def compute_coupling(
self,
S,
indexA,
indexB,
doETF=False, # Do Joe Subotnik ETF?
):
if indexA == indexB:
raise ValueError('indexA == indexB: you want a gradient?')
# Sizes
nao = self.sizes['nao']
nmo = self.sizes['nmo']
nocc = self.sizes['nocc']
nvir = self.sizes['nvir']
# Energy difference between states
dE = self.evals[S][indexB] - self.evals[S][indexA]
CA = self.evecs[S][indexA]
CB = self.evecs[S][indexB]
Cocc = self.tensors['Cocc']
Cvir = self.tensors['Cvir']
# Difference transition OPDM in AO basis
D1dao = ls.Tensor((nao, ) * 2)
if CA is None:
# <0|B>
# T_jb = + sqrt(2) CB_jb
D1dao[...] += np.sqrt(2.0) * ls.Tensor.chain([Cocc, CB, Cvir],
[False, False, True])
elif CB is None:
# <A|0>
# T_ai = + sqrt(2) CA_ia
D1dao[...] += np.sqrt(2.0) * ls.Tensor.chain([Cvir, CA, Cocc],
[False, True, True])
else:
# T_ab <- + CA_ia CB_ib
D1dao[...] = ls.Tensor.chain([Cvir, CA, CB, Cvir],
[False, True, False, True])
# T_ji <- - CA_ia CB_ja (watch the tanspose!)
D1dao[...] -= ls.Tensor.chain([Cocc, CB, CA, Cocc],
[False, False, True, True])
raise ValueError("Not implemented")
def orbital_atomic_charges(
self,
C,
):
""" Compute the orbital atomic charges Q_A^i for a set of orbitals C_mi
Only the electronic contribution is considered.
Params:
C (ls.Tensor of shape (nao, ni)) - Orbital coefficients
Returns:
Q (ls.Tensor of shape (natom, ni)) - Orbital atomic charges
"""
L = ls.Tensor.chain([C,self.S,self.A],[True,False,False])
Q = ls.Tensor((self.minbasis.natom,C.shape[1]), 'Q IBO')
for A, inds2 in enumerate(self.minao_inds):
Q[A,:] = np.sum(L[:,inds2]**2,1)
return Q
def test_casbox_orbital_transformation_det(
S=0,
M=6,
Na=3,
Nb=3,
H1=None,
I1=None,
):
# Random rotation matrix
A = ls.Tensor.array(np.random.rand(M, M) + 0.3 * np.eye(M))
Q, R = sp.qr(A)
Q = ls.Tensor.array(Q)
# Random permutation matrix (forces pivoting)
perm = np.random.permutation(list(range(M)))
Q2 = ls.Tensor((M,)*2)
for k, k2 in enumerate(perm):
Q2[k,k2] = 1.0
# Orbital transformation matrix (some rotation, required pivoting in LU)
Q3 = ls.Tensor.chain([Q, Q2], [False, False])
# Integrals in transformed basis
H2 = ls.Tensor.array(np.einsum('ae,bf,ab->ef', Q3, Q3, H1))
I2 = ls.Tensor.array(np.einsum('ae,bf,cg,dh,abcd->efgh', Q3, Q3, Q3, Q3, I1))
casbox1 = ls.CASBox(M, Na, Nb, H1, I1)
casbox2 = ls.CASBox(M, Na, Nb, H2, I2)
ebox1 = ls.ExplicitCASBox(casbox1)
ebox2 = ls.ExplicitCASBox(casbox2)
evec1 = ebox1.evec(S,0)
evec2 = ebox2.evec(S,0)
evec1d = casbox1.CSF_basis(S).transform_CSF_to_det(evec1)
evec2d = casbox2.CSF_basis(S).transform_CSF_to_det(evec2)
evec1dp = casbox1.orbital_transformation_det(Q3, evec1d)
O = evec1dp.vector_dot(evec2d)
OK = abs(abs(O) - 1.0) < 1.0E-13
return OK
def atomic_charges(
self,
D,
):
""" Compute the atomic charges Q_A for an OPDM D_mn.
Only the electronic contribution is considered.
Params:
D (ls.Tensor of shape (nao, nao)) - density matrix
Returns:
Q (ls.Tensor of shape (natom,)) - atomic charges
"""
V = ls.Tensor.chain([self.A, self.S, D, self.S, self.A], [True, False, False, False, False])
V2 = np.diag(V)
Q = ls.Tensor((self.minbasis.natom,), 'Q IBO')
for A, inds2 in enumerate(self.minao_inds):
Q[A] = np.sum(V2[inds2])
return Q
def compute_external_potential(
self,
pairlist,
):
""" Return the complete external potential of this Geometry, including the
nuclear attraction potential of the QM molecule, and any external
potential terms involving other structures in the Geometry. """
V = ls.Tensor((pairlist.basis1.nao, pairlist.basis2.nao))
ls.IntBox.potential(self.resources, self.ewald, pairlist,
self.qm_molecule_ecp.xyzZ, V)
# QM/MM
if self.qmmm:
V[...] += self.qmmm.compute_mm_potential(self.resources,
self.ewald, pairlist)
# ECP
if self.ecp:
V[...] += ls.IntBox.ecp(
self.resources,
pairlist,
self.ecp,
self.options['threecp'],
)
return V
O 0.000000000000 0.000000000000 -0.129476890157
H 0.000000000000 -1.494186750504 1.027446102928
H 0.000000000000 1.494186750504 1.027446102928""",
name='h2o',
scale=1.0)
bas = ls.Basis.from_gbs_file(mol, 'cc-pvdz')
minao = ls.Basis.from_gbs_file(mol, 'cc-pvdz-minao')
res = ls.ResourceList.build_cpu()
nocc = ls.SAD.sad_nocc_neutral(mol)
print(nocc)
Q = ls.Tensor((3, ))
Q[0] = 4.5
Q[1] = 0.5
Q[2] = 0.5
nocc = ls.SAD.sad_nocc(mol, Q)
print(nocc)
print(ls.SAD.sad_nocc_atoms())
S = ls.IntBox.overlap(res, ls.PairList.build_schwarz(bas, bas, True, 1.0E-14))
print(S)
C = ls.SAD.sad_orbitals(res, nocc, minao, bas)
print(C)
def __init__(
self,
options, # A dictionary of user options
):
# => Default Options <= #
self.options = RHF.options.copy()
# => Override Options <= #
for key, val in options.items():
if not key in list(self.options.keys()):
raise ValueError('Invalid user option: %s' % key)
self.options[key] = val
# => Useful Registers <= #
self.sizes = {}
self.scalars = {}
self.tensors = {}
# => Title Bars <= #
print('==> RHF <==\n')
# => Problem Geometry <= #
self.resources = self.options['resources']
self.molecule = self.options['molecule']
self.basis = self.options['basis']
self.minbasis = self.options['minbasis']
print(self.resources)
print(self.molecule)
print(self.basis)
print(self.minbasis)
self.sizes['natom'] = self.molecule.natom
self.sizes['nao'] = self.basis.nao
self.sizes['nmin'] = self.minbasis.nao
# => Nuclear Repulsion <= #
self.scalars['Enuc'] = self.molecule.nuclear_repulsion_energy()
print('Nuclear Repulsion Energy = %20.14f\n' % self.scalars['Enuc'])
# => Integral Thresholds <= #
print('Integral Thresholds:')
print(' Threshold PQ = %11.3E' % self.options['thre_pq'])
print(' Threshold DP = %11.3E' % self.options['thre_dp'])
print(' Threshold SP = %11.3E' % self.options['thre_sp'])
print('')
# => PairList <= #
self.pairlist = ls.PairList.build_schwarz(
self.basis,
self.basis,
True,
self.options['thre_pq'])
print(self.pairlist)
# => One-Electron Integrals <= #
print('One-Electron Integrals:\n')
self.tensors['S'] = ls.IntBox.overlap(
self.resources,
self.pairlist)
self.tensors['T'] = ls.IntBox.kinetic(
self.resources,
self.pairlist)
self.tensors['V'] = ls.IntBox.potential(
self.resources,
ls.Ewald.coulomb(),
self.pairlist,
self.molecule.xyzZ)
self.tensors['H'] = ls.Tensor.array(self.tensors['T'].np + self.tensors['V'].np)
# => Canonical Orthogonalization <= #
print('Canonical Orthogonalization:')
print(' Threshold = %11.3E' % self.options['thre_canonical'])
self.tensors['X'] = ls.Tensor.canonical_orthogonalize(self.tensors['S'], self.options['thre_canonical'])
self.sizes['nmo'] = self.tensors['X'].shape[1]
print(' Nmo = %11d' % self.sizes['nmo'])
print(' Ndiscard = %11d' % (self.sizes['nao'] - self.sizes['nmo']))
print('')
# => SAD Guess <= #
print('SAD Guess:\n')
self.tensors['CSAD'] = ls.SAD.orbitals(
self.resources,
self.molecule,
self.basis,
self.minbasis)
self.tensors['DSAD'] = ls.Tensor.chain([self.tensors['CSAD'],self.tensors['CSAD']],[False,True])
# => DIIS <= #
diis = ls.DIIS(
self.options['diis_max_vecs'],
)
print(diis)
# => Determine number of electrons (and check for integral singlet) <= #
if self.options['nocc'] is None:
if self.options['charge'] is None:
charge = self.molecule.charge
else:
charge = self.options['charge']
nelec = self.molecule.nuclear_charge - charge
nalpha = 0.5 * nelec
if nalpha != round(nalpha):
raise ValueError('Cannot do fractional electrons. Possibly charge/multiplicity are wrong.')
self.sizes['nocc'] = int(nalpha)
else:
self.sizes['nocc'] = int(self.options['nocc'])
self.sizes['nvir'] = self.sizes['nmo'] - self.sizes['nocc']
print('Orbital Spaces:')
print(' Nocc = %d' % self.sizes['nocc'])
print(' Nvir = %d' % self.sizes['nvir'])
print('')
# ==> SCF Iterations <== #
print('Convergence Options:')
print(' Max Iterations = %11d' % self.options['maxiter'])
print(' E Convergence = %11.3E' % self.options['e_convergence'])
print(' G Convergence = %11.3E' % self.options['g_convergence'])
print('')
self.tensors['D'] = ls.Tensor.array(self.tensors['DSAD'])
Eold = 0.
converged = False
print('SCF Iterations:\n')
print('%4s: %24s %11s %11s' % ('Iter', 'Energy', 'dE', 'dG'))
for iter in range(self.options['maxiter']):
# => Compute J/K Matrices <= #
import time
start = time.time()
self.tensors['J'] = ls.IntBox.coulomb(
self.resources,
ls.Ewald.coulomb(),
self.pairlist,
self.pairlist,
self.tensors['D'],
self.options['thre_sp'],
self.options['thre_dp'],
)
print('J: %11.3E' % (time.time() - start))
start = time.time()
self.tensors['K'] = ls.IntBox.exchange(
self.resources,
ls.Ewald.coulomb(),
self.pairlist,
self.pairlist,
self.tensors['D'],
True,
self.options['thre_sp'],
self.options['thre_dp'],
)
print('K: %11.3E' % (time.time() - start))
start = time.time()
# => Build Fock Matrix <= #
self.tensors['F'] = ls.Tensor.array(self.tensors['H'])
self.tensors['F'].np[...] += 2. * self.tensors['J'].np
self.tensors['F'].np[...] -= 1. * self.tensors['K'].np
# => Compute Energy <= #
self.scalars['Escf'] = self.scalars['Enuc'] + \
self.tensors['D'].vector_dot(self.tensors['H']) + \
self.tensors['D'].vector_dot(self.tensors['F'])
dE = self.scalars['Escf'] - Eold
Eold = self.scalars['Escf']
# => Compute Orbital Gradient <= #
G1 = ls.Tensor.chain([self.tensors[x] for x in ['X', 'S', 'D', 'F', 'X']], [True] + [False]*4)
G1.antisymmetrize()
G1[...] *= 2.0
self.tensors['G'] = G1
dG = np.max(np.abs(self.tensors['G']))
# => Print Iteration <= #
print('%4d: %24.16E %11.3E %11.3E' % (iter, self.scalars['Escf'], dE, dG))
# => Check Convergence <= #
if iter > 0 and abs(dE) < self.options['e_convergence'] and dG < self.options['g_convergence']:
converged = True
break
# => DIIS Fock Matrix <= #
if iter > 0:
self.tensors['F'] = diis.iterate(self.tensors['F'], self.tensors['G'])
# => Diagonalize Fock Matrix <= #
F2 = ls.Tensor.chain([self.tensors[x] for x in ['X', 'F', 'X']],[True,False,False])
e2, U2 = ls.Tensor.eigh(F2)
C2 = ls.Tensor.chain([self.tensors['X'], U2],[False,False])
e2.name = 'eps'
C2.name = 'C'
self.tensors['C'] = C2
self.tensors['eps'] = e2
# => Aufbau Occupy Orbitals <= #
self.tensors['Cocc'] = ls.Tensor((self.sizes['nao'], self.sizes['nocc']),'Cocc')
self.tensors['Cocc'].np[...] = self.tensors['C'].np[:,:self.sizes['nocc']]
# => Compute Density Matrix <= #
self.tensors['D'] = ls.Tensor.chain([self.tensors['Cocc'], self.tensors['Cocc']], [False, True])
print('T: %11.3E' % (time.time() - start))
# => Print Convergence <= #
print('')
if converged:
print('SCF Converged\n')
else:
print('SCF Failed\n')
# => Print Final Energy <= #
print('SCF Energy = %24.16E\n' % self.scalars['Escf'])
# => Cache the Orbitals/Eigenvalues (for later use) <= #
self.tensors['Cvir'] = ls.Tensor((self.sizes['nao'], self.sizes['nvir']), 'Cvir')
self.tensors['Cvir'].np[...] = self.tensors['C'].np[:,self.sizes['nocc']:]
self.tensors['eps_occ'] = ls.Tensor((self.sizes['nocc'],), 'eps_occ')
self.tensors['eps_occ'].np[...] = self.tensors['eps'].np[:self.sizes['nocc']]
self.tensors['eps_vir'] = ls.Tensor((self.sizes['nvir'],), 'eps_vir')
self.tensors['eps_vir'].np[...] = self.tensors['eps'].np[self.sizes['nocc']:]
# => Print Orbital Energies <= #
print(self.tensors['eps_occ'])
print(self.tensors['eps_vir'])
# => Trailer Bars <= #
print('"I love it when a plan comes together!"')
print(' --LTC John "Hannibal" Smith\n')
print('==> End RHF <==\n')
def diffraction_pattern(
self,
S,
index1,
index2,
):
""" Compute ab initio elastic or inelastic diffraction pattern for xray
or ued probes, using a variety of computational methods.
If it is tractable to use moments to exactly compute the scattering
signal (isotropic, parallel, perpendicular cases) this is done first.
If this is not tractable, the full diffraction pattern is directly
computed.
Params:
S (int) - spin index
index1 (int) - index of bra state
index2 (int) - index of ket state
Elastic scattering is assumed if index1==index2 (scattering off of total state density)
Inelastic scattering is assumed if index1!=index2 (scattering off of transition density)
Returns:
I (ls.Tensor of shape (ns,neta)) - diffraction pattern.
"""
# First try to compute via moments
if self.anisotropy in ['isotropic', 'parallel', 'perpendicular']:
IM = self.diffraction_moments(S=S,index1=index1,index2=index2)
return AISCAT.pattern_from_moments(IM,eta=self.eta)
# Otherwise, must compute aligned scattering signal
# Grid density collocation
xyzq = self.compute_xyzq(
D=self.lot.compute_opdm_ao(S, index1, index2),
include_nuclei=self.mode=='ued' and index1==index2,
)
print('Grid Density: %12.6f\n' % np.sum(xyzq[:,3]))
# Scattering collocation points
theta = 2.0 * np.arcsin(self.s[...] * self.L / (4.0 * np.pi))
tt, ee = np.meshgrid(theta, self.eta, indexing='ij')
ss, ee = np.meshgrid(self.s, self.eta, indexing='ij')
# Compute scattering vectors
sx = ss * np.cos(tt / 2.0) * np.sin(ee)
sy = ss * np.sin(tt / 2.0)
sz = ss * np.cos(tt / 2.0) * np.cos(ee)
# Pack for LS
sxyz = ls.Tensor((sx.size,3))
sxyz[:,0] = np.ravel(sx)
sxyz[:,1] = np.ravel(sy)
sxyz[:,2] = np.ravel(sz)
# Diffraction function
if self.algorithm == 'cpu': fun = ls2.aligned_diffraction2
elif self.algorithm == 'gpu_f_f': fun = ls2.aligned_diffraction_gpu_f_f
elif self.algorithm == 'gpu_f_d': fun = ls2.aligned_diffraction_gpu_f_d
elif self.algorithm == 'gpu_d_d': fun = ls2.aligned_diffraction_gpu_d_d
# Compute diffraction pattern
I = fun(
self.lot.geometry.resources,
sxyz,
xyzq,
)
# Make sure return is (ns, neta)
I = ls.Tensor.array(np.reshape(I, (self.s.shape[0], self.eta.shape[0])))
# 1/s^4 weight in UED
if self.mode == 'ued':
I[...] /= ss**4
return I
def compute_overlap(
cisA,
cisB,
S,
):
""" Compute the overlap between all states in spin block S in two CIS object.
Params:
cisA (CIS) - the bra-side CIS object
cisB (CIS) - the ket-side CIS object
S (int) - the spin index
Returns:
O (ls.Tensor, shape (nstateA, nstateB)) - the overlap matrix elements
"""
# TODO: Benchmark these overlaps
# Build the overlap integrals (p|q') in the AO basis
pairlist = ls.PairList.build_schwarz(cisA.basis, cisB.basis, False,
cisA.pairlist.thre)
Sao = ls.IntBox.overlap(cisA.resources, pairlist)
# Build the orbital overlap integrals in the occupied and active blocks of the MO basis
Sij = ls.Tensor.chain(
[cisA.tensors['Cocc'], Sao, cisB.tensors['Cocc']],
[True, False, False])
Sib = ls.Tensor.chain(
[cisA.tensors['Cocc'], Sao, cisB.tensors['Cvir']],
[True, False, False])
Saj = ls.Tensor.chain(
[cisA.tensors['Cvir'], Sao, cisB.tensors['Cocc']],
[True, False, False])
Sab = ls.Tensor.chain(
[cisA.tensors['Cvir'], Sao, cisB.tensors['Cvir']],
[True, False, False])
# Compute the overlap inverse and determinant in the core space
detC = Sij.invert_lu()
# Form modified metric integrals
Mij = Sij
Mia = ls.Tensor((cisA.sizes['nocc'], cisA.sizes['nvir']))
Mjb = ls.Tensor((cisB.sizes['nocc'], cisB.sizes['nvir']))
Mab = ls.Tensor.array(Sab)
if detC != 0.0:
# Mai[...] = ls.Tensor.chain([Saj, Mij], [False, False])
Mia[...] = ls.Tensor.chain(
[Mij, Saj],
[True, True]) # Transposed from the notes for easier dot
Mjb[...] = ls.Tensor.chain([Mij, Sib], [False, False])
Mab[...] -= ls.Tensor.chain([Saj, Mjb], [False, False])
# Compute the intermediates for connected overlap term
A2s = []
for A, evecA in enumerate(cisA.evecs[S]):
if S == 0 and A == 0:
A2s.append(None)
continue
A2s.append(ls.Tensor.chain([evecA, Mab], [False, False]))
B2s = []
for B, evecB in enumerate(cisB.evecs[S]):
if S == 0 and B == 0:
B2s.append(None)
continue
B2s.append(ls.Tensor.chain([Mij, evecB], [True, False]))
# Compute the overlaps
O = ls.Tensor((len(cisA.evecs[S]), len(cisB.evecs[S])))
for A, evecA in enumerate(cisA.evecs[S]):
for B, evecB in enumerate(cisB.evecs[S]):
if S == 0 and A == 0 and B == 0:
# <0|0>
O[A, B] = 1.0
continue
if S == 0 and A == 0:
# <0|B>
O[A, B] = np.sqrt(2.0) * evecB.vector_dot(Mjb)
continue
if S == 0 and B == 0:
# <A|0>
O[A, B] = np.sqrt(2.0) * evecA.vector_dot(Mia)
continue
else:
# <A|B>
O[A, B] = A2s[A].vector_dot(B2s[B])
if S == 0:
O[A, B] += 2.0 * evecA.vector_dot(
Mia) * evecB.vector_dot(Mjb)
# Account for the core overlap
O[...] *= detC**2
return O
def compute_gradient(
self,
S,
index,
):
# Handle the reference gradient separately
if S == 0 and index == 0: return self.reference.compute_gradient()
# Sizes
nao = self.sizes['nao']
nmo = self.sizes['nmo']
nocc = self.sizes['nocc']
nvir = self.sizes['nvir']
# CI vector and orbitals
Cvec = self.evecs[S][index]
C = self.tensors['C']
Cocc = self.tensors['Cocc']
Cvir = self.tensors['Cvir']
# Difference OPDM in AO basis
D1dao = ls.Tensor.chain([Cvir, Cvec, Cvec, Cvir],
[False, True, False, True])
D1dao[...] -= ls.Tensor.chain([Cocc, Cvec, Cvec, Cocc],
[False, False, True, True])
# Total OPDM in AO basis
D1ao = ls.Tensor.chain([Cocc, Cocc], [False, True])
D1ao[...] *= 2.0
D1ao[...] += D1dao
# CI Vector in AO basis
C1ao = ls.Tensor.chain([Cocc, Cvec, Cvir], [False, False, True])
# => J/K contributions <= #
JD1 = ls.IntBox.coulomb(
self.resources,
ls.Ewald.coulomb(),
self.pairlist,
self.pairlist,
D1dao,
self.options['thre_sp'],
self.options['thre_dp'],
)
KD1 = ls.IntBox.exchange(
self.resources,
ls.Ewald.coulomb(),
self.pairlist,
self.pairlist,
D1dao,
True,
self.options['thre_sp'],
self.options['thre_dp'],
)
JC1 = ls.IntBox.coulomb(
self.resources,
ls.Ewald.coulomb(),
self.pairlist,
self.pairlist,
C1ao,
self.options['thre_sp'],
self.options['thre_dp'],
)
KC1 = ls.IntBox.exchange(
self.resources,
ls.Ewald.coulomb(),
self.pairlist,
self.pairlist,
C1ao,
False,
self.options['thre_sp'],
self.options['thre_dp'],
)
# TODO: The following manipulations can be *much* faster if one exploits block sparsity
# => Fock Matrices (Long Way) <= #
FO2 = ls.Tensor.chain([C, self.reference.tensors['F'], C],
[True, False, False])
FD2 = ls.Tensor.chain([C, JD1, C], [True, False, False])
FD2.np[...] -= 0.5 * ls.Tensor.chain([C, KD1, C],
[True, False, False]).np
FA2 = ls.Tensor.array(FO2)
FA2.np[...] += FD2
# => MO-Basis OPDMs (Long Way) <= #
D2 = ls.Tensor((nmo, ) * 2)
D2[nocc:, nocc:] += ls.Tensor.chain([Cvec, Cvec], [True, False])
D2[:nocc, :nocc] -= ls.Tensor.chain([Cvec, Cvec], [False, True])
A2 = ls.Tensor.array(np.diag(self.reference.tensors['n']))
A2[...] *= 2.0
A2[...] += D2
# => MO-Basis Amplitudes (Long Way) <= #
C2 = ls.Tensor((nmo, ) * 2)
C2[:nocc, nocc:] = Cvec
# => Lagrangian (Long Way) <= #
X = ls.Tensor([self.sizes['nmo']] * 2)
X.np[...] += ls.Tensor.chain([A2, FA2], [False, False])
X.np[...] -= ls.Tensor.chain([D2, FD2], [False, False])
if S == 0:
X.np[...] += 2. * ls.Tensor.chain([C2, C, JC1, C],
[False, True, True, False]).np
X.np[...] += 2. * ls.Tensor.chain([C2, C, JC1, C],
[True, True, False, False]).np
X.np[...] -= 1. * ls.Tensor.chain([C2, C, KC1, C],
[False, True, True, False]).np
X.np[...] -= 1. * ls.Tensor.chain([C2, C, KC1, C],
[True, True, False, False]).np
X[...] *= 2.0 # Spin-summed convention
X = X.transpose(
) # Ed's convention: X_pq = 2 h_pr D1_qr + 4 (pr|st) D2_qrst
# => TPDM Gradient <= #
grads = collections.OrderedDict()
# Coulomb integral gradient 1
grads['J1'] = ls.IntBox.coulombGrad(
self.resources,
ls.Ewald.coulomb(),
self.pairlist,
D1ao,
D1ao,
self.options['thre_sp'],
self.options['thre_dp'],
)
grads['J1'].np[...] *= +0.5
# Coulomb integral gradient 2
grads['J2'] = ls.IntBox.coulombGrad(
self.resources,
ls.Ewald.coulomb(),
self.pairlist,
D1dao,
D1dao,
self.options['thre_sp'],
self.options['thre_dp'],
)
grads['J2'].np[...] *= -0.5
# Exchange integral gradient 1
grads['K1'] = ls.IntBox.exchangeGrad(
self.resources,
ls.Ewald.coulomb(),
self.pairlist,
D1ao,
D1ao,
True,
True,
True,
self.options['thre_sp'],
self.options['thre_dp'],
)
grads['K1'].np[...] *= -0.25
# Exchange integral gradient 2
grads['K2'] = ls.IntBox.exchangeGrad(
self.resources,
ls.Ewald.coulomb(),
self.pairlist,
D1dao,
D1dao,
True,
True,
True,
self.options['thre_sp'],
self.options['thre_dp'],
)
grads['K2'].np[...] *= +0.25
# Coulomb integral gradient 3
grads['J3'] = ls.IntBox.coulombGrad(
self.resources,
ls.Ewald.coulomb(),
self.pairlist,
C1ao,
C1ao,
self.options['thre_sp'],
self.options['thre_dp'],
)
grads['J3'].np[...] *= +2.0 if S == 0 else 0.0
# Exchange integral gradient 2
grads['K3'] = ls.IntBox.exchangeGrad(
self.resources,
ls.Ewald.coulomb(),
self.pairlist,
C1ao,
C1ao,
False,
False,
True,
self.options['thre_sp'],
self.options['thre_dp'],
)
grads['K3'].np[...] *= -1.0
grad2e = ls.Tensor.zeros_like(grads['J1'])
for grad in list(grads.values()):
grad2e[...] += grad
# for key, grad in grads.iteritems():
# grad.name = key
# print grad
return self.reference.compute_hf_based_gradient(D1ao, X, grad2e)
def compute_dipoles(
self,
S,
x0=0.0,
y0=0.0,
z0=0.0,
):
"""Calculates total and transition dipole moments for all states in
spin block S.
Params:
S (int) - spin block index
x0 (float) - origin
y0 (float) - origin
z0 (float) - origin
Returns:
XYZ ((nstates, nstates) ls.Tensor.array) - transition dipole matrix
"""
# xyz dipole matrix in AO basis
XYZ = ls.IntBox.dipole(
self.resources,
self.pairlist,
x0,
y0,
z0,
)
evecs = self.evecs[S]
nstate = len(evecs)
Cocc = self.tensors['Cocc']
Cvir = self.tensors['Cvir']
XYZ3 = [ls.Tensor((nstate, nstate)) for x in range(3)]
for A, evecA in enumerate(evecs):
for B, evecB in enumerate(evecs):
if A > B: continue
if evecA is None and evecB is None: continue # <0|D|0>
if evecA is None: # <0|D|0>
# D_ia = + sqrt(2) C_ia
Dao = ls.Tensor.chain([Cocc, evecB, Cvir],
[False, False, True])
Dao[...] *= np.sqrt(2.0)
else:
# D_ab = + C_ia C_ib
Dao = ls.Tensor.chain([Cvir, evecA, evecB, Cvir],
[False, True, False, True])
# D_ij = - C_ja C_ia
Dao[...] -= ls.Tensor.chain([Cocc, evecB, evecA, Cocc],
[False, False, True, True])
# Dot with AB-basis
XYZ3[0][A, B] = XYZ3[0][B, A] = Dao.vector_dot(XYZ[0])
XYZ3[1][A, B] = XYZ3[1][B, A] = Dao.vector_dot(XYZ[1])
XYZ3[2][A, B] = XYZ3[2][B, A] = Dao.vector_dot(XYZ[2])
# Reference density matrix
Dcore = ls.Tensor.chain([Cocc, Cocc], [False, True])
Dcore[...] *= 2.0
Xcore = Dcore.vector_dot(XYZ[0])
Ycore = Dcore.vector_dot(XYZ[1])
Zcore = Dcore.vector_dot(XYZ[2])
# Get nuclear dipole
for A, atomA in enumerate(self.qm_molecule.atoms):
Xcore -= atomA.Z * (atomA.x - x0)
Ycore -= atomA.Z * (atomA.y - y0)
Zcore -= atomA.Z * (atomA.z - z0)
for A in range(nstate):
XYZ3[0][A, A] += Xcore
XYZ3[1][A, A] += Ycore
XYZ3[2][A, A] += Zcore
return XYZ3
def compute_states(
self,
Sindex,
nstate,
):
# => Title <= #
title = 'S=%d' % Sindex
if self.print_level:
print('=> %s States <=\n' % title)
if Sindex not in [0, 2]:
raise RuntimeError('Invalid Sindex for CIS: %d' % Sindex)
# => Preconditioner <= #
F = ls.Tensor((self.sizes['nocc'], self.sizes['nvir']))
F.np[...] += np.einsum('i,a->ia', np.ones(self.sizes['nocc']),
self.tensors['eps_vir'])
F.np[...] -= np.einsum('i,a->ia', self.tensors['eps_occ'],
np.ones(self.sizes['nvir']))
# => Guess Vectors <= #
nstate_new = nstate - 1 if Sindex == 0 else nstate
nguess = min(self.sizes['nocc'] * self.sizes['nvir'],
nstate_new * self.options['nguess_per_root'])
if self.print_level > 1:
print('Guess Details:')
print(' Nguess: %11d' % nguess)
Forder = sorted([(x, xind[0], xind[1])
for xind, x in np.ndenumerate(F)])
Cs = []
for k in range(nguess):
C = ls.Tensor((self.sizes['nocc'], self.sizes['nvir']))
r = Forder[k][1]
c = Forder[k][2]
if self.print_level > 1:
print(' %3d: %5d -> %-5d' % (k, r, c + self.sizes['nocc']))
C.np[r, c] = +1.0
Cs.append(C)
if self.print_level > 1:
print('')
# => Convergence Info <= #
if self.print_level > 1:
print('Convergence:')
print(' Maxiter: %11d' % self.options['maxiter'])
print('')
# => Davidson Object <= #
dav = ls.Davidson(
nstate_new,
self.options['nmax'],
self.options['r_convergence'],
self.options['norm_cutoff'],
)
if self.print_level > 1:
print(dav)
# ==> Davidson Iterations <== #
if self.print_level:
print('%s CIS Iterations:\n' % title)
print('%4s: %11s' % ('Iter', '|R|'))
converged = False
for iter in range(self.options['maxiter']):
# Sigma Vector Builds
Ss = [ls.Tensor.clone(C) for C in Cs]
for C, S in zip(Cs, Ss):
# One-Particle Term
S.np[...] *= F
# Two-Particle Term
D = ls.Tensor.chain(
[self.tensors['Cocc'], C, self.tensors['Cvir']],
[False, False, True])
if Sindex == 0:
J = ls.IntBox.coulomb(
self.resources,
ls.Ewald.coulomb(),
self.pairlist,
self.pairlist,
D,
self.options['thre_sp'],
self.options['thre_dp'],
)
J2 = ls.Tensor.chain(
[self.tensors['Cocc'], J, self.tensors['Cvir']],
[True, False, False])
K = ls.IntBox.exchange(
self.resources,
ls.Ewald.coulomb(),
self.pairlist,
self.pairlist,
D,
False,
self.options['thre_sp'],
self.options['thre_dp'],
)
K2 = ls.Tensor.chain(
[self.tensors['Cocc'], K, self.tensors['Cvir']],
[True, False, False])
if Sindex == 0:
S.np[...] += 2. * J2.np - K2.np
else:
S.np[...] -= K2.np
# Add vectors/diagonalize Davidson subspace
Rs, Es = dav.add_vectors(Cs, Ss, use_disk=self.options['use_disk'])
# Print Iteration Trace
if self.print_level:
print('%4d: %11.3E' % (iter, dav.max_rnorm))
# Check for convergence
if dav.is_converged:
converged = True
break
# Precondition the desired residuals
for R, E in zip(Rs, Es):
R.np[...] /= -(F.np[...] - E)
# Get new trial vectors
Cs = dav.add_preconditioned(Rs, use_disk=self.options['use_disk'])
# => Output Quantities <= #
# Print Convergence
if self.print_level:
print('')
if converged:
print('%s CIS Converged\n' % title)
else:
print('%s CIS Failed\n' % title)
# Cache quantities
self.converged[Sindex] = converged
self.evals[Sindex] = []
self.evecs[Sindex] = []
# Make allowance for the reference state
if Sindex == 0:
self.evals[Sindex] += [self.scalars['Escf']]
self.evecs[Sindex] += [None]
self.evals[Sindex] += [x + self.scalars['Escf'] for x in dav.evals]
self.evecs[Sindex] += [
ls.Storage.from_storage(x, Ss[0]) for x in dav.evecs
]
# Print residuals
if self.print_level:
print('CIS %s Residuals:\n' % title)
print('%4s: %11s' % ('I', '|R|'))
for rind, r in enumerate(dav.rnorms):
Soffset = 1 if Sindex == 0 else 0 # offset for the ground state
print('%4d: %11.3E %s' %
(rind + Soffset, r, 'Converged' if
r < self.options['r_convergence'] else 'Not Converged'))
print('')
# Print energies
if self.print_level:
print('CIS %s Energies:\n' % title)
print('%4s: %24s' % ('I', 'Total E'))
for Eind, E in enumerate(self.evals[Sindex]):
print('%4d: %24.16E' % (Eind, E))
print('')
if self.print_level:
print('=> End %s States <=\n' % title)
def compute_cphf(
self,
G, # A tensor which is nocc x nvir
options={}, # Override options
):
# => Override Options <= #
options2 = options
options = RHF.cphf_options.copy()
for key, val in options2.items():
if not key in list(options.keys()):
raise ValueError('Invalid user option: %s' % key)
options[key] = val
# Check that G has correct shape
G.shape_error((self.sizes['nocc'], self.sizes['nvir']))
# => Header <= #
#print '==> CPHF <==\n'
# => DIIS <= #
diis = ls.DIIS(options['diis_max_vecs'], )
#print diis
# => Preconditioner <= #
# Fock-Matrix Contribution (Preconditioner)
F = ls.Tensor((self.sizes['nocc'], self.sizes['nvir']), 'F')
F.np[...] += np.einsum('i,a->ia', np.ones(self.sizes['nocc']),
self.tensors['eps_vir'])
F.np[...] -= np.einsum('i,a->ia', self.tensors['eps_occ'],
np.ones(self.sizes['nvir']))
# => Initial Guess (UCHF Result) <= #
X = ls.Tensor.array(G)
X.np[...] /= 4. * F.np[...]
# ==> Iterations <== #
converged = False
#print 'CPHF Iterations:\n'
#print '%4s: %11s' % ('Iter', 'dR')
for iter in range(options['maxiter'] + 1):
# => Compute the Residual <= #
R = ls.Tensor.array(G)
# One-electron term
R.np[...] -= 4. * F.np[...] * X.np[...]
# Two-electron terms
D = ls.Tensor.chain(
[self.tensors['Cocc'], X, self.tensors['Cvir']],
[False, False, True])
D.symmetrize()
I = ls.Tensor.zeros_like(D)
I.np[...] += 16. * ls.IntBox.coulomb(
self.resources,
ls.Ewald.coulomb(),
self.pairlist,
self.pairlist,
D,
options['thre_sp'],
options['thre_dp'],
).np
I.np[...] -= 8. * ls.IntBox.exchange(
self.resources,
ls.Ewald.coulomb(),
self.pairlist,
self.pairlist,
D,
True,
options['thre_sp'],
options['thre_dp'],
).np
R.np[...] -= ls.Tensor.chain(
[self.tensors['Cocc'], I, self.tensors['Cvir']],
[True, False, False])
# => Precondition the Residual <= #
R.np[...] /= 4. * F.np
X.np[...] += R.np # Approximate NR-Step
# => Check Convergence <= #
Rmax = np.max(np.abs(R))
#print '%4d: %11.3E' % (iter, Rmax)
if Rmax < options['convergence']:
converged = True
break
# => Perform DIIS <= #
X = diis.iterate(X, R, use_disk=options['diis_use_disk'])
# => Print Convergence <= #
#print ''
if converged:
#print 'CPHF Converged\n'
pass
else:
#print 'CPHF Failed\n'
return False
# => Trailer <= #
#print '==> End CPHF <==\n'
return X
def localize(
self,
C,
F,
print_level=0,
):
""" Localize orbitals.
Params:
C (ls.Tensor of shape (nao, ni)) - Orbitals to localize - these
must live inside the span of Cref.
F (ls.Tensor of shape, (ni, ni)) - Fock matrix in orbital basis.
Used to sort localized orbitals to ascending orbital energies.
print_level (int) - 0 - no printing, 1 - print iterative history
and converence info.
Returns:
U (ls.Tensor of shape (ni, ni)) - Rotation from original orbitals
(rows) to localized orbitals (cols).
L (ls.Tensor of shape (nao, ni)) - Localized orbital coefficients.
F (ls.Tensor of shape (ni, ni)) - Fock matrix in local orbital basis.
converged (bool) - Did the localization procedure converge (True)
or not (False).
Definitions:
L = C * U
F2 = L' * F * L
Localized orbitals are sorted to have ascending orbital energies.
"""
if print_level:
print('==> IBO Localization <==\n')
print('IBO Convergence Options:')
print(' Power = %11d' % self.options['power'])
print(' Maxiter = %11d' % self.options['maxiter'])
print(' G Convergence = %11.3E' % self.options['g_convergence'])
print('')
L = ls.Tensor.chain([C,self.S,self.A],[True,False,False])
U = ls.Tensor((C.shape[1],)*2)
ret = ls.Local.localize(
self.options['power'],
self.options['maxiter'],
self.options['g_convergence'],
self.minbasis,
L,
U,
)
converged = ret[-1,1] < self.options['g_convergence']
if print_level:
print('IBO %4s: %24s %11s %11s' % ('Iter', 'Metric', 'Delta', 'Gradient'))
retnp = ret.np
Eold = 0.0
for ind in range(ret.shape[0]):
E = retnp[ind,0]
G = retnp[ind,1]
print('IBO %4d: %24.16E %11.3E %11.3E' % (
ind+1,
E,
E-Eold,
G,
))
Eold = E
print('')
if converged:
print('IBO converged\n')
else:
print('IBO failed\n')
# Energy ordering
eps = np.diag(ls.Tensor.chain([U,F,U],[True,False,False]))
U = ls.Tensor.array(U[:,np.argsort(eps)])
# Localized orbitals
C2 = ls.Tensor.chain([C,U],[False,False])
# Localized Fock matrix
F = ls.Tensor.chain([U,F,U],[True,False,False])
if print_level:
print('==> End IBO Localization <==\n')
return U, C2, F, converged
