvir = %d', \
self.nelecas[0], self.nelecas[1], ncas, ncore, nvir)
assert(self.ncas > 0)
log.info('natorb = %s', self.natorb)
log.info('canonicalization = %s', self.canonicalization)
log.info('sorting_mo_energy = %s', self.sorting_mo_energy)
log.info('max_memory %d (MB)', self.max_memory)
if getattr(self.fcisolver, 'dump_flags', None):
self.fcisolver.dump_flags(log.verbose)
if self.mo_coeff is None:
log.error('Orbitals for CASCI are not specified. The relevant SCF '
'object may not be initialized.')
if (getattr(self._scf, 'with_solvent', None) and
not getattr(self, 'with_solvent', None)):
log.warn('''Solvent model %s was found in SCF object.
It is not applied to the CASSCF object. The CASSCF result is not affected by the SCF solvent model.
To enable the solvent model for CASSCF, a decoration to CASSCF object as below needs be called
from pyscf import solvent
mc = mcscf.CASSCF(...)
mc = solvent.ddCOSMO(mc)
''',
self._scf.with_solvent.__class__)
return self
def rhf_internal(mf, verbose=None):
log = logger.new_logger(mf, verbose)
g, hop, hdiag = newton_ah.gen_g_hop_rhf(mf, mf.mo_coeff, mf.mo_occ)
def precond(dx, e, x0):
hdiagd = hdiag*2 - e
hdiagd[abs(hdiagd)<1e-8] = 1e-8
return dx/hdiagd
# The results of hop(x) corresponds to a displacement that reduces
# gradients g. It is the vir-occ block of the matrix vector product
# (Hessian*x). The occ-vir block equals to x2.T.conj(). The overall
# Hessian for internal reotation is x2 + x2.T.conj(). This is
# the reason we apply (.real * 2) below
def hessian_x(x):
return hop(x).real * 2
x0 = numpy.zeros_like(g)
x0[g!=0] = 1. / hdiag[g!=0]
e, v = lib.davidson(hessian_x, x0, precond, tol=1e-4, verbose=log)
if e < -1e-5:
log.log('KRHF/KRKS wavefunction has an internal instablity')
mo = _rotate_mo(mf.mo_coeff, mf.mo_occ, v)
else:
log.log('KRHF/KRKS wavefunction is stable in the intenral stability analysis')
mo = mf.mo_coeff
return mo
def mulliken_pop(mol, dm, s=None, verbose=logger.DEBUG):
r'''Mulliken population analysis
.. math:: M_{ij} = D_{ij} S_{ji}
Mulliken charges
.. math:: \delta_i = \sum_j M_{ij}
'''
if s is None: s = get_ovlp(mol)
log = logger.new_logger(mol, verbose)
pop = numpy.einsum('ij,ji->i', dm, s).real
log.info(' ** Mulliken pop **')
for i, s in enumerate(mol.spinor_labels()):
log.info('pop of %s %10.5f', s, pop[i])
log.note(' ** Mulliken atomic charges **')
chg = numpy.zeros(mol.natm)
for i, s in enumerate(mol.spinor_labels(fmt=None)):
chg[s[0]] += pop[i]
chg = mol.atom_charges() - chg
for ia in range(mol.natm):
symb = mol.atom_symbol(ia)
log.note('charge of %d%s = %10.5f', ia, symb, chg[ia])
return pop, chg
def get_jk_coulomb(mol, dm, hermi=1, coulomb_allow='SSSS',
opt_llll=None, opt_ssll=None, opt_ssss=None, verbose=None):
log = logger.new_logger(mol, verbose)
if coulomb_allow.upper() == 'LLLL':
log.debug('Coulomb integral: (LL|LL)')
j1, k1 = _call_veff_llll(mol, dm, hermi, opt_llll)
n2c = j1.shape[1]
vj = numpy.zeros_like(dm)
vk = numpy.zeros_like(dm)
vj[...,:n2c,:n2c] = j1
vk[...,:n2c,:n2c] = k1
elif coulomb_allow.upper() == 'SSLL' \
or coulomb_allow.upper() == 'LLSS':
log.debug('Coulomb integral: (LL|LL) + (SS|LL)')
vj, vk = _call_veff_ssll(mol, dm, hermi, opt_ssll)
j1, k1 = _call_veff_llll(mol, dm, hermi, opt_llll)
n2c = j1.shape[1]
vj[...,:n2c,:n2c] += j1
vk[...,:n2c,:n2c] += k1
else: # coulomb_allow == 'SSSS'
log.debug('Coulomb integral: (LL|LL) + (SS|LL) + (SS|SS)')
vj, vk = _call_veff_ssll(mol, dm, hermi, opt_ssll)
j1, k1 = _call_veff_llll(mol, dm, hermi, opt_llll)
n2c = j1.shape[1]
vj[...,:n2c,:n2c] += j1
vk[...,:n2c,:n2c] += k1
j1, k1 = _call_veff_ssss(mol, dm, hermi, opt_ssss)
vj[...,n2c:,n2c:] += j1
vk[...,n2c:,n2c:] += k1
return vj, vk
def get_jk(self, mol=None, dm=None, hermi=1):
if mol is None: mol = self.mol
if dm is None: dm = self.make_rdm1()
t0 = (time.clock(), time.time())
log = logger.new_logger(self)
if self.direct_scf and self.opt[0] is None:
self.opt = self.init_direct_scf(mol)
opt_llll, opt_ssll, opt_ssss, opt_gaunt = self.opt
vj, vk = get_jk_coulomb(mol, dm, hermi, self._coulomb_now,
opt_llll, opt_ssll, opt_ssss, log)
if self.with_breit:
if 'SSSS' in self._coulomb_now.upper():
vj1, vk1 = _call_veff_gaunt_breit(mol, dm, hermi, opt_gaunt, True)
log.debug('Add Breit term')
vj += vj1
vk += vk1
elif self.with_gaunt and 'SS' in self._coulomb_now.upper():
log.debug('Add Gaunt term')
vj1, vk1 = _call_veff_gaunt_breit(mol, dm, hermi, opt_gaunt, False)
vj += vj1
vk += vk1
log.timer('vj and vk', *t0)
return vj, vk
def mulliken_meta(cell, dm_ao_kpts, verbose=logger.DEBUG,
pre_orth_method=PRE_ORTH_METHOD, s=None):
'''A modified Mulliken population analysis, based on meta-Lowdin AOs.
Note this function only computes the Mulliken population for the gamma
point density matrix.
'''
from pyscf.lo import orth
if s is None:
s = khf.get_ovlp(cell)
log = logger.new_logger(cell, verbose)
log.note('Analyze output for *gamma point*.')
log.info(' To include the contributions from k-points, transform to a '
'supercell then run the population analysis on the supercell\n'
' from pyscf.pbc.tools import k2gamma\n'
' k2gamma.k2gamma(mf).mulliken_meta()')
log.note("KUHF mulliken_meta")
dm_ao_gamma = dm_ao_kpts[:,0,:,:].real
s_gamma = s[0,:,:].real
c = orth.restore_ao_character(cell, pre_orth_method)
orth_coeff = orth.orth_ao(cell, 'meta_lowdin', pre_orth_ao=c, s=s_gamma)
c_inv = np.dot(orth_coeff.T, s_gamma)
dm_a = reduce(np.dot, (c_inv, dm_ao_gamma[0], c_inv.T.conj()))
dm_b = reduce(np.dot, (c_inv, dm_ao_gamma[1], c_inv.T.conj()))
log.note(' ** Mulliken pop alpha/beta on meta-lowdin orthogonal AOs **')
return mol_uhf.mulliken_pop(cell, (dm_a,dm_b), np.eye(orth_coeff.shape[0]), log)
def casci(self, mo_coeff, ci0=None, eris=None, verbose=None, envs=None):
log = logger.new_logger(self, verbose)
log.debug('Running CASCI with solvent. Note the total energy '
'has duplicated contributions from solvent.')
# In oldCAS.casci function, dE was computed based on the total
# energy without removing the duplicated solvent contributions.
# However, envs['elast'] is the last total energy with correct
# solvent effects. Hack envs['elast'] to make oldCAS.casci print
# the correct energy difference.
envs['elast'] = self._e_tot_without_solvent
e_tot, e_cas, fcivec = oldCAS.casci(self, mo_coeff, ci0, eris,
verbose, envs)
self._e_tot_without_solvent = e_tot
log.debug('Computing corrections to the total energy.')
dm = self.make_rdm1(ci=fcivec, ao_repr=True)
with_solvent = self.with_solvent
if with_solvent.epcm is not None:
edup = numpy.einsum('ij,ji->', with_solvent.vpcm, dm)
ediel = with_solvent.epcm
e_tot = e_tot - edup + ediel
log.info('Removing duplication %.15g, '
'adding E_diel = %.15g to total energy:\n'
' E(CASSCF+solvent) = %.15g', edup, ediel, e_tot)
# Update solvent effects for next iteration if needed
if not with_solvent.frozen:
with_solvent.epcm, with_solvent.vpcm = with_solvent.kernel(dm)
return e_tot, e_cas, fcivec
def rhf_internal(mf, verbose=None):
log = logger.new_logger(mf, verbose)
mol = mf.mol
mo_coeff = mf.mo_coeff
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
nmo = mo_coeff.shape[1]
nocc = numpy.count_nonzero(mo_occ)
nvir = nmo - nocc
eri_mo = ao2mo.full(mol, mo_coeff)
eri_mo = ao2mo.restore(1, eri_mo, nmo)
eai = lib.direct_sum('a-i->ai', mo_energy[nocc:], mo_energy[:nocc])
# A
h = numpy.einsum('ckld->kcld', eri_mo[nocc:,:nocc,:nocc,nocc:]) * 2
h-= numpy.einsum('cdlk->kcld', eri_mo[nocc:,nocc:,:nocc,:nocc])
for a in range(nvir):
for i in range(nocc):
h[i,a,i,a] += eai[a,i]
# B
h+= numpy.einsum('ckdl->kcld', eri_mo[nocc:,:nocc,nocc:,:nocc]) * 2
h-= numpy.einsum('cldk->kcld', eri_mo[nocc:,:nocc,nocc:,:nocc])
nov = nocc * nvir
e = scipy.linalg.eigh(h.reshape(nov,nov))[0]
log.debug('rhf_internal: lowest eigs = %s', e[e<=max(e[0],1e-5)])
if e[0] < -1e-5:
log.log('RHF wavefunction has an internal instablity')
else:
log.log('RHF wavefunction is stable in the intenral stablity analysis')
def kernel(casci, mo_coeff=None, ci0=None, verbose=logger.NOTE):
'''CASCI solver
'''
if mo_coeff is None: mo_coeff = casci.mo_coeff
log = logger.new_logger(casci, verbose)
t0 = (time.clock(), time.time())
log.debug('Start CASCI')
ncas = casci.ncas
nelecas = casci.nelecas
# 2e
eri_cas = casci.get_h2eff(mo_coeff)
t1 = log.timer('integral transformation to CAS space', *t0)
# 1e
h1eff, energy_core = casci.get_h1eff(mo_coeff)
log.debug('core energy = %.15g', energy_core)
t1 = log.timer('effective h1e in CAS space', *t1)
if h1eff.shape[0] != ncas:
raise RuntimeError('Active space size error. nmo=%d ncore=%d ncas=%d' %
(mo_coeff.shape[1], casci.ncore, ncas))
# FCI
max_memory = max(400, casci.max_memory-lib.current_memory()[0])
e_tot, fcivec = casci.fcisolver.kernel(h1eff, eri_cas, ncas, nelecas,
ci0=ci0, verbose=log,
max_memory=max_memory,
ecore=energy_core)
t1 = log.timer('FCI solver', *t1)
e_cas = e_tot - energy_core
return e_tot, e_cas, fcivec
def kernel(casci, mo_coeff=None, ci0=None, verbose=logger.NOTE):
'''UHF-CASCI solver
'''
if mo_coeff is None: mo_coeff = casci.mo_coeff
log = logger.new_logger(casci, verbose)
t0 = (time.clock(), time.time())
log.debug('Start uhf-based CASCI')
ncas = casci.ncas
nelecas = casci.nelecas
ncore = casci.ncore
mo_core, mo_cas, mo_vir = extract_orbs(mo_coeff, ncas, nelecas, ncore)
# 1e
h1eff, energy_core = casci.h1e_for_cas(mo_coeff)
log.debug('core energy = %.15g', energy_core)
t1 = log.timer('effective h1e in CAS space', *t0)
# 2e
eri_cas = casci.get_h2eff(mo_cas)
t1 = log.timer('integral transformation to CAS space', *t1)
# FCI
max_memory = max(400, casci.max_memory-lib.current_memory()[0])
e_tot, fcivec = casci.fcisolver.kernel(h1eff, eri_cas, ncas, nelecas,
ci0=ci0, verbose=log,
max_memory=max_memory,
ecore=energy_core)
t1 = log.timer('FCI solver', *t1)
e_cas = e_tot - energy_core
return e_tot, e_cas, fcivec
def polarizability_with_freq(polobj, freq=None):
from pyscf.prop.nmr import rhf as rhf_nmr
log = logger.new_logger(polobj)
mf = polobj._scf
mol = mf.mol
mo_energy = mf.mo_energy
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
occidx = mo_occ > 0
orbo = mo_coeff[:, occidx]
orbv = mo_coeff[:,~occidx]
charges = mol.atom_charges()
coords = mol.atom_coords()
charge_center = numpy.einsum('i,ix->x', charges, coords) / charges.sum()
with mol.with_common_orig(charge_center):
int_r = mol.intor_symmetric('int1e_r', comp=3)
h1 = lib.einsum('xpq,pi,qj->xij', int_r, orbv.conj(), orbo)
mo1 = cphf_with_freq(mf, mo_energy, mo_occ, h1, freq,
polobj.max_cycle_cphf, polobj.conv_tol, verbose=log)[0]
e2 = numpy.einsum('xpi,ypi->xy', h1, mo1[0])
e2 += numpy.einsum('xpi,ypi->xy', h1, mo1[1])
# *-1 from the definition of dipole moment. *2 for double occupancy
e2 *= -2
log.debug('Polarizability tensor with freq %s', freq)
log.debug('%s', e2)
return e2
def mulliken_pop(mol, dm, s=None, verbose=logger.DEBUG):
'''Mulliken population analysis
'''
if s is None: s = hf.get_ovlp(mol)
log = logger.new_logger(mol, verbose)
if isinstance(dm, numpy.ndarray) and dm.ndim == 2:
dm = numpy.array((dm*.5, dm*.5))
pop_a = numpy.einsum('ij,ji->i', dm[0], s).real
pop_b = numpy.einsum('ij,ji->i', dm[1], s).real
log.info(' ** Mulliken pop alpha | beta **')
for i, s in enumerate(mol.ao_labels()):
log.info('pop of %s %10.5f | %-10.5f',
s, pop_a[i], pop_b[i])
log.info('In total %10.5f | %-10.5f', sum(pop_a), sum(pop_b))
log.note(' ** Mulliken atomic charges ( Nelec_alpha | Nelec_beta ) **')
nelec_a = numpy.zeros(mol.natm)
nelec_b = numpy.zeros(mol.natm)
for i, s in enumerate(mol.ao_labels(fmt=None)):
nelec_a[s[0]] += pop_a[i]
nelec_b[s[0]] += pop_b[i]
chg = mol.atom_charges() - (nelec_a + nelec_b)
for ia in range(mol.natm):
symb = mol.atom_symbol(ia)
log.note('charge of %d%s = %10.5f ( %10.5f %10.5f )',
ia, symb, chg[ia], nelec_a[ia], nelec_b[ia])
return (pop_a,pop_b), chg
def make_fcdip(hfcobj, dm0, hfc_nuc=None, verbose=None):
'''The contribution of Fermi-contact term and dipole-dipole interactions'''
log = logger.new_logger(hfcobj, verbose)
mol = hfcobj.mol
if hfc_nuc is None:
hfc_nuc = range(mol.natm)
if isinstance(dm0, numpy.ndarray) and dm0.ndim == 2: # RHF DM
return numpy.zeros((3,3))
dma, dmb = dm0
spindm = dma - dmb
effspin = mol.spin * .5
e_gyro = .5 * nist.G_ELECTRON
nuc_mag = .5 * (nist.E_MASS/nist.PROTON_MASS) # e*hbar/2m
au2MHz = nist.HARTREE2J / nist.PLANCK * 1e-6
fac = nist.ALPHA**2 / 2 / effspin * e_gyro * au2MHz
hfc = []
for i, atm_id in enumerate(hfc_nuc):
nuc_gyro = get_nuc_g_factor(mol.atom_symbol(atm_id)) * nuc_mag
h1 = _get_integrals_fcdip(mol, atm_id)
fcsd = numpy.einsum('xyij,ji->xy', h1, spindm)
h1fc = _get_integrals_fc(mol, atm_id)
fc = numpy.einsum('ij,ji', h1fc, spindm)
sd = fcsd + numpy.eye(3) * fc
log.info('FC of atom %d %s (in MHz)', atm_id, fac * nuc_gyro * fc)
if hfcobj.verbose >= logger.INFO:
_write(hfcobj, align(fac*nuc_gyro*sd)[0], 'SD of atom %d (in MHz)' % atm_id)
hfc.append(fac * nuc_gyro * fcsd)
return numpy.asarray(hfc)
def kernel(self, mo_coeff=None, ci=None, atmlst=None, mf_grad=None,
state=None, verbose=None):
cput0 = (time.clock(), time.time())
log = logger.new_logger(self, verbose)
if ci is None: ci = self.base.ci
if isinstance(ci, (list, tuple)):
if state is None:
state = self.state
else:
self.state = state
ci = ci[state]
logger.info(self, 'Multiple roots are found in CASCI solver. '
'Nuclear gradients of root %d are computed.', state)
if atmlst is None:
atmlst = self.atmlst
else:
self.atmlst = atmlst
if self.verbose >= logger.WARN:
self.check_sanity()
if self.verbose >= logger.INFO:
self.dump_flags()
self.de = kernel(self.base, mo_coeff, ci, atmlst, mf_grad, log)
log.timer('CASCI gradients', *cput0)
self._finalize()
return self.de
def analyze(mf, verbose=logger.DEBUG, **kwargs):
from pyscf.tools import dump_mat
log = logger.new_logger(mf, verbose)
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
mo_coeff = mf.mo_coeff
log.info('**** MO energy ****')
for i in range(len(mo_energy)):
if mo_occ[i] > 0:
log.info('occupied MO #%d energy= %.15g occ= %g', \
i+1, mo_energy[i], mo_occ[i])
else:
log.info('virtual MO #%d energy= %.15g occ= %g', \
i+1, mo_energy[i], mo_occ[i])
mol = mf.mol
if mf.verbose >= logger.DEBUG1:
log.debug(' ** MO coefficients of large component of postive state (real part) **')
label = mol.spinor_labels()
n2c = mo_coeff.shape[0] // 2
dump_mat.dump_rec(mf.stdout, mo_coeff[n2c:,:n2c].real, label, start=1)
dm = mf.make_rdm1(mo_coeff, mo_occ)
pop_chg = mf.mulliken_pop(mol, dm, mf.get_ovlp(), log)
dip = mf.dip_moment(mol, dm, verbose=log)
return pop_chg, dip
def kernel(self, *args, **kwargs):
with_solvent = self.with_solvent
# The underlying ._scf object is decorated with solvent effects.
# The resultant Fock matrix and orbital energies both include the
# effects from solvent. It means that solvent effects for post-HF
# methods are automatically counted if solvent is enabled at scf
# level.
if with_solvent.frozen:
return old_method.kernel(self, *args, **kwargs)
log = logger.new_logger(self)
log.info('\n** Self-consistently update the solvent effects for %s **',
old_method)
##TODO: Suppress a few output messages
#log1 = copy.copy(log)
#log1.note, log1.info = log1.info, log1.debug
e_last = 0
for cycle in range(self.with_solvent.max_cycle):
log.info('\n** Solvent self-consistent cycle %d:', cycle)
# Solvent effects are applied when accessing the
# underlying ._scf objects. The flag frozen=True ensures that
# the generated potential with_solvent.vpcm is passed to the
# the post-HF object, without being updated in the implicit
# call to the _scf iterations.
with lib.temporary_env(with_solvent, frozen=True):
e_tot = basic_scanner(self.mol)
dm = basic_scanner.make_rdm1(ao_repr=True)
if with_solvent.epcm is not None:
edup = numpy.einsum('ij,ji->', with_solvent.vpcm, dm)
e_tot = e_tot - edup + with_solvent.epcm
log.debug(' E_diel = %.15g', with_solvent.epcm)
# To generate the solvent potential for ._scf object. Since
# frozen is set when calling basic_scanner, the solvent
# effects are frozen during the scf iterations.
with_solvent.epcm, with_solvent.vpcm = with_solvent.kernel(dm)
de = e_tot - e_last
log.info('Sovlent cycle %d E_tot = %.15g dE = %g',
cycle, e_tot, de)
if abs(e_tot-e_last).max() < with_solvent.conv_tol:
break
e_last = e_tot
# An extra cycle to compute the total energy
log.info('\n** Extra cycle for solvent effects')
res = old_method.kernel(self)
with lib.temporary_env(with_solvent, frozen=True):
#Update everything except the _scf object and _keys
basic_scanner(self.mol)
new_keys = self._keys
self.__dict__.update(basic_scanner.__dict__)
self._keys = new_keys
self._scf = scf_with_solvent
self._finalize()
return res
def hess_elec(hessobj, mo_energy=None, mo_coeff=None, mo_occ=None,
mo1=None, mo_e1=None, h1ao=None,
atmlst=None, max_memory=4000, verbose=None):
log = logger.new_logger(hessobj, verbose)
time0 = t1 = (time.clock(), time.time())
mol = hessobj.mol
mf = hessobj.base
if mo_energy is None: mo_energy = mf.mo_energy
if mo_occ is None: mo_occ = mf.mo_occ
if mo_coeff is None: mo_coeff = mf.mo_coeff
if atmlst is None: atmlst = range(mol.natm)
de2 = hessobj.partial_hess_elec(mo_energy, mo_coeff, mo_occ, atmlst,
max_memory, log)
if h1ao is None:
h1ao = hessobj.make_h1(mo_coeff, mo_occ, hessobj.chkfile, atmlst, log)
t1 = log.timer_debug1('making H1', *time0)
if mo1 is None or mo_e1 is None:
mo1, mo_e1 = hessobj.solve_mo1(mo_energy, mo_coeff, mo_occ, h1ao,
None, atmlst, max_memory, log)
t1 = log.timer_debug1('solving MO1', *t1)
if isinstance(h1ao, str):
h1ao = lib.chkfile.load(h1ao, 'scf_f1ao')
h1ao = dict([(int(k), h1ao[k]) for k in h1ao])
if isinstance(mo1, str):
mo1 = lib.chkfile.load(mo1, 'scf_mo1')
mo1 = dict([(int(k), mo1[k]) for k in mo1])
nao, nmo = mo_coeff.shape
mocc = mo_coeff[:,mo_occ>0]
s1a = -mol.intor('int1e_ipovlp', comp=3)
aoslices = mol.aoslice_by_atom()
for i0, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = aoslices[ia]
s1ao = numpy.zeros((3,nao,nao))
s1ao[:,p0:p1] += s1a[:,p0:p1]
s1ao[:,:,p0:p1] += s1a[:,p0:p1].transpose(0,2,1)
s1oo = numpy.einsum('xpq,pi,qj->xij', s1ao, mocc, mocc)
for j0 in range(i0+1):
ja = atmlst[j0]
q0, q1 = aoslices[ja][2:]
# *2 for double occupancy, *2 for +c.c.
dm1 = numpy.einsum('ypi,qi->ypq', mo1[ja], mocc)
de2[i0,j0] += numpy.einsum('xpq,ypq->xy', h1ao[ia], dm1) * 4
dm1 = numpy.einsum('ypi,qi,i->ypq', mo1[ja], mocc, mo_energy[mo_occ>0])
de2[i0,j0] -= numpy.einsum('xpq,ypq->xy', s1ao, dm1) * 4
de2[i0,j0] -= numpy.einsum('xpq,ypq->xy', s1oo, mo_e1[ja]) * 2
for j0 in range(i0):
de2[j0,i0] = de2[i0,j0].T
log.timer('RHF hessian', *time0)
return de2
def dump_flags(self, verbose=None):
log = logger.new_logger(self, verbose)
log.info('')
log.info('******** SHCI flags ********')
log.info('executable = %s', self.executable)
log.info('mpiprefix = %s', self.mpiprefix)
log.info('runtimedir = %s', self.runtimedir)
log.debug1('config = %s', self.config)
log.info('')
return self
def solve_withs1(fvind, mo_energy, mo_occ, h1, s1,
max_cycle=20, tol=1e-9, hermi=False, verbose=logger.WARN):
'''For field dependent basis. First order overlap matrix is non-zero.
The first order orbitals are set to
C^1_{ij} = -1/2 S1
e1 = h1 - s1*e0 + (e0_j-e0_i)*c1 + vhf[c1]
Kwargs:
hermi : boolean
Whether the matrix defined by fvind is Hermitian or not.
Returns:
First order orbital coefficients (in MO basis) and first order orbital
energy matrix
'''
log = logger.new_logger(verbose=verbose)
t0 = (time.clock(), time.time())
occidx = mo_occ > 0
viridx = mo_occ == 0
e_a = mo_energy[viridx]
e_i = mo_energy[occidx]
e_ai = 1 / lib.direct_sum('a-i->ai', e_a, e_i)
nvir, nocc = e_ai.shape
nmo = nocc + nvir
s1 = s1.reshape(-1,nmo,nocc)
hs = mo1base = h1.reshape(-1,nmo,nocc) - s1*e_i
mo_e1 = hs[:,occidx,:].copy()
mo1base[:,viridx] *= -e_ai
mo1base[:,occidx] = -s1[:,occidx] * .5
def vind_vo(mo1):
v = fvind(mo1.reshape(h1.shape)).reshape(-1,nmo,nocc)
v[:,viridx,:] *= e_ai
v[:,occidx,:] = 0
return v.ravel()
mo1 = lib.krylov(vind_vo, mo1base.ravel(),
tol=tol, max_cycle=max_cycle, hermi=hermi, verbose=log)
mo1 = mo1.reshape(mo1base.shape)
log.timer('krylov solver in CPHF', *t0)
v1mo = fvind(mo1.reshape(h1.shape)).reshape(-1,nmo,nocc)
mo1[:,viridx] = mo1base[:,viridx] - v1mo[:,viridx]*e_ai
# mo_e1 has the same symmetry as the first order Fock matrix (hermitian or
# anti-hermitian). mo_e1 = v1mo - s1*lib.direct_sum('i+j->ij',e_i,e_i)
mo_e1 += mo1[:,occidx] * lib.direct_sum('i-j->ij', e_i, e_i)
mo_e1 += v1mo[:,occidx,:]
if h1.ndim == 3:
return mo1, mo_e1
else:
return mo1.reshape(h1.shape), mo_e1.reshape(nocc,nocc)
def _make_eris(mp, mo_coeff=None, ao2mofn=None, verbose=None):
log = logger.new_logger(mp, verbose)
time0 = (time.clock(), time.time())
eris = _ChemistsERIs(mp, mo_coeff)
nocca, noccb = mp.get_nocc()
nmoa, nmob = mp.get_nmo()
nvira, nvirb = nmoa-nocca, nmob-noccb
nao = eris.mo_coeff[0].shape[0]
nmo_pair = nmoa * (nmoa+1) // 2
nao_pair = nao * (nao+1) // 2
mem_incore = (nao_pair**2 + nmo_pair**2) * 8/1e6
mem_now = lib.current_memory()[0]
max_memory = max(0, mp.max_memory-mem_now)
moa = eris.mo_coeff[0]
mob = eris.mo_coeff[1]
orboa = moa[:,:nocca]
orbob = mob[:,:noccb]
orbva = moa[:,nocca:]
orbvb = mob[:,noccb:]
if (mp.mol.incore_anyway or
(mp._scf._eri is not None and mem_incore+mem_now < mp.max_memory)):
log.debug('transform (ia|jb) incore')
if callable(ao2mofn):
eris.ovov = ao2mofn((orboa,orbva,orboa,orbva)).reshape(nocca*nvira,nocca*nvira)
eris.ovOV = ao2mofn((orboa,orbva,orbob,orbvb)).reshape(nocca*nvira,noccb*nvirb)
eris.OVOV = ao2mofn((orbob,orbvb,orbob,orbvb)).reshape(noccb*nvirb,noccb*nvirb)
else:
eris.ovov = ao2mo.general(mp._scf._eri, (orboa,orbva,orboa,orbva))
eris.ovOV = ao2mo.general(mp._scf._eri, (orboa,orbva,orbob,orbvb))
eris.OVOV = ao2mo.general(mp._scf._eri, (orbob,orbvb,orbob,orbvb))
elif getattr(mp._scf, 'with_df', None):
logger.warn(mp, 'UMP2 detected DF being used in the HF object. '
'MO integrals are computed based on the DF 3-index tensors.\n'
'It\'s recommended to use DF-UMP2 module.')
log.debug('transform (ia|jb) with_df')
eris.ovov = mp._scf.with_df.ao2mo((orboa,orbva,orboa,orbva))
eris.ovOV = mp._scf.with_df.ao2mo((orboa,orbva,orbob,orbvb))
eris.OVOV = mp._scf.with_df.ao2mo((orbob,orbvb,orbob,orbvb))
else:
log.debug('transform (ia|jb) outcore')
eris.feri = lib.H5TmpFile()
_ao2mo_ovov(mp, (orboa,orbva,orbob,orbvb), eris.feri,
max(2000, max_memory), log)
eris.ovov = eris.feri['ovov']
eris.ovOV = eris.feri['ovOV']
eris.OVOV = eris.feri['OVOV']
time1 = log.timer('Integral transformation', *time0)
return eris
def hyper_polarizability(polobj, with_cphf=True):
from pyscf.prop.nmr import uhf as uhf_nmr
log = logger.new_logger(polobj)
mf = polobj._scf
mol = mf.mol
mo_energy = mf.mo_energy
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
occidxa = mo_occ[0] > 0
occidxb = mo_occ[1] > 0
mo0a, mo0b = mo_coeff
orboa = mo0a[:, occidxa]
orbva = mo0a[:,~occidxa]
orbob = mo0b[:, occidxb]
orbvb = mo0b[:,~occidxb]
charges = mol.atom_charges()
coords = mol.atom_coords()
charge_center = numpy.einsum('i,ix->x', charges, coords) / charges.sum()
with mol.with_common_orig(charge_center):
int_r = mol.intor_symmetric('int1e_r', comp=3)
h1a = lib.einsum('xpq,pi,qj->xij', int_r, mo0a.conj(), orboa)
h1b = lib.einsum('xpq,pi,qj->xij', int_r, mo0b.conj(), orbob)
s1a = numpy.zeros_like(h1a)
s1b = numpy.zeros_like(h1b)
vind = polobj.gen_vind(mf, mo_coeff, mo_occ)
if with_cphf:
mo1, e1 = ucphf.solve(vind, mo_energy, mo_occ, (h1a,h1b), (s1a,s1b),
polobj.max_cycle_cphf, polobj.conv_tol, verbose=log)
else:
mo1, e1 = uhf_nmr._solve_mo1_uncoupled(mo_energy, mo_occ, (h1a,h1b),
(s1a,s1b))
mo1a = lib.einsum('xqi,pq->xpi', mo1[0], mo0a)
mo1b = lib.einsum('xqi,pq->xpi', mo1[1], mo0b)
dm1a = lib.einsum('xpi,qi->xpq', mo1a, orboa)
dm1b = lib.einsum('xpi,qi->xpq', mo1b, orbob)
dm1a = dm1a + dm1a.transpose(0,2,1)
dm1b = dm1b + dm1b.transpose(0,2,1)
vresp = _gen_uhf_response(mf, hermi=1)
h1ao = int_r + vresp(numpy.stack((dm1a, dm1b)))
s0 = mf.get_ovlp()
e3 = lib.einsum('xpq,ypi,zqi->xyz', h1ao[0], mo1a, mo1a)
e3 += lib.einsum('xpq,ypi,zqi->xyz', h1ao[1], mo1b, mo1b)
e3 -= lib.einsum('pq,xpi,yqj,zij->xyz', s0, mo1a, mo1a, e1[0])
e3 -= lib.einsum('pq,xpi,yqj,zij->xyz', s0, mo1b, mo1b, e1[1])
e3 = (e3 + e3.transpose(1,2,0) + e3.transpose(2,0,1) +
e3.transpose(0,2,1) + e3.transpose(1,0,2) + e3.transpose(2,1,0))
e3 = -e3
log.debug('Static hyper polarizability tensor\n%s', e3)
return e3
def make_h10(mol, dm0, gauge_orig=None, verbose=logger.WARN):
log = logger.new_logger(mol, verbose=verbose)
if gauge_orig is None:
# A10_i dot p + p dot A10_i consistents with <p^2 g>
# A10_j dot p + p dot A10_j consistents with <g p^2>
# A10_j dot p + p dot A10_j => i/2 (rjxp - pxrj) = irjxp
log.debug('First-order GIAO Fock matrix')
h1 = -.5 * mol.intor('int1e_giao_irjxp', 3) + make_h10giao(mol, dm0)
else:
with mol.with_common_origin(gauge_orig):
h1 = -.5 * mol.intor('int1e_cg_irxp', 3)
h1 = (h1, h1)
return h1
def kernel(self, t2=None, atmlst=None, mf_grad=None, verbose=None,
_kern=kernel):
log = logger.new_logger(self, verbose)
if t2 is None: t2 = self.base.t2
if t2 is None: t2 = self.base.kernel()
if atmlst is None:
atmlst = self.atmlst
else:
self.atmlst = atmlst
self.de = _kern(self.base, t2, atmlst, mf_grad, verbose=log)
self._finalize()
return self.de
def guess_wfnsym(self, norb, nelec, fcivec=None, orbsym=None, wfnsym=None,
**kwargs):
if orbsym is None:
orbsym = self.orbsym
if fcivec is None:
wfnsym = direct_spin1_symm._id_wfnsym(self, norb, nelec, orbsym,
wfnsym)
else:
strsa, strsb = getattr(fcivec, '_strs', self._strs)
wfnsym = addons._guess_wfnsym(fcivec, strsa, strsb, orbsym)
verbose = kwargs.get('verbose', None)
log = logger.new_logger(self, verbose)
log.debug('Guessing CI wfn symmetry = %s', wfnsym)
return wfnsym
def _partial_hess_ejk(hessobj, mo_energy=None, mo_coeff=None, mo_occ=None,
atmlst=None, max_memory=4000, verbose=None, with_k=True):
'''Partial derivative
'''
log = logger.new_logger(hessobj, verbose)
time0 = t1 = (time.clock(), time.time())
mol = hessobj.mol
mf = hessobj.base
if mo_energy is None: mo_energy = mf.mo_energy
if mo_occ is None: mo_occ = mf.mo_occ
if mo_coeff is None: mo_coeff = mf.mo_coeff
if atmlst is None: atmlst = range(mol.natm)
nao, nmo = mo_coeff.shape
mocc = mo_coeff[:,mo_occ>0]
mocc_2 = np.einsum('pi,i->pi', mocc, mo_occ[mo_occ>0]**.5)
nocc = mocc.shape[1]
dm0 = numpy.dot(mocc, mocc.T) * 2
# Energy weighted density matrix
dme0 = numpy.einsum('pi,qi,i->pq', mocc, mocc, mo_energy[mo_occ>0]) * 2
auxmol = hessobj.base.with_df.auxmol
naux = auxmol.nao
nbas = mol.nbas
auxslices = auxmol.aoslice_by_atom()
aoslices = mol.aoslice_by_atom()
aux_loc = auxmol.ao_loc
blksize = min(480, hessobj.max_memory*.3e6/8/nao**2)
aux_ranges = ao2mo.outcore.balance_partition(auxmol.ao_loc, blksize)
hcore_deriv = hessobj.hcore_generator(mol)
s1aa, s1ab, s1a = rhf_hess.get_ovlp(mol)
ftmp = lib.H5TmpFile()
get_int3c = _int3c_wrapper(mol, auxmol, 'int3c2e', 's1')
# Without RI basis response
# (20|0)(0|00)
# (11|0)(0|00)
# (10|0)(0|10)
int2c = auxmol.intor('int2c2e', aosym='s1')
int2c_low = scipy.linalg.cho_factor(int2c, lower=True)
int2c_ip1 = auxmol.intor('int2c2e_ip1', aosym='s1')
rhoj0_P = 0
if with_k:
if hessobj.max_memory*.8e6/8 < naux*nocc*(nocc+nao):
raise RuntimeError('Memory not enough. You need to increase mol.max_memory')
rhok0_Pl_ = np.empty((naux,nao,nocc))
for i, (shl0, shl1, p0, p1) in enumerate(aoslices):
int3c = get_int3c((shl0, shl1, 0, nbas, 0, auxmol.nbas))
rhoj0_P += np.einsum('klp,kl->p', int3c, dm0[p0:p1])
if with_k:
tmp = lib.einsum('ijp,jk->pik', int3c, mocc_2)
tmp = scipy.linalg.cho_solve(int2c_low, tmp.reshape(naux,-1), overwrite_b=True)
rhok0_Pl_[:,p0:p1] = tmp.reshape(naux,p1-p0,nocc)
int3c = tmp = None
rhoj0_P = scipy.linalg.cho_solve(int2c_low, rhoj0_P)
get_int3c_ipip1 = _int3c_wrapper(mol, auxmol, 'int3c2e_ipip1', 's1')
vj1_diag = 0
vk1_diag = 0
for shl0, shl1, nL in aux_ranges:
shls_slice = (0, nbas, 0, nbas, shl0, shl1)
p0, p1 = aux_loc[shl0], aux_loc[shl1]
int3c_ipip1 = get_int3c_ipip1(shls_slice)
vj1_diag += np.einsum('xijp,p->xij', int3c_ipip1, rhoj0_P[p0:p1]).reshape(3,3,nao,nao)
if with_k:
tmp = lib.einsum('Plj,Jj->PlJ', rhok0_Pl_[p0:p1], mocc_2)
vk1_diag += lib.einsum('xijp,plj->xil', int3c_ipip1, tmp).reshape(3,3,nao,nao)
int3c_ipip1 = get_int3c_ipip1 = tmp = None
t1 = log.timer_debug1('contracting int2e_ipip1', *t1)
get_int3c_ip1 = _int3c_wrapper(mol, auxmol, 'int3c2e_ip1', 's1')
rho_ip1 = ftmp.create_dataset('rho_ip1', (nao,nao,naux,3), 'f8')
rhok_ip1_IkP = ftmp.create_group('rhok_ip1_IkP')
rhok_ip1_PkI = ftmp.create_group('rhok_ip1_PkI')
rhoj1 = np.empty((mol.natm,naux,3))
wj1 = np.empty((mol.natm,naux,3))
for i0, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = aoslices[ia]
shls_slice = (shl0, shl1, 0, nbas, 0, auxmol.nbas)
int3c_ip1 = get_int3c_ip1(shls_slice)
tmp_ip1 = scipy.linalg.cho_solve(int2c_low, int3c_ip1.reshape(-1,naux).T,
overwrite_b=True).reshape(naux,3,p1-p0,nao)
rhoj1[i0] = np.einsum('pxij,ji->px', tmp_ip1, dm0[:,p0:p1])
wj1[i0] = np.einsum('xijp,ji->px', int3c_ip1, dm0[:,p0:p1])
rho_ip1[p0:p1] = tmp_ip1.transpose(2,3,0,1)
if with_k:
tmp = lib.einsum('pykl,li->ikpy', tmp_ip1, dm0)
rhok_ip1_IkP['%.4d'%ia] = tmp
rhok_ip1_PkI['%.4d'%ia] = tmp.transpose(2,1,0,3)
tmp = None
ej = lib.einsum('ipx,jpy->ijxy', rhoj1, wj1) * 4
ek = np.zeros_like(ej)
e1 = np.zeros_like(ej)
rhoj1 = wj1 = None
if with_k:
vk2buf = 0
for shl0, shl1, nL in aux_ranges:
shls_slice = (0, nbas, 0, nbas, shl0, shl1)
p0, p1 = aux_loc[shl0], aux_loc[shl1]
int3c_ip1 = get_int3c_ip1(shls_slice)
vk2buf += lib.einsum('xijp,pkjy->xyki', int3c_ip1,
_load_dim0(rhok_ip1_PkI, p0, p1))
int3c_ip1 = None
get_int3c_ip2 = _int3c_wrapper(mol, auxmol, 'int3c2e_ip2', 's1')
wj_ip2 = np.empty((naux,3))
wk_ip2_Ipk = ftmp.create_dataset('wk_ip2', (nao,naux,3,nao), 'f8')
if hessobj.auxbasis_response > 1:
wk_ip2_P__ = np.empty((naux,3,nocc,nocc))
for shl0, shl1, nL in aux_ranges:
shls_slice = (0, nbas, 0, nbas, shl0, shl1)
p0, p1 = aux_loc[shl0], aux_loc[shl1]
int3c_ip2 = get_int3c_ip2(shls_slice)
wj_ip2[p0:p1] = np.einsum('yklp,lk->py', int3c_ip2, dm0)
if with_k:
wk_ip2_Ipk[:,p0:p1] = lib.einsum('yklp,il->ipyk', int3c_ip2, dm0)
if hessobj.auxbasis_response > 1:
wk_ip2_P__[p0:p1] = lib.einsum('xuvp,ui,vj->pxij', int3c_ip2, mocc_2, mocc_2)
int3c_ip2 = None
if hessobj.auxbasis_response > 1:
get_int3c_ipip2 = _int3c_wrapper(mol, auxmol, 'int3c2e_ipip2', 's1')
rhok0_P__ = lib.einsum('plj,li->pij', rhok0_Pl_, mocc_2)
rho2c_0 = lib.einsum('pij,qji->pq', rhok0_P__, rhok0_P__)
int2c_inv = np.linalg.inv(int2c)
int2c_ipip1 = auxmol.intor('int2c2e_ipip1', aosym='s1')
int2c_ip_ip = lib.einsum('xpq,qr,ysr->xyps', int2c_ip1, int2c_inv, int2c_ip1)
int2c_ip_ip -= auxmol.intor('int2c2e_ip1ip2', aosym='s1').reshape(3,3,naux,naux)
int2c = int2c_low = None
get_int3c_ipvip1 = _int3c_wrapper(mol, auxmol, 'int3c2e_ipvip1', 's1')
get_int3c_ip1ip2 = _int3c_wrapper(mol, auxmol, 'int3c2e_ip1ip2', 's1')
for i0, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = aoslices[ia]
shls_slice = (shl0, shl1, 0, nbas, 0, auxmol.nbas)
# (10|0)(0|10) without response of RI basis
if with_k:
int3c_ip1 = get_int3c_ip1(shls_slice)
vk1 = lib.einsum('xijp,ikpy->xykj', int3c_ip1, _load_dim0(rhok_ip1_IkP, p0, p1))
vk1[:,:,:,p0:p1] += vk2buf[:,:,:,p0:p1]
t1 = log.timer_debug1('contracting int2e_ip1ip2 for atom %d'%ia, *t1)
int3c_ip1 = None
# (11|0)(0|00) without response of RI basis
int3c_ipvip1 = get_int3c_ipvip1(shls_slice)
vj1 = np.einsum('xijp,p->xji', int3c_ipvip1, rhoj0_P).reshape(3,3,nao,p1-p0)
if with_k:
tmp = lib.einsum('pki,ji->pkj', rhok0_Pl_, mocc_2[p0:p1])
vk1 += lib.einsum('xijp,pki->xjk', int3c_ipvip1, tmp).reshape(3,3,nao,nao)
t1 = log.timer_debug1('contracting int2e_ipvip1 for atom %d'%ia, *t1)
int3c_ipvip1 = tmp = None
e1[i0,i0] -= numpy.einsum('xypq,pq->xy', s1aa[:,:,p0:p1], dme0[p0:p1])*2
ej[i0,i0] += numpy.einsum('xypq,pq->xy', vj1_diag[:,:,p0:p1], dm0[p0:p1])*2
if with_k:
ek[i0,i0] += numpy.einsum('xypq,pq->xy', vk1_diag[:,:,p0:p1], dm0[p0:p1])
for j0, ja in enumerate(atmlst[:i0+1]):
q0, q1 = aoslices[ja][2:]
ej[i0,j0] += numpy.einsum('xypq,pq->xy', vj1[:,:,q0:q1], dm0[q0:q1,p0:p1])*2
e1[i0,j0] -= numpy.einsum('xypq,pq->xy', s1ab[:,:,p0:p1,q0:q1], dme0[p0:p1,q0:q1])*2
if with_k:
ek[i0,j0] += numpy.einsum('xypq,pq->xy', vk1[:,:,q0:q1], dm0[q0:q1])
h1ao = hcore_deriv(ia, ja)
e1[i0,j0] += numpy.einsum('xypq,pq->xy', h1ao, dm0)
#
# The first order RI basis response
# (10|1)(0|00)
# (10|0)(1|0)(0|00)
# (10|0)(0|1)(0|00)
# (10|0)(1|00)
#
if hessobj.auxbasis_response:
wk1_Pij = rho_ip1[p0:p1].transpose(2,3,0,1)
rhoj1_P = np.einsum('pxij,ji->px', wk1_Pij, dm0[:,p0:p1])
# (10|1)(0|0)(0|00)
int3c_ip1ip2 = get_int3c_ip1ip2(shls_slice)
wj11_p = np.einsum('xijp,ji->xp', int3c_ip1ip2, dm0[:,p0:p1])
# (10|0)(1|0)(0|00)
wj0_01 = np.einsum('ypq,q->yp', int2c_ip1, rhoj0_P)
if with_k:
rhok0_P_I = lib.einsum('plj,il->pji', rhok0_Pl_, dm0[p0:p1])
rhok0_PJI = lib.einsum('pji,Jj->pJi', rhok0_P_I, mocc_2)
wk1_pJI = lib.einsum('ypq,qji->ypji', int2c_ip1, rhok0_PJI)
wk1_IpJ = lib.einsum('ipyk,kj->ipyj', wk_ip2_Ipk[p0:p1], dm0)
#rho2c_PQ = lib.einsum('qij,uj,iupx->xqp', rhok0_Pl_, mocc_2[p0:p1], rhok_ip1_IkP['%.4d'%ia])
rho2c_PQ = lib.einsum('pxij,qji->xqp', wk1_Pij, rhok0_PJI)
for j0, (q0, q1) in enumerate(auxslices[:,2:]):
# (10|1)(0|00)
_ej = np.einsum('xp,p->x', wj11_p[:,q0:q1], rhoj0_P[q0:q1]).reshape(3,3)
# (10|0)(0|1)(0|00)
_ej -= lib.einsum('yqp,q,px->xy', int2c_ip1[:,q0:q1], rhoj0_P[q0:q1], rhoj1_P)
# (10|0)(1|0)(0|00)
_ej -= lib.einsum('px,yp->xy', rhoj1_P[q0:q1], wj0_01[:,q0:q1])
# (10|0)(1|00)
_ej += lib.einsum('px,py->xy', rhoj1_P[q0:q1], wj_ip2[q0:q1])
if hessobj.auxbasis_response > 1:
ej[i0,j0] += _ej * 2
ej[j0,i0] += _ej.T * 2
else:
ej[i0,j0] += _ej
ej[j0,i0] += _ej.T
if with_k:
_ek = lib.einsum('xijp,pji->x', int3c_ip1ip2[:,:,:,q0:q1],
rhok0_PJI[q0:q1]).reshape(3,3)
_ek -= lib.einsum('pxij,ypji->xy', wk1_Pij[q0:q1], wk1_pJI[:,q0:q1])
_ek -= lib.einsum('xqp,yqp->xy', rho2c_PQ[:,q0:q1], int2c_ip1[:,q0:q1])
_ek += lib.einsum('pxij,ipyj->xy', wk1_Pij[q0:q1], wk1_IpJ[:,q0:q1])
if hessobj.auxbasis_response > 1:
ek[i0,j0] += _ek
ek[j0,i0] += _ek.T
else:
ek[i0,j0] += _ek * .5
ek[j0,i0] += _ek.T * .5
int3c_ip1ip2 = rhok0_P_I = rhok0_PJI = wk1_pJI = wk1_IpJ = rho2c_PQ = None
#
# The second order RI basis response
#
if hessobj.auxbasis_response > 1:
# (00|2)(0|00)
# (00|0)(2|0)(0|00)
shl0, shl1, p0, p1 = auxslices[ia]
shls_slice = (0, nbas, 0, nbas, shl0, shl1)
int3c_ipip2 = get_int3c_ipip2(shls_slice)
ej[i0,i0] += np.einsum('xijp,ji,p->x', int3c_ipip2, dm0, rhoj0_P[p0:p1]).reshape(3,3)
ej[i0,i0] -= np.einsum('p,xpq,q->x', rhoj0_P[p0:p1], int2c_ipip1[:,p0:p1], rhoj0_P).reshape(3,3)
if with_k:
rhok0_PJI = lib.einsum('Pij,Jj,Ii->PJI', rhok0_P__[p0:p1], mocc_2, mocc_2)
ek[i0,i0] += .5 * np.einsum('xijp,pij->x', int3c_ipip2, rhok0_PJI).reshape(3,3)
ek[i0,i0] -= .5 * np.einsum('pq,xpq->x', rho2c_0[p0:p1], int2c_ipip1[:,p0:p1]).reshape(3,3)
rhok0_PJI = None
# (00|0)(1|1)(0|00)
# (00|1)(1|0)(0|00)
# (00|1)(0|1)(0|00)
# (00|1)(1|00)
rhoj1 = lib.einsum('px,pq->xq', wj_ip2[p0:p1], int2c_inv[p0:p1])
# (00|0)(0|1)(1|0)(0|00)
rhoj0_01 = lib.einsum('xp,pq->xq', wj0_01[:,p0:p1], int2c_inv[p0:p1])
# (00|0)(1|0)(1|0)(0|00)
ip1_2c_2c = lib.einsum('xpq,qr->xpr', int2c_ip1[:,p0:p1], int2c_inv)
rhoj0_10 = lib.einsum('p,xpq->xq', rhoj0_P[p0:p1], ip1_2c_2c)
if with_k:
# (00|0)(0|1)(1|0)(0|00)
ip1_rho2c = .5 * lib.einsum('xpq,qr->xpr', int2c_ip1[:,p0:p1], rho2c_0)
rho2c_1 = lib.einsum('xrq,rp->xpq', ip1_rho2c, int2c_inv[p0:p1])
# (00|0)(1|0)(1|0)(0|00)
rho2c_1 += lib.einsum('xrp,rq->xpq', ip1_2c_2c, rho2c_0[p0:p1])
# (00|1)(0|1)(0|00)
# (00|1)(1|0)(0|00)
int3c_ip2 = get_int3c_ip2(shls_slice)
tmp = lib.einsum('xuvr,vj,ui->xrij', int3c_ip2, mocc_2, mocc_2)
tmp = lib.einsum('xrij,qij,rp->xpq', tmp, rhok0_P__, int2c_inv[p0:p1])
rho2c_1 -= tmp
rho2c_1 -= tmp.transpose(0,2,1)
int3c_ip2 = tmp = None
for j0, (q0, q1) in enumerate(auxslices[:,2:]):
_ej = 0
# (00|0)(1|1)(0|00)
# (00|0)(1|0)(0|1)(0|00)
_ej += .5 * np.einsum('p,xypq,q->xy', rhoj0_P[p0:p1], int2c_ip_ip[:,:,p0:p1,q0:q1], rhoj0_P[q0:q1])
# (00|1)(1|0)(0|00)
_ej -= lib.einsum('xp,yp->xy', rhoj1[:,q0:q1], wj0_01[:,q0:q1])
# (00|1)(1|00)
_ej += .5 * lib.einsum('xp,py->xy', rhoj1[:,q0:q1], wj_ip2[q0:q1])
# (00|0)(0|1)(1|0)(0|00)
_ej += .5 * np.einsum('xp,yp->xy', rhoj0_01[:,q0:q1], wj0_01[:,q0:q1])
# (00|1)(0|1)(0|00)
_ej -= lib.einsum('yqp,q,xp->xy', int2c_ip1[:,q0:q1], rhoj0_P[q0:q1], rhoj1)
# (00|0)(1|0)(1|0)(0|00)
_ej += np.einsum('xp,yp->xy', rhoj0_10[:,q0:q1], wj0_01[:,q0:q1])
ej[i0,j0] += _ej
ej[j0,i0] += _ej.T
if with_k:
# (00|0)(1|1)(0|00)
# (00|0)(1|0)(0|1)(0|00)
_ek = .5 * np.einsum('pq,xypq->xy', rho2c_0[p0:p1,q0:q1], int2c_ip_ip[:,:,p0:p1,q0:q1])
# (00|1)(0|1)(0|00)
# (00|1)(1|0)(0|00)
# (00|0)(0|1)(1|0)(0|00)
# (00|0)(1|0)(1|0)(0|00)
_ek += np.einsum('xpq,ypq->xy', rho2c_1[:,q0:q1], int2c_ip1[:,q0:q1])
# (00|1)(1|00)
_ek += .5 * lib.einsum('pxij,pq,qyij->xy', wk_ip2_P__[p0:p1],
int2c_inv[p0:p1,q0:q1], wk_ip2_P__[q0:q1])
ek[i0,j0] += _ek * .5
ek[j0,i0] += _ek.T * .5
for i0, ia in enumerate(atmlst):
for j0 in range(i0):
e1[j0,i0] = e1[i0,j0].T
ej[j0,i0] = ej[i0,j0].T
ek[j0,i0] = ek[i0,j0].T
log.timer('RHF partial hessian', *time0)
return e1, ej, ek
def cas_natorb(mc,
mo_coeff=None,
ci=None,
eris=None,
sort=False,
casdm1=None,
verbose=None,
with_meta_lowdin=WITH_META_LOWDIN):
'''Transform active orbitals to natrual orbitals, and update the CI wfn
Args:
mc : a CASSCF/CASCI object or RHF object
Kwargs:
sort : bool
Sort natural orbitals wrt the occupancy.
Returns:
A tuple, the first item is natural orbitals, the second is updated CI
coefficients, the third is the natural occupancy associated to the
natural orbitals.
'''
from pyscf.lo import orth
from pyscf.tools import dump_mat
from pyscf.tools.mo_mapping import mo_1to1map
if mo_coeff is None: mo_coeff = mc.mo_coeff
if ci is None: ci = mc.ci
log = logger.new_logger(mc, verbose)
ncore = mc.ncore
ncas = mc.ncas
nocc = ncore + ncas
nelecas = mc.nelecas
if casdm1 is None:
casdm1 = mc.fcisolver.make_rdm1(ci, ncas, nelecas)
# orbital symmetry is reserved in this _eig call
occ, ucas = mc._eig(-casdm1, ncore, nocc)
if sort:
casorb_idx = numpy.argsort(occ.round(9), kind='mergesort')
occ = occ[casorb_idx]
ucas = ucas[:, casorb_idx]
# restore phase
# where_natorb gives the location of the natural orbital for the input cas
# orbitals. gen_strings4orblist map thes sorted strings (on CAS orbital) to
# the unsorted determinant strings (on natural orbital). e.g. (3o,2e) system
# CAS orbital 1 2 3
# natural orbital 3 1 2 <= by mo_1to1map
# CASorb-strings 0b011, 0b101, 0b110
# == (1,2), (1,3), (2,3)
# natorb-strings (3,1), (3,2), (1,2)
# == 0B101, 0B110, 0B011 <= by gen_strings4orblist
# then argsort to translate the string representation to the address
# [2(=0B011), 0(=0B101), 1(=0B110)]
# to indicate which CASorb-strings address to be loaded in each natorb-strings slot
where_natorb = mo_1to1map(ucas)
occ = -occ
mo_occ = numpy.zeros(mo_coeff.shape[1])
mo_occ[:ncore] = 2
mo_occ[ncore:nocc] = occ
mo_coeff1 = mo_coeff.copy()
mo_coeff1[:, ncore:nocc] = numpy.dot(mo_coeff[:, ncore:nocc], ucas)
if hasattr(mo_coeff, 'orbsym'):
orbsym = numpy.copy(mo_coeff.orbsym)
if sort:
orbsym[ncore:nocc] = orbsym[ncore:nocc][casorb_idx]
mo_coeff1 = lib.tag_array(mo_coeff1, orbsym=orbsym)
if isinstance(ci, numpy.ndarray):
fcivec = fci.addons.transform_ci_for_orbital_rotation(
ci, ncas, nelecas, ucas)
elif isinstance(ci, (tuple, list)) and isinstance(ci[0], numpy.ndarray):
# for state-average eigenfunctions
fcivec = [
fci.addons.transform_ci_for_orbital_rotation(
x, ncas, nelecas, ucas) for x in ci
]
else:
log.info('FCI vector not available, call CASCI for wavefunction')
mocas = mo_coeff1[:, ncore:nocc]
hcore = mc.get_hcore()
dm_core = numpy.dot(mo_coeff1[:, :ncore] * 2, mo_coeff1[:, :ncore].T)
ecore = mc._scf.energy_nuc()
ecore += numpy.einsum('ij,ji', hcore, dm_core)
h1eff = reduce(numpy.dot, (mocas.T, hcore, mocas))
if eris is not None and hasattr(eris, 'ppaa'):
ecore += eris.vhf_c[:ncore, :ncore].trace()
h1eff += reduce(numpy.dot,
(ucas.T, eris.vhf_c[ncore:nocc, ncore:nocc], ucas))
aaaa = ao2mo.restore(4, eris.ppaa[ncore:nocc, ncore:nocc, :, :],
ncas)
aaaa = ao2mo.incore.full(aaaa, ucas)
else:
if getattr(mc, 'with_df', None):
raise NotImplementedError('cas_natorb for DFCASCI/DFCASSCF')
corevhf = mc.get_veff(mc.mol, dm_core)
ecore += numpy.einsum('ij,ji', dm_core, corevhf) * .5
h1eff += reduce(numpy.dot, (mocas.T, corevhf, mocas))
aaaa = ao2mo.kernel(mc.mol, mocas)
# See label_symmetry_ function in casci_symm.py which initialize the
# orbital symmetry information in fcisolver. This orbital symmetry
# labels should be reordered to match the sorted active space orbitals.
if hasattr(mo_coeff1, 'orbsym') and sort:
mc.fcisolver.orbsym = mo_coeff1.orbsym[ncore:nocc]
max_memory = max(400, mc.max_memory - lib.current_memory()[0])
e, fcivec = mc.fcisolver.kernel(h1eff,
aaaa,
ncas,
nelecas,
ecore=ecore,
max_memory=max_memory,
verbose=log)
log.debug('In Natural orbital, CASCI energy = %s', e)
if log.verbose >= logger.INFO:
ovlp_ao = mc._scf.get_ovlp()
log.debug('where_natorb %s', str(where_natorb))
log.info('Natural occ %s', str(occ))
if with_meta_lowdin:
log.info(
'Natural orbital (expansion on meta-Lowdin AOs) in CAS space')
label = mc.mol.ao_labels()
orth_coeff = orth.orth_ao(mc.mol, 'meta_lowdin', s=ovlp_ao)
mo_cas = reduce(numpy.dot,
(orth_coeff.T, ovlp_ao, mo_coeff1[:, ncore:nocc]))
else:
log.info('Natural orbital (expansion on AOs) in CAS space')
label = mc.mol.ao_labels()
mo_cas = mo_coeff1[:, ncore:nocc]
dump_mat.dump_rec(log.stdout, mo_cas, label, start=1)
if mc._scf.mo_coeff is not None:
s = reduce(numpy.dot, (mo_coeff1[:, ncore:nocc].T,
mc._scf.get_ovlp(), mc._scf.mo_coeff))
idx = numpy.argwhere(abs(s) > .4)
for i, j in idx:
log.info('<CAS-nat-orb|mo-hf> %d %d %12.8f', ncore + i + 1,
j + 1, s[i, j])
return mo_coeff1, fcivec, mo_occ
def analyze(casscf, mo_coeff=None, ci=None, verbose=logger.INFO,
large_ci_tol=.1, **kwargs):
from pyscf.lo import orth
from pyscf.tools import dump_mat
log = logger.new_logger(casscf, verbose)
if mo_coeff is None: mo_coeff = casscf.mo_coeff
if ci is None: ci = casscf.ci
nelecas = casscf.nelecas
ncas = casscf.ncas
ncore = casscf.ncore
nocc = ncore + ncas
label = casscf.mol.ao_labels()
if isinstance(ci, (tuple, list)):
ci0 = ci[0]
log.info('** Natural natural orbitals are based on the first root **')
else:
ci0 = ci
if ci0 is None and hasattr(casscf, 'casdm1'):
casdm1 = casscf.casdm1
mocore = mo_coeff[:,:ncore]
mocas = mo_coeff[:,ncore:nocc]
dm1a =(numpy.dot(mocore, mocore.T) * 2
+ reduce(numpy.dot, (mocas, casdm1, mocas.T)))
dm1b = None
dm1 = dm1a
elif hasattr(casscf.fcisolver, 'make_rdm1s'):
casdm1a, casdm1b = casscf.fcisolver.make_rdm1s(ci0, ncas, nelecas)
casdm1 = casdm1a + casdm1b
mocore = mo_coeff[:,:ncore]
mocas = mo_coeff[:,ncore:nocc]
dm1b = numpy.dot(mocore, mocore.T)
dm1a = dm1b + reduce(numpy.dot, (mocas, casdm1a, mocas.T))
dm1b += reduce(numpy.dot, (mocas, casdm1b, mocas.T))
dm1 = dm1a + dm1b
if log.verbose >= logger.DEBUG2:
log.info('alpha density matrix (on AO)')
dump_mat.dump_tri(log.stdout, dm1a, label, **kwargs)
log.info('beta density matrix (on AO)')
dump_mat.dump_tri(log.stdout, dm1b, label, **kwargs)
else:
casdm1 = casscf.fcisolver.make_rdm1(ci0, ncas, nelecas)
mocore = mo_coeff[:,:ncore]
mocas = mo_coeff[:,ncore:nocc]
dm1a =(numpy.dot(mocore, mocore.T) * 2
+ reduce(numpy.dot, (mocas, casdm1, mocas.T)))
dm1b = None
dm1 = dm1a
if log.verbose >= logger.INFO:
ovlp_ao = casscf._scf.get_ovlp()
# note the last two args of ._eig for mc1step_symm
occ, ucas = casscf._eig(-casdm1, ncore, nocc)
log.info('Natural occ %s', str(-occ))
for i, k in enumerate(numpy.argmax(abs(ucas), axis=0)):
if ucas[k,i] < 0:
ucas[:,i] *= -1
orth_coeff = orth.orth_ao(casscf.mol, 'meta_lowdin', s=ovlp_ao)
mo_cas = reduce(numpy.dot, (orth_coeff.T, ovlp_ao, mo_coeff[:,ncore:nocc], ucas))
log.info('Natural orbital (expansion on meta-Lowdin AOs) in CAS space')
dump_mat.dump_rec(log.stdout, mo_cas, label, start=1, **kwargs)
if log.verbose >= logger.DEBUG2:
if not casscf.natorb:
log.debug2('NOTE: mc.mo_coeff in active space is different to '
'the natural orbital coefficients printed in above.')
log.debug2(' ** CASCI/CASSCF orbital coefficients (expansion on meta-Lowdin AOs) **')
c = reduce(numpy.dot, (orth_coeff.T, ovlp_ao, mo_coeff))
dump_mat.dump_rec(log.stdout, c, label, start=1, **kwargs)
if casscf._scf.mo_coeff is not None:
s = reduce(numpy.dot, (casscf.mo_coeff.T, ovlp_ao, casscf._scf.mo_coeff))
idx = numpy.argwhere(abs(s)>.4)
for i,j in idx:
log.info('<mo-mcscf|mo-hf> %d %d %12.8f', i+1, j+1, s[i,j])
if hasattr(casscf.fcisolver, 'large_ci') and ci is not None:
log.info('** Largest CI components **')
if isinstance(ci, (tuple, list)):
for i, civec in enumerate(ci):
res = casscf.fcisolver.large_ci(civec, casscf.ncas, casscf.nelecas,
large_ci_tol, return_strs=False)
log.info(' [alpha occ-orbitals] [beta occ-orbitals] state %-3d CI coefficient', i)
for c,ia,ib in res:
log.info(' %-20s %-30s %.12f', ia, ib, c)
else:
log.info(' [alpha occ-orbitals] [beta occ-orbitals] CI coefficient')
res = casscf.fcisolver.large_ci(ci, casscf.ncas, casscf.nelecas,
large_ci_tol, return_strs=False)
for c,ia,ib in res:
log.info(' %-20s %-30s %.12f', ia, ib, c)
casscf._scf.mulliken_meta(casscf.mol, dm1, s=ovlp_ao, verbose=log)
return dm1a, dm1b
def _contract_vvvv_t2(mycc, mol, vvL, t2, out=None, verbose=None):
'''Ht2 = numpy.einsum('ijcd,acdb->ijab', t2, vvvv)
Args:
vvvv : None or integral object
if vvvv is None, contract t2 to AO-integrals using AO-direct algorithm
'''
_dgemm = lib.numpy_helper._dgemm
time0 = time.clock(), time.time()
log = logger.new_logger(mol, verbose)
naux = vvL.shape[-1]
nvira, nvirb = t2.shape[-2:]
x2 = t2.reshape(-1, nvira, nvirb)
nocc2 = x2.shape[0]
nvir2 = nvira * nvirb
Ht2 = numpy.ndarray(x2.shape, buffer=out)
Ht2[:] = 0
max_memory = max(MEMORYMIN, mycc.max_memory - lib.current_memory()[0])
def contract_blk_(eri, i0, i1, j0, j1):
ic = i1 - i0
jc = j1 - j0
#:Ht2[:,j0:j1] += numpy.einsum('xef,efab->xab', x2[:,i0:i1], eri)
_dgemm('N', 'N', nocc2, jc * nvirb, ic * nvirb, x2.reshape(-1, nvir2),
eri.reshape(-1, jc * nvirb), Ht2.reshape(-1, nvir2), 1, 1,
i0 * nvirb, 0, j0 * nvirb)
if i0 > j0:
#:Ht2[:,i0:i1] += numpy.einsum('xef,abef->xab', x2[:,j0:j1], eri)
_dgemm('N', 'T', nocc2, ic * nvirb, jc * nvirb,
x2.reshape(-1, nvir2), eri.reshape(-1, jc * nvirb),
Ht2.reshape(-1, nvir2), 1, 1, j0 * nvirb, 0, i0 * nvirb)
#TODO: check if vvL can be entirely loaded into memory
nvir_pair = nvirb * (nvirb + 1) // 2
dmax = numpy.sqrt(max_memory * .7e6 / 8 / nvirb**2 / 2)
dmax = int(min((nvira + 3) // 4, max(ccsd.BLKMIN, dmax)))
vvblk = (max_memory * 1e6 / 8 - dmax**2 * (nvirb**2 * 1.5 + naux)) / naux
vvblk = int(min((nvira + 3) // 4, max(ccsd.BLKMIN, vvblk / naux)))
eribuf = numpy.empty((dmax, dmax, nvir_pair))
loadbuf = numpy.empty((dmax, dmax, nvirb, nvirb))
tril2sq = lib.square_mat_in_trilu_indices(nvira)
for i0, i1 in lib.prange(0, nvira, dmax):
off0 = i0 * (i0 + 1) // 2
off1 = i1 * (i1 + 1) // 2
vvL0 = _cp(vvL[off0:off1])
for j0, j1 in lib.prange(0, i1, dmax):
ijL = vvL0[tril2sq[i0:i1, j0:j1] - off0].reshape(-1, naux)
eri = numpy.ndarray(((i1 - i0) * (j1 - j0), nvir_pair),
buffer=eribuf)
for p0, p1 in lib.prange(0, nvir_pair, vvblk):
vvL1 = _cp(vvL[p0:p1])
eri[:, p0:p1] = lib.ddot(ijL, vvL1.T)
vvL1 = None
tmp = numpy.ndarray((i1 - i0, nvirb, j1 - j0, nvirb),
buffer=loadbuf)
_ccsd.libcc.CCload_eri(tmp.ctypes.data_as(ctypes.c_void_p),
eri.ctypes.data_as(ctypes.c_void_p),
(ctypes.c_int * 4)(i0, i1, j0, j1),
ctypes.c_int(nvirb))
contract_blk_(tmp, i0, i1, j0, j1)
time0 = log.timer_debug1('vvvv [%d:%d,%d:%d]' % (i0, i1, j0, j1),
*time0)
return Ht2.reshape(t2.shape)
def analyze(casscf,
mo_coeff=None,
ci=None,
verbose=None,
large_ci_tol=LARGE_CI_TOL,
with_meta_lowdin=WITH_META_LOWDIN,
**kwargs):
from pyscf.lo import orth
from pyscf.tools import dump_mat
from pyscf.mcscf import addons
log = logger.new_logger(casscf, verbose)
if mo_coeff is None: mo_coeff = casscf.mo_coeff
if ci is None: ci = casscf.ci
nelecas = casscf.nelecas
ncas = casscf.ncas
ncore = casscf.ncore
nocc = ncore + ncas
mocore = mo_coeff[:, :ncore]
mocas = mo_coeff[:, ncore:nocc]
label = casscf.mol.ao_labels()
if (isinstance(ci, (list, tuple)) and
not isinstance(casscf.fcisolver, addons.StateAverageFCISolver)):
log.warn('Mulitple states found in CASCI/CASSCF solver. Density '
'matrix of first state is generated in .analyze() function.')
civec = ci[0]
else:
civec = ci
if hasattr(casscf.fcisolver, 'make_rdm1s'):
casdm1a, casdm1b = casscf.fcisolver.make_rdm1s(civec, ncas, nelecas)
casdm1 = casdm1a + casdm1b
dm1b = numpy.dot(mocore, mocore.T)
dm1a = dm1b + reduce(numpy.dot, (mocas, casdm1a, mocas.T))
dm1b += reduce(numpy.dot, (mocas, casdm1b, mocas.T))
dm1 = dm1a + dm1b
if log.verbose >= logger.DEBUG2:
log.info('alpha density matrix (on AO)')
dump_mat.dump_tri(log.stdout, dm1a, label, **kwargs)
log.info('beta density matrix (on AO)')
dump_mat.dump_tri(log.stdout, dm1b, label, **kwargs)
else:
casdm1 = casscf.fcisolver.make_rdm1(civec, ncas, nelecas)
dm1a = (numpy.dot(mocore, mocore.T) * 2 +
reduce(numpy.dot, (mocas, casdm1, mocas.T)))
dm1b = None
dm1 = dm1a
if log.verbose >= logger.INFO:
ovlp_ao = casscf._scf.get_ovlp()
# note the last two args of ._eig for mc1step_symm
occ, ucas = casscf._eig(-casdm1, ncore, nocc)
log.info('Natural occ %s', str(-occ))
mocas = numpy.dot(mocas, ucas)
if with_meta_lowdin:
log.info(
'Natural orbital (expansion on meta-Lowdin AOs) in CAS space')
orth_coeff = orth.orth_ao(casscf.mol, 'meta_lowdin', s=ovlp_ao)
mocas = reduce(numpy.dot, (orth_coeff.T, ovlp_ao, mocas))
else:
log.info('Natural orbital (expansion on AOs) in CAS space')
dump_mat.dump_rec(log.stdout, mocas, label, start=1, **kwargs)
if log.verbose >= logger.DEBUG2:
if not casscf.natorb:
log.debug2(
'NOTE: mc.mo_coeff in active space is different to '
'the natural orbital coefficients printed in above.')
if with_meta_lowdin:
c = reduce(numpy.dot, (orth_coeff.T, ovlp_ao, mo_coeff))
log.debug2('MCSCF orbital (expansion on meta-Lowdin AOs)')
else:
c = mo_coeff
log.debug2('MCSCF orbital (expansion on AOs)')
dump_mat.dump_rec(log.stdout, c, label, start=1, **kwargs)
if casscf._scf.mo_coeff is not None:
addons.map2hf(casscf, casscf._scf.mo_coeff)
if hasattr(casscf.fcisolver, 'large_ci') and ci is not None:
log.info('** Largest CI components **')
if isinstance(ci, (tuple, list)):
for i, civec in enumerate(ci):
res = casscf.fcisolver.large_ci(civec,
casscf.ncas,
casscf.nelecas,
large_ci_tol,
return_strs=False)
log.info(
' [alpha occ-orbitals] [beta occ-orbitals] state %-3d CI coefficient',
i)
for c, ia, ib in res:
log.info(' %-20s %-30s %.12f', ia, ib, c)
else:
log.info(
' [alpha occ-orbitals] [beta occ-orbitals] CI coefficient'
)
res = casscf.fcisolver.large_ci(ci,
casscf.ncas,
casscf.nelecas,
large_ci_tol,
return_strs=False)
for c, ia, ib in res:
log.info(' %-20s %-30s %.12f', ia, ib, c)
if with_meta_lowdin:
casscf._scf.mulliken_meta(casscf.mol, dm1, s=ovlp_ao, verbose=log)
else:
casscf._scf.mulliken_pop(casscf.mol, dm1, s=ovlp_ao, verbose=log)
return dm1a, dm1b
def ucphf_with_freq(mf,
mo_energy,
mo_occ,
h1,
freq=0,
max_cycle=20,
tol=1e-9,
hermi=False,
verbose=logger.WARN):
log = logger.new_logger(verbose=verbose)
t0 = (logger.process_clock(), logger.perf_counter())
occidxa = mo_occ[0] > 0
occidxb = mo_occ[1] > 0
viridxa = ~occidxa
viridxb = ~occidxb
mo_ea, mo_eb = mo_energy
# e_ai - freq may produce very small elements which can cause numerical
# issue in krylov solver
LEVEL_SHIF = 0.1
e_ai_a = lib.direct_sum('a-i->ai', mo_ea[viridxa], mo_ea[occidxa]).ravel()
e_ai_b = lib.direct_sum('a-i->ai', mo_eb[viridxb], mo_eb[occidxb]).ravel()
diag = (e_ai_a - freq, e_ai_b - freq, e_ai_a + freq, e_ai_b + freq)
diag[0][diag[0] < LEVEL_SHIF] += LEVEL_SHIF
diag[1][diag[1] < LEVEL_SHIF] += LEVEL_SHIF
diag[2][diag[2] < LEVEL_SHIF] += LEVEL_SHIF
diag[3][diag[3] < LEVEL_SHIF] += LEVEL_SHIF
mo0a, mo0b = mf.mo_coeff
nao, nmoa = mo0a.shape
orbva = mo0a[:, viridxa]
orbvb = mo0b[:, viridxb]
orboa = mo0a[:, occidxa]
orbob = mo0b[:, occidxb]
nvira = orbva.shape[1]
nvirb = orbvb.shape[1]
nocca = orboa.shape[1]
noccb = orbob.shape[1]
h1a = h1[0].reshape(-1, nvira * nocca)
h1b = h1[1].reshape(-1, nvirb * noccb)
ncomp = h1a.shape[0]
mo1base = numpy.hstack(
(-h1a / diag[0], -h1b / diag[1], -h1a / diag[2], -h1b / diag[3]))
offsets = numpy.cumsum((nocca * nvira, noccb * nvirb, nocca * nvira))
vresp = mf.gen_response(hermi=0)
def vind(xys):
nz = len(xys)
dm1a = numpy.empty((nz, nao, nao))
dm1b = numpy.empty((nz, nao, nao))
for i in range(nz):
xa, xb, ya, yb = numpy.split(xys[i], offsets)
dmx = reduce(numpy.dot, (orbva, xa.reshape(nvira, nocca), orboa.T))
dmy = reduce(numpy.dot,
(orboa, ya.reshape(nvira, nocca).T, orbva.T))
dm1a[i] = dmx + dmy # AX + BY
dmx = reduce(numpy.dot, (orbvb, xb.reshape(nvirb, noccb), orbob.T))
dmy = reduce(numpy.dot,
(orbob, yb.reshape(nvirb, noccb).T, orbvb.T))
dm1b[i] = dmx + dmy # AX + BY
v1ao = vresp(numpy.stack((dm1a, dm1b)))
v1voa = lib.einsum('xpq,pi,qj->xij', v1ao[0], orbva,
orboa).reshape(nz, -1)
v1vob = lib.einsum('xpq,pi,qj->xij', v1ao[1], orbvb,
orbob).reshape(nz, -1)
v1ova = lib.einsum('xpq,pi,qj->xji', v1ao[0], orboa,
orbva).reshape(nz, -1)
v1ovb = lib.einsum('xpq,pi,qj->xji', v1ao[1], orbob,
orbvb).reshape(nz, -1)
for i in range(nz):
xa, xb, ya, yb = numpy.split(xys[i], offsets)
v1voa[i] += (e_ai_a - freq - diag[0]) * xa
v1voa[i] /= diag[0]
v1vob[i] += (e_ai_b - freq - diag[1]) * xb
v1vob[i] /= diag[1]
v1ova[i] += (e_ai_a + freq - diag[2]) * ya
v1ova[i] /= diag[2]
v1ovb[i] += (e_ai_b + freq - diag[3]) * yb
v1ovb[i] /= diag[3]
v = numpy.hstack((v1voa, v1vob, v1ova, v1ovb))
return v
# FIXME: krylov solver is not accurate enough for many freqs. Using tight
# tol and lindep could offer small help. A better linear equation solver
# is needed.
mo1 = lib.krylov(vind,
mo1base,
tol=tol,
max_cycle=max_cycle,
hermi=hermi,
lindep=1e-18,
verbose=log)
log.timer('krylov solver in CPHF', *t0)
dm1a = numpy.empty((ncomp, nao, nao))
dm1b = numpy.empty((ncomp, nao, nao))
for i in range(ncomp):
xa, xb, ya, yb = numpy.split(mo1[i], offsets)
dmx = reduce(numpy.dot, (orbva, xa.reshape(nvira, nocca) * 2, orboa.T))
dmy = reduce(numpy.dot,
(orboa, ya.reshape(nvira, nocca).T * 2, orbva.T))
dm1a[i] = dmx + dmy
dmx = reduce(numpy.dot, (orbvb, xb.reshape(nvirb, noccb) * 2, orbob.T))
dmy = reduce(numpy.dot,
(orbob, yb.reshape(nvirb, noccb).T * 2, orbvb.T))
dm1b[i] = dmx + dmy
v1ao = vresp(numpy.stack((dm1a, dm1b)))
mo_e1_a = lib.einsum('xpq,pi,qj->xij', v1ao[0], orboa, orboa)
mo_e1_b = lib.einsum('xpq,pi,qj->xij', v1ao[1], orbob, orbob)
mo_e1 = (mo_e1_a, mo_e1_b)
xa, xb, ya, yb = numpy.split(mo1, offsets, axis=1)
mo1 = (xa.reshape(ncomp, nvira, nocca), xb.reshape(ncomp, nvirb, noccb),
ya.reshape(ncomp, nvira, nocca), yb.reshape(ncomp, nvirb, noccb))
return mo1, mo_e1
def kernel(mf, mo_coeff, mo_occ, conv_tol=1e-10, conv_tol_grad=None,
max_cycle=50, dump_chk=True,
callback=None, verbose=logger.NOTE):
cput0 = (time.clock(), time.time())
log = logger.new_logger(mf, verbose)
mol = mf._scf.mol
if mol != mf.mol:
logger.warn(mf, 'dual-basis SOSCF is an experimental feature. It is '
'still in testing.')
if conv_tol_grad is None:
conv_tol_grad = numpy.sqrt(conv_tol)
log.info('Set conv_tol_grad to %g', conv_tol_grad)
scf_conv = False
e_tot = mf.e_tot
# call mf._scf.get_hcore, mf._scf.get_ovlp because they might be overloaded
h1e = mf._scf.get_hcore(mol)
s1e = mf._scf.get_ovlp(mol)
dm = mf.make_rdm1(mo_coeff, mo_occ)
# call mf._scf.get_veff, to avoid "newton().density_fit()" polluting get_veff
vhf = mf._scf.get_veff(mol, dm)
e_tot = mf._scf.energy_tot(dm, h1e, vhf)
fock = mf.get_fock(h1e, s1e, vhf, dm, level_shift_factor=0)
log.info('Initial guess E= %.15g |g|= %g', e_tot,
numpy.linalg.norm(mf._scf.get_grad(mo_coeff, mo_occ, fock)))
# NOTE: DO NOT change the initial guess mo_occ, mo_coeff
mo_energy, mo_tmp = mf.eig(fock, s1e)
mf.get_occ(mo_energy, mo_tmp)
if dump_chk and mf.chkfile:
chkfile.save_mol(mol, mf.chkfile)
# Copy the integral file to soscf object to avoid the integrals being cached
# twice.
if mol == mf.mol and not getattr(mf, 'with_df', None):
mf._eri = mf._scf._eri
rotaiter = rotate_orb_cc(mf, mo_coeff, mo_occ, fock, h1e, conv_tol_grad, log)
u, g_orb, kfcount, jkcount = next(rotaiter)
kftot = kfcount + 1
jktot = jkcount
cput1 = log.timer('initializing second order scf', *cput0)
for imacro in range(max_cycle):
dm_last = dm
last_hf_e = e_tot
norm_gorb = numpy.linalg.norm(g_orb)
mo_coeff = mf.rotate_mo(mo_coeff, u, log)
dm = mf.make_rdm1(mo_coeff, mo_occ)
vhf = mf._scf.get_veff(mol, dm, dm_last=dm_last, vhf_last=vhf)
fock = mf.get_fock(h1e, s1e, vhf, dm, level_shift_factor=0)
# NOTE: DO NOT change the initial guess mo_occ, mo_coeff
if mf.verbose >= logger.DEBUG:
mo_energy, mo_tmp = mf.eig(fock, s1e)
mf.get_occ(mo_energy, mo_tmp)
# call mf._scf.energy_tot for dft, because the (dft).get_veff step saved _exc in mf._scf
e_tot = mf._scf.energy_tot(dm, h1e, vhf)
log.info('macro= %d E= %.15g delta_E= %g |g|= %g %d KF %d JK',
imacro, e_tot, e_tot-last_hf_e, norm_gorb,
kfcount+1, jkcount)
cput1 = log.timer('cycle= %d'%(imacro+1), *cput1)
if (abs((e_tot-last_hf_e)/e_tot)*1e2 < conv_tol and
norm_gorb < conv_tol_grad):
scf_conv = True
if dump_chk:
mf.dump_chk(locals())
if callable(callback):
callback(locals())
if scf_conv:
break
u, g_orb, kfcount, jkcount = rotaiter.send((mo_coeff, mo_occ, fock))
kftot += kfcount + 1
jktot += jkcount
if callable(callback):
callback(locals())
rotaiter.close()
mo_energy, mo_coeff1 = mf._scf.canonicalize(mo_coeff, mo_occ, fock)
if mf.canonicalization:
log.info('Canonicalize SCF orbitals')
mo_coeff = mo_coeff1
if dump_chk:
mf.dump_chk(locals())
log.info('macro X = %d E=%.15g |g|= %g total %d KF %d JK',
imacro+1, e_tot, norm_gorb, kftot, jktot)
if (numpy.any(mo_occ==0) and
mo_energy[mo_occ>0].max() > mo_energy[mo_occ==0].min()):
log.warn('H**O %s > LUMO %s was found in the canonicalized orbitals.',
mo_energy[mo_occ>0].max(), mo_energy[mo_occ==0].min())
return scf_conv, e_tot, mo_energy, mo_coeff, mo_occ
def get_nto(tdobj, state=1, threshold=OUTPUT_THRESHOLD, verbose=None):
r'''
Natural transition orbital analysis.
The natural transition density matrix between ground state and excited
state :math:`Tia = \langle \Psi_{ex} | i a^\dagger | \Psi_0 \rangle` can
be transformed to diagonal form through SVD
:math:`T = O \sqrt{\lambda} V^\dagger`. O and V are occupied and virtual
natural transition orbitals. The diagonal elements :math:`\lambda` are the
weights of the occupied-virtual orbital pair in the excitation.
Ref: Martin, R. L., JCP, 118, 4775-4777
Note in the TDHF/TDDFT calculations, the excitation part (X) is
interpreted as the CIS coefficients and normalized to 1. The de-excitation
part (Y) is ignored.
Args:
state : int
Excited state ID. state = 1 means the first excited state.
If state < 0, state ID is counted from the last excited state.
Kwargs:
threshold : float
Above which the NTO coefficients will be printed in the output.
Returns:
A list (weights, NTOs). NTOs are natural orbitals represented in AO
basis. The first N_occ NTOs are occupied NTOs and the rest are virtual
NTOs.
'''
if state == 0:
logger.warn(
tdobj, 'Excited state starts from 1. '
'Set state=1 for first excited state.')
state_id = state
elif state < 0:
state_id = state
else:
state_id = state - 1
mol = tdobj.mol
mo_coeff = tdobj._scf.mo_coeff
mo_occ = tdobj._scf.mo_occ
orbo_a = mo_coeff[0][:, mo_occ[0] == 1]
orbv_a = mo_coeff[0][:, mo_occ[0] == 0]
orbo_b = mo_coeff[1][:, mo_occ[1] == 1]
orbv_b = mo_coeff[1][:, mo_occ[1] == 0]
nocc_a = orbo_a.shape[1]
nvir_a = orbv_a.shape[1]
nocc_b = orbo_b.shape[1]
nvir_b = orbv_b.shape[1]
cis_t1a, cis_t1b = tdobj.xy[state_id][0]
norm = numpy.linalg.norm(cis_t1a)**2 + numpy.linalg.norm(cis_t1b)**2
cis_t1a *= 1. / norm
cis_t1b *= 1. / norm
if mol.symmetry:
orbsyma, orbsymb = uhf_symm.get_orbsym(mol, mo_coeff)
o_sym_a = orbsyma[mo_occ[0] == 1]
v_sym_a = orbsyma[mo_occ[0] == 0]
o_sym_b = orbsymb[mo_occ[1] == 1]
v_sym_b = orbsymb[mo_occ[1] == 0]
nto_o_a = numpy.eye(nocc_a)
nto_v_a = numpy.eye(nvir_a)
nto_o_b = numpy.eye(nocc_b)
nto_v_b = numpy.eye(nvir_b)
weights_o_a = numpy.zeros(nocc_a)
weights_v_a = numpy.zeros(nvir_a)
weights_o_b = numpy.zeros(nocc_b)
weights_v_b = numpy.zeros(nvir_b)
for ir in set(orbsyma):
idx = numpy.where(o_sym_a == ir)[0]
if idx.size > 0:
dm_oo = numpy.dot(cis_t1a[idx], cis_t1a[idx].T)
weights_o_a[idx], nto_o_a[idx[:, None],
idx] = numpy.linalg.eigh(dm_oo)
idx = numpy.where(v_sym_a == ir)[0]
if idx.size > 0:
dm_vv = numpy.dot(cis_t1a[:, idx].T, cis_t1a[:, idx])
weights_v_a[idx], nto_v_a[idx[:, None],
idx] = numpy.linalg.eigh(dm_vv)
for ir in set(orbsymb):
idx = numpy.where(o_sym_b == ir)[0]
if idx.size > 0:
dm_oo = numpy.dot(cis_t1b[idx], cis_t1b[idx].T)
weights_o_b[idx], nto_o_b[idx[:, None],
idx] = numpy.linalg.eigh(dm_oo)
idx = numpy.where(v_sym_b == ir)[0]
if idx.size > 0:
dm_vv = numpy.dot(cis_t1b[:, idx].T, cis_t1b[:, idx])
weights_v_b[idx], nto_v_b[idx[:, None],
idx] = numpy.linalg.eigh(dm_vv)
def sort(weights, nto, sym):
# weights in descending order
idx = numpy.argsort(-weights)
weights = weights[idx]
nto = nto[:, idx]
sym = sym[idx]
return weights, nto, sym
weights_o_a, nto_o_a, o_sym_a = sort(weights_o_a, nto_o_a, o_sym_a)
weights_v_a, nto_v_a, v_sym_a = sort(weights_v_a, nto_v_a, v_sym_a)
weights_o_b, nto_o_b, o_sym_b = sort(weights_o_b, nto_o_b, o_sym_b)
weights_v_b, nto_v_b, v_sym_b = sort(weights_v_b, nto_v_b, v_sym_b)
nto_orbsyma = numpy.hstack((o_sym_a, v_sym_a))
nto_orbsymb = numpy.hstack((o_sym_b, v_sym_b))
if nocc_a < nvir_a:
weights_a = weights_o_a
else:
weights_a = weights_v_a
if nocc_b < nvir_b:
weights_b = weights_o_b
else:
weights_b = weights_v_b
else:
nto_o_a, w_a, nto_v_aT = numpy.linalg.svd(cis_t1a)
nto_o_b, w_b, nto_v_bT = numpy.linalg.svd(cis_t1b)
nto_v_a = nto_v_aT.conj().T
nto_v_b = nto_v_bT.conj().T
weights_a = w_a**2
weights_b = w_b**2
nto_orbsyma = nto_orbsymb = None
def _set_phase_(c):
idx = numpy.argmax(abs(c.real), axis=0)
c[:, c[idx, numpy.arange(c.shape[1])].real < 0] *= -1
_set_phase_(nto_o_a)
_set_phase_(nto_o_b)
_set_phase_(nto_v_a)
_set_phase_(nto_v_b)
occupied_nto_a = numpy.dot(orbo_a, nto_o_a)
occupied_nto_b = numpy.dot(orbo_b, nto_o_b)
virtual_nto_a = numpy.dot(orbv_a, nto_v_a)
virtual_nto_b = numpy.dot(orbv_b, nto_v_b)
nto_coeff = (numpy.hstack((occupied_nto_a, virtual_nto_a)),
numpy.hstack((occupied_nto_b, virtual_nto_b)))
if mol.symmetry:
nto_coeff = (lib.tag_array(nto_coeff[0], orbsym=nto_orbsyma),
lib.tag_array(nto_coeff[1], orbsym=nto_orbsymb))
log = logger.new_logger(tdobj, verbose)
if log.verbose >= logger.INFO:
log.info('State %d: %g eV NTO largest component %s', state_id + 1,
tdobj.e[state_id] * nist.HARTREE2EV,
weights_a[0] + weights_b[0])
fmt = '%' + str(lib.param.OUTPUT_DIGITS) + 'f (MO #%d)'
o_idx_a = numpy.where(abs(nto_o_a[:, 0]) > threshold)[0]
v_idx_a = numpy.where(abs(nto_v_a[:, 0]) > threshold)[0]
o_idx_b = numpy.where(abs(nto_o_b[:, 0]) > threshold)[0]
v_idx_b = numpy.where(abs(nto_v_b[:, 0]) > threshold)[0]
log.info(' alpha occ-NTO: ' +
' + '.join([(fmt % (nto_o_a[i, 0], i + MO_BASE))
for i in o_idx_a]))
log.info(' alpha vir-NTO: ' +
' + '.join([(fmt % (nto_v_a[i, 0], i + MO_BASE + nocc_a))
for i in v_idx_a]))
log.info(' beta occ-NTO: ' +
' + '.join([(fmt % (nto_o_b[i, 0], i + MO_BASE))
for i in o_idx_b]))
log.info(' beta vir-NTO: ' +
' + '.join([(fmt % (nto_v_b[i, 0], i + MO_BASE + nocc_b))
for i in v_idx_b]))
return (weights_a, weights_b), nto_coeff
def analyze(tdobj, verbose=None):
log = logger.new_logger(tdobj, verbose)
mol = tdobj.mol
mo_coeff = tdobj._scf.mo_coeff
mo_occ = tdobj._scf.mo_occ
nocc_a = numpy.count_nonzero(mo_occ[0] == 1)
nocc_b = numpy.count_nonzero(mo_occ[1] == 1)
e_ev = numpy.asarray(tdobj.e) * nist.HARTREE2EV
e_wn = numpy.asarray(tdobj.e) * nist.HARTREE2WAVENUMBER
wave_length = 1e11 / e_wn
log.note('\n** Excitation energies and oscillator strengths **')
if mol.symmetry:
orbsyma, orbsymb = uhf_symm.get_orbsym(mol, mo_coeff)
orbsyma = orbsyma % 10
x_syma = (orbsyma[mo_occ[0] == 1, None]
^ orbsyma[mo_occ[0] == 0]).ravel()
else:
x_syma = None
f_oscillator = tdobj.oscillator_strength()
for i, ei in enumerate(tdobj.e):
x, y = tdobj.xy[i]
if x_syma is None:
log.note('Excited State %3d: %12.5f eV %9.2f nm f=%.4f', i + 1,
e_ev[i], wave_length[i], f_oscillator[i])
else:
wfnsym_id = x_syma[abs(x[0]).argmax()]
wfnsym = symm.irrep_id2name(mol.groupname, wfnsym_id)
log.note('Excited State %3d: %4s %12.5f eV %9.2f nm f=%.4f',
i + 1, wfnsym, e_ev[i], wave_length[i], f_oscillator[i])
if log.verbose >= logger.INFO:
for o, v in zip(*numpy.where(abs(x[0]) > 0.1)):
log.info(' %4da -> %4da %12.5f', o + MO_BASE,
v + MO_BASE + nocc_a, x[0][o, v])
for o, v in zip(*numpy.where(abs(x[1]) > 0.1)):
log.info(' %4db -> %4db %12.5f', o + MO_BASE,
v + MO_BASE + nocc_b, x[1][o, v])
if log.verbose >= logger.INFO:
log.info('\n** Transition electric dipole moments (AU) **')
log.info(
'state X Y Z Dip. S. Osc.'
)
trans_dip = tdobj.transition_dipole()
for i, ei in enumerate(tdobj.e):
dip = trans_dip[i]
log.info('%3d %11.4f %11.4f %11.4f %11.4f %11.4f', i + 1,
dip[0], dip[1], dip[2], numpy.dot(dip,
dip), f_oscillator[i])
log.info(
'\n** Transition velocity dipole moments (imaginary part AU) **')
log.info(
'state X Y Z Dip. S. Osc.'
)
trans_v = tdobj.transition_velocity_dipole()
f_v = tdobj.oscillator_strength(gauge='velocity', order=0)
for i, ei in enumerate(tdobj.e):
v = trans_v[i]
log.info('%3d %11.4f %11.4f %11.4f %11.4f %11.4f', i + 1, v[0],
v[1], v[2], numpy.dot(v, v), f_v[i])
log.info('\n** Transition magnetic dipole moments (AU) **')
log.info('state X Y Z')
trans_m = tdobj.transition_magnetic_dipole()
for i, ei in enumerate(tdobj.e):
m = trans_m[i]
log.info('%3d %11.4f %11.4f %11.4f', i + 1, m[0], m[1], m[2])
return tdobj
def analyze(mf, verbose=logger.DEBUG, with_meta_lowdin=WITH_META_LOWDIN,
**kwargs):
'''Analyze the given SCF object: print orbital energies, occupancies;
print orbital coefficients; Occupancy for each irreps; Mulliken population analysis
'''
from pyscf.lo import orth
from pyscf.tools import dump_mat
mol = mf.mol
if not mol.symmetry:
return hf.analyze(mf, verbose, with_meta_lowdin, **kwargs)
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
mo_coeff = mf.mo_coeff
ovlp_ao = mf.get_ovlp()
log = logger.new_logger(mf, verbose)
if log.verbose >= logger.NOTE:
mf.dump_scf_summary(log)
nirrep = len(mol.irrep_id)
orbsym = get_orbsym(mf.mol, mo_coeff, ovlp_ao, False)
wfnsym = 0
noccs = [sum(orbsym[mo_occ>0]==ir) for ir in mol.irrep_id]
if mol.groupname in ('SO3', 'Dooh', 'Coov'):
log.note('TODO: total wave-function symmetry for %s', mol.groupname)
else:
log.note('Wave-function symmetry = %s',
symm.irrep_id2name(mol.groupname, wfnsym))
log.note('occupancy for each irrep: ' + (' %4s'*nirrep), *mol.irrep_name)
log.note(' ' + (' %4d'*nirrep), *noccs)
log.note('**** MO energy ****')
irname_full = {}
for k,ir in enumerate(mol.irrep_id):
irname_full[ir] = mol.irrep_name[k]
irorbcnt = {}
for k, j in enumerate(orbsym):
if j in irorbcnt:
irorbcnt[j] += 1
else:
irorbcnt[j] = 1
log.note('MO #%d (%s #%d), energy= %.15g occ= %g',
k+MO_BASE, irname_full[j], irorbcnt[j],
mo_energy[k], mo_occ[k])
if log.verbose >= logger.DEBUG:
label = mol.ao_labels()
molabel = []
irorbcnt = {}
for k, j in enumerate(orbsym):
if j in irorbcnt:
irorbcnt[j] += 1
else:
irorbcnt[j] = 1
molabel.append('#%-d(%s #%d)' %
(k+MO_BASE, irname_full[j], irorbcnt[j]))
if with_meta_lowdin:
log.debug(' ** MO coefficients (expansion on meta-Lowdin AOs) **')
orth_coeff = orth.orth_ao(mol, 'meta_lowdin', s=ovlp_ao)
c = reduce(numpy.dot, (orth_coeff.conj().T, ovlp_ao, mo_coeff))
else:
log.debug(' ** MO coefficients (expansion on AOs) **')
c = mo_coeff
dump_mat.dump_rec(mf.stdout, c, label, molabel, start=MO_BASE, **kwargs)
dm = mf.make_rdm1(mo_coeff, mo_occ)
if with_meta_lowdin:
pop_and_charge = mf.mulliken_meta(mol, dm, s=ovlp_ao, verbose=log)
else:
pop_and_charge = mf.mulliken_pop(mol, dm, s=ovlp_ao, verbose=log)
dip = mf.dip_moment(mol, dm, verbose=log)
return pop_and_charge, dip
def analyze(self, verbose=None, with_meta_lowdin=WITH_META_LOWDIN,
**kwargs):
if verbose is None: verbose = self.verbose
from pyscf.lo import orth
from pyscf.tools import dump_mat
if not self.mol.symmetry:
return rohf.ROHF.analyze(self, verbose, with_meta_lowdin, **kwargs)
mol = self.mol
mo_energy = self.mo_energy
mo_occ = self.mo_occ
mo_coeff = self.mo_coeff
ovlp_ao = self.get_ovlp()
log = logger.new_logger(self, verbose)
if log.verbose >= logger.NOTE:
self.dump_scf_summary(log)
nirrep = len(mol.irrep_id)
orbsym = get_orbsym(self.mol, mo_coeff)
wfnsym = 0
ndoccs = []
nsoccs = []
for k,ir in enumerate(mol.irrep_id):
ndoccs.append(sum(orbsym[mo_occ==2] == ir))
nsoccs.append(sum(orbsym[mo_occ==1] == ir))
if nsoccs[k] % 2 == 1:
wfnsym ^= ir
if mol.groupname in ('SO3', 'Dooh', 'Coov'):
log.note('TODO: total wave-function symmetry for %s', mol.groupname)
else:
log.note('Wave-function symmetry = %s',
symm.irrep_id2name(mol.groupname, wfnsym))
log.note('occupancy for each irrep: ' + (' %4s'*nirrep),
*mol.irrep_name)
log.note('double occ ' + (' %4d'*nirrep), *ndoccs)
log.note('single occ ' + (' %4d'*nirrep), *nsoccs)
log.note('**** MO energy ****')
irname_full = {}
for k,ir in enumerate(mol.irrep_id):
irname_full[ir] = mol.irrep_name[k]
irorbcnt = {}
if getattr(mo_energy, 'mo_ea', None) is not None:
mo_ea = mo_energy.mo_ea
mo_eb = mo_energy.mo_eb
log.note(' Roothaan | alpha | beta')
for k, j in enumerate(orbsym):
if j in irorbcnt:
irorbcnt[j] += 1
else:
irorbcnt[j] = 1
log.note('MO #%-4d(%-3s #%-2d) energy= %-18.15g | %-18.15g | %-18.15g occ= %g',
k+MO_BASE, irname_full[j], irorbcnt[j],
mo_energy[k], mo_ea[k], mo_eb[k], mo_occ[k])
else:
for k, j in enumerate(orbsym):
if j in irorbcnt:
irorbcnt[j] += 1
else:
irorbcnt[j] = 1
log.note('MO #%-3d (%s #%-2d), energy= %-18.15g occ= %g',
k+MO_BASE, irname_full[j], irorbcnt[j],
mo_energy[k], mo_occ[k])
if log.verbose >= logger.DEBUG:
label = mol.ao_labels()
molabel = []
irorbcnt = {}
for k, j in enumerate(orbsym):
if j in irorbcnt:
irorbcnt[j] += 1
else:
irorbcnt[j] = 1
molabel.append('#%-d(%s #%d)' %
(k+MO_BASE, irname_full[j], irorbcnt[j]))
if with_meta_lowdin:
log.debug(' ** MO coefficients (expansion on meta-Lowdin AOs) **')
orth_coeff = orth.orth_ao(mol, 'meta_lowdin', s=ovlp_ao)
c = reduce(numpy.dot, (orth_coeff.conj().T, ovlp_ao, mo_coeff))
else:
log.debug(' ** MO coefficients (expansion on AOs) **')
c = mo_coeff
dump_mat.dump_rec(self.stdout, c, label, molabel, start=MO_BASE, **kwargs)
dm = self.make_rdm1(mo_coeff, mo_occ)
if with_meta_lowdin:
pop_and_charge = self.mulliken_meta(mol, dm, s=ovlp_ao, verbose=log)
else:
pop_and_charge = self.mulliken_pop(mol, dm, s=ovlp_ao, verbose=log)
dip = self.dip_moment(mol, dm, verbose=log)
return pop_and_charge, dip
def _ao2mo_ovov(mp, orbs, feri, max_memory=2000, verbose=None):
time0 = (time.clock(), time.time())
log = logger.new_logger(mp, verbose)
orboa = numpy.asarray(orbs[0], order='F')
orbva = numpy.asarray(orbs[1], order='F')
orbob = numpy.asarray(orbs[2], order='F')
orbvb = numpy.asarray(orbs[3], order='F')
nao, nocca = orboa.shape
noccb = orbob.shape[1]
nvira = orbva.shape[1]
nvirb = orbvb.shape[1]
mol = mp.mol
int2e = mol._add_suffix('int2e')
ao2mopt = _ao2mo.AO2MOpt(mol, int2e, 'CVHFnr_schwarz_cond',
'CVHFsetnr_direct_scf')
nbas = mol.nbas
assert (nvira <= nao)
assert (nvirb <= nao)
ao_loc = mol.ao_loc_nr()
dmax = max(
4, min(nao / 3, numpy.sqrt(max_memory * .95e6 / 8 / (nao + nocca)**2)))
sh_ranges = ao2mo.outcore.balance_partition(ao_loc, dmax)
dmax = max(x[2] for x in sh_ranges)
eribuf = numpy.empty((nao, dmax, dmax, nao))
ftmp = lib.H5TmpFile()
disk = (nocca**2 * (nao * (nao + dmax) / 2 + nvira**2) + noccb**2 *
(nao * (nao + dmax) / 2 + nvirb**2) + nocca * noccb *
(nao**2 + nvira * nvirb))
log.debug('max_memory %s MB (dmax = %s) required disk space %g MB',
max_memory, dmax, disk * 8 / 1e6)
fint = gto.moleintor.getints4c
aa_blk_slices = []
ab_blk_slices = []
count_ab = 0
count_aa = 0
time1 = time0
with lib.call_in_background(ftmp.__setitem__) as save:
for ish0, ish1, ni in sh_ranges:
for jsh0, jsh1, nj in sh_ranges:
i0, i1 = ao_loc[ish0], ao_loc[ish1]
j0, j1 = ao_loc[jsh0], ao_loc[jsh1]
eri = fint(int2e,
mol._atm,
mol._bas,
mol._env,
shls_slice=(0, nbas, ish0, ish1, jsh0, jsh1, 0,
nbas),
aosym='s1',
ao_loc=ao_loc,
cintopt=ao2mopt._cintopt,
out=eribuf)
tmp_i = lib.ddot(orboa.T,
eri.reshape(nao, (i1 - i0) * (j1 - j0) * nao))
tmp_li = lib.ddot(
orbob.T,
tmp_i.reshape(nocca * (i1 - i0) * (j1 - j0), nao).T)
tmp_li = tmp_li.reshape(noccb, nocca, (i1 - i0), (j1 - j0))
save('ab/%d' % count_ab, tmp_li.transpose(1, 0, 2, 3))
ab_blk_slices.append((i0, i1, j0, j1))
count_ab += 1
if ish0 >= jsh0:
tmp_li = lib.ddot(
orboa.T,
tmp_i.reshape(nocca * (i1 - i0) * (j1 - j0), nao).T)
tmp_li = tmp_li.reshape(nocca, nocca, (i1 - i0), (j1 - j0))
save('aa/%d' % count_aa, tmp_li.transpose(1, 0, 2, 3))
tmp_i = lib.ddot(
orbob.T, eri.reshape(nao, (i1 - i0) * (j1 - j0) * nao))
tmp_li = lib.ddot(
orbob.T,
tmp_i.reshape(noccb * (i1 - i0) * (j1 - j0), nao).T)
tmp_li = tmp_li.reshape(noccb, noccb, (i1 - i0), (j1 - j0))
save('bb/%d' % count_aa, tmp_li.transpose(1, 0, 2, 3))
aa_blk_slices.append((i0, i1, j0, j1))
count_aa += 1
time1 = log.timer_debug1(
'partial ao2mo [%d:%d,%d:%d]' % (ish0, ish1, jsh0, jsh1),
*time1)
time1 = time0 = log.timer('mp2 ao2mo_ovov pass1', *time0)
eri = eribuf = tmp_i = tmp_li = None
fovov = feri.create_dataset('ovov', (nocca * nvira, nocca * nvira),
'f8',
chunks=(nvira, nvira))
fovOV = feri.create_dataset('ovOV', (nocca * nvira, noccb * nvirb),
'f8',
chunks=(nvira, nvirb))
fOVOV = feri.create_dataset('OVOV', (noccb * nvirb, noccb * nvirb),
'f8',
chunks=(nvirb, nvirb))
occblk = int(
min(max(nocca, noccb),
max(4, 250 / nocca, max_memory * .9e6 / 8 / (nao**2 * nocca) / 5)))
def load_aa(h5g, nocc, i0, eri):
if i0 < nocc:
i1 = min(i0 + occblk, nocc)
for k, (p0, p1, q0, q1) in enumerate(aa_blk_slices):
eri[:i1 - i0, :, p0:p1, q0:q1] = h5g[str(k)][i0:i1]
if p0 != q0:
dat = numpy.asarray(h5g[str(k)][:, i0:i1])
eri[:i1 - i0, :, q0:q1, p0:p1] = dat.transpose(1, 0, 3, 2)
def load_ab(h5g, nocca, i0, eri):
if i0 < nocca:
i1 = min(i0 + occblk, nocca)
for k, (p0, p1, q0, q1) in enumerate(ab_blk_slices):
eri[:i1 - i0, :, p0:p1, q0:q1] = h5g[str(k)][i0:i1]
def save(h5dat, nvir, i0, i1, dat):
for i in range(i0, i1):
h5dat[i * nvir:(i + 1) * nvir] = dat[i - i0].reshape(nvir, -1)
with lib.call_in_background(save) as bsave:
with lib.call_in_background(load_aa) as prefetch:
buf_prefecth = numpy.empty((occblk, nocca, nao, nao))
buf = numpy.empty_like(buf_prefecth)
load_aa(ftmp['aa'], nocca, 0, buf_prefecth)
for i0, i1 in lib.prange(0, nocca, occblk):
buf, buf_prefecth = buf_prefecth, buf
prefetch(ftmp['aa'], nocca, i1, buf_prefecth)
eri = buf[:i1 - i0].reshape((i1 - i0) * nocca, nao, nao)
dat = _ao2mo.nr_e2(eri, orbva, (0, nvira, 0, nvira), 's1',
's1')
bsave(
fovov, nvira, i0, i1,
dat.reshape(i1 - i0, nocca, nvira,
nvira).transpose(0, 2, 1, 3))
time1 = log.timer_debug1(
'pass2 ao2mo for aa [%d:%d]' % (i0, i1), *time1)
buf_prefecth = numpy.empty((occblk, noccb, nao, nao))
buf = numpy.empty_like(buf_prefecth)
load_aa(ftmp['bb'], noccb, 0, buf_prefecth)
for i0, i1 in lib.prange(0, noccb, occblk):
buf, buf_prefecth = buf_prefecth, buf
prefetch(ftmp['bb'], noccb, i1, buf_prefecth)
eri = buf[:i1 - i0].reshape((i1 - i0) * noccb, nao, nao)
dat = _ao2mo.nr_e2(eri, orbvb, (0, nvirb, 0, nvirb), 's1',
's1')
bsave(
fOVOV, nvirb, i0, i1,
dat.reshape(i1 - i0, noccb, nvirb,
nvirb).transpose(0, 2, 1, 3))
time1 = log.timer_debug1(
'pass2 ao2mo for bb [%d:%d]' % (i0, i1), *time1)
orbvab = numpy.asarray(numpy.hstack((orbva, orbvb)), order='F')
with lib.call_in_background(load_ab) as prefetch:
load_ab(ftmp['ab'], nocca, 0, buf_prefecth)
for i0, i1 in lib.prange(0, nocca, occblk):
buf, buf_prefecth = buf_prefecth, buf
prefetch(ftmp['ab'], nocca, i1, buf_prefecth)
eri = buf[:i1 - i0].reshape((i1 - i0) * noccb, nao, nao)
dat = _ao2mo.nr_e2(eri, orbvab,
(0, nvira, nvira, nvira + nvirb), 's1',
's1')
bsave(
fovOV, nvira, i0, i1,
dat.reshape(i1 - i0, noccb, nvira,
nvirb).transpose(0, 2, 1, 3))
time1 = log.timer_debug1(
'pass2 ao2mo for ab [%d:%d]' % (i0, i1), *time1)
time0 = log.timer('mp2 ao2mo_ovov pass2', *time0)
def kernel(mycc, eris, t1=None, t2=None, verbose=logger.NOTE):
cpu1 = cpu0 = (time.clock(), time.time())
log = logger.new_logger(mycc, verbose)
if t1 is None: t1 = mycc.t1
if t2 is None: t2 = mycc.t2
nocc, nvir = t1.shape
nmo = nocc + nvir
_tmpfile = tempfile.NamedTemporaryFile(dir=lib.param.TMPDIR)
ftmp = h5py.File(_tmpfile.name)
eris_vvop = ftmp.create_dataset('vvop', (nvir, nvir, nocc, nmo), 'f8')
orbsym = _sort_eri(mycc, eris, nocc, nvir, eris_vvop, log)
ftmp[
't2'] = t2 # read back late. Cache t2T in t2 to reduce memory footprint
mo_energy, t1T, t2T, vooo = _sort_t2_vooo_(mycc, orbsym, t1, t2, eris)
cpu1 = log.timer_debug1('CCSD(T) sort_eri', *cpu1)
cpu2 = list(cpu1)
orbsym = numpy.hstack(
(numpy.sort(orbsym[:nocc]), numpy.sort(orbsym[nocc:])))
o_ir_loc = numpy.append(
0, numpy.cumsum(numpy.bincount(orbsym[:nocc], minlength=8)))
v_ir_loc = numpy.append(
0, numpy.cumsum(numpy.bincount(orbsym[nocc:], minlength=8)))
o_sym = orbsym[:nocc]
oo_sym = (o_sym[:, None] ^ o_sym).ravel()
oo_ir_loc = numpy.append(0,
numpy.cumsum(numpy.bincount(oo_sym, minlength=8)))
nirrep = max(oo_sym) + 1
orbsym = orbsym.astype(numpy.int32)
o_ir_loc = o_ir_loc.astype(numpy.int32)
v_ir_loc = v_ir_loc.astype(numpy.int32)
oo_ir_loc = oo_ir_loc.astype(numpy.int32)
et_sum = [0]
def contract(a0, a1, b0, b1, cache):
cache_row_a, cache_col_a, cache_row_b, cache_col_b = cache
drv = _ccsd.libcc.CCsd_t_contract
drv.restype = ctypes.c_double
et = drv(mo_energy.ctypes.data_as(ctypes.c_void_p),
t1T.ctypes.data_as(ctypes.c_void_p),
t2T.ctypes.data_as(ctypes.c_void_p),
vooo.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(nocc),
ctypes.c_int(nvir), ctypes.c_int(a0), ctypes.c_int(a1),
ctypes.c_int(b0), ctypes.c_int(b1), ctypes.c_int(nirrep),
o_ir_loc.ctypes.data_as(ctypes.c_void_p),
v_ir_loc.ctypes.data_as(ctypes.c_void_p),
oo_ir_loc.ctypes.data_as(ctypes.c_void_p),
orbsym.ctypes.data_as(ctypes.c_void_p),
cache_row_a.ctypes.data_as(ctypes.c_void_p),
cache_col_a.ctypes.data_as(ctypes.c_void_p),
cache_row_b.ctypes.data_as(ctypes.c_void_p),
cache_col_b.ctypes.data_as(ctypes.c_void_p))
cpu2[:] = log.timer_debug1('contract %d:%d,%d:%d' % (a0, a1, b0, b1),
*cpu2)
et_sum[0] += et
return et
# The rest 20% memory for cache b
mem_now = lib.current_memory()[0]
max_memory = max(2000, mycc.max_memory - mem_now)
bufsize = max(1,
(max_memory * 1e6 / 8 - nocc**3 * 100) * .7 / (nocc * nmo))
log.debug('max_memory %d MB (%d MB in use)', max_memory, mem_now)
for a0, a1 in reversed(list(lib.prange_tril(0, nvir, bufsize))):
with lib.call_in_background(contract) as async_contract:
cache_row_a = numpy.asarray(eris_vvop[a0:a1, :a1], order='C')
if a0 == 0:
cache_col_a = cache_row_a
else:
cache_col_a = numpy.asarray(eris_vvop[:a0, a0:a1], order='C')
async_contract(
a0, a1, a0, a1,
(cache_row_a, cache_col_a, cache_row_a, cache_col_a))
for b0, b1 in lib.prange_tril(0, a0, bufsize / 6):
cache_row_b = numpy.asarray(eris_vvop[b0:b1, :b1], order='C')
if b0 == 0:
cache_col_b = cache_row_b
else:
cache_col_b = numpy.asarray(eris_vvop[:b0, b0:b1],
order='C')
async_contract(
a0, a1, b0, b1,
(cache_row_a, cache_col_a, cache_row_b, cache_col_b))
cache_row_b = cache_col_b = None
cache_row_a = cache_col_a = None
t2[:] = ftmp['t2']
ftmp.close()
_tmpfile = None
et = et_sum[0] * 2
log.timer('CCSD(T)', *cpu0)
log.note('CCSD(T) correction = %.15g', et)
return et
def dump_flags(self, verbose=None):
log = logger.new_logger(self, verbose)
hf.RHF.dump_flags(self, log)
log.info('atom = %s', self.mol.atom_symbol(0))
def grad_elec(mc_grad, mo_coeff=None, ci=None, atmlst=None, verbose=None):
mc = mc_grad.base
with_df = mc.with_df
if mo_coeff is None: mo_coeff = mc.mo_coeff
if ci is None: ci = mc.ci
if mc.frozen is not None:
raise NotImplementedError
time0 = time.clock(), time.time()
log = logger.new_logger(mc_grad, verbose)
mol = mc_grad.mol
auxmol = with_df.auxmol
ncore = mc.ncore
ncas = mc.ncas
nocc = ncore + ncas
nelecas = mc.nelecas
nao, nmo = mo_coeff.shape
nao_pair = nao * (nao + 1) // 2
# Necessary kludge because gfock isn't zero in occ-virt space in SA-CASSCf
# Among many other potential applications!
if hasattr(mc, '_tag_gfock_ov_nonzero'):
if mc._tag_gfock_ov_nonzero:
nocc = nmo
mo_occ = mo_coeff[:, :nocc]
mo_core = mo_coeff[:, :ncore]
mo_cas = mo_coeff[:, ncore:ncore + ncas]
casdm1, casdm2 = mc.fcisolver.make_rdm12(ci, ncas, nelecas)
# gfock = Generalized Fock, Adv. Chem. Phys., 69, 63
dm_core = numpy.dot(mo_core, mo_core.T) * 2
dm_cas = reduce(numpy.dot, (mo_cas, casdm1, mo_cas.T))
# MRH flag: this is one of my kludges
# It would be better to just pass the ERIS object used in orbital optimization
# But I am too lazy at the moment
aapa = with_df.ao2mo((mo_cas, mo_cas, mo_occ, mo_cas), compact=False)
aapa = aapa.reshape(ncas, ncas, nocc, ncas)
vj, vk = mc._scf.get_jk(mol, (dm_core, dm_cas))
h1 = mc.get_hcore()
vhf_c = vj[0] - vk[0] * .5
vhf_a = vj[1] - vk[1] * .5
gfock = numpy.zeros((nocc, nocc))
gfock[:, :ncore] = reduce(numpy.dot,
(mo_occ.T, h1 + vhf_c + vhf_a, mo_core)) * 2
gfock[:,
ncore:ncore + ncas] = reduce(numpy.dot,
(mo_occ.T, h1 + vhf_c, mo_cas, casdm1))
gfock[:, ncore:ncore + ncas] += numpy.einsum('uviw,vuwt->it', aapa, casdm2)
dme0 = reduce(numpy.dot, (mo_occ, (gfock + gfock.T) * .5, mo_occ.T))
aapa = vj = vk = vhf_c = vhf_a = h1 = gfock = None
dm1 = dm_core + dm_cas
vj, vk = mc_grad.get_jk(mol, (dm_core, dm_cas))
vhf1c, vhf1a = vj - vk * .5
hcore_deriv = mc_grad.hcore_generator(mol)
s1 = mc_grad.get_ovlp(mol)
dfcasdm2 = casdm2 = solve_df_rdm2(mc_grad, mo_cas=mo_cas, casdm2=casdm2)
if atmlst is None:
atmlst = range(mol.natm)
aoslices = mol.aoslice_by_atom()
de = grad_elec_dferi(mc_grad,
mo_cas=mo_cas,
dfcasdm2=dfcasdm2,
atmlst=atmlst,
max_memory=mc_grad.max_memory)[0]
if mc_grad.auxbasis_response:
de_aux = vj.aux - vk.aux * .5
de_aux = de_aux.sum((0, 1)) - de_aux[1, 1]
de_aux += grad_elec_auxresponse_dferi(mc_grad,
mo_cas=mo_cas,
dfcasdm2=dfcasdm2,
atmlst=atmlst,
max_memory=mc_grad.max_memory)[0]
de += de_aux
dfcasdm2 = casdm2 = None
for k, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = aoslices[ia]
h1ao = hcore_deriv(ia)
de[k] += numpy.einsum('xij,ij->x', h1ao, dm1)
de[k] -= numpy.einsum('xij,ij->x', s1[:, p0:p1], dme0[p0:p1]) * 2
de[k] += numpy.einsum('xij,ij->x', vhf1c[:, p0:p1], dm1[p0:p1]) * 2
de[k] += numpy.einsum('xij,ij->x', vhf1a[:, p0:p1], dm_core[p0:p1]) * 2
log.timer('CASSCF nuclear gradients', *time0)
return de
def _make_eris(mp, mo_coeff=None, ao2mofn=None, verbose=None):
log = logger.new_logger(mp, verbose)
time0 = (time.clock(), time.time())
eris = _ChemistsERIs(mp, mo_coeff)
nocca, noccb = mp.get_nocc()
nmoa, nmob = mp.get_nmo()
nvira, nvirb = nmoa - nocca, nmob - noccb
nao = eris.mo_coeff[0].shape[0]
nmo_pair = nmoa * (nmoa + 1) // 2
nao_pair = nao * (nao + 1) // 2
mem_incore = (nao_pair**2 + nmo_pair**2) * 8 / 1e6
mem_now = lib.current_memory()[0]
max_memory = max(0, mp.max_memory - mem_now)
moa = eris.mo_coeff[0]
mob = eris.mo_coeff[1]
orboa = moa[:, :nocca]
orbob = mob[:, :noccb]
orbva = moa[:, nocca:]
orbvb = mob[:, noccb:]
if (mp.mol.incore_anyway or
(mp._scf._eri is not None and mem_incore + mem_now < mp.max_memory)):
log.debug('transform (ia|jb) incore')
if callable(ao2mofn):
eris.ovov = ao2mofn(
(orboa, orbva, orboa, orbva)).reshape(nocca * nvira,
nocca * nvira)
eris.ovOV = ao2mofn(
(orboa, orbva, orbob, orbvb)).reshape(nocca * nvira,
noccb * nvirb)
eris.OVOV = ao2mofn(
(orbob, orbvb, orbob, orbvb)).reshape(noccb * nvirb,
noccb * nvirb)
else:
eris.ovov = ao2mo.general(mp._scf._eri,
(orboa, orbva, orboa, orbva))
eris.ovOV = ao2mo.general(mp._scf._eri,
(orboa, orbva, orbob, orbvb))
eris.OVOV = ao2mo.general(mp._scf._eri,
(orbob, orbvb, orbob, orbvb))
elif hasattr(mp._scf, 'with_df'):
logger.warn(
mp, 'UMP2 detected DF being used in the HF object. '
'MO integrals are computed based on the DF 3-index tensors.\n'
'It\'s recommended to use DF-UMP2 module.')
log.debug('transform (ia|jb) with_df')
eris.ovov = mp._scf.with_df.ao2mo((orboa, orbva, orboa, orbva))
eris.ovOV = mp._scf.with_df.ao2mo((orboa, orbva, orbob, orbvb))
eris.OVOV = mp._scf.with_df.ao2mo((orbob, orbvb, orbob, orbvb))
else:
log.debug('transform (ia|jb) outcore')
eris.feri = lib.H5TmpFile()
_ao2mo_ovov(mp, (orboa, orbva, orbob, orbvb), eris.feri,
max(2000, max_memory), log)
eris.ovov = eris.feri['ovov']
eris.ovOV = eris.feri['ovOV']
eris.OVOV = eris.feri['OVOV']
time1 = log.timer('Integral transformation', *time0)
return eris
def grad_elec(mc_grad, mo_coeff=None, ci=None, atmlst=None, verbose=None):
mc = mc_grad.base
if mo_coeff is None: mo_coeff = mc._scf.mo_coeff
if ci is None: ci = mc.ci
time0 = time.clock(), time.time()
log = logger.new_logger(mc_grad, verbose)
mol = mc_grad.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_energy = mc._scf.mo_energy
mo_occ = mo_coeff[:, :nocc]
mo_core = mo_coeff[:, :ncore]
mo_cas = mo_coeff[:, ncore:nocc]
neleca, nelecb = mol.nelec
assert (neleca == nelecb)
orbo = mo_coeff[:, :neleca]
orbv = mo_coeff[:, neleca:]
casdm1, casdm2 = mc.fcisolver.make_rdm12(ci, ncas, nelecas)
dm_core = numpy.dot(mo_core, mo_core.T) * 2
dm_cas = reduce(numpy.dot, (mo_cas, casdm1, mo_cas.T))
aapa = ao2mo.kernel(mol, (mo_cas, mo_cas, mo_coeff, mo_cas), compact=False)
aapa = aapa.reshape(ncas, ncas, nmo, ncas)
vj, vk = mc._scf.get_jk(mol, (dm_core, dm_cas))
h1 = mc.get_hcore()
vhf_c = vj[0] - vk[0] * .5
vhf_a = vj[1] - vk[1] * .5
# Imat = h1_{pi} gamma1_{iq} + h2_{pijk} gamma_{iqkj}
Imat = numpy.zeros((nmo, nmo))
Imat[:, :nocc] = reduce(numpy.dot,
(mo_coeff.T, h1 + vhf_c + vhf_a, mo_occ)) * 2
Imat[:, ncore:nocc] = reduce(numpy.dot,
(mo_coeff.T, h1 + vhf_c, mo_cas, casdm1))
Imat[:, ncore:nocc] += lib.einsum('uviw,vuwt->it', aapa, casdm2)
aapa = vj = vk = vhf_c = vhf_a = h1 = None
ee = mo_energy[:, None] - mo_energy
zvec = numpy.zeros_like(Imat)
zvec[:ncore,
ncore:neleca] = Imat[:ncore, ncore:neleca] / -ee[:ncore, ncore:neleca]
zvec[ncore:neleca, :ncore] = Imat[
ncore:neleca, :ncore] / -ee[ncore:neleca, :ncore]
zvec[nocc:,
neleca:nocc] = Imat[nocc:, neleca:nocc] / -ee[nocc:, neleca:nocc]
zvec[neleca:nocc,
nocc:] = Imat[neleca:nocc, nocc:] / -ee[neleca:nocc, nocc:]
zvec_ao = reduce(numpy.dot, (mo_coeff, zvec + zvec.T, mo_coeff.T))
vhf = mc._scf.get_veff(mol, zvec_ao) * 2
xvo = reduce(numpy.dot, (orbv.T, vhf, orbo))
xvo += Imat[neleca:, :neleca] - Imat[:neleca, neleca:].T
def fvind(x):
x = x.reshape(xvo.shape)
dm = reduce(numpy.dot, (orbv, x, orbo.T))
v = mc._scf.get_veff(mol, dm + dm.T)
v = reduce(numpy.dot, (orbv.T, v, orbo))
return v * 2
dm1resp = cphf.solve(fvind, mo_energy, mc._scf.mo_occ, xvo,
max_cycle=30)[0]
zvec[neleca:, :neleca] = dm1resp
zeta = numpy.einsum('ij,j->ij', zvec, mo_energy)
zeta = reduce(numpy.dot, (mo_coeff, zeta, mo_coeff.T))
zvec_ao = reduce(numpy.dot, (mo_coeff, zvec + zvec.T, mo_coeff.T))
p1 = numpy.dot(mo_coeff[:, :neleca], mo_coeff[:, :neleca].T)
vhf_s1occ = reduce(numpy.dot, (p1, mc._scf.get_veff(mol, zvec_ao), p1))
Imat[:ncore, ncore:neleca] = 0
Imat[ncore:neleca, :ncore] = 0
Imat[nocc:, neleca:nocc] = 0
Imat[neleca:nocc, nocc:] = 0
Imat[neleca:, :neleca] = Imat[:neleca, neleca:].T
im1 = reduce(numpy.dot, (mo_coeff, Imat, mo_coeff.T))
casci_dm1 = dm_core + dm_cas
hf_dm1 = mc._scf.make_rdm1(mo_coeff, mc._scf.mo_occ)
hcore_deriv = mc_grad.hcore_generator(mol)
s1 = mc_grad.get_ovlp(mol)
diag_idx = numpy.arange(nao)
diag_idx = diag_idx * (diag_idx + 1) // 2 + diag_idx
casdm2_cc = casdm2 + casdm2.transpose(0, 1, 3, 2)
dm2buf = ao2mo._ao2mo.nr_e2(casdm2_cc.reshape(ncas**2, ncas**2), mo_cas.T,
(0, nao, 0, nao)).reshape(ncas**2, nao, nao)
dm2buf = lib.pack_tril(dm2buf)
dm2buf[:, diag_idx] *= .5
dm2buf = dm2buf.reshape(ncas, ncas, nao_pair)
casdm2 = casdm2_cc = None
if atmlst is None:
atmlst = range(mol.natm)
aoslices = mol.aoslice_by_atom()
de = numpy.zeros((len(atmlst), 3))
max_memory = mc_grad.max_memory - lib.current_memory()[0]
blksize = int(max_memory * .9e6 / 8 /
((aoslices[:, 3] - aoslices[:, 2]).max() * nao_pair))
blksize = min(nao, max(2, blksize))
for k, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = aoslices[ia]
h1ao = hcore_deriv(ia)
de[k] += numpy.einsum('xij,ij->x', h1ao, casci_dm1)
de[k] += numpy.einsum('xij,ij->x', h1ao, zvec_ao)
vhf1 = numpy.zeros((3, nao, nao))
q1 = 0
for b0, b1, nf in _shell_prange(mol, 0, mol.nbas, blksize):
q0, q1 = q1, q1 + nf
dm2_ao = lib.einsum('ijw,pi,qj->pqw', dm2buf, mo_cas[p0:p1],
mo_cas[q0:q1])
shls_slice = (shl0, shl1, b0, b1, 0, mol.nbas, 0, mol.nbas)
eri1 = mol.intor('int2e_ip1',
comp=3,
aosym='s2kl',
shls_slice=shls_slice).reshape(
3, p1 - p0, nf, nao_pair)
de[k] -= numpy.einsum('xijw,ijw->x', eri1, dm2_ao) * 2
for i in range(3):
eri1tmp = lib.unpack_tril(eri1[i].reshape((p1 - p0) * nf, -1))
eri1tmp = eri1tmp.reshape(p1 - p0, nf, nao, nao)
de[k, i] -= numpy.einsum('ijkl,ij,kl', eri1tmp,
hf_dm1[p0:p1, q0:q1], zvec_ao) * 2
de[k, i] -= numpy.einsum('ijkl,kl,ij', eri1tmp, hf_dm1,
zvec_ao[p0:p1, q0:q1]) * 2
de[k, i] += numpy.einsum('ijkl,il,kj', eri1tmp, hf_dm1[p0:p1],
zvec_ao[q0:q1])
de[k, i] += numpy.einsum('ijkl,jk,il', eri1tmp, hf_dm1[q0:q1],
zvec_ao[p0:p1])
#:vhf1c, vhf1a = mc_grad.get_veff(mol, (dm_core, dm_cas))
#:de[k] += numpy.einsum('xij,ij->x', vhf1c[:,p0:p1], casci_dm1[p0:p1]) * 2
#:de[k] += numpy.einsum('xij,ij->x', vhf1a[:,p0:p1], dm_core[p0:p1]) * 2
de[k, i] -= numpy.einsum('ijkl,lk,ij', eri1tmp, dm_core[q0:q1],
casci_dm1[p0:p1]) * 2
de[k, i] += numpy.einsum('ijkl,jk,il', eri1tmp, dm_core[q0:q1],
casci_dm1[p0:p1])
de[k, i] -= numpy.einsum('ijkl,lk,ij', eri1tmp, dm_cas[q0:q1],
dm_core[p0:p1]) * 2
de[k, i] += numpy.einsum('ijkl,jk,il', eri1tmp, dm_cas[q0:q1],
dm_core[p0:p1])
eri1 = eri1tmp = None
de[k] -= numpy.einsum('xij,ij->x', s1[:, p0:p1], im1[p0:p1])
de[k] -= numpy.einsum('xij,ji->x', s1[:, p0:p1], im1[:, p0:p1])
de[k] -= numpy.einsum('xij,ij->x', s1[:, p0:p1], zeta[p0:p1]) * 2
de[k] -= numpy.einsum('xij,ji->x', s1[:, p0:p1], zeta[:, p0:p1]) * 2
de[k] -= numpy.einsum('xij,ij->x', s1[:, p0:p1], vhf_s1occ[p0:p1]) * 2
de[k] -= numpy.einsum('xij,ji->x', s1[:, p0:p1], vhf_s1occ[:,
p0:p1]) * 2
log.timer('CASCI nuclear gradients', *time0)
return de
def grad_elec(td_grad, x_y, singlet=True, atmlst=None,
max_memory=2000, verbose=logger.INFO):
'''
Electronic part of TDA, TDDFT nuclear gradients
Args:
td_grad : grad.tdrhf.Gradients or grad.tdrks.Gradients object.
x_y : a two-element list of numpy arrays
TDDFT X and Y amplitudes. If Y is set to 0, this function computes
TDA energy gradients.
'''
log = logger.new_logger(td_grad, verbose)
time0 = time.clock(), time.time()
mol = td_grad.mol
mf = td_grad.base._scf
mo_coeff = mf.mo_coeff
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
nao, nmo = mo_coeff.shape
nocc = (mo_occ>0).sum()
nvir = nmo - nocc
x, y = x_y
xpy = (x+y).reshape(nocc,nvir).T
xmy = (x-y).reshape(nocc,nvir).T
orbv = mo_coeff[:,nocc:]
orbo = mo_coeff[:,:nocc]
dvv = numpy.einsum('ai,bi->ab', xpy, xpy) + numpy.einsum('ai,bi->ab', xmy, xmy)
doo =-numpy.einsum('ai,aj->ij', xpy, xpy) - numpy.einsum('ai,aj->ij', xmy, xmy)
dmxpy = reduce(numpy.dot, (orbv, xpy, orbo.T))
dmxmy = reduce(numpy.dot, (orbv, xmy, orbo.T))
dmzoo = reduce(numpy.dot, (orbo, doo, orbo.T))
dmzoo+= reduce(numpy.dot, (orbv, dvv, orbv.T))
mem_now = lib.current_memory()[0]
max_memory = max(2000, td_grad.max_memory*.9-mem_now)
ni = mf._numint
ni.libxc.test_deriv_order(mf.xc, 3, raise_error=True)
omega, alpha, hyb = ni.rsh_and_hybrid_coeff(mf.xc, mol.spin)
# dm0 = mf.make_rdm1(mo_coeff, mo_occ), but it is not used when computing
# fxc since rho0 is passed to fxc function.
dm0 = None
rho0, vxc, fxc = ni.cache_xc_kernel(mf.mol, mf.grids, mf.xc,
[mo_coeff]*2, [mo_occ*.5]*2, spin=1)
f1vo, f1oo, vxc1, k1ao = \
_contract_xc_kernel(td_grad, mf.xc, dmxpy,
dmzoo, True, True, singlet, max_memory)
if abs(hyb) > 1e-10:
dm = (dmzoo, dmxpy+dmxpy.T, dmxmy-dmxmy.T)
vj, vk = mf.get_jk(mol, dm, hermi=0)
vk *= hyb
if abs(omega) > 1e-10:
vk += mf.get_k(mol, dm, hermi=0, omega=omega) * (alpha-hyb)
veff0doo = vj[0] * 2 - vk[0] + f1oo[0] + k1ao[0] * 2
wvo = reduce(numpy.dot, (orbv.T, veff0doo, orbo)) * 2
if singlet:
veff = vj[1] * 2 - vk[1] + f1vo[0] * 2
else:
veff = -vk[1] + f1vo[0] * 2
veff0mop = reduce(numpy.dot, (mo_coeff.T, veff, mo_coeff))
wvo -= numpy.einsum('ki,ai->ak', veff0mop[:nocc,:nocc], xpy) * 2
wvo += numpy.einsum('ac,ai->ci', veff0mop[nocc:,nocc:], xpy) * 2
veff = -vk[2]
veff0mom = reduce(numpy.dot, (mo_coeff.T, veff, mo_coeff))
wvo -= numpy.einsum('ki,ai->ak', veff0mom[:nocc,:nocc], xmy) * 2
wvo += numpy.einsum('ac,ai->ci', veff0mom[nocc:,nocc:], xmy) * 2
else:
vj = mf.get_j(mol, (dmzoo, dmxpy+dmxpy.T), hermi=1)
veff0doo = vj[0] * 2 + f1oo[0] + k1ao[0] * 2
wvo = reduce(numpy.dot, (orbv.T, veff0doo, orbo)) * 2
if singlet:
veff = vj[1] * 2 + f1vo[0] * 2
else:
veff = f1vo[0] * 2
veff0mop = reduce(numpy.dot, (mo_coeff.T, veff, mo_coeff))
wvo -= numpy.einsum('ki,ai->ak', veff0mop[:nocc,:nocc], xpy) * 2
wvo += numpy.einsum('ac,ai->ci', veff0mop[nocc:,nocc:], xpy) * 2
veff0mom = numpy.zeros((nmo,nmo))
# set singlet=None, generate function for CPHF type response kernel
vresp = mf.gen_response(singlet=None, hermi=1)
def fvind(x):
dm = reduce(numpy.dot, (orbv, x.reshape(nvir,nocc)*2, orbo.T))
v1ao = vresp(dm+dm.T)
return reduce(numpy.dot, (orbv.T, v1ao, orbo)).ravel()
z1 = cphf.solve(fvind, mo_energy, mo_occ, wvo,
max_cycle=td_grad.cphf_max_cycle,
tol=td_grad.cphf_conv_tol)[0]
z1 = z1.reshape(nvir,nocc)
time1 = log.timer('Z-vector using CPHF solver', *time0)
z1ao = reduce(numpy.dot, (orbv, z1, orbo.T))
veff = vresp(z1ao+z1ao.T)
im0 = numpy.zeros((nmo,nmo))
im0[:nocc,:nocc] = reduce(numpy.dot, (orbo.T, veff0doo+veff, orbo))
im0[:nocc,:nocc]+= numpy.einsum('ak,ai->ki', veff0mop[nocc:,:nocc], xpy)
im0[:nocc,:nocc]+= numpy.einsum('ak,ai->ki', veff0mom[nocc:,:nocc], xmy)
im0[nocc:,nocc:] = numpy.einsum('ci,ai->ac', veff0mop[nocc:,:nocc], xpy)
im0[nocc:,nocc:]+= numpy.einsum('ci,ai->ac', veff0mom[nocc:,:nocc], xmy)
im0[nocc:,:nocc] = numpy.einsum('ki,ai->ak', veff0mop[:nocc,:nocc], xpy)*2
im0[nocc:,:nocc]+= numpy.einsum('ki,ai->ak', veff0mom[:nocc,:nocc], xmy)*2
zeta = lib.direct_sum('i+j->ij', mo_energy, mo_energy) * .5
zeta[nocc:,:nocc] = mo_energy[:nocc]
zeta[:nocc,nocc:] = mo_energy[nocc:]
dm1 = numpy.zeros((nmo,nmo))
dm1[:nocc,:nocc] = doo
dm1[nocc:,nocc:] = dvv
dm1[nocc:,:nocc] = z1
dm1[:nocc,:nocc] += numpy.eye(nocc)*2 # for ground state
im0 = reduce(numpy.dot, (mo_coeff, im0+zeta*dm1, mo_coeff.T))
# Initialize hcore_deriv with the underlying SCF object because some
# extensions (e.g. QM/MM, solvent) modifies the SCF object only.
mf_grad = td_grad.base._scf.nuc_grad_method()
hcore_deriv = mf_grad.hcore_generator(mol)
s1 = mf_grad.get_ovlp(mol)
dmz1doo = z1ao + dmzoo
oo0 = reduce(numpy.dot, (orbo, orbo.T))
if abs(hyb) > 1e-10:
dm = (oo0, dmz1doo+dmz1doo.T, dmxpy+dmxpy.T, dmxmy-dmxmy.T)
vj, vk = td_grad.get_jk(mol, dm)
vk *= hyb
if abs(omega) > 1e-10:
with mol.with_range_coulomb(omega):
vk += td_grad.get_k(mol, dm) * (alpha-hyb)
vj = vj.reshape(-1,3,nao,nao)
vk = vk.reshape(-1,3,nao,nao)
if singlet:
veff1 = vj * 2 - vk
else:
veff1 = numpy.vstack((vj[:2]*2-vk[:2], -vk[2:]))
else:
vj = td_grad.get_j(mol, (oo0, dmz1doo+dmz1doo.T, dmxpy+dmxpy.T))
vj = vj.reshape(-1,3,nao,nao)
veff1 = numpy.zeros((4,3,nao,nao))
if singlet:
veff1[:3] = vj * 2
else:
veff1[:2] = vj[:2] * 2
fxcz1 = _contract_xc_kernel(td_grad, mf.xc, z1ao, None,
False, False, True, max_memory)[0]
veff1[0] += vxc1[1:]
veff1[1] +=(f1oo[1:] + fxcz1[1:] + k1ao[1:]*2)*2 # *2 for dmz1doo+dmz1oo.T
veff1[2] += f1vo[1:] * 2
time1 = log.timer('2e AO integral derivatives', *time1)
if atmlst is None:
atmlst = range(mol.natm)
offsetdic = mol.offset_nr_by_atom()
de = numpy.zeros((len(atmlst),3))
for k, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = offsetdic[ia]
# Ground state gradients
h1ao = hcore_deriv(ia)
h1ao[:,p0:p1] += veff1[0,:,p0:p1]
h1ao[:,:,p0:p1] += veff1[0,:,p0:p1].transpose(0,2,1)
# oo0*2 for doubly occupied orbitals
e1 = numpy.einsum('xpq,pq->x', h1ao, oo0) * 2
e1 += numpy.einsum('xpq,pq->x', h1ao, dmz1doo)
e1 -= numpy.einsum('xpq,pq->x', s1[:,p0:p1], im0[p0:p1])
e1 -= numpy.einsum('xqp,pq->x', s1[:,p0:p1], im0[:,p0:p1])
e1 += numpy.einsum('xij,ij->x', veff1[1,:,p0:p1], oo0[p0:p1])
e1 += numpy.einsum('xij,ij->x', veff1[2,:,p0:p1], dmxpy[p0:p1,:]) * 2
e1 += numpy.einsum('xij,ij->x', veff1[3,:,p0:p1], dmxmy[p0:p1,:]) * 2
e1 += numpy.einsum('xji,ij->x', veff1[2,:,p0:p1], dmxpy[:,p0:p1]) * 2
e1 -= numpy.einsum('xji,ij->x', veff1[3,:,p0:p1], dmxmy[:,p0:p1]) * 2
de[k] = e1
log.timer('TDDFT nuclear gradients', *time0)
return de
def _ao2mo_ovov(mp, orbo, orbv, feri, max_memory=2000, verbose=None):
time0 = (time.clock(), time.time())
log = logger.new_logger(mp, verbose)
mol = mp.mol
int2e = mol._add_suffix('int2e')
ao2mopt = _ao2mo.AO2MOpt(mol, int2e, 'CVHFnr_schwarz_cond',
'CVHFsetnr_direct_scf')
nao, nocc = orbo.shape
nvir = orbv.shape[1]
nbas = mol.nbas
assert (nvir <= nao)
ao_loc = mol.ao_loc_nr()
dmax = max(
4, min(nao / 3, numpy.sqrt(max_memory * .95e6 / 8 / (nao + nocc)**2)))
sh_ranges = ao2mo.outcore.balance_partition(ao_loc, dmax)
dmax = max(x[2] for x in sh_ranges)
eribuf = numpy.empty((nao, dmax, dmax, nao))
ftmp = lib.H5TmpFile()
log.debug('max_memory %s MB (dmax = %s) required disk space %g MB',
max_memory, dmax,
nocc**2 * (nao * (nao + dmax) / 2 + nvir**2) * 8 / 1e6)
buf_i = numpy.empty((nocc * dmax**2 * nao))
buf_li = numpy.empty((nocc**2 * dmax**2))
buf1 = numpy.empty_like(buf_li)
fint = gto.moleintor.getints4c
jk_blk_slices = []
count = 0
time1 = time0
with lib.call_in_background(ftmp.__setitem__) as save:
for ip, (ish0, ish1, ni) in enumerate(sh_ranges):
for jsh0, jsh1, nj in sh_ranges[:ip + 1]:
i0, i1 = ao_loc[ish0], ao_loc[ish1]
j0, j1 = ao_loc[jsh0], ao_loc[jsh1]
jk_blk_slices.append((i0, i1, j0, j1))
eri = fint(int2e,
mol._atm,
mol._bas,
mol._env,
shls_slice=(0, nbas, ish0, ish1, jsh0, jsh1, 0,
nbas),
aosym='s1',
ao_loc=ao_loc,
cintopt=ao2mopt._cintopt,
out=eribuf)
tmp_i = numpy.ndarray((nocc, (i1 - i0) * (j1 - j0) * nao),
buffer=buf_i)
tmp_li = numpy.ndarray((nocc, nocc * (i1 - i0) * (j1 - j0)),
buffer=buf_li)
lib.ddot(orbo.T,
eri.reshape(nao, (i1 - i0) * (j1 - j0) * nao),
c=tmp_i)
lib.ddot(orbo.T,
tmp_i.reshape(nocc * (i1 - i0) * (j1 - j0), nao).T,
c=tmp_li)
tmp_li = tmp_li.reshape(nocc, nocc, (i1 - i0), (j1 - j0))
save(str(count), tmp_li.transpose(1, 0, 2, 3))
buf_li, buf1 = buf1, buf_li
count += 1
time1 = log.timer_debug1(
'partial ao2mo [%d:%d,%d:%d]' % (ish0, ish1, jsh0, jsh1),
*time1)
time1 = time0 = log.timer('mp2 ao2mo_ovov pass1', *time0)
eri = eribuf = tmp_i = tmp_li = buf_i = buf_li = buf1 = None
h5dat = feri.create_dataset('ovov', (nocc * nvir, nocc * nvir),
'f8',
chunks=(nvir, nvir))
occblk = int(
min(nocc,
max(4, 250 / nocc, max_memory * .9e6 / 8 / (nao**2 * nocc) / 5)))
def load(i0, eri):
if i0 < nocc:
i1 = min(i0 + occblk, nocc)
for k, (p0, p1, q0, q1) in enumerate(jk_blk_slices):
eri[:i1 - i0, :, p0:p1, q0:q1] = ftmp[str(k)][i0:i1]
if p0 != q0:
dat = numpy.asarray(ftmp[str(k)][:, i0:i1])
eri[:i1 - i0, :, q0:q1, p0:p1] = dat.transpose(1, 0, 3, 2)
def save(i0, i1, dat):
for i in range(i0, i1):
h5dat[i * nvir:(i + 1) * nvir] = dat[i - i0].reshape(
nvir, nocc * nvir)
orbv = numpy.asarray(orbv, order='F')
buf_prefecth = numpy.empty((occblk, nocc, nao, nao))
buf = numpy.empty_like(buf_prefecth)
bufw = numpy.empty((occblk * nocc, nvir**2))
bufw1 = numpy.empty_like(bufw)
with lib.call_in_background(load) as prefetch:
with lib.call_in_background(save) as bsave:
load(0, buf_prefecth)
for i0, i1 in lib.prange(0, nocc, occblk):
buf, buf_prefecth = buf_prefecth, buf
prefetch(i1, buf_prefecth)
eri = buf[:i1 - i0].reshape((i1 - i0) * nocc, nao, nao)
dat = _ao2mo.nr_e2(eri,
orbv, (0, nvir, 0, nvir),
's1',
's1',
out=bufw)
bsave(
i0, i1,
dat.reshape(i1 - i0, nocc, nvir,
nvir).transpose(0, 2, 1, 3))
bufw, bufw1 = bufw1, bufw
time1 = log.timer_debug1('pass2 ao2mo [%d:%d]' % (i0, i1),
*time1)
time0 = log.timer('mp2 ao2mo_ovov pass2', *time0)
return h5dat
def get_nto(tdobj, state=1, threshold=OUTPUT_THRESHOLD, verbose=None):
r'''
Natural transition orbital analysis.
The natural transition density matrix between ground state and excited
state :math:`Tia = \langle \Psi_{ex} | i a^\dagger | \Psi_0 \rangle` can
be transformed to diagonal form through SVD
:math:`T = O \sqrt{\lambda} V^\dagger`. O and V are occupied and virtual
natural transition orbitals. The diagonal elements :math:`\lambda` are the
weights of the occupied-virtual orbital pair in the excitation.
Ref: Martin, R. L., JCP, 118, 4775-4777
Note in the TDHF/TDDFT calculations, the excitation part (X) is
interpreted as the CIS coefficients and normalized to 1. The de-excitation
part (Y) is ignored.
Args:
tdobj : TDA, or TDHF, or TDDFT object
state : int
Excited state ID. state = 1 means the first excited state.
If state < 0, state ID is counted from the last excited state.
Kwargs:
threshold : float
Above which the NTO coefficients will be printed in the output.
Returns:
A list (weights, NTOs). NTOs are natural orbitals represented in AO
basis. The first N_occ NTOs are occupied NTOs and the rest are virtual
NTOs.
'''
if state == 0:
logger.warn(
tdobj, 'Excited state starts from 1. '
'Set state=1 for first excited state.')
state_id = state
elif state < 0:
state_id = state
else:
state_id = state - 1
mol = tdobj.mol
mo_coeff = tdobj._scf.mo_coeff
mo_occ = tdobj._scf.mo_occ
orbo = mo_coeff[:, mo_occ == 2]
orbv = mo_coeff[:, mo_occ == 0]
nocc = orbo.shape[1]
nvir = orbv.shape[1]
cis_t1 = tdobj.xy[state_id][0]
# TDDFT (X,Y) has X^2-Y^2=1.
# Renormalizing X (X^2=1) to map it to CIS coefficients
cis_t1 *= 1. / numpy.linalg.norm(cis_t1)
# TODO: Comparing to the NTOs defined in JCP, 142, 244103. JCP, 142, 244103
# provides a method to incorporate the Y matrix in the transition density
# matrix. However, it may break the point group symmetry of the NTO orbitals
# when the system has degenerated irreducible representations.
if mol.symmetry:
orbsym = hf_symm.get_orbsym(mol, mo_coeff)
orbsym_in_d2h = numpy.asarray(orbsym) % 10 # convert to D2h irreps
o_sym = orbsym_in_d2h[mo_occ == 2]
v_sym = orbsym_in_d2h[mo_occ == 0]
nto_o = numpy.eye(nocc)
nto_v = numpy.eye(nvir)
weights_o = numpy.zeros(nocc)
weights_v = numpy.zeros(nvir)
for ir in set(orbsym_in_d2h):
idx = numpy.where(o_sym == ir)[0]
if idx.size > 0:
dm_oo = numpy.dot(cis_t1[idx], cis_t1[idx].T)
weights_o[idx], nto_o[idx[:, None],
idx] = numpy.linalg.eigh(dm_oo)
idx = numpy.where(v_sym == ir)[0]
if idx.size > 0:
dm_vv = numpy.dot(cis_t1[:, idx].T, cis_t1[:, idx])
weights_v[idx], nto_v[idx[:, None],
idx] = numpy.linalg.eigh(dm_vv)
# weights in descending order
idx = numpy.argsort(-weights_o)
weights_o = weights_o[idx]
nto_o = nto_o[:, idx]
o_sym = o_sym[idx]
idx = numpy.argsort(-weights_v)
weights_v = weights_v[idx]
nto_v = nto_v[:, idx]
v_sym = v_sym[idx]
nto_orbsym = numpy.hstack((o_sym, v_sym))
if nocc < nvir:
weights = weights_o
else:
weights = weights_v
else:
nto_o, w, nto_vT = numpy.linalg.svd(cis_t1)
nto_v = nto_vT.conj().T
weights = w**2
nto_orbsym = None
idx = numpy.argmax(abs(nto_o.real), axis=0)
nto_o[:, nto_o[idx, numpy.arange(nocc)].real < 0] *= -1
idx = numpy.argmax(abs(nto_v.real), axis=0)
nto_v[:, nto_v[idx, numpy.arange(nvir)].real < 0] *= -1
occupied_nto = numpy.dot(orbo, nto_o)
virtual_nto = numpy.dot(orbv, nto_v)
nto_coeff = numpy.hstack((occupied_nto, virtual_nto))
if mol.symmetry:
nto_coeff = lib.tag_array(nto_coeff, orbsym=nto_orbsym)
log = logger.new_logger(tdobj, verbose)
if log.verbose >= logger.INFO:
log.info('State %d: %g eV NTO largest component %s', state_id + 1,
tdobj.e[state_id] * nist.HARTREE2EV, weights[0])
o_idx = numpy.where(abs(nto_o[:, 0]) > threshold)[0]
v_idx = numpy.where(abs(nto_v[:, 0]) > threshold)[0]
fmt = '%' + str(lib.param.OUTPUT_DIGITS) + 'f (MO #%d)'
log.info(' occ-NTO: ' + ' + '.join([(fmt %
(nto_o[i, 0], i + MO_BASE))
for i in o_idx]))
log.info(' vir-NTO: ' +
' + '.join([(fmt % (nto_v[i, 0], i + MO_BASE + nocc))
for i in v_idx]))
return weights, nto_coeff
def rotate_orb_cc(mf, mo_coeff, mo_occ, fock_ao, h1e,
conv_tol_grad=None, max_stepsize=None, verbose=None):
log = logger.new_logger(mf, verbose)
if conv_tol_grad is None:
conv_tol_grad = numpy.sqrt(mf.conv_tol*.1)
#TODO: dynamically adjust max_stepsize, as done in mc1step.py
t2m = (time.clock(), time.time())
g_orb, h_op, h_diag = mf.gen_g_hop(mo_coeff, mo_occ, fock_ao)
g_kf = g_orb
norm_gkf = norm_gorb = numpy.linalg.norm(g_orb)
log.debug(' |g|= %4.3g (keyframe)', norm_gorb)
t3m = log.timer('gen h_op', *t2m)
def precond(x, e):
hdiagd = h_diag-(e-mf.ah_level_shift)
hdiagd[abs(hdiagd)<1e-8] = 1e-8
x = x/hdiagd
## Because of DFT, donot norm to 1 which leads 1st DM too large.
# norm_x = numpy.linalg.norm(x)
# if norm_x < 1e-2:
# x *= 1e-2/norm_x
return x
g_op = lambda: g_orb
x0_guess = g_orb
kf_trust_region = mf.kf_trust_region
while True:
ah_conv_tol = min(norm_gorb**2, mf.ah_conv_tol)
# increase the AH accuracy when approach convergence
#ah_start_cycle = max(mf.ah_start_cycle, int(-numpy.log10(norm_gorb)))
ah_start_cycle = mf.ah_start_cycle
imic = 0
dr = 0
ukf = None
jkcount = 0
kfcount = 0
ikf = 0
dm0 = mf.make_rdm1(mo_coeff, mo_occ)
# NOTE: vhf0 cannot be computed as (fock_ao - h1e) because mf.get_fock
# may be overloaded and fock_ao != h1e + vhf0
vhf0 = mf._scf.get_veff(mf._scf.mol, dm0)
for ah_end, ihop, w, dxi, hdxi, residual, seig \
in ciah.davidson_cc(h_op, g_op, precond, x0_guess,
tol=ah_conv_tol, max_cycle=mf.ah_max_cycle,
lindep=mf.ah_lindep, verbose=log):
norm_residual = numpy.linalg.norm(residual)
ah_start_tol = min(norm_gorb*5, mf.ah_start_tol)
if (ah_end or ihop == mf.ah_max_cycle or # make sure to use the last step
((norm_residual < ah_start_tol) and (ihop >= ah_start_cycle)) or
(seig < mf.ah_lindep)):
imic += 1
dxmax = numpy.max(abs(dxi))
if dxmax > mf.max_stepsize:
scale = mf.max_stepsize / dxmax
log.debug1('... scale rotation size %g', scale)
dxi *= scale
hdxi *= scale
else:
scale = None
dr = dr + dxi
g_orb = g_orb + hdxi
norm_dr = numpy.linalg.norm(dr)
norm_gorb = numpy.linalg.norm(g_orb)
norm_dxi = numpy.linalg.norm(dxi)
log.debug(' imic %d(%d) |g|= %4.3g |dxi|= %4.3g '
'max(|x|)= %4.3g |dr|= %4.3g eig= %4.3g seig= %4.3g',
imic, ihop, norm_gorb, norm_dxi,
dxmax, norm_dr, w, seig)
max_cycle = max(mf.max_cycle_inner,
mf.max_cycle_inner-int(numpy.log(norm_gkf+1e-9)*2))
log.debug1('Set ah_start_tol %g, ah_start_cycle %d, max_cycle %d',
ah_start_tol, ah_start_cycle, max_cycle)
ikf += 1
if imic > 3 and norm_gorb > norm_gkf*mf.ah_grad_trust_region:
g_orb = g_orb - hdxi
dr -= dxi
norm_gorb = numpy.linalg.norm(g_orb)
log.debug('|g| >> keyframe, Restore previouse step')
break
elif (imic >= max_cycle or norm_gorb < conv_tol_grad*.5):
break
elif (ikf > 2 and # avoid frequent keyframe
#TODO: replace it with keyframe_scheduler
(ikf >= max(mf.kf_interval, mf.kf_interval-numpy.log(norm_dr+1e-9)) or
# Insert keyframe if the keyframe and the esitimated g_orb are too different
norm_gorb < norm_gkf/kf_trust_region)):
ikf = 0
u = mf.update_rotate_matrix(dr, mo_occ, mo_coeff=mo_coeff)
if ukf is not None:
u = mf.rotate_mo(ukf, u)
ukf = u
dr[:] = 0
mo1 = mf.rotate_mo(mo_coeff, u)
dm = mf.make_rdm1(mo1, mo_occ)
# use mf._scf.get_veff to avoid density-fit mf polluting get_veff
vhf0 = mf._scf.get_veff(mf._scf.mol, dm, dm_last=dm0, vhf_last=vhf0)
kfcount += 1
dm0 = dm
# Use API to compute fock instead of "fock=h1e+vhf0". This is because get_fock
# is the hook being overloaded in many places.
fock = mf.get_fock(h1e, vhf=vhf0)
g_kf1 = mf.get_grad(mo1, mo_occ, fock)
norm_gkf1 = numpy.linalg.norm(g_kf1)
norm_dg = numpy.linalg.norm(g_kf1-g_orb)
jkcount += 1
log.debug('Adjust keyframe g_orb to |g|= %4.3g '
'|g-correction|= %4.3g', norm_gkf1, norm_dg)
if (norm_dg < norm_gorb*mf.ah_grad_trust_region # kf not too diff
#or norm_gkf1 < norm_gkf # grad is decaying
# close to solution
or norm_gkf1 < conv_tol_grad*mf.ah_grad_trust_region):
kf_trust_region = min(max(norm_gorb/(norm_dg+1e-9), mf.kf_trust_region), 10)
log.debug1('Set kf_trust_region = %g', kf_trust_region)
g_orb = g_kf = g_kf1
norm_gorb = norm_gkf = norm_gkf1
else:
g_orb = g_orb - hdxi
dr -= dxi
norm_gorb = numpy.linalg.norm(g_orb)
log.debug('Out of trust region. Restore previouse step')
break
u = mf.update_rotate_matrix(dr, mo_occ, mo_coeff=mo_coeff)
if ukf is not None:
u = mf.rotate_mo(ukf, u)
jkcount += ihop + 1
log.debug(' tot inner=%d %d JK |g|= %4.3g |u-1|= %4.3g',
imic, jkcount, norm_gorb, numpy.linalg.norm(dr))
h_op = h_diag = None
t3m = log.timer('aug_hess in %d inner iters' % imic, *t3m)
mo_coeff, mo_occ, fock_ao = (yield u, g_kf, kfcount, jkcount)
g_kf, h_op, h_diag = mf.gen_g_hop(mo_coeff, mo_occ, fock_ao)
norm_gkf = numpy.linalg.norm(g_kf)
norm_dg = numpy.linalg.norm(g_kf-g_orb)
log.debug(' |g|= %4.3g (keyframe), |g-correction|= %4.3g',
norm_gkf, norm_dg)
kf_trust_region = min(max(norm_gorb/(norm_dg+1e-9), mf.kf_trust_region), 10)
log.debug1('Set kf_trust_region = %g', kf_trust_region)
g_orb = g_kf
norm_gorb = norm_gkf
if norm_dxi != 0:
x0_guess = dxi
else:
x0_guess = g_kf
def kernel(self, mo_coeff=None, ci0=None, verbose=None):
with_solvent = self.with_solvent
log = logger.new_logger(self)
log.info(
'\n** Self-consistently update the solvent effects for %s **',
oldCAS)
log1 = copy.copy(log)
log1.verbose -= 1 # Suppress a few output messages
def casci_iter_(ci0, log):
# self.e_tot, self.e_cas, and self.ci are updated in the call
# to oldCAS.kernel
e_tot, e_cas, ci0 = oldCAS.kernel(self, mo_coeff, ci0, log)[:3]
if isinstance(self.e_cas, (float, numpy.number)):
dm = self.make_rdm1(ci=ci0)
else:
log.debug('Computing solvent responses to DM of state %d',
with_solvent.state_id)
dm = self.make_rdm1(ci=ci0[with_solvent.state_id])
if with_solvent.e is not None:
edup = numpy.einsum('ij,ji->', with_solvent.v, dm)
self.e_tot += with_solvent.e - edup
if not with_solvent.frozen:
with_solvent.e, with_solvent.v = with_solvent.kernel(dm)
return self.e_tot, e_cas, ci0
if with_solvent.frozen:
with lib.temporary_env(self, _finalize=lambda: None):
casci_iter_(ci0, log)
log.note('Total energy with solvent effects')
self._finalize()
return self.e_tot, self.e_cas, self.ci, self.mo_coeff, self.mo_energy
self.converged = False
with lib.temporary_env(self, canonicalization=False):
e_tot = e_last = 0
for cycle in range(self.with_solvent.max_cycle):
log.info('\n** Solvent self-consistent cycle %d:', cycle)
e_tot, e_cas, ci0 = casci_iter_(ci0, log1)
de = e_tot - e_last
if isinstance(e_cas, (float, numpy.number)):
log.info(
'Sovlent cycle %d E(CASCI+solvent) = %.15g '
'dE = %g', cycle, e_tot, de)
else:
for i, e in enumerate(e_tot):
log.info(
'Solvent cycle %d CASCI root %d '
'E(CASCI+solvent) = %.15g dE = %g', cycle, i,
e, de[i])
if abs(e_tot - e_last).max() < with_solvent.conv_tol:
self.converged = True
break
e_last = e_tot
# An extra cycle to canonicalize CASCI orbitals
with lib.temporary_env(self, _finalize=lambda: None):
casci_iter_(ci0, log)
if self.converged:
log.info('self-consistent CASCI+solvent converged')
else:
log.info('self-consistent CASCI+solvent not converged')
log.note('Total energy with solvent effects')
self._finalize()
return self.e_tot, self.e_cas, self.ci, self.mo_coeff, self.mo_energy
def analyze(self, mo_coeff=None, ci=None, verbose=None,
large_ci_tol=LARGE_CI_TOL, with_meta_lowdin=WITH_META_LOWDIN,
**kwargs):
from pyscf.lo import orth
from pyscf.tools import dump_mat
if mo_coeff is None: mo_coeff = self.mo_coeff
if ci is None: ci = self.ci
log = logger.new_logger(self, verbose)
nelecas = self.nelecas
ncas = self.ncas
ncore = self.ncore
mocore_a = mo_coeff[0][:,:ncore[0]]
mocas_a = mo_coeff[0][:,ncore[0]:ncore[0]+ncas]
mocore_b = mo_coeff[1][:,:ncore[1]]
mocas_b = mo_coeff[1][:,ncore[1]:ncore[1]+ncas]
label = self.mol.ao_labels()
if (isinstance(ci, (list, tuple, RANGE_TYPE)) and
not isinstance(self.fcisolver, addons.StateAverageFCISolver)):
log.warn('Mulitple states found in UCASCI solver. Density '
'matrix of first state is generated in .analyze() function.')
civec = ci[0]
else:
civec = ci
casdm1a, casdm1b = self.fcisolver.make_rdm1s(civec, ncas, nelecas)
dm1a = numpy.dot(mocore_a, mocore_a.T)
dm1a += reduce(numpy.dot, (mocas_a, casdm1a, mocas_a.T))
dm1b = numpy.dot(mocore_b, mocore_b.T)
dm1b += reduce(numpy.dot, (mocas_b, casdm1b, mocas_b.T))
if log.verbose >= logger.DEBUG2:
log.debug2('alpha density matrix (on AO)')
dump_mat.dump_tri(self.stdout, dm1a, label)
log.debug2('beta density matrix (on AO)')
dump_mat.dump_tri(self.stdout, dm1b, label)
if log.verbose >= logger.INFO:
ovlp_ao = self._scf.get_ovlp()
occa, ucasa = self._eig(-casdm1a, ncore[0], ncore[0]+ncas)
occb, ucasb = self._eig(-casdm1b, ncore[1], ncore[1]+ncas)
log.info('Natural alpha-occupancy %s', str(-occa))
log.info('Natural beta-occupancy %s', str(-occb))
mocas_a = numpy.dot(mocas_a, ucasa)
mocas_b = numpy.dot(mocas_b, ucasb)
if with_meta_lowdin:
orth_coeff = orth.orth_ao(self.mol, 'meta_lowdin', s=ovlp_ao)
mocas_a = reduce(numpy.dot, (orth_coeff.T, ovlp_ao, mocas_a))
mocas_b = reduce(numpy.dot, (orth_coeff.T, ovlp_ao, mocas_b))
log.info('Natural alpha-orbital (expansion on meta-Lowdin AOs) in CAS space')
dump_mat.dump_rec(log.stdout, mocas_a, label, start=1, **kwargs)
log.info('Natural beta-orbital (expansion on meta-Lowdin AOs) in CAS space')
dump_mat.dump_rec(log.stdout, mocas_b, label, start=1, **kwargs)
else:
log.info('Natural alpha-orbital (expansion on AOs) in CAS space')
dump_mat.dump_rec(log.stdout, mocas_a, label, start=1, **kwargs)
log.info('Natural beta-orbital (expansion on AOs) in CAS space')
dump_mat.dump_rec(log.stdout, mocas_b, label, start=1, **kwargs)
tol = getattr(__config__, 'mcscf_addons_map2hf_tol', 0.4)
s = reduce(numpy.dot, (mo_coeff[0].T, ovlp_ao, self._scf.mo_coeff[0]))
idx = numpy.argwhere(abs(s)>tol)
for i,j in idx:
log.info('alpha <mo-mcscf|mo-hf> %d %d %12.8f' % (i+1,j+1,s[i,j]))
s = reduce(numpy.dot, (mo_coeff[1].T, ovlp_ao, self._scf.mo_coeff[1]))
idx = numpy.argwhere(abs(s)>tol)
for i,j in idx:
log.info('beta <mo-mcscf|mo-hf> %d %d %12.8f' % (i+1,j+1,s[i,j]))
if getattr(self.fcisolver, 'large_ci', None) and ci is not None:
log.info('\n** Largest CI components **')
if isinstance(ci, (list, tuple, RANGE_TYPE)):
for i, state in enumerate(ci):
log.info(' [alpha occ-orbitals] [beta occ-orbitals] state %-3d CI coefficient', i)
res = self.fcisolver.large_ci(state, self.ncas, self.nelecas,
large_ci_tol, return_strs=False)
for c,ia,ib in res:
log.info(' %-20s %-30s %.12f', ia, ib, c)
else:
log.info(' [alpha occ-orbitals] [beta occ-orbitals] CI coefficient')
res = self.fcisolver.large_ci(ci, self.ncas, self.nelecas,
large_ci_tol, return_strs=False)
for c,ia,ib in res:
log.info(' %-20s %-30s %.12f', ia, ib, c)
return dm1a, dm1b
def grad_elec(mc_grad, mo_coeff=None, ci=None, atmlst=None, verbose=None):
mc = mc_grad.base
if mo_coeff is None: mo_coeff = mc.mo_coeff
if ci is None: ci = mc.ci
if mc.frozen is not None:
raise NotImplementedError
time0 = time.clock(), time.time()
log = logger.new_logger(mc_grad, verbose)
mol = mc_grad.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 = numpy.dot(mo_core, mo_core.T) * 2
dm_cas = reduce(numpy.dot, (mo_cas, casdm1, mo_cas.T))
# MRH flag: this is one of my kludges
# It would be better to just pass the ERIS object used in orbital optimization
# But I am too lazy at the moment
aapa = ao2mo.kernel(mol, (mo_cas, mo_cas, mo_coeff, mo_cas), compact=False)
aapa = aapa.reshape(ncas, ncas, nmo, ncas)
vj, vk = mc._scf.get_jk(mol, (dm_core, dm_cas))
h1 = mc.get_hcore()
vhf_c = vj[0] - vk[0] * .5
vhf_a = vj[1] - vk[1] * .5
gfock = numpy.zeros((nmo, nmo))
gfock[:, :ncore] = reduce(numpy.dot,
(mo_coeff.T, h1 + vhf_c + vhf_a, mo_core)) * 2
gfock[:, ncore:nocc] = reduce(numpy.dot,
(mo_coeff.T, h1 + vhf_c, mo_cas, casdm1))
gfock[:, ncore:nocc] += numpy.einsum('uviw,vuwt->it', aapa, casdm2)
dme0 = reduce(numpy.dot, (mo_coeff, (gfock + gfock.T) * .5, mo_coeff.T))
aapa = vj = vk = vhf_c = vhf_a = h1 = gfock = None
dm1 = dm_core + dm_cas
vj, vk = mc_grad.get_jk(mol, (dm_core, dm_cas))
vhf1c, vhf1a = vj - vk * .5
hcore_deriv = mc_grad.hcore_generator(mol)
s1 = mc_grad.get_ovlp(mol)
diag_idx = numpy.arange(nao)
diag_idx = diag_idx * (diag_idx + 1) // 2 + diag_idx
casdm2_cc = casdm2 + casdm2.transpose(0, 1, 3, 2)
dm2buf = ao2mo._ao2mo.nr_e2(casdm2_cc.reshape(ncas**2, ncas**2), mo_cas.T,
(0, nao, 0, nao)).reshape(ncas**2, nao, nao)
dm2buf = lib.pack_tril(dm2buf)
dm2buf[:, diag_idx] *= .5
dm2buf = dm2buf.reshape(ncas, ncas, nao_pair)
casdm2 = casdm2_cc = None
if atmlst is None:
atmlst = range(mol.natm)
aoslices = mol.aoslice_by_atom()
de = numpy.zeros((len(atmlst), 3))
max_memory = mc_grad.max_memory - lib.current_memory()[0]
# MRH: this originally implied that the memory footprint would be max(p1-p0) * max(q1-q0) * nao_pair
# In fact, that's the size of dm2_ao AND EACH COMPONENT of the differentiated eris
# So the actual memory footprint is 4 times that!
blksize = int(max_memory * .9e6 / 8 /
(4 * (aoslices[:, 3] - aoslices[:, 2]).max() * nao_pair))
blksize = min(nao, max(2, blksize))
for k, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = aoslices[ia]
h1ao = hcore_deriv(ia)
de[k] += numpy.einsum('xij,ij->x', h1ao, dm1)
de[k] -= numpy.einsum('xij,ij->x', s1[:, p0:p1], dme0[p0:p1]) * 2
q1 = 0
for b0, b1, nf in _shell_prange(mol, 0, mol.nbas, blksize):
q0, q1 = q1, q1 + nf
dm2_ao = lib.einsum('ijw,pi,qj->pqw', dm2buf, mo_cas[p0:p1],
mo_cas[q0:q1])
shls_slice = (shl0, shl1, b0, b1, 0, mol.nbas, 0, mol.nbas)
eri1 = mol.intor('int2e_ip1',
comp=3,
aosym='s2kl',
shls_slice=shls_slice).reshape(
3, p1 - p0, nf, nao_pair)
de[k] -= numpy.einsum('xijw,ijw->x', eri1, dm2_ao) * 2
eri1 = None
de[k] += numpy.einsum('xij,ij->x', vhf1c[:, p0:p1], dm1[p0:p1]) * 2
de[k] += numpy.einsum('xij,ij->x', vhf1a[:, p0:p1], dm_core[p0:p1]) * 2
log.timer('CASSCF nuclear gradients', *time0)
return de
def canonicalize(mc,
mo_coeff=None,
ci=None,
eris=None,
sort=False,
cas_natorb=False,
casdm1=None,
verbose=logger.NOTE,
with_meta_lowdin=WITH_META_LOWDIN):
'''Canonicalized CASCI/CASSCF orbitals of effecitve Fock matrix.
Effective Fock matrix is built with one-particle density matrix (see
also :func:`mcscf.casci.get_fock`). For state-average CASCI/CASSCF object,
the canonicalized orbitals are based on the state-average density matrix.
To obtain canonicalized orbitals for an individual state, you need to pass
"casdm1" of the specific state to this function.
Args:
mc: a CASSCF/CASCI object or RHF object
Kwargs:
mo_coeff (ndarray): orbitals that span the core, active and external
space.
ci (ndarray): CI coefficients (or objects to represent the CI
wavefunctions in DMRG/QMC-MCSCF calculations).
eris: Integrals for the MCSCF object. Input this object to reduce the
overhead of computing integrals. It can be generated by
:func:`mc.ao2mo` method.
sort (bool): Whether the canonicalized orbitals are sorted based on
orbital energy (diagonal part of the effective Fock matrix)
within each subspace (core, active, external). If the point group
symmetry is not available in the system, the orbitals are always
sorted. When the point group symmetry is available, sort=False
will keep the symmetry label of input orbitals and only sort the
orbitals in each symmetry block while sort=True will reorder all
orbitals in each subspace and the symmetry labels may be changed.
cas_natorb (bool): Whether to transform the active orbitals to natual
orbitals
casdm1 (ndarray): 1-particle density matrix in active space. This
density matrix is used to build effective fock matrix. Without
input casdm1, the density matrix is computed with the input ci
coefficients/object. If neither ci nor casdm1 were given, density
matrix is computed by :func:`mc.fcisolver.make_rdm1` method. For
state-average CASCI/CASCF calculation, this results in a set of
canonicalized orbitals of state-average effective Fock matrix.
To canonicalize the orbitals for one particular state, you can
assign the density matrix of that state to the kwarg casdm1.
Returns:
A tuple, (natural orbitals, CI coefficients, orbital energies)
The orbital energies are the diagonal terms of effective Fock matrix.
'''
from pyscf.lo import orth
from pyscf.tools import dump_mat
from pyscf.mcscf import addons
log = logger.new_logger(mc, verbose)
if mo_coeff is None: mo_coeff = mc.mo_coeff
if ci is None: ci = mc.ci
if casdm1 is None:
if (isinstance(ci, (list, tuple)) and
not isinstance(mc.fcisolver, addons.StateAverageFCISolver)):
log.warn('Mulitple states found in CASCI solver. First state is '
'used to compute the natural orbitals in active space.')
casdm1 = mc.fcisolver.make_rdm1(ci[0], mc.ncas, mc.nelecas)
else:
casdm1 = mc.fcisolver.make_rdm1(ci, mc.ncas, mc.nelecas)
ncore = mc.ncore
nocc = ncore + mc.ncas
nmo = mo_coeff.shape[1]
fock_ao = mc.get_fock(mo_coeff, ci, eris, casdm1, verbose)
if cas_natorb:
mo_coeff1, ci, occ = mc.cas_natorb(mo_coeff, ci, eris, sort, casdm1,
verbose, with_meta_lowdin)
else:
# Keep the active space unchanged by default. The rotation in active space
# may cause problem for external CI solver eg DMRG.
mo_coeff1 = mo_coeff.copy()
log.info('Density matrix diagonal elements %s', casdm1.diagonal())
fock = reduce(numpy.dot, (mo_coeff1.T, fock_ao, mo_coeff1))
mo_energy = fock.diagonal().copy()
mask = numpy.ones(nmo, dtype=bool)
frozen = getattr(mc, 'frozen', None)
if frozen is not None:
if isinstance(frozen, (int, numpy.integer)):
mask[:frozen] = False
else:
mask[frozen] = False
core_idx = numpy.where(mask[:ncore])[0]
vir_idx = numpy.where(mask[nocc:])[0] + nocc
if hasattr(mo_coeff, 'orbsym'):
orbsym = mo_coeff.orbsym
else:
orbsym = numpy.zeros(nmo, dtype=int)
if len(core_idx) > 0:
# note the last two args of ._eig for mc1step_symm
# mc._eig function is called to handle symmetry adapated fock
w, c1 = mc._eig(fock[core_idx[:, None], core_idx], 0, ncore,
orbsym[core_idx])
if sort:
idx = numpy.argsort(w.round(9), kind='mergesort')
w = w[idx]
c1 = c1[:, idx]
orbsym[core_idx] = orbsym[core_idx][idx]
mo_coeff1[:, core_idx] = numpy.dot(mo_coeff1[:, core_idx], c1)
mo_energy[core_idx] = w
if len(vir_idx) > 0:
w, c1 = mc._eig(fock[vir_idx[:, None], vir_idx], nocc, nmo,
orbsym[vir_idx])
if sort:
idx = numpy.argsort(w.round(9), kind='mergesort')
w = w[idx]
c1 = c1[:, idx]
orbsym[vir_idx] = orbsym[vir_idx][idx]
mo_coeff1[:, vir_idx] = numpy.dot(mo_coeff1[:, vir_idx], c1)
mo_energy[vir_idx] = w
if hasattr(mo_coeff, 'orbsym'):
mo_coeff1 = lib.tag_array(mo_coeff1, orbsym=orbsym)
if log.verbose >= logger.DEBUG:
for i in range(nmo):
log.debug('i = %d <i|F|i> = %12.8f', i + 1, mo_energy[i])
# still return ci coefficients, in case the canonicalization funciton changed
# cas orbitals, the ci coefficients should also be updated.
return mo_coeff1, ci, mo_energy
def kernel_ms0(fci,
h1e,
eri,
norb,
nelec,
ci0=None,
link_index=None,
tol=None,
lindep=None,
max_cycle=None,
max_space=None,
nroots=None,
davidson_only=None,
pspace_size=None,
max_memory=None,
verbose=None,
ecore=0,
**kwargs):
if nroots is None: nroots = fci.nroots
if davidson_only is None: davidson_only = fci.davidson_only
if pspace_size is None: pspace_size = fci.pspace_size
if max_memory is None:
max_memory = fci.max_memory - lib.current_memory()[0]
log = logger.new_logger(fci, verbose)
assert (fci.spin is None or fci.spin == 0)
assert (0 <= numpy.sum(nelec) <= norb * 2)
link_index = _unpack(norb, nelec, link_index)
h1e = numpy.ascontiguousarray(h1e)
eri = numpy.ascontiguousarray(eri)
na = link_index.shape[0]
if max_memory < na**2 * 6 * 8e-6:
log.warn(
'Not enough memory for FCI solver. '
'The minimal requirement is %.0f MB', na**2 * 60e-6)
hdiag = fci.make_hdiag(h1e, eri, norb, nelec)
nroots = min(hdiag.size, nroots)
try:
addr, h0 = fci.pspace(h1e, eri, norb, nelec, hdiag,
max(pspace_size, nroots))
if pspace_size > 0:
pw, pv = fci.eig(h0)
else:
pw = pv = None
if pspace_size >= na * na and ci0 is None and not davidson_only:
# The degenerated wfn can break symmetry. The davidson iteration with proper
# initial guess doesn't have this issue
if na * na == 1:
return pw[0] + ecore, pv[:, 0].reshape(1, 1)
elif nroots > 1:
civec = numpy.empty((nroots, na * na))
civec[:, addr] = pv[:, :nroots].T
civec = civec.reshape(nroots, na, na)
try:
return pw[:nroots] + ecore, [_check_(ci) for ci in civec]
except ValueError:
pass
elif abs(pw[0] - pw[1]) > 1e-12:
civec = numpy.empty((na * na))
civec[addr] = pv[:, 0]
civec = civec.reshape(na, na)
civec = lib.transpose_sum(civec) * .5
# direct diagonalization may lead to triplet ground state
##TODO: optimize initial guess. Using pspace vector as initial guess may have
## spin problems. The 'ground state' of psapce vector may have different spin
## state to the true ground state.
try:
return pw[0] + ecore, _check_(civec.reshape(na, na))
except ValueError:
pass
except NotImplementedError:
addr = [0]
pw = pv = None
precond = fci.make_precond(hdiag, pw, pv, addr)
h2e = fci.absorb_h1e(h1e, eri, norb, nelec, .5)
def hop(c):
hc = fci.contract_2e(h2e, c.reshape(na, na), norb, nelec, link_index)
return hc.ravel()
#TODO: check spin of initial guess
if ci0 is None:
if callable(getattr(fci, 'get_init_guess', None)):
ci0 = lambda: fci.get_init_guess(norb, nelec, nroots, hdiag)
else:
def ci0():
x0 = []
for i in range(nroots):
x = numpy.zeros((na, na))
addra = addr[i] // na
addrb = addr[i] % na
if addra == addrb:
x[addra, addrb] = 1
else:
x[addra, addrb] = x[addrb, addra] = numpy.sqrt(.5)
x0.append(x.ravel())
return x0
elif not callable(ci0):
if isinstance(ci0, numpy.ndarray) and ci0.size == na * na:
ci0 = [ci0.ravel()]
else:
ci0 = [x.ravel() for x in ci0]
if tol is None: tol = fci.conv_tol
if lindep is None: lindep = fci.lindep
if max_cycle is None: max_cycle = fci.max_cycle
if max_space is None: max_space = fci.max_space
tol_residual = getattr(fci, 'conv_tol_residual', None)
with lib.with_omp_threads(fci.threads):
#e, c = lib.davidson(hop, ci0, precond, tol=fci.conv_tol, lindep=fci.lindep)
e, c = fci.eig(hop,
ci0,
precond,
tol=tol,
lindep=lindep,
max_cycle=max_cycle,
max_space=max_space,
nroots=nroots,
max_memory=max_memory,
verbose=log,
follow_state=True,
tol_residual=tol_residual,
**kwargs)
if nroots > 1:
return e + ecore, [_check_(ci.reshape(na, na)) for ci in c]
else:
return e + ecore, _check_(c.reshape(na, na))
def grad_elec(cc_grad,
t1=None,
t2=None,
l1=None,
l2=None,
eris=None,
atmlst=None,
d1=None,
d2=None,
verbose=logger.INFO):
mycc = cc_grad.base
if eris is not None:
if (abs(eris.focka - numpy.diag(eris.focka.diagonal())).max() > 1e-3
or abs(eris.fockb - numpy.diag(eris.fockb.diagonal())).max() >
1e-3):
raise RuntimeError(
'UCCSD gradients does not support NHF (non-canonical HF)')
if t1 is None: t1 = mycc.t1
if t2 is None: t2 = mycc.t2
if l1 is None: l1 = mycc.l1
if l2 is None: l2 = mycc.l2
log = logger.new_logger(mycc, verbose)
time0 = time.clock(), time.time()
log.debug('Build uccsd rdm1 intermediates')
if d1 is None:
d1 = uccsd_rdm._gamma1_intermediates(mycc, t1, t2, l1, l2)
time1 = log.timer_debug1('rdm1 intermediates', *time0)
log.debug('Build uccsd rdm2 intermediates')
fdm2 = lib.H5TmpFile()
if d2 is None:
d2 = uccsd_rdm._gamma2_outcore(mycc, t1, t2, l1, l2, fdm2, True)
time1 = log.timer_debug1('rdm2 intermediates', *time1)
mol = cc_grad.mol
mo_a, mo_b = mycc.mo_coeff
mo_ea, mo_eb = mycc._scf.mo_energy
nao, nmoa = mo_a.shape
nmob = mo_b.shape[1]
nocca = numpy.count_nonzero(mycc.mo_occ[0] > 0)
noccb = numpy.count_nonzero(mycc.mo_occ[1] > 0)
with_frozen = not ((mycc.frozen is None) or
(isinstance(mycc.frozen,
(int, numpy.integer)) and mycc.frozen == 0)
or (len(mycc.frozen) == 0))
moidx = mycc.get_frozen_mask()
OA_a, VA_a, OF_a, VF_a = ccsd_grad._index_frozen_active(
moidx[0], mycc.mo_occ[0])
OA_b, VA_b, OF_b, VF_b = ccsd_grad._index_frozen_active(
moidx[1], mycc.mo_occ[1])
log.debug('symmetrized rdm2 and MO->AO transformation')
# Roughly, dm2*2 is computed in _rdm2_mo2ao
mo_active = (mo_a[:, numpy.hstack((OA_a, VA_a))], mo_b[:,
numpy.hstack(
(OA_b, VA_b))])
_rdm2_mo2ao(mycc, d2, mo_active, fdm2) # transform the active orbitals
time1 = log.timer_debug1('MO->AO transformation', *time1)
hf_dm1a, hf_dm1b = mycc._scf.make_rdm1(mycc.mo_coeff, mycc.mo_occ)
hf_dm1 = hf_dm1a + hf_dm1b
if atmlst is None:
atmlst = range(mol.natm)
offsetdic = mol.offset_nr_by_atom()
diagidx = numpy.arange(nao)
diagidx = diagidx * (diagidx + 1) // 2 + diagidx
de = numpy.zeros((len(atmlst), 3))
Imata = numpy.zeros((nao, nao))
Imatb = numpy.zeros((nao, nao))
vhf1 = fdm2.create_dataset('vhf1', (len(atmlst), 2, 3, nao, nao), 'f8')
# 2e AO integrals dot 2pdm
max_memory = max(0, mycc.max_memory - lib.current_memory()[0])
blksize = max(1, int(max_memory * .9e6 / 8 / (nao**3 * 2.5)))
for k, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = offsetdic[ia]
ip1 = p0
vhf = numpy.zeros((2, 3, nao, nao))
for b0, b1, nf in ccsd_grad._shell_prange(mol, shl0, shl1, blksize):
ip0, ip1 = ip1, ip1 + nf
dm2bufa = ccsd_grad._load_block_tril(fdm2['dm2aa+ab'], ip0, ip1,
nao)
dm2bufb = ccsd_grad._load_block_tril(fdm2['dm2bb+ab'], ip0, ip1,
nao)
dm2bufa[:, :, diagidx] *= .5
dm2bufb[:, :, diagidx] *= .5
shls_slice = (b0, b1, 0, mol.nbas, 0, mol.nbas, 0, mol.nbas)
eri0 = mol.intor('int2e', aosym='s2kl', shls_slice=shls_slice)
Imata += lib.einsum('ipx,iqx->pq', eri0.reshape(nf, nao, -1),
dm2bufa)
Imatb += lib.einsum('ipx,iqx->pq', eri0.reshape(nf, nao, -1),
dm2bufb)
eri0 = None
eri1 = mol.intor('int2e_ip1',
comp=3,
aosym='s2kl',
shls_slice=shls_slice).reshape(3, nf, nao, -1)
de[k] -= numpy.einsum('xijk,ijk->x', eri1, dm2bufa) * 2
de[k] -= numpy.einsum('xijk,ijk->x', eri1, dm2bufb) * 2
dm2bufa = dm2bufb = None
# HF part
for i in range(3):
eri1tmp = lib.unpack_tril(eri1[i].reshape(nf * nao, -1))
eri1tmp = eri1tmp.reshape(nf, nao, nao, nao)
vhf[:, i] += numpy.einsum('ijkl,ij->kl', eri1tmp,
hf_dm1[ip0:ip1])
vhf[0, i] -= numpy.einsum('ijkl,il->kj', eri1tmp,
hf_dm1a[ip0:ip1])
vhf[1, i] -= numpy.einsum('ijkl,il->kj', eri1tmp,
hf_dm1b[ip0:ip1])
vhf[:, i, ip0:ip1] += numpy.einsum('ijkl,kl->ij', eri1tmp,
hf_dm1)
vhf[0, i, ip0:ip1] -= numpy.einsum('ijkl,jk->il', eri1tmp,
hf_dm1a)
vhf[1, i, ip0:ip1] -= numpy.einsum('ijkl,jk->il', eri1tmp,
hf_dm1b)
eri1 = eri1tmp = None
vhf1[k] = vhf
log.debug('2e-part grad of atom %d %s = %s', ia, mol.atom_symbol(ia),
de[k])
time1 = log.timer_debug1('2e-part grad of atom %d' % ia, *time1)
s0 = mycc._scf.get_ovlp()
Imata = reduce(numpy.dot, (mo_a.T, Imata, s0, mo_a)) * -1
Imatb = reduce(numpy.dot, (mo_b.T, Imatb, s0, mo_b)) * -1
dm1a = numpy.zeros((nmoa, nmoa))
dm1b = numpy.zeros((nmob, nmob))
doo, dOO = d1[0]
dov, dOV = d1[1]
dvo, dVO = d1[2]
dvv, dVV = d1[3]
if with_frozen:
dco = Imata[OF_a[:, None], OA_a] / (mo_ea[OF_a, None] - mo_ea[OA_a])
dfv = Imata[VF_a[:, None], VA_a] / (mo_ea[VF_a, None] - mo_ea[VA_a])
dm1a[OA_a[:, None], OA_a] = (doo + doo.T) * .5
dm1a[OF_a[:, None], OA_a] = dco
dm1a[OA_a[:, None], OF_a] = dco.T
dm1a[VA_a[:, None], VA_a] = (dvv + dvv.T) * .5
dm1a[VF_a[:, None], VA_a] = dfv
dm1a[VA_a[:, None], VF_a] = dfv.T
dco = Imatb[OF_b[:, None], OA_b] / (mo_eb[OF_b, None] - mo_eb[OA_b])
dfv = Imatb[VF_b[:, None], VA_b] / (mo_eb[VF_b, None] - mo_eb[VA_b])
dm1b[OA_b[:, None], OA_b] = (dOO + dOO.T) * .5
dm1b[OF_b[:, None], OA_b] = dco
dm1b[OA_b[:, None], OF_b] = dco.T
dm1b[VA_b[:, None], VA_b] = (dVV + dVV.T) * .5
dm1b[VF_b[:, None], VA_b] = dfv
dm1b[VA_b[:, None], VF_b] = dfv.T
else:
dm1a[:nocca, :nocca] = (doo + doo.T) * .5
dm1a[nocca:, nocca:] = (dvv + dvv.T) * .5
dm1b[:noccb, :noccb] = (dOO + dOO.T) * .5
dm1b[noccb:, noccb:] = (dVV + dVV.T) * .5
dm1 = (reduce(numpy.dot,
(mo_a, dm1a, mo_a.T)), reduce(numpy.dot,
(mo_b, dm1b, mo_b.T)))
vhf = mycc._scf.get_veff(mycc.mol, dm1)
Xvo = reduce(numpy.dot, (mo_a[:, nocca:].T, vhf[0], mo_a[:, :nocca]))
XVO = reduce(numpy.dot, (mo_b[:, noccb:].T, vhf[1], mo_b[:, :noccb]))
Xvo += Imata[:nocca, nocca:].T - Imata[nocca:, :nocca]
XVO += Imatb[:noccb, noccb:].T - Imatb[noccb:, :noccb]
dm1_resp = _response_dm1(mycc, (Xvo, XVO), eris)
dm1a += dm1_resp[0]
dm1b += dm1_resp[1]
time1 = log.timer_debug1('response_rdm1 intermediates', *time1)
Imata[nocca:, :nocca] = Imata[:nocca, nocca:].T
Imatb[noccb:, :noccb] = Imatb[:noccb, noccb:].T
im1 = reduce(numpy.dot, (mo_a, Imata, mo_a.T))
im1 += reduce(numpy.dot, (mo_b, Imatb, mo_b.T))
time1 = log.timer_debug1('response_rdm1', *time1)
log.debug('h1 and JK1')
# Initialize hcore_deriv with the underlying SCF object because some
# extensions (e.g. QM/MM, solvent) modifies the SCF object only.
mf_grad = cc_grad.base._scf.nuc_grad_method()
hcore_deriv = mf_grad.hcore_generator(mol)
s1 = mf_grad.get_ovlp(mol)
zeta = (mo_ea[:, None] + mo_ea) * .5
zeta[nocca:, :nocca] = mo_ea[:nocca]
zeta[:nocca, nocca:] = mo_ea[:nocca].reshape(-1, 1)
zeta_a = reduce(numpy.dot, (mo_a, zeta * dm1a, mo_a.T))
zeta = (mo_eb[:, None] + mo_eb) * .5
zeta[noccb:, :noccb] = mo_eb[:noccb]
zeta[:noccb, noccb:] = mo_eb[:noccb].reshape(-1, 1)
zeta_b = reduce(numpy.dot, (mo_b, zeta * dm1b, mo_b.T))
dm1 = (reduce(numpy.dot,
(mo_a, dm1a, mo_a.T)), reduce(numpy.dot,
(mo_b, dm1b, mo_b.T)))
vhf_s1occ = mycc._scf.get_veff(mol, (dm1[0] + dm1[0].T, dm1[1] + dm1[1].T))
p1a = numpy.dot(mo_a[:, :nocca], mo_a[:, :nocca].T)
p1b = numpy.dot(mo_b[:, :noccb], mo_b[:, :noccb].T)
vhf_s1occ = (reduce(numpy.dot, (p1a, vhf_s1occ[0], p1a)) +
reduce(numpy.dot, (p1b, vhf_s1occ[1], p1b))) * .5
time1 = log.timer_debug1('h1 and JK1', *time1)
# Hartree-Fock part contribution
dm1pa = hf_dm1a + dm1[0] * 2
dm1pb = hf_dm1b + dm1[1] * 2
dm1 = dm1[0] + dm1[1] + hf_dm1
zeta_a += rhf_grad.make_rdm1e(mo_ea, mo_a, mycc.mo_occ[0])
zeta_b += rhf_grad.make_rdm1e(mo_eb, mo_b, mycc.mo_occ[1])
zeta = zeta_a + zeta_b
for k, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = offsetdic[ia]
# s[1] dot I, note matrix im1 is not hermitian
de[k] += numpy.einsum('xij,ij->x', s1[:, p0:p1], im1[p0:p1])
de[k] += numpy.einsum('xji,ij->x', s1[:, p0:p1], im1[:, p0:p1])
# h[1] \dot DM, contribute to f1
h1ao = hcore_deriv(ia)
de[k] += numpy.einsum('xij,ji->x', h1ao, dm1)
# -s[1]*e \dot DM, contribute to f1
de[k] -= numpy.einsum('xij,ij->x', s1[:, p0:p1], zeta[p0:p1])
de[k] -= numpy.einsum('xji,ij->x', s1[:, p0:p1], zeta[:, p0:p1])
# -vhf[s_ij[1]], contribute to f1, *2 for s1+s1.T
de[k] -= numpy.einsum('xij,ij->x', s1[:, p0:p1], vhf_s1occ[p0:p1]) * 2
de[k] -= numpy.einsum('xij,ij->x', vhf1[k, 0], dm1pa)
de[k] -= numpy.einsum('xij,ij->x', vhf1[k, 1], dm1pb)
log.timer('%s gradients' % mycc.__class__.__name__, *time0)
return de
def analyze(mf, verbose=logger.DEBUG, **kwargs):
from pyscf.lo import orth
from pyscf.tools import dump_mat
mol = mf.mol
if not mol.symmetry:
return uhf.analyze(mf, verbose, **kwargs)
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
mo_coeff = mf.mo_coeff
ovlp_ao = mf.get_ovlp()
log = logger.new_logger(mf, verbose)
if log.verbose >= logger.NOTE:
nirrep = len(mol.irrep_id)
ovlp_ao = mf.get_ovlp()
orbsyma, orbsymb = get_orbsym(mf.mol, mo_coeff, ovlp_ao, False)
tot_sym = 0
noccsa = [sum(orbsyma[mo_occ[0] > 0] == ir) for ir in mol.irrep_id]
noccsb = [sum(orbsymb[mo_occ[1] > 0] == ir) for ir in mol.irrep_id]
for i, ir in enumerate(mol.irrep_id):
if (noccsa[i] + noccsb[i]) % 2:
tot_sym ^= ir
if mol.groupname in ('Dooh', 'Coov', 'SO3'):
log.note('TODO: total symmetry for %s', mol.groupname)
else:
log.note('total symmetry = %s',
symm.irrep_id2name(mol.groupname, tot_sym))
log.note('alpha occupancy for each irrep: ' + (' %4s' * nirrep),
*mol.irrep_name)
log.note(' ' + (' %4d' * nirrep),
*noccsa)
log.note('beta occupancy for each irrep: ' + (' %4s' * nirrep),
*mol.irrep_name)
log.note(' ' + (' %4d' * nirrep),
*noccsb)
log.note('**** MO energy ****')
irname_full = {}
for k, ir in enumerate(mol.irrep_id):
irname_full[ir] = mol.irrep_name[k]
irorbcnt = {}
for k, j in enumerate(orbsyma):
if j in irorbcnt:
irorbcnt[j] += 1
else:
irorbcnt[j] = 1
log.note('alpha MO #%d (%s #%d), energy= %.15g occ= %g', k + 1,
irname_full[j], irorbcnt[j], mo_energy[0][k],
mo_occ[0][k])
irorbcnt = {}
for k, j in enumerate(orbsymb):
if j in irorbcnt:
irorbcnt[j] += 1
else:
irorbcnt[j] = 1
log.note('beta MO #%d (%s #%d), energy= %.15g occ= %g', k + 1,
irname_full[j], irorbcnt[j], mo_energy[1][k],
mo_occ[1][k])
if mf.verbose >= logger.DEBUG:
label = mol.ao_labels()
molabel = []
irorbcnt = {}
for k, j in enumerate(orbsyma):
if j in irorbcnt:
irorbcnt[j] += 1
else:
irorbcnt[j] = 1
molabel.append('#%-d(%s #%d)' %
(k + 1, irname_full[j], irorbcnt[j]))
log.debug(
' ** alpha MO coefficients (expansion on meta-Lowdin AOs) **')
orth_coeff = orth.orth_ao(mol, 'meta_lowdin', s=ovlp_ao)
c_inv = numpy.dot(orth_coeff.T, ovlp_ao)
dump_mat.dump_rec(mol.stdout,
c_inv.dot(mo_coeff[0]),
label,
molabel,
start=1,
**kwargs)
molabel = []
irorbcnt = {}
for k, j in enumerate(orbsymb):
if j in irorbcnt:
irorbcnt[j] += 1
else:
irorbcnt[j] = 1
molabel.append('#%-d(%s #%d)' %
(k + 1, irname_full[j], irorbcnt[j]))
log.debug(' ** beta MO coefficients (expansion on meta-Lowdin AOs) **')
dump_mat.dump_rec(mol.stdout,
c_inv.dot(mo_coeff[1]),
label,
molabel,
start=1,
**kwargs)
dm = mf.make_rdm1(mo_coeff, mo_occ)
return mf.mulliken_meta(mol, dm, s=ovlp_ao, verbose=log)
def canonicalize(mc, mo_coeff=None, ci=None, eris=None, sort=False,
cas_natorb=False, casdm1=None, verbose=logger.NOTE):
'''Canonicalized CASCI/CASSCF orbitals of effecitve Fock matrix.
Effective Fock matrix is built with one-particle density matrix (see
also :func:`mcscf.casci.get_fock`)
Args:
mc : a CASSCF/CASCI object or RHF object
Returns:
A tuple, (natural orbitals, CI coefficients, orbital energies)
The orbital energies are the diagonal terms of general Fock matrix.
'''
from pyscf.lo import orth
from pyscf.tools import dump_mat
log = logger.new_logger(mc, verbose)
if mo_coeff is None: mo_coeff = mc.mo_coeff
if ci is None: ci = mc.ci
if casdm1 is None:
casdm1 = mc.fcisolver.make_rdm1(ci, mc.ncas, mc.nelecas)
ncore = mc.ncore
nocc = ncore + mc.ncas
nmo = mo_coeff.shape[1]
fock_ao = mc.get_fock(mo_coeff, ci, eris, casdm1, verbose)
fock = reduce(numpy.dot, (mo_coeff.T, fock_ao, mo_coeff))
mo_energy = fock.diagonal().copy()
if cas_natorb:
mo_coeff1, ci, occ = mc.cas_natorb(mo_coeff, ci, eris, sort, casdm1,
verbose)
ma = mo_coeff1[:,ncore:nocc]
mo_energy[ncore:nocc] = numpy.einsum('ji,ji->i', ma, fock_ao.dot(ma))
else:
# Keep the active space unchanged by default. The rotation in active space
# may cause problem for external CI solver eg DMRG.
mo_coeff1 = numpy.empty_like(mo_coeff)
mo_coeff1[:,ncore:nocc] = mo_coeff[:,ncore:nocc]
if ncore > 0:
# note the last two args of ._eig for mc1step_symm
# mc._eig function is called to handle symmetry adapated fock
w, c1 = mc._eig(fock[:ncore,:ncore], 0, ncore)
if sort:
idx = numpy.argsort(w.round(9), kind='mergesort')
w = w[idx]
c1 = c1[:,idx]
mo_coeff1[:,:ncore] = numpy.dot(mo_coeff[:,:ncore], c1)
mo_energy[:ncore] = w
if nmo-nocc > 0:
w, c1 = mc._eig(fock[nocc:,nocc:], nocc, nmo)
if sort:
idx = numpy.argsort(w.round(9), kind='mergesort')
w = w[idx]
c1 = c1[:,idx]
mo_coeff1[:,nocc:] = numpy.dot(mo_coeff[:,nocc:], c1)
mo_energy[nocc:] = w
if hasattr(mo_coeff, 'orbsym'):
if sort:
orbsym = symm.label_orb_symm(mc.mol, mc.mol.irrep_id,
mc.mol.symm_orb, mo_coeff1)
else:
orbsym = mo_coeff.orbsym
mo_coeff1 = lib.tag_array(mo_coeff1, orbsym=orbsym)
if log.verbose >= logger.DEBUG:
for i in range(nmo):
log.debug('i = %d <i|F|i> = %12.8f', i+1, mo_energy[i])
# still return ci coefficients, in case the canonicalization funciton changed
# cas orbitals, the ci coefficients should also be updated.
return mo_coeff1, ci, mo_energy
def analyze(tdobj, verbose=None):
log = logger.new_logger(tdobj, verbose)
mol = tdobj.mol
mo_coeff = tdobj._scf.mo_coeff
mo_occ = tdobj._scf.mo_occ
nocc = numpy.count_nonzero(mo_occ == 2)
e_ev = numpy.asarray(tdobj.e) * nist.HARTREE2EV
e_wn = numpy.asarray(tdobj.e) * nist.HARTREE2WAVENUMBER
wave_length = 1e7 / e_wn
if tdobj.singlet:
log.note(
'\n** Singlet excitation energies and oscillator strengths **')
else:
log.note(
'\n** Triplet excitation energies and oscillator strengths **')
if mol.symmetry:
orbsym = hf_symm.get_orbsym(mol, mo_coeff)
x_sym = symm.direct_prod(orbsym[mo_occ == 2], orbsym[mo_occ == 0],
mol.groupname)
else:
x_sym = None
f_oscillator = tdobj.oscillator_strength()
for i, ei in enumerate(tdobj.e):
x, y = tdobj.xy[i]
if x_sym is None:
log.note('Excited State %3d: %12.5f eV %9.2f nm f=%.4f', i + 1,
e_ev[i], wave_length[i], f_oscillator[i])
else:
wfnsym = analyze_wfnsym(tdobj, x_sym, x)
log.note('Excited State %3d: %4s %12.5f eV %9.2f nm f=%.4f',
i + 1, wfnsym, e_ev[i], wave_length[i], f_oscillator[i])
if log.verbose >= logger.INFO:
o_idx, v_idx = numpy.where(abs(x) > 0.1)
for o, v in zip(o_idx, v_idx):
log.info(' %4d -> %-4d %12.5f', o + MO_BASE,
v + MO_BASE + nocc, x[o, v])
if log.verbose >= logger.INFO:
log.info('\n** Transition electric dipole moments (AU) **')
log.info(
'state X Y Z Dip. S. Osc.'
)
trans_dip = tdobj.transition_dipole()
for i, ei in enumerate(tdobj.e):
dip = trans_dip[i]
log.info('%3d %11.4f %11.4f %11.4f %11.4f %11.4f', i + 1,
dip[0], dip[1], dip[2], numpy.dot(dip,
dip), f_oscillator[i])
log.info(
'\n** Transition velocity dipole moments (imaginary part, AU) **')
log.info(
'state X Y Z Dip. S. Osc.'
)
trans_v = tdobj.transition_velocity_dipole()
f_v = tdobj.oscillator_strength(gauge='velocity', order=0)
for i, ei in enumerate(tdobj.e):
v = trans_v[i]
log.info('%3d %11.4f %11.4f %11.4f %11.4f %11.4f', i + 1, v[0],
v[1], v[2], numpy.dot(v, v), f_v[i])
log.info(
'\n** Transition magnetic dipole moments (imaginary part, AU) **')
log.info('state X Y Z')
trans_m = tdobj.transition_magnetic_dipole()
for i, ei in enumerate(tdobj.e):
m = trans_m[i]
log.info('%3d %11.4f %11.4f %11.4f', i + 1, m[0], m[1], m[2])
return tdobj