def test_inversion() -> None:
"""Test that each kind of inversion function gives identical results."""
mol = molecules_pyscf.molecule_glycine_sto3g()
mol.charge = 1
mol.spin = 1
mol.build()
mf = pyscf.scf.uhf.UHF(mol)
mf.scf()
assert isinstance(mf.mo_coeff, np.ndarray)
assert len(mf.mo_coeff) == 2
C = utils.fix_mocoeffs_shape(mf.mo_coeff)
E = utils.fix_moenergies_shape(mf.mo_energy)
occupations = occupations_from_pyscf_mol(mol, C)
calculator_ref = magnetic.Magnetizability(
Program.PySCF,
mol,
cphf.CPHF(solvers.ExactInv(C, E, occupations)),
C,
E,
occupations,
)
calculator_ref.form_operators()
calculator_ref.run(hamiltonian=Hamiltonian.RPA, spin=Spin.singlet)
calculator_ref.form_results()
inv_funcs = (sp.linalg.inv, sp.linalg.pinv, sp.linalg.pinv2)
thresh = 6.0e-14
for inv_func in inv_funcs:
calculator_res = magnetic.Magnetizability(
Program.PySCF,
mol,
cphf.CPHF(solvers.ExactInv(C, E, occupations)),
C,
E,
occupations,
)
calculator_res.form_operators()
calculator_res.run(hamiltonian=Hamiltonian.RPA, spin=Spin.singlet)
calculator_res.form_results()
np.testing.assert_equal(
np.sign(calculator_ref.magnetizability),
np.sign(calculator_res.magnetizability),
)
diff = calculator_ref.magnetizability - calculator_res.magnetizability
abs_diff = np.abs(diff)
print(abs_diff)
assert np.all(abs_diff < thresh)
def test_final_result_rhf_h2o_sto3g_rpa_singlet_iter() -> None:
mol = molecules_psi4.molecule_physicists_water_sto3g()
psi4.core.set_active_molecule(mol)
psi4.set_options({
"scf_type": "direct",
"df_scf_guess": False,
"e_convergence": 1e-11,
"d_convergence": 1e-11,
})
_, wfn = psi4.energy("hf", return_wfn=True)
C = mocoeffs_from_psi4wfn(wfn)
E = moenergies_from_psi4wfn(wfn)
occupations = occupations_from_psi4wfn(wfn)
frequencies = [0.0, 0.0773178]
ref_polarizability = electric.Polarizability(
Program.Psi4,
mol,
cphf.CPHF(solvers.ExactInv(C, E, occupations)),
C,
E,
occupations,
frequencies=frequencies,
)
ref_polarizability.form_operators()
ref_polarizability.run(hamiltonian=Hamiltonian.RPA, spin=Spin.singlet)
ref_polarizability.form_results()
ref_operator = ref_polarizability.driver.solver.operators[0]
res_polarizability = electric.Polarizability(
Program.Psi4,
mol,
cphf.CPHF(
solvers.IterativeLinEqSolver(C,
E,
occupations,
integrals.JKPsi4(wfn),
conv=1.0e-12)),
C,
E,
occupations,
frequencies=frequencies,
)
res_polarizability.form_operators()
res_polarizability.run(hamiltonian=Hamiltonian.RPA, spin=Spin.singlet)
res_polarizability.form_results()
res_operator = res_polarizability.driver.solver.operators[0]
np.testing.assert_allclose(
ref_polarizability.polarizabilities,
res_polarizability.polarizabilities,
rtol=0.0,
atol=1.0e-6,
)
def test_magnetizability_uhf() -> None:
mol = molecules.molecule_glycine_sto3g()
mol.charge = 1
mol.spin = 1
mol.build()
mf = pyscf.scf.uhf.UHF(mol)
mf.scf()
C = utils.fix_mocoeffs_shape(mf.mo_coeff)
E = utils.fix_moenergies_shape(mf.mo_energy)
occupations = occupations_from_pyscf_mol(mol, C)
calculator_common = magnetic.Magnetizability(
Program.PySCF,
mol,
cphf.CPHF(solvers.ExactInv(C, E, occupations)),
C,
E,
occupations,
)
calculator_common.form_operators()
calculator_common.run(hamiltonian=Hamiltonian.RPA, spin=Spin.singlet)
calculator_common.form_results()
ref_eigvals, ref_iso, _ = utils.tensor_printer(ref_magnetizability_rohf)
res_eigvals, res_iso, _ = utils.tensor_printer(
calculator_common.magnetizability)
thresh_eigval = 1.0e-1
for i in range(3):
assert abs(ref_eigvals[i] - res_eigvals[i]) < thresh_eigval
def test_electronicgtensor_small() -> None:
mol = molecules.molecule_bc2h4_neutral_radical_sto3g()
mol.build()
mf = pyscf.scf.uhf.UHF(mol)
mf.scf()
C = utils.fix_mocoeffs_shape(mf.mo_coeff)
E = utils.fix_moenergies_shape(mf.mo_energy)
occupations = occupations_from_pyscf_mol(mol, C)
gtensor_calculator = magnetic.ElectronicGTensor(
Program.PySCF,
mol,
cphf.CPHF(solvers.ExactInv(C, E, occupations)),
C,
E,
occupations,
)
gtensor_calculator.form_operators()
gtensor_calculator.run(hamiltonian=Hamiltonian.RPA, spin=Spin.singlet)
gtensor_calculator.form_results()
print(ref_electronicgtensor_small)
print(gtensor_calculator.g_oz_soc_1)
assert np.all(
np.equal(np.sign(ref_electronicgtensor_small),
np.sign(gtensor_calculator.g_oz_soc_1)))
def test_ORD_RPA_singlet_BC2H4_HF_STO3G():
ref = BC2H4_HF_STO3G_RPA_singlet_nwchem
pyscfmol = molecules.molecule_bc2h4_neutral_radical_sto3g()
pyscfmol.build()
mf = pyscf.scf.UHF(pyscfmol)
mf.scf()
C = utils.fix_mocoeffs_shape(mf.mo_coeff)
E = utils.fix_moenergies_shape(mf.mo_energy)
occupations = occupations_from_pyscf_mol(pyscfmol, C)
frequencies = [0.0, 0.001, 0.0773178, 0.128347]
ord_solver = optrot.ORD(
Program.PySCF,
pyscfmol,
cphf.CPHF(solvers.ExactInv(C, E, occupations)),
C,
E,
occupations,
frequencies=frequencies,
do_dipvel=False,
)
ord_solver.form_operators()
ord_solver.run(hamiltonian=Hamiltonian.RPA, spin=Spin.singlet)
ord_solver.form_results()
print("Polarizabilities")
assert len(frequencies) == len(ord_solver.polarizabilities)
thresh = 6.5e-4
for idxf, frequency in enumerate(frequencies):
ref_polar = ref[frequency]["polar"]
res_polar = ord_solver.polarizabilities[idxf]
abs_diff = abs(res_polar - ref_polar)
print(idxf, frequency)
print(res_polar)
print(abs_diff)
if frequency == 0.128347:
thresh = 6.0e-3
assert (abs_diff < thresh).all()
print(r"\beta(\omega)")
thresh = 0.09
for idxf, frequency in enumerate(frequencies):
if "orbeta" in ref[frequency]:
ref_beta = ref[frequency]["orbeta"]
# TODO why no speed of light?
# TODO why the (1/2)?
res_beta = -(0.5 /
frequency) * ord_solver.driver.results[idxf][3:6, 0:3]
abs_diff = abs(res_beta - ref_beta)
print(idxf, frequency)
print(res_beta)
print(ref_beta)
print(abs_diff)
assert (abs_diff < thresh).all()
def test_uncoupled_rhf() -> None:
mol = molecules.molecule_trithiolane_sto3g()
mol.build()
mf = pyscf.scf.RHF(mol)
mf.scf()
C = utils.fix_mocoeffs_shape(mf.mo_coeff)
E = utils.fix_moenergies_shape(mf.mo_energy)
occupations = occupations_from_pyscf_mol(mol, C)
solver = solvers.ExactInv(C, E, occupations)
ao2mo = AO2MOpyscf(C, mol.verbose, mol)
ao2mo.perform_rhf_partial()
solver.tei_mo = ao2mo.tei_mo
solver.tei_mo_type = AO2MOTransformationType.partial
driver = cphf.CPHF(solver)
operator_diplen = operators.Operator(label="dipole",
is_imaginary=False,
is_spin_dependent=False,
triplet=False)
integrals_diplen_ao = mol.intor("cint1e_r_sph", comp=3)
operator_diplen.ao_integrals = integrals_diplen_ao
driver.add_operator(operator_diplen)
frequencies = [0.0, 0.0773178, 0.128347]
driver.set_frequencies(frequencies)
driver.run(
hamiltonian=Hamiltonian.RPA,
spin=Spin.singlet,
program=Program.PySCF,
program_obj=mol,
)
for idxf, frequency in enumerate(frequencies):
print(idxf, frequency)
print("uncoupled")
diag_res = np.diag(driver.uncoupled_results[idxf])
diag_ref = np.diag(rhf_uncoupled[frequency]["result"])
diff = diag_res - diag_ref
print(diag_res)
print(diag_ref)
print(diff)
assert np.max(
np.abs(diff)) < rhf_uncoupled[frequency]["error_max_diag"]
print("coupled")
diag_res = np.diag(driver.results[idxf])
diag_ref = np.diag(rhf_coupled[frequency]["result"])
diff = diag_res - diag_ref
print(diag_res)
print(diag_ref)
print(diff)
assert np.max(np.abs(diff)) < rhf_coupled[frequency]["error_max_diag"]
def test_uncoupled_uhf():
mol = molecules.molecule_trithiolane_sto3g()
mol.charge = 1
mol.spin = 1
mol.build()
mf = pyscf.scf.uhf.UHF(mol)
mf.scf()
C = utils.fix_mocoeffs_shape(mf.mo_coeff)
E = utils.fix_moenergies_shape(mf.mo_energy)
occupations = utils.occupations_from_pyscf_mol(mol, C)
solver = iterators.ExactInv(C, E, occupations)
ao2mo = AO2MOpyscf(C, mol.verbose, mol)
ao2mo.perform_uhf_partial()
solver.tei_mo = ao2mo.tei_mo
solver.tei_mo_type = "partial"
driver = cphf.CPHF(solver)
operator_diplen = operators.Operator(
label="dipole", is_imaginary=False, is_spin_dependent=False, triplet=False
)
integrals_diplen_ao = mol.intor("cint1e_r_sph", comp=3)
operator_diplen.ao_integrals = integrals_diplen_ao
driver.add_operator(operator_diplen)
frequencies = [0.0, 0.0773178, 0.128347, 0.4556355]
driver.set_frequencies(frequencies)
driver.run(solver_type="exact", hamiltonian="rpa", spin="singlet")
for idxf, frequency in enumerate(frequencies):
print(idxf, frequency)
print("uncoupled")
diag_res = np.diag(driver.uncoupled_results[idxf])
diag_ref = np.diag(uhf_uncoupled[frequency]["result"])
diff = diag_res - diag_ref
print(diag_res)
print(diag_ref)
print(diff)
assert np.max(np.abs(diff)) < uhf_uncoupled[frequency]["error_max_diag"]
print("coupled")
diag_res = np.diag(driver.results[idxf])
diag_ref = np.diag(uhf_coupled[frequency]["result"])
diff = diag_res - diag_ref
print(diag_res)
print(diag_ref)
print(diff)
assert np.max(np.abs(diff)) < uhf_coupled[frequency]["error_max_diag"]
return
def test_explicit_uhf():
mol = molecules.molecule_water_sto3g()
mol.charge = 1
mol.spin = 1
mol.build()
mf = pyscf.scf.UHF(mol)
mf.kernel()
C = np.stack(mf.mo_coeff, axis=0)
E_a = np.diag(mf.mo_energy[0])
E_b = np.diag(mf.mo_energy[1])
assert E_a.shape == E_b.shape
E = np.stack((E_a, E_b), axis=0)
integrals_dipole_ao = mol.intor("cint1e_r_sph", comp=3)
occupations = utils.occupations_from_pyscf_mol(mol, C)
solver = iterators.ExactInv(C, E, occupations)
ao2mo = AO2MOpyscf(C, mol.verbose, mol)
ao2mo.perform_uhf_full()
solver.tei_mo = ao2mo.tei_mo
solver.tei_mo_type = "full"
driver = cphf.CPHF(solver)
operator_dipole = operators.Operator(label="dipole",
is_imaginary=False,
is_spin_dependent=False)
operator_dipole.ao_integrals = integrals_dipole_ao
driver.add_operator(operator_dipole)
driver.set_frequencies()
driver.run(solver_type="exact", hamiltonian="rpa", spin="singlet")
assert len(driver.frequencies) == len(driver.results) == 1
res = driver.results[0]
print(res)
atol = 1.0e-5
rtol = 0.0
np.testing.assert_allclose(res,
ref_water_cation_UHF_HF_STO3G,
rtol=rtol,
atol=atol)
def test_ORD_RPA_singlet_trithiolane_HF_STO3G():
ref = trithiolane_HF_STO3G_RPA_singlet
pyscfmol = molecules.molecule_trithiolane_sto3g()
pyscfmol.build()
mf = pyscf.scf.RHF(pyscfmol)
mf.scf()
C = utils.fix_mocoeffs_shape(mf.mo_coeff)
E = utils.fix_moenergies_shape(mf.mo_energy)
occupations = occupations_from_pyscf_mol(pyscfmol, C)
frequencies = [0.0, 0.0773178, 0.128347]
ord_solver = optrot.ORD(
Program.PySCF,
pyscfmol,
cphf.CPHF(solvers.ExactInv(C, E, occupations)),
C,
E,
occupations,
frequencies=frequencies,
do_dipvel=False,
)
ord_solver.form_operators()
ord_solver.run(hamiltonian=Hamiltonian.RPA, spin=Spin.singlet)
ord_solver.form_results()
print("Polarizabilities")
assert len(frequencies) == len(ord_solver.polarizabilities)
thresh = 5.0e-4
for idxf, frequency in enumerate(frequencies):
ref_polar = ref[frequency]["polar"]
res_polar = ord_solver.polarizabilities[idxf]
abs_diff = abs(res_polar - ref_polar)
print(idxf, frequency)
print(res_polar)
print(abs_diff)
assert (abs_diff < thresh).all()
def test_first_hyperpolarizability_shg_rhf_wigner_explicit_psi4numpy_pyscf_large():
mol = molecule_physicists_water_augccpvdz()
mol.build()
mf = pyscf.scf.RHF(mol)
mf.kernel()
C = utils.fix_mocoeffs_shape(mf.mo_coeff)
E = utils.fix_moenergies_shape(mf.mo_energy)
occupations = occupations_from_pyscf_mol(mol, C)
nocc_alph, nvirt_alph, _, _ = occupations
nov_alph = nocc_alph * nvirt_alph
norb = nocc_alph + nvirt_alph
# calculate linear response vectors for electric dipole operator
f1 = 0.0773178
f2 = 2 * f1
frequencies = [f1, f2]
calculator = electric.Polarizability(
Program.PySCF,
mol,
cphf.CPHF(solvers.ExactInv(C, E, occupations)),
C,
E,
occupations,
frequencies=frequencies,
)
calculator.form_operators()
calculator.run(hamiltonian=Hamiltonian.RPA, spin=Spin.singlet)
calculator.form_results()
polarizability_1 = calculator.polarizabilities[0]
polarizability_2 = calculator.polarizabilities[1]
print("polarizability: {} a.u.".format(f1))
print(polarizability_1)
print("polarizability: {} a.u. (frequency doubled)".format(f2))
print(polarizability_2)
# each operator contains multiple sets of response vectors, one
# set of components for each frequency
assert isinstance(calculator.driver.solver.operators, list)
assert len(calculator.driver.solver.operators) == 1
operator = calculator.driver.solver.operators[0]
rhsvecs = operator.mo_integrals_ai_supervector_alph
assert isinstance(operator.rspvecs_alph, list)
assert len(operator.rspvecs_alph) == 2
rspvecs_1 = operator.rspvecs_alph[0]
rspvecs_2 = operator.rspvecs_alph[1]
## Form the full [norb, norb] representation of everything.
# Response vectors: transform X_{ia} and Y_{ia} -> U_{p,q}
# 0. 'a' is fast index, 'i' slow
# 1. rspvec == [X Y]
# 2. U_{p, q} -> zero
# 3. place X_{ia} into U_{i, a}
# 4. place Y_{ia} into U_{a, i}
ncomp = rhsvecs.shape[0]
rspmats_1 = np.zeros(shape=(ncomp, norb, norb))
rspmats_2 = np.zeros(shape=(ncomp, norb, norb))
for i in range(ncomp):
rspvec_1 = rspvecs_1[i, :, 0]
rspvec_2 = rspvecs_2[i, :, 0]
x_1 = rspvec_1[:nov_alph]
y_1 = rspvec_1[nov_alph:]
x_2 = rspvec_2[:nov_alph]
y_2 = rspvec_2[nov_alph:]
x_full_1 = utils.repack_vector_to_matrix(x_1, (nvirt_alph, nocc_alph))
y_full_1 = utils.repack_vector_to_matrix(y_1, (nvirt_alph, nocc_alph))
x_full_2 = utils.repack_vector_to_matrix(x_2, (nvirt_alph, nocc_alph))
y_full_2 = utils.repack_vector_to_matrix(y_2, (nvirt_alph, nocc_alph))
rspmats_1[i, :nocc_alph, nocc_alph:] = y_full_1.T
rspmats_1[i, nocc_alph:, :nocc_alph] = x_full_1
rspmats_2[i, :nocc_alph, nocc_alph:] = y_full_2.T
rspmats_2[i, nocc_alph:, :nocc_alph] = x_full_2
rhsmats = np.zeros(shape=(ncomp, norb, norb))
for i in range(ncomp):
rhsvec = rhsvecs[i, :, 0]
rhsvec_top = rhsvec[:nov_alph]
rhsvec_bot = rhsvec[nov_alph:]
rhsvec_top_mat = utils.repack_vector_to_matrix(rhsvec_top, (nvirt_alph, nocc_alph))
rhsvec_bot_mat = utils.repack_vector_to_matrix(rhsvec_bot, (nvirt_alph, nocc_alph))
rhsmats[i, :nocc_alph, nocc_alph:] = rhsvec_top_mat.T
rhsmats[i, nocc_alph:, :nocc_alph] = rhsvec_bot_mat
polarizability_full_1 = np.empty_like(polarizability_1)
polarizability_full_2 = np.empty_like(polarizability_2)
for a in (0, 1, 2):
for b in (0, 1, 2):
polarizability_full_1[a, b] = 2 * np.trace(np.dot(rhsmats[a].T, rspmats_1[b]))
polarizability_full_2[a, b] = 2 * np.trace(np.dot(rhsmats[a].T, rspmats_2[b]))
np.testing.assert_almost_equal(polarizability_1, -polarizability_full_1)
np.testing.assert_almost_equal(polarizability_2, -polarizability_full_2)
# V_{p,q} <- full MO transformation of right hand side
integrals_ao = operator.ao_integrals
integrals_mo = np.empty_like(integrals_ao)
for i in range(ncomp):
integrals_mo[i] = (C[0].T).dot(integrals_ao[i]).dot(C[0])
G_1 = np.empty_like(rspmats_1)
G_2 = np.empty_like(rspmats_2)
C = mf.mo_coeff
# TODO I feel as though if I have all the MO-basis two-electron
# integrals, I shouldn't need another JK build.
for i in range(ncomp):
V = integrals_mo[i]
Dl_1 = (C[:, :nocc_alph]).dot(rspmats_1[i, :nocc_alph, :]).dot(C.T)
Dr_1 = (-C).dot(rspmats_1[i, :, :nocc_alph]).dot(C[:, :nocc_alph].T)
D_1 = Dl_1 + Dr_1
Dl_2 = (C[:, :nocc_alph]).dot(rspmats_2[i, :nocc_alph, :]).dot(C.T)
Dr_2 = (-C).dot(rspmats_2[i, :, :nocc_alph]).dot(C[:, :nocc_alph].T)
D_2 = Dl_2 + Dr_2
J_1, K_1 = mf.get_jk(mol, D_1, hermi=0)
J_2, K_2 = mf.get_jk(mol, D_2, hermi=0)
F_AO_1 = 2 * J_1 - K_1
F_AO_2 = 2 * J_2 - K_2
F_MO_1 = (C.T).dot(F_AO_1).dot(C)
F_MO_2 = (C.T).dot(F_AO_2).dot(C)
G_1[i] = V + F_MO_1
G_2[i] = V + F_MO_2
E_diag = np.diag(E[0, ...])
epsilon_1 = G_1.copy()
epsilon_2 = G_2.copy()
for i in range(ncomp):
eoU_1 = (E_diag[..., np.newaxis] + f1) * rspmats_1[i]
Ue_1 = rspmats_1[i] * E_diag[np.newaxis, ...]
epsilon_1[i] += eoU_1 - Ue_1
eoU_2 = (E_diag[..., np.newaxis] + f2) * rspmats_2[i]
Ue_2 = rspmats_2[i] * E_diag[np.newaxis, ...]
epsilon_2[i] += eoU_2 - Ue_2
# Assume some symmetry and calculate only part of the tensor.
hyperpolarizability = np.zeros(shape=(6, 3))
off1 = [0, 1, 2, 0, 0, 1]
off2 = [0, 1, 2, 1, 2, 2]
for r in range(6):
b = off1[r]
c = off2[r]
for a in range(3):
tl1 = np.trace(rspmats_2[a].T.dot(G_1[b]).dot(rspmats_1[c])[:nocc_alph, :nocc_alph])
tl2 = np.trace(rspmats_1[c].dot(G_1[b]).dot(rspmats_2[a].T)[:nocc_alph, :nocc_alph])
tl3 = np.trace(rspmats_2[a].T.dot(G_1[c]).dot(rspmats_1[b])[:nocc_alph, :nocc_alph])
tl4 = np.trace(rspmats_1[b].dot(G_1[c]).dot(rspmats_2[a].T)[:nocc_alph, :nocc_alph])
tl5 = np.trace(rspmats_1[c].dot(-G_2[a].T).dot(rspmats_1[b])[:nocc_alph, :nocc_alph])
tl6 = np.trace(rspmats_1[b].dot(-G_2[a].T).dot(rspmats_1[c])[:nocc_alph, :nocc_alph])
tr1 = np.trace(
rspmats_1[c].dot(rspmats_1[b]).dot(-epsilon_2[a].T)[:nocc_alph, :nocc_alph]
)
tr2 = np.trace(
rspmats_1[b].dot(rspmats_1[c]).dot(-epsilon_2[a].T)[:nocc_alph, :nocc_alph]
)
tr3 = np.trace(
rspmats_1[c].dot(rspmats_2[a].T).dot(epsilon_1[b])[:nocc_alph, :nocc_alph]
)
tr4 = np.trace(
rspmats_2[a].T.dot(rspmats_1[c]).dot(epsilon_1[b])[:nocc_alph, :nocc_alph]
)
tr5 = np.trace(
rspmats_1[b].dot(rspmats_2[a].T).dot(epsilon_1[c])[:nocc_alph, :nocc_alph]
)
tr6 = np.trace(
rspmats_2[a].T.dot(rspmats_1[b]).dot(epsilon_1[c])[:nocc_alph, :nocc_alph]
)
tl = tl1 + tl2 + tl3 + tl4 + tl5 + tl6
tr = tr1 + tr2 + tr3 + tr4 + tr5 + tr6
hyperpolarizability[r, a] = -2 * (tl - tr)
# pylint: disable=C0326
ref = np.array(
[
[0.00000000, 0.00000000, 1.92505358],
[0.00000000, 0.00000000, -31.33652886],
[0.00000000, 0.00000000, -13.92830863],
[0.00000000, 0.00000000, 0.00000000],
[-1.80626084, 0.00000000, 0.00000000],
[0.00000000, -31.13504192, 0.00000000],
]
)
ref_avgs = np.array([0.00000000, 0.00000000, 45.69300223])
ref_avg = 45.69300223
diff = np.abs(ref - hyperpolarizability)
print("abs diff")
print(diff)
thresh = 2.5e-04
assert np.all(diff < thresh)
print("hyperpolarizability: SHG, (-{}; {}, {}), symmetry-unique components".format(f2, f1, f1))
print(hyperpolarizability)
print("ref")
print(ref)
# Transpose all frequency-doubled quantities (+2w) to get -2w.
for i in range(ncomp):
rspmats_2[i] = rspmats_2[i].T
G_2[i] = -G_2[i].T
epsilon_2[i] = -epsilon_2[i].T
# Assume some symmetry and calculate only part of the tensor. This
# time, work with the in-place manipulated quantities (this tests
# their correctness).
mU = (rspmats_2, rspmats_1)
mG = (G_2, G_1)
me = (epsilon_2, epsilon_1)
hyperpolarizability = np.zeros(shape=(6, 3))
off1 = [0, 1, 2, 0, 0, 1]
off2 = [0, 1, 2, 1, 2, 2]
for r in range(6):
b = off1[r]
c = off2[r]
for a in range(3):
tl1 = np.trace(mU[0][a].dot(mG[1][b]).dot(mU[1][c])[:nocc_alph, :nocc_alph])
tl2 = np.trace(mU[1][c].dot(mG[1][b]).dot(mU[0][a])[:nocc_alph, :nocc_alph])
tl3 = np.trace(mU[0][a].dot(mG[1][c]).dot(mU[1][b])[:nocc_alph, :nocc_alph])
tl4 = np.trace(mU[1][b].dot(mG[1][c]).dot(mU[0][a])[:nocc_alph, :nocc_alph])
tl5 = np.trace(mU[1][c].dot(mG[0][a]).dot(mU[1][b])[:nocc_alph, :nocc_alph])
tl6 = np.trace(mU[1][b].dot(mG[0][a]).dot(mU[1][c])[:nocc_alph, :nocc_alph])
tr1 = np.trace(mU[1][c].dot(mU[1][b]).dot(me[0][a])[:nocc_alph, :nocc_alph])
tr2 = np.trace(mU[1][b].dot(mU[1][c]).dot(me[0][a])[:nocc_alph, :nocc_alph])
tr3 = np.trace(mU[1][c].dot(mU[0][a]).dot(me[1][b])[:nocc_alph, :nocc_alph])
tr4 = np.trace(mU[0][a].dot(mU[1][c]).dot(me[1][b])[:nocc_alph, :nocc_alph])
tr5 = np.trace(mU[1][b].dot(mU[0][a]).dot(me[1][c])[:nocc_alph, :nocc_alph])
tr6 = np.trace(mU[0][a].dot(mU[1][b]).dot(me[1][c])[:nocc_alph, :nocc_alph])
tl = [tl1, tl2, tl3, tl4, tl5, tl6]
tr = [tr1, tr2, tr3, tr4, tr5, tr6]
hyperpolarizability[r, a] = -2 * (sum(tl) - sum(tr))
assert np.all(np.abs(ref - hyperpolarizability) < thresh)
# Assume no symmetry and calculate the full tensor.
hyperpolarizability_full = np.zeros(shape=(3, 3, 3))
# components x, y, z
for ip, p in enumerate(list(product(range(3), range(3), range(3)))):
a, b, c = p
tl, tr = [], []
# 1st tuple -> index a, b, c (*not* x, y, z!)
# 2nd tuple -> index frequency (0 -> -2w, 1 -> +w)
for iq, q in enumerate(list(permutations(zip(p, (0, 1, 1)), 3))):
d, e, f = q
tlp = (mU[d[1]][d[0]]).dot(mG[e[1]][e[0]]).dot(mU[f[1]][f[0]])
tle = np.trace(tlp[:nocc_alph, :nocc_alph])
tl.append(tle)
trp = (mU[d[1]][d[0]]).dot(mU[e[1]][e[0]]).dot(me[f[1]][f[0]])
tre = np.trace(trp[:nocc_alph, :nocc_alph])
tr.append(tre)
hyperpolarizability_full[a, b, c] = -2 * (sum(tl) - sum(tr))
print("hyperpolarizability: SHG, (-{}; {}, {}), full tensor".format(f2, f1, f1))
print(hyperpolarizability_full)
# Check that the elements of the reduced and full tensors are
# equivalent.
for r in range(6):
b = off1[r]
c = off2[r]
for a in range(3):
diff = hyperpolarizability[r, a] - hyperpolarizability_full[a, b, c]
# TODO why not 14?
assert abs(diff) < 1.0e-13
# Compute averages and compare to reference.
avgs, avg = utils.form_first_hyperpolarizability_averages(hyperpolarizability_full)
assert np.allclose(ref_avgs, avgs, rtol=0, atol=1.0e-3)
assert np.allclose([ref_avg], [avg], rtol=0, atol=1.0e-3)
print(avgs)
print(avg)
return
def test_final_result_rhf_h2o_sto3g_tda_triplet() -> None:
"""Test correctness of the final result for water/STO-3G with the TDA
approximation/CIS for triplet response induced by the dipole length
operator computed with quantities from disk.
"""
hamiltonian = Hamiltonian.TDA
spin = Spin.triplet
C = utils.fix_mocoeffs_shape(utils.np_load(REFDIR / "C.npz"))
E = utils.fix_moenergies_shape(utils.np_load(REFDIR / "F_MO.npz"))
TEI_MO = utils.np_load(REFDIR / "TEI_MO.npz")
# nocc_alph, nvirt_alph, nocc_beta, nvirt_beta
occupations = np.asarray([5, 2, 5, 2], dtype=int)
stub = "h2o_sto3g_"
dim = occupations[0] + occupations[1]
mat_dipole_x = utils.parse_int_file_2(REFDIR / f"{stub}mux.dat", dim)
mat_dipole_y = utils.parse_int_file_2(REFDIR / f"{stub}muy.dat", dim)
mat_dipole_z = utils.parse_int_file_2(REFDIR / f"{stub}muz.dat", dim)
solver = solvers.ExactInv(C, E, occupations)
solver.tei_mo = (TEI_MO, )
solver.tei_mo_type = AO2MOTransformationType.full
driver = cphf.CPHF(solver)
ao_integrals_dipole = np.stack((mat_dipole_x, mat_dipole_y, mat_dipole_z),
axis=0)
operator_dipole = operators.Operator(label="dipole",
is_imaginary=False,
is_spin_dependent=False)
operator_dipole.ao_integrals = ao_integrals_dipole
driver.add_operator(operator_dipole)
frequencies = (0.0, 0.02, 0.06, 0.1)
driver.set_frequencies(frequencies)
driver.run(hamiltonian=hamiltonian,
spin=spin,
program=None,
program_obj=None)
assert len(driver.results) == len(frequencies)
result__0_00 = np.array([[14.64430714, 0.0, 0.0], [0.0, 8.80921432, 0.0],
[0.0, 0.0, 0.06859496]])
result__0_02 = np.array([[14.68168443, 0.0, 0.0], [0.0, 8.83562647, 0.0],
[0.0, 0.0, 0.0689291]])
result__0_06 = np.array([[14.98774296, 0.0, 0.0], [0.0, 9.0532224, 0.0],
[0.0, 0.0, 0.07172414]])
result__0_10 = np.array([[15.63997724, 0.0, 0.0], [0.0, 9.52504267, 0.0],
[0.0, 0.0, 0.07805428]])
atol = 1.0e-8
rtol = 0.0
np.testing.assert_allclose(driver.results[0],
result__0_00,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(driver.results[1],
result__0_02,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(driver.results[2],
result__0_06,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(driver.results[3],
result__0_10,
rtol=rtol,
atol=atol)
mol = molecules.molecule_water_sto3g()
mol.build()
polarizability = electric.Polarizability(
Program.PySCF,
mol,
cphf.CPHF(solvers.ExactInv(C, E, occupations)),
C,
E,
occupations,
frequencies=frequencies,
)
polarizability.form_operators()
polarizability.run(hamiltonian=hamiltonian, spin=spin)
polarizability.form_results()
np.testing.assert_allclose(polarizability.polarizabilities[0],
result__0_00,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(polarizability.polarizabilities[1],
result__0_02,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(polarizability.polarizabilities[2],
result__0_06,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(polarizability.polarizabilities[3],
result__0_10,
rtol=rtol,
atol=atol)
def test_final_result_rhf_h2o_sto3g_rpa_singlet() -> None:
"""Test correctness of the final result for water/STO-3G with full RPA for
singlet response induced by the dipole length operator (the electric
polarizability) computed with quantities from disk.
"""
hamiltonian = Hamiltonian.RPA
spin = Spin.singlet
C = utils.fix_mocoeffs_shape(utils.np_load(REFDIR / "C.npz"))
E = utils.fix_moenergies_shape(utils.np_load(REFDIR / "F_MO.npz"))
TEI_MO = utils.np_load(REFDIR / "TEI_MO.npz")
# nocc_alph, nvirt_alph, nocc_beta, nvirt_beta
occupations = np.asarray([5, 2, 5, 2], dtype=int)
stub = "h2o_sto3g_"
dim = occupations[0] + occupations[1]
mat_dipole_x = utils.parse_int_file_2(REFDIR / f"{stub}mux.dat", dim)
mat_dipole_y = utils.parse_int_file_2(REFDIR / f"{stub}muy.dat", dim)
mat_dipole_z = utils.parse_int_file_2(REFDIR / f"{stub}muz.dat", dim)
solver = solvers.ExactInv(C, E, occupations)
solver.tei_mo = (TEI_MO, )
solver.tei_mo_type = AO2MOTransformationType.full
driver = cphf.CPHF(solver)
ao_integrals_dipole = np.stack((mat_dipole_x, mat_dipole_y, mat_dipole_z),
axis=0)
operator_dipole = operators.Operator(label="dipole",
is_imaginary=False,
is_spin_dependent=False)
operator_dipole.ao_integrals = ao_integrals_dipole
driver.add_operator(operator_dipole)
frequencies = (0.0, 0.02, 0.06, 0.1)
driver.set_frequencies(frequencies)
driver.run(hamiltonian=hamiltonian,
spin=spin,
program=None,
program_obj=None)
assert len(driver.results) == len(frequencies)
result__0_00 = np.array([[7.93556221, 0.0, 0.0], [0.0, 3.06821077, 0.0],
[0.0, 0.0, 0.05038621]])
result__0_02 = np.array([[7.94312371, 0.0, 0.0], [0.0, 3.07051688, 0.0],
[0.0, 0.0, 0.05054685]])
result__0_06 = np.array([[8.00414009, 0.0, 0.0], [0.0, 3.08913608, 0.0],
[0.0, 0.0, 0.05186977]])
result__0_10 = np.array([[8.1290378, 0.0, 0.0], [0.0, 3.12731363, 0.0],
[0.0, 0.0, 0.05473482]])
atol = 1.0e-8
rtol = 0.0
np.testing.assert_allclose(driver.results[0],
result__0_00,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(driver.results[1],
result__0_02,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(driver.results[2],
result__0_06,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(driver.results[3],
result__0_10,
rtol=rtol,
atol=atol)
# Reminder: there's no call to do SCF here because we already have
# the MO coefficients.
mol = molecules.molecule_water_sto3g()
mol.build()
polarizability = electric.Polarizability(
Program.PySCF,
mol,
cphf.CPHF(solvers.ExactInv(C, E, occupations)),
C,
E,
occupations,
frequencies=frequencies,
)
polarizability.form_operators()
polarizability.run(hamiltonian=hamiltonian, spin=spin)
polarizability.form_results()
np.testing.assert_allclose(polarizability.polarizabilities[0],
result__0_00,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(polarizability.polarizabilities[1],
result__0_02,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(polarizability.polarizabilities[2],
result__0_06,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(polarizability.polarizabilities[3],
result__0_10,
rtol=rtol,
atol=atol)
def test_final_result_rhf_h2o_sto3g_rpa_triplet() -> None:
"""Test correctness of the final result for water/STO-3G with full RPA for
triplet response induced by the dipole length operator computed with
quantities from disk.
"""
hamiltonian = Hamiltonian.RPA
spin = Spin.triplet
C = utils.fix_mocoeffs_shape(utils.np_load(REFDIR / "C.npz"))
E = utils.fix_moenergies_shape(utils.np_load(REFDIR / "F_MO.npz"))
TEI_MO = utils.np_load(REFDIR / "TEI_MO.npz")
# nocc_alph, nvirt_alph, nocc_beta, nvirt_beta
occupations = np.asarray([5, 2, 5, 2], dtype=int)
stub = "h2o_sto3g_"
dim = occupations[0] + occupations[1]
mat_dipole_x = utils.parse_int_file_2(REFDIR / f"{stub}mux.dat", dim)
mat_dipole_y = utils.parse_int_file_2(REFDIR / f"{stub}muy.dat", dim)
mat_dipole_z = utils.parse_int_file_2(REFDIR / f"{stub}muz.dat", dim)
solver = solvers.ExactInv(C, E, occupations)
solver.tei_mo = (TEI_MO, )
solver.tei_mo_type = AO2MOTransformationType.full
driver = cphf.CPHF(solver)
ao_integrals_dipole = np.stack((mat_dipole_x, mat_dipole_y, mat_dipole_z),
axis=0)
operator_dipole = operators.Operator(label="dipole",
is_imaginary=False,
is_spin_dependent=False)
operator_dipole.ao_integrals = ao_integrals_dipole
driver.add_operator(operator_dipole)
frequencies = (0.0, 0.02, 0.06, 0.1)
driver.set_frequencies(frequencies)
driver.run(hamiltonian=hamiltonian,
spin=spin,
program=None,
program_obj=None)
assert len(driver.results) == len(frequencies)
result__0_00 = np.array([[26.59744305, 0.0, 0.0], [0.0, 18.11879557, 0.0],
[0.0, 0.0, 0.07798969]])
result__0_02 = np.array([[26.68282287, 0.0, 0.0], [0.0, 18.19390051, 0.0],
[0.0, 0.0, 0.07837521]])
result__0_06 = np.array([[27.38617401, 0.0, 0.0], [0.0, 18.81922578, 0.0],
[0.0, 0.0, 0.08160226]])
result__0_10 = np.array([[28.91067234, 0.0, 0.0], [0.0, 20.21670386, 0.0],
[0.0, 0.0, 0.08892512]])
atol = 1.0e-8
rtol = 0.0
np.testing.assert_allclose(driver.results[0],
result__0_00,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(driver.results[1],
result__0_02,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(driver.results[2],
result__0_06,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(driver.results[3],
result__0_10,
rtol=rtol,
atol=atol)
mol = molecules.molecule_water_sto3g()
mol.build()
polarizability = electric.Polarizability(
Program.PySCF,
mol,
cphf.CPHF(solvers.ExactInv(C, E, occupations)),
C,
E,
occupations,
frequencies=frequencies,
)
polarizability.form_operators()
polarizability.run(hamiltonian=hamiltonian, spin=spin)
polarizability.form_results()
np.testing.assert_allclose(polarizability.polarizabilities[0],
result__0_00,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(polarizability.polarizabilities[1],
result__0_02,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(polarizability.polarizabilities[2],
result__0_06,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(polarizability.polarizabilities[3],
result__0_10,
rtol=rtol,
atol=atol)
def test_first_hyperpolarizability_static_rhf_wigner_explicit():
mol = molecule_water_sto3g_angstrom()
mol.build()
mf = pyscf.scf.RHF(mol)
mf.kernel()
C = utils.fix_mocoeffs_shape(mf.mo_coeff)
E = utils.fix_moenergies_shape(mf.mo_energy)
occupations = occupations_from_pyscf_mol(mol, C)
nocc_alph, nvirt_alph, _, _ = occupations
nov_alph = nocc_alph * nvirt_alph
norb = nocc_alph + nvirt_alph
# calculate linear response vectors for electric dipole operator
calculator = electric.Polarizability(
Program.PySCF,
mol,
cphf.CPHF(solvers.ExactInv(C, E, occupations)),
C,
E,
occupations,
frequencies=[0.0],
)
calculator.form_operators()
calculator.run(hamiltonian=Hamiltonian.RPA, spin=Spin.singlet)
calculator.form_results()
polarizability = calculator.polarizabilities[0]
print("polarizability (static)")
print(polarizability)
operator = calculator.driver.solver.operators[0]
rhsvecs = operator.mo_integrals_ai_supervector_alph
rspvecs = operator.rspvecs_alph[0]
## Form the full [norb, norb] representation of everything.
# Response vectors: transform X_{ia} and Y_{ia} -> U_{p,q}
# 0. 'a' is fast index, 'i' slow
# 1. rspvec == [X Y]
# 2. U_{p, q} -> zero
# 3. place X_{ia} into U_{i, a}
# 4. place Y_{ia} into U_{a, i}
ncomp = rhsvecs.shape[0]
rspmats = np.zeros(shape=(ncomp, norb, norb))
for i in range(ncomp):
rspvec = rspvecs[i, :, 0]
x = rspvec[:nov_alph]
y = rspvec[nov_alph:]
x_full = utils.repack_vector_to_matrix(x, (nvirt_alph, nocc_alph))
y_full = utils.repack_vector_to_matrix(y, (nvirt_alph, nocc_alph))
rspmats[i, :nocc_alph, nocc_alph:] = x_full.T
rspmats[i, nocc_alph:, :nocc_alph] = y_full
rhsmats = np.zeros(shape=(ncomp, norb, norb))
for i in range(ncomp):
rhsvec = rhsvecs[i, :, 0]
rhsvec_top = rhsvec[:nov_alph]
rhsvec_bot = rhsvec[nov_alph:]
rhsvec_top_mat = utils.repack_vector_to_matrix(rhsvec_top,
(nvirt_alph, nocc_alph))
rhsvec_bot_mat = utils.repack_vector_to_matrix(rhsvec_bot,
(nvirt_alph, nocc_alph))
rhsmats[i, :nocc_alph, nocc_alph:] = rhsvec_top_mat.T
rhsmats[i, nocc_alph:, :nocc_alph] = rhsvec_bot_mat
polarizability_full = np.empty_like(polarizability)
for a in (0, 1, 2):
for b in (0, 1, 2):
polarizability_full[a, b] = 2 * np.trace(rhsmats[a, ...].T.dot(
rspmats[b, ...]))
np.testing.assert_almost_equal(polarizability, polarizability_full)
# V_{p,q} <- full MO transformation of right hand side
integrals_ao = operator.ao_integrals
integrals_mo = np.empty_like(integrals_ao)
for i in range(ncomp):
integrals_mo[i, ...] = (C[0, ...].T).dot(integrals_ao[i,
...]).dot(C[0,
...])
G = np.empty_like(rspmats)
C = mf.mo_coeff
# TODO I feel as though if I have all the MO-basis two-electron
# integrals, I shouldn't need another JK build.
for i in range(ncomp):
V = integrals_mo[i, ...]
Dl = (C[:, nocc_alph:].dot(
utils.repack_vector_to_matrix(rspvecs[i, :nov_alph, 0],
(nvirt_alph, nocc_alph))).dot(
C[:, :nocc_alph].T))
J, K = mf.get_jk(mol, Dl, hermi=0)
F_AO = -(4 * J - K - K.T)
F_MO = (C.T).dot(F_AO).dot(C)
G[i, ...] = V + F_MO
E_diag = np.diag(E[0, ...])
epsilon = G.copy()
omega = 0
for i in range(ncomp):
eoU = (E_diag[..., np.newaxis] + omega) * rspmats[i, ...]
Ue = rspmats[i, ...] * E_diag[np.newaxis, ...]
epsilon[i, ...] += eoU - Ue
# Assume some symmetry and calculate only part of the tensor.
hyperpolarizability = np.zeros(shape=(6, 3))
off1 = [0, 1, 2, 0, 0, 1]
off2 = [0, 1, 2, 1, 2, 2]
for r in range(6):
b = off1[r]
c = off2[r]
for a in range(3):
tl1 = 2 * np.trace(rspmats[a, ...].dot(G[b, ...]).dot(
rspmats[c, ...])[:nocc_alph, :nocc_alph])
tl2 = 2 * np.trace(rspmats[a, ...].dot(G[c, ...]).dot(
rspmats[b, ...])[:nocc_alph, :nocc_alph])
tl3 = 2 * np.trace(rspmats[c, ...].dot(G[a, ...]).dot(
rspmats[b, ...])[:nocc_alph, :nocc_alph])
tr1 = np.trace(rspmats[c, ...].dot(rspmats[b, ...]).dot(
epsilon[a, ...])[:nocc_alph, :nocc_alph])
tr2 = np.trace(rspmats[b, ...].dot(rspmats[c, ...]).dot(
epsilon[a, ...])[:nocc_alph, :nocc_alph])
tr3 = np.trace(rspmats[c, ...].dot(rspmats[a, ...]).dot(
epsilon[b, ...])[:nocc_alph, :nocc_alph])
tr4 = np.trace(rspmats[a, ...].dot(rspmats[c, ...]).dot(
epsilon[b, ...])[:nocc_alph, :nocc_alph])
tr5 = np.trace(rspmats[b, ...].dot(rspmats[a, ...]).dot(
epsilon[c, ...])[:nocc_alph, :nocc_alph])
tr6 = np.trace(rspmats[a, ...].dot(rspmats[b, ...]).dot(
epsilon[c, ...])[:nocc_alph, :nocc_alph])
tl = tl1 + tl2 + tl3
tr = tr1 + tr2 + tr3 + tr4 + tr5 + tr6
hyperpolarizability[r, a] = 2 * (tl - tr)
# pylint: disable=C0326
ref = np.array([
[-8.86822254, 0.90192130, -0.50796586],
[1.98744058, 5.13635628, -2.95319400],
[0.66008119, 1.62699646, -0.85632412],
[0.90192130, 1.98744058, -1.09505123],
[-0.50796586, -1.09505123, 0.66008119],
[-1.09505123, -2.95319400, 1.62699646],
])
ref_avgs = np.array([6.22070078, -7.66527404, 4.31748398])
ref_avg = 10.77470242
thresh = 1.5e-4
assert np.all(np.abs(ref - hyperpolarizability) < thresh)
print("hyperpolarizability (static), symmetry-unique components")
print(hyperpolarizability)
# Assume no symmetry and calculate the full tensor.
hyperpolarizability_full = np.zeros(shape=(3, 3, 3))
for p in product(range(3), range(3), range(3)):
a, b, c = p
tl, tr = 0, 0
for q in permutations(p, 3):
d, e, f = q
tl += np.trace(rspmats[d, ...].dot(G[e, ...]).dot(
rspmats[f, ...])[:nocc_alph, :nocc_alph])
tr += np.trace(rspmats[d, ...].dot(rspmats[e, ...]).dot(
epsilon[f, ...])[:nocc_alph, :nocc_alph])
hyperpolarizability_full[a, b, c] = 2 * (tl - tr)
print("hyperpolarizability (static), full tensor")
print(hyperpolarizability_full)
# Check that the elements of the reduced and full tensors are
# equivalent.
thresh = 1.0e-14
for r in range(6):
b = off1[r]
c = off2[r]
for a in range(3):
diff = hyperpolarizability[r, a] - hyperpolarizability_full[a, b,
c]
assert abs(diff) < thresh
# Compute averages and compare to reference.
# This is the slow way.
# avgs = []
# for i in range(3):
# avg_c = 0
# for j in range(3):
# avg_c += hyperpolarizability_full[i, j, j] + hyperpolarizability_full[j, i, j] + hyperpolarizability_full[j, j, i]
# avgs.append((-1/3) * avg_c)
# print(np.asarray(avgs))
x = hyperpolarizability_full
# This is the simplest non-einsum way.
# avgs = (-1 / 3) * np.asarray([np.trace(x[i, :, :] + x[:, i, :] + x[:, :, i]) for i in range(3)])
# This is the best way.
avgs = (-1 / 3) * (np.einsum("ijj->i", x) + np.einsum("jij->i", x) +
np.einsum("jji->i", x))
# print(list(set([''.join(p) for p in list(permutations('ijj', 3))])))
assert np.allclose(ref_avgs, avgs, rtol=0, atol=1.0e-3)
avg = np.sum(avgs**2)**(1 / 2)
assert np.allclose([ref_avg], [avg], rtol=0, atol=1.0e-3)
print(avgs)
print(avg)
utils_avgs, utils_avg = utils.form_first_hyperpolarizability_averages(x)
assert np.allclose(avgs, utils_avgs, rtol=0, atol=1.0e-13)
assert np.allclose([avg], [utils_avg], rtol=0, atol=1.0e-13)
return
def test_first_hyperpolarizability_or_rhf_wigner_explicit():
mol = molecule_water_sto3g_angstrom()
mol.build()
mf = pyscf.scf.RHF(mol)
mf.kernel()
C = utils.fix_mocoeffs_shape(mf.mo_coeff)
E = utils.fix_moenergies_shape(mf.mo_energy)
occupations = occupations_from_pyscf_mol(mol, C)
nocc_alph, nvirt_alph, _, _ = occupations
nov_alph = nocc_alph * nvirt_alph
norb = nocc_alph + nvirt_alph
# calculate linear response vectors for electric dipole operator
f1 = 0.0
f2 = 0.0773178
frequencies = [f1, f2]
calculator = electric.Polarizability(
Program.PySCF,
mol,
cphf.CPHF(solvers.ExactInv(C, E, occupations)),
C,
E,
occupations,
frequencies=frequencies,
)
calculator.form_operators()
calculator.run(hamiltonian=Hamiltonian.RPA, spin=Spin.singlet)
calculator.form_results()
polarizability_1 = calculator.polarizabilities[0]
polarizability_2 = calculator.polarizabilities[1]
print("polarizability (static)")
print(polarizability_1)
print("polarizability: {} a.u.".format(f2))
print(polarizability_2)
# each operator contains multiple sets of response vectors, one
# set of components for each frequency
assert isinstance(calculator.driver.solver.operators, list)
assert len(calculator.driver.solver.operators) == 1
operator = calculator.driver.solver.operators[0]
rhsvecs = operator.mo_integrals_ai_supervector_alph
assert isinstance(operator.rspvecs_alph, list)
assert len(operator.rspvecs_alph) == 2
rspvecs_1 = operator.rspvecs_alph[0]
rspvecs_2 = operator.rspvecs_alph[1]
## Form the full [norb, norb] representation of everything.
# Response vectors: transform X_{ia} and Y_{ia} -> U_{p,q}
# 0. 'a' is fast index, 'i' slow
# 1. rspvec == [X Y]
# 2. U_{p, q} -> zero
# 3. place X_{ia} into U_{i, a}
# 4. place Y_{ia} into U_{a, i}
ncomp = rhsvecs.shape[0]
rspmats_1 = np.zeros(shape=(ncomp, norb, norb))
rspmats_2 = np.zeros(shape=(ncomp, norb, norb))
for i in range(ncomp):
rspvec_1 = rspvecs_1[i, :, 0]
rspvec_2 = rspvecs_2[i, :, 0]
x_1 = rspvec_1[:nov_alph]
y_1 = rspvec_1[nov_alph:]
x_2 = rspvec_2[:nov_alph]
y_2 = rspvec_2[nov_alph:]
x_full_1 = utils.repack_vector_to_matrix(x_1, (nvirt_alph, nocc_alph))
y_full_1 = utils.repack_vector_to_matrix(y_1, (nvirt_alph, nocc_alph))
x_full_2 = utils.repack_vector_to_matrix(x_2, (nvirt_alph, nocc_alph))
y_full_2 = utils.repack_vector_to_matrix(y_2, (nvirt_alph, nocc_alph))
rspmats_1[i, :nocc_alph, nocc_alph:] = y_full_1.T
rspmats_1[i, nocc_alph:, :nocc_alph] = x_full_1
rspmats_2[i, :nocc_alph, nocc_alph:] = y_full_2.T
rspmats_2[i, nocc_alph:, :nocc_alph] = x_full_2
rhsmats = np.zeros(shape=(ncomp, norb, norb))
for i in range(ncomp):
rhsvec = rhsvecs[i, :, 0]
rhsvec_top = rhsvec[:nov_alph]
rhsvec_bot = rhsvec[nov_alph:]
rhsvec_top_mat = utils.repack_vector_to_matrix(rhsvec_top,
(nvirt_alph, nocc_alph))
rhsvec_bot_mat = utils.repack_vector_to_matrix(rhsvec_bot,
(nvirt_alph, nocc_alph))
rhsmats[i, :nocc_alph, nocc_alph:] = rhsvec_top_mat.T
rhsmats[i, nocc_alph:, :nocc_alph] = rhsvec_bot_mat
polarizability_full_1 = np.empty_like(polarizability_1)
polarizability_full_2 = np.empty_like(polarizability_2)
for a in (0, 1, 2):
for b in (0, 1, 2):
polarizability_full_1[a, b] = 2 * np.trace(rhsmats[a, ...].T.dot(
rspmats_1[b, ...]))
polarizability_full_2[a, b] = 2 * np.trace(rhsmats[a, ...].T.dot(
rspmats_2[b, ...]))
np.testing.assert_almost_equal(polarizability_1, -polarizability_full_1)
np.testing.assert_almost_equal(polarizability_2, -polarizability_full_2)
# V_{p,q} <- full MO transformation of right hand side
integrals_ao = operator.ao_integrals
integrals_mo = np.empty_like(integrals_ao)
for i in range(ncomp):
integrals_mo[i, ...] = (C[0, ...].T).dot(integrals_ao[i,
...]).dot(C[0,
...])
# from pyresponse.ao2mo import AO2MOpyscf
# ao2mo = AO2MOpyscf(C, pyscfmol=mol)
# ao2mo.perform_rhf_full()
# tei_mo = ao2mo.tei_mo[0]
G_1 = np.empty_like(rspmats_1)
G_2 = np.empty_like(rspmats_2)
C = mf.mo_coeff
# TODO I feel as though if I have all the MO-basis two-electron
# integrals, I shouldn't need another JK build.
for i in range(ncomp):
V = integrals_mo[i, ...]
Dl_1 = (C[:, :nocc_alph]).dot(rspmats_1[i, :nocc_alph, :]).dot(C.T)
Dr_1 = (-C).dot(rspmats_1[i, :, :nocc_alph]).dot(C[:, :nocc_alph].T)
D_1 = Dl_1 + Dr_1
Dl_2 = (C[:, :nocc_alph]).dot(rspmats_2[i, :nocc_alph, :]).dot(C.T)
Dr_2 = (-C).dot(rspmats_2[i, :, :nocc_alph]).dot(C[:, :nocc_alph].T)
D_2 = Dl_2 + Dr_2
J_1, K_1 = mf.get_jk(mol, D_1, hermi=0)
J_2, K_2 = mf.get_jk(mol, D_2, hermi=0)
F_AO_1 = 2 * J_1 - K_1
F_AO_2 = 2 * J_2 - K_2
F_MO_1 = (C.T).dot(F_AO_1).dot(C)
F_MO_2 = (C.T).dot(F_AO_2).dot(C)
G_1[i, ...] = V + F_MO_1
G_2[i, ...] = V + F_MO_2
E_diag = np.diag(E[0, ...])
epsilon_1 = G_1.copy()
epsilon_2 = G_2.copy()
for i in range(ncomp):
eoU_1 = (E_diag[..., np.newaxis] + f1) * rspmats_1[i, ...]
Ue_1 = rspmats_1[i, ...] * E_diag[np.newaxis, ...]
epsilon_1[i, ...] += eoU_1 - Ue_1
eoU_2 = (E_diag[..., np.newaxis] + f2) * rspmats_2[i, ...]
Ue_2 = rspmats_2[i, ...] * E_diag[np.newaxis, ...]
epsilon_2[i, ...] += eoU_2 - Ue_2
# Assume some symmetry and calculate only part of the tensor.
hyperpolarizability = np.zeros(shape=(6, 3))
off1 = [0, 1, 2, 0, 0, 1]
off2 = [0, 1, 2, 1, 2, 2]
for r in range(6):
b = off1[r]
c = off2[r]
for a in range(3):
# _1 -> 0
# _2 -> +w
# a is _1, b is _2, c is _2 transposed/negated
tl1 = np.trace(rspmats_1[a, ...].dot(G_2[b, ...]).dot(
rspmats_2[c, ...].T)[:nocc_alph, :nocc_alph])
tl2 = np.trace(rspmats_2[c, ...].T.dot(G_2[b, ...]).dot(
rspmats_1[a, ...])[:nocc_alph, :nocc_alph])
tl3 = np.trace(rspmats_1[a, ...].dot(-G_2[c, ...].T).dot(
rspmats_2[b, ...])[:nocc_alph, :nocc_alph])
tl4 = np.trace(rspmats_2[b, ...].dot(-G_2[c, ...].T).dot(
rspmats_1[a, ...])[:nocc_alph, :nocc_alph])
tl5 = np.trace(rspmats_2[c, ...].T.dot(G_1[a, ...]).dot(
rspmats_2[b, ...])[:nocc_alph, :nocc_alph])
tl6 = np.trace(rspmats_2[b, ...].dot(G_1[a, ...]).dot(
rspmats_2[c, ...].T)[:nocc_alph, :nocc_alph])
tr1 = np.trace(rspmats_2[c, ...].T.dot(rspmats_2[b, ...]).dot(
epsilon_1[a, ...])[:nocc_alph, :nocc_alph])
tr2 = np.trace(rspmats_2[b, ...].dot(rspmats_2[c, ...].T).dot(
epsilon_1[a, ...])[:nocc_alph, :nocc_alph])
tr3 = np.trace(rspmats_2[c, ...].T.dot(rspmats_1[a, ...]).dot(
epsilon_2[b, ...])[:nocc_alph, :nocc_alph])
tr4 = np.trace(rspmats_1[a, ...].dot(rspmats_2[c, ...].T).dot(
epsilon_2[b, ...])[:nocc_alph, :nocc_alph])
tr5 = np.trace(rspmats_2[b, ...].dot(
rspmats_1[a,
...]).dot(-epsilon_2[c,
...].T)[:nocc_alph, :nocc_alph])
tr6 = np.trace(rspmats_1[a, ...].dot(
rspmats_2[b,
...]).dot(-epsilon_2[c,
...].T)[:nocc_alph, :nocc_alph])
tl = tl1 + tl2 + tl3 + tl4 + tl5 + tl6
tr = tr1 + tr2 + tr3 + tr4 + tr5 + tr6
hyperpolarizability[r, a] = -2 * (tl - tr)
# pylint: disable=C0326
ref = np.array([
[-9.02854579, 0.92998934, -0.52377445],
[2.01080066, 5.23470702, -3.01208409],
[0.66669794, 1.66112712, -0.87205853],
[0.92021130, 2.01769267, -1.11067223],
[-0.51824440, -1.11067586, 0.67140102],
[-1.10887175, -3.00950655, 1.65659586],
])
ref_avgs = np.array([6.34331713, -7.81628395, 4.40251201])
ref_avg = 10.98699590
thresh = 4.0e-5
assert np.all(np.abs(ref - hyperpolarizability) < thresh)
print("hyperpolarizability: OR, (0; {}, -{}), symmetry-unique components".
format(f2, f2))
print(hyperpolarizability)
return
def test_final_result_rhf_h2o_sto3g_tda_singlet():
hamiltonian = "tda"
spin = "singlet"
C = utils.fix_mocoeffs_shape(utils.np_load(REFDIR / "C.npz"))
E = utils.fix_moenergies_shape(utils.np_load(REFDIR / "F_MO.npz"))
TEI_MO = utils.np_load(REFDIR / "TEI_MO.npz")
# nocc_alph, nvirt_alph, nocc_beta, nvirt_beta
occupations = [5, 2, 5, 2]
stub = "h2o_sto3g_"
dim = occupations[0] + occupations[1]
mat_dipole_x = utils.parse_int_file_2(REFDIR / f"{stub}mux.dat", dim)
mat_dipole_y = utils.parse_int_file_2(REFDIR / f"{stub}muy.dat", dim)
mat_dipole_z = utils.parse_int_file_2(REFDIR / f"{stub}muz.dat", dim)
solver = iterators.ExactInv(C, E, occupations)
solver.tei_mo = (TEI_MO, )
solver.tei_mo_type = "full"
driver = cphf.CPHF(solver)
ao_integrals_dipole = np.stack((mat_dipole_x, mat_dipole_y, mat_dipole_z),
axis=0)
operator_dipole = operators.Operator(label="dipole",
is_imaginary=False,
is_spin_dependent=False)
operator_dipole.ao_integrals = ao_integrals_dipole
driver.add_operator(operator_dipole)
frequencies = (0.0, 0.02, 0.06, 0.1)
driver.set_frequencies(frequencies)
driver.run(solver_type="exact", hamiltonian=hamiltonian, spin=spin)
assert len(driver.results) == len(frequencies)
result__0_00 = np.array([[8.89855952, 0.0, 0.0], [0.0, 4.00026556, 0.0],
[0.0, 0.0, 0.0552774]])
result__0_02 = np.array([[8.90690928, 0.0, 0.0], [0.0, 4.00298342, 0.0],
[0.0, 0.0, 0.05545196]])
result__0_06 = np.array([[8.97427725, 0.0, 0.0], [0.0, 4.02491517, 0.0],
[0.0, 0.0, 0.05688918]])
result__0_10 = np.array([[9.11212633, 0.0, 0.0], [0.0, 4.06981937, 0.0],
[0.0, 0.0, 0.05999934]])
atol = 1.0e-8
rtol = 0.0
np.testing.assert_allclose(driver.results[0],
result__0_00,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(driver.results[1],
result__0_02,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(driver.results[2],
result__0_06,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(driver.results[3],
result__0_10,
rtol=rtol,
atol=atol)
mol = molecules.molecule_water_sto3g()
mol.build()
polarizability = electric.Polarizability(Program.PySCF, mol, C, E,
occupations, frequencies)
polarizability.form_operators()
polarizability.run(hamiltonian=hamiltonian, spin=spin)
polarizability.form_results()
np.testing.assert_allclose(polarizability.polarizabilities[0],
result__0_00,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(polarizability.polarizabilities[1],
result__0_02,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(polarizability.polarizabilities[2],
result__0_06,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(polarizability.polarizabilities[3],
result__0_10,
rtol=rtol,
atol=atol)
return
def test_final_result_rhf_h2o_sto3g_rpa_singlet():
hamiltonian = "rpa"
spin = "singlet"
C = utils.fix_mocoeffs_shape(utils.np_load(REFDIR / "C.npz"))
E = utils.fix_moenergies_shape(utils.np_load(REFDIR / "F_MO.npz"))
TEI_MO = utils.np_load(REFDIR / "TEI_MO.npz")
# nocc_alph, nvirt_alph, nocc_beta, nvirt_beta
occupations = [5, 2, 5, 2]
stub = "h2o_sto3g_"
dim = occupations[0] + occupations[1]
mat_dipole_x = utils.parse_int_file_2(REFDIR / f"{stub}mux.dat", dim)
mat_dipole_y = utils.parse_int_file_2(REFDIR / f"{stub}muy.dat", dim)
mat_dipole_z = utils.parse_int_file_2(REFDIR / f"{stub}muz.dat", dim)
solver = iterators.ExactInv(C, E, occupations)
solver.tei_mo = (TEI_MO, )
solver.tei_mo_type = "full"
driver = cphf.CPHF(solver)
ao_integrals_dipole = np.stack((mat_dipole_x, mat_dipole_y, mat_dipole_z),
axis=0)
operator_dipole = operators.Operator(label="dipole",
is_imaginary=False,
is_spin_dependent=False)
operator_dipole.ao_integrals = ao_integrals_dipole
driver.add_operator(operator_dipole)
frequencies = (0.0, 0.02, 0.06, 0.1)
driver.set_frequencies(frequencies)
driver.run(solver_type="exact", hamiltonian=hamiltonian, spin=spin)
assert len(driver.results) == len(frequencies)
result__0_00 = np.array([[7.93556221, 0.0, 0.0], [0.0, 3.06821077, 0.0],
[0.0, 0.0, 0.05038621]])
result__0_02 = np.array([[7.94312371, 0.0, 0.0], [0.0, 3.07051688, 0.0],
[0.0, 0.0, 0.05054685]])
result__0_06 = np.array([[8.00414009, 0.0, 0.0], [0.0, 3.08913608, 0.0],
[0.0, 0.0, 0.05186977]])
result__0_10 = np.array([[8.1290378, 0.0, 0.0], [0.0, 3.12731363, 0.0],
[0.0, 0.0, 0.05473482]])
atol = 1.0e-8
rtol = 0.0
np.testing.assert_allclose(driver.results[0],
result__0_00,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(driver.results[1],
result__0_02,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(driver.results[2],
result__0_06,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(driver.results[3],
result__0_10,
rtol=rtol,
atol=atol)
# Reminder: there's no call to do SCF here because we already have
# the MO coefficients.
mol = molecules.molecule_water_sto3g()
mol.build()
polarizability = electric.Polarizability(Program.PySCF, mol, C, E,
occupations, frequencies)
polarizability.form_operators()
polarizability.run(hamiltonian=hamiltonian, spin=spin)
polarizability.form_results()
np.testing.assert_allclose(polarizability.polarizabilities[0],
result__0_00,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(polarizability.polarizabilities[1],
result__0_02,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(polarizability.polarizabilities[2],
result__0_06,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(polarizability.polarizabilities[3],
result__0_10,
rtol=rtol,
atol=atol)
return
def calculate_disk_uhf(testcasedir, hamiltonian, spin, frequency, label_1,
label_2):
occupations = utils.read_file_occupations(testcasedir / "occupations")
nocc_alph, nvirt_alph, nocc_beta, nvirt_beta = occupations
norb = nocc_alph + nvirt_alph
C = utils.read_file_3(testcasedir / "C")
assert C.shape[0] == 2
assert C.shape[2] == norb
nbasis = C.shape[1]
moene = utils.read_file_2(testcasedir / "moene")
assert moene.shape == (norb, 2)
moints_iajb_aaaa = utils.read_file_4(testcasedir / "moints_iajb_aaaa")
moints_iajb_aabb = utils.read_file_4(testcasedir / "moints_iajb_aabb")
moints_iajb_bbaa = utils.read_file_4(testcasedir / "moints_iajb_bbaa")
moints_iajb_bbbb = utils.read_file_4(testcasedir / "moints_iajb_bbbb")
moints_ijab_aaaa = utils.read_file_4(testcasedir / "moints_ijab_aaaa")
moints_ijab_bbbb = utils.read_file_4(testcasedir / "moints_ijab_bbbb")
assert moints_iajb_aaaa.shape == (nocc_alph, nvirt_alph, nocc_alph,
nvirt_alph)
assert moints_iajb_aabb.shape == (nocc_alph, nvirt_alph, nocc_beta,
nvirt_beta)
assert moints_iajb_bbaa.shape == (nocc_beta, nvirt_beta, nocc_alph,
nvirt_alph)
assert moints_iajb_bbbb.shape == (nocc_beta, nvirt_beta, nocc_beta,
nvirt_beta)
assert moints_ijab_aaaa.shape == (nocc_alph, nocc_alph, nvirt_alph,
nvirt_alph)
assert moints_ijab_bbbb.shape == (nocc_beta, nocc_beta, nvirt_beta,
nvirt_beta)
operator_1 = utils.dalton_label_to_operator(label_1)
operator_2 = utils.dalton_label_to_operator(label_2)
operator_1_integrals_mn = utils.read_file_3(
testcasedir / f"operator_mn_{operator_1.label}")
operator_2_integrals_mn = utils.read_file_3(
testcasedir / f"operator_mn_{operator_2.label}")
# The first dimension can"t be checked since there may be multiple
# components.
assert operator_1_integrals_mn.shape[1:] == (nbasis, nbasis)
assert operator_2_integrals_mn.shape[1:] == (nbasis, nbasis)
# Only take the component/slice from the integral as determined
# from the DALTON operator label.
operator_1_integrals_mn = operator_1_integrals_mn[operator_1.slice_idx]
operator_2_integrals_mn = operator_2_integrals_mn[operator_2.slice_idx]
# However, this eliminates an axis, which needs to be added back.
operator_1_integrals_mn = operator_1_integrals_mn[np.newaxis, ...]
operator_2_integrals_mn = operator_2_integrals_mn[np.newaxis, ...]
operator_1.ao_integrals = operator_1_integrals_mn
operator_2.ao_integrals = operator_2_integrals_mn
moene_alph = np.diag(moene[:, 0])
moene_beta = np.diag(moene[:, 1])
moene = np.stack((moene_alph, moene_beta), axis=0)
assert moene.shape == (2, norb, norb)
solver = iterators.ExactInv(C, moene, occupations)
solver.tei_mo = (
moints_iajb_aaaa,
moints_iajb_aabb,
moints_iajb_bbaa,
moints_iajb_bbbb,
moints_ijab_aaaa,
moints_ijab_bbbb,
)
solver.tei_mo_type = "partial"
driver = cphf.CPHF(solver)
driver.add_operator(operator_1)
driver.add_operator(operator_2)
driver.set_frequencies([float(frequency)])
driver.run(solver_type="exact", hamiltonian=hamiltonian, spin=spin)
assert len(driver.frequencies) == len(driver.results) == 1
res = driver.results[0]
assert res.shape == (2, 2)
bl = res[1, 0]
tr = res[0, 1]
diff = abs(abs(bl) - abs(tr))
# Results should be symmetric w.r.t. interchange between operators
# in the LR equations.
thresh = 1.0e-14
assert diff < thresh
return bl
def calculate_uhf(
dalton_tmpdir,
hamiltonian=None,
spin=None,
operator_label=None,
operator=None,
source_moenergies=None,
source_mocoeffs=None,
source_operator=None,
):
if operator_label:
# TODO add dipvel
assert operator_label in ("dipole", "angmom", "spinorb")
assert source_moenergies in ("pyscf", "dalton")
assert source_mocoeffs in ("pyscf", "dalton")
dalton_molecule = dalmol.readin(dalton_tmpdir / "DALTON.BAS")
lines = []
for atom in dalton_molecule:
label = atom["label"][0]
center = atom["center"][0]
center_str = " ".join(["{:f}".format(pos) for pos in center])
line = "{:3} {}".format(label, center_str)
lines.append(line)
lines = "\n".join(lines)
# PySCF molecule setup, needed for generating the TEIs in the MO
# basis.
mol = pyscf.gto.Mole()
verbose = 1
mol.verbose = verbose
mol.atom = lines
mol.unit = "Bohr"
# TODO read basis from DALTON molecule
mol.basis = "sto-3g"
mol.symmetry = False
# TODO read charge from DALTON molecule?
mol.charge = 1
# TODO read spin from DALTON molecule?
mol.spin = 1
mol.build()
ifc = sirifc.sirifc(dalton_tmpdir / "SIRIFC")
occupations = utils.occupations_from_sirifc(ifc)
if source_moenergies == "pyscf" or source_mocoeffs == "pyscf":
mf = pyscf.scf.UHF(mol)
mf.kernel()
if source_moenergies == "pyscf":
E_alph = np.diag(mf.mo_energy[0])
E_beta = np.diag(mf.mo_energy[1])
E = np.stack((E_alph, E_beta), axis=0)
elif source_moenergies == "dalton":
job = ccopen(dalton_tmpdir / "DALTON.OUT")
data = job.parse()
# pylint: disable=no-member
E = np.diag([
convertor(x, "eV", "hartree") for x in data.moenergies[0]
])[np.newaxis, ...]
E = np.concatenate((E, E), axis=0)
else:
pass
if source_mocoeffs == "pyscf":
C = mf.mo_coeff
elif source_mocoeffs == "dalton":
C = ifc.cmo[0][np.newaxis, ...]
C = np.concatenate((C, C), axis=0)
else:
pass
solver = iterators.ExactInv(C, E, occupations)
solver.tei_mo = ao2mo.perform_tei_ao2mo_uhf_partial(mol, C)
solver.tei_mo_type = "partial"
driver = cphf.CPHF(solver)
if operator:
driver.add_operator(operator)
elif operator_label:
if operator_label == "dipole":
operator_dipole = operators.Operator(label="dipole",
is_imaginary=False,
is_spin_dependent=False,
triplet=False)
integrals_dipole_ao = mol.intor("cint1e_r_sph", comp=3)
operator_dipole.ao_integrals = integrals_dipole_ao
driver.add_operator(operator_dipole)
elif operator_label == "angmom":
operator_angmom = operators.Operator(label="angmom",
is_imaginary=True,
is_spin_dependent=False,
triplet=False)
integrals_angmom_ao = mol.intor("cint1e_cg_irxp_sph", comp=3)
operator_angmom.ao_integrals = integrals_angmom_ao
driver.add_operator(operator_angmom)
elif operator_label == "spinorb":
operator_spinorb = operators.Operator(label="spinorb",
is_imaginary=True,
is_spin_dependent=False,
triplet=False)
integrals_spinorb_ao = 0
for atm_id in range(mol.natm):
mol.set_rinv_orig(mol.atom_coord(atm_id))
chg = mol.atom_charge(atm_id)
integrals_spinorb_ao += chg * mol.intor("cint1e_prinvxp_sph",
comp=3)
operator_spinorb.ao_integrals = integrals_spinorb_ao
driver.add_operator(operator_spinorb)
else:
pass
else:
pass
driver.set_frequencies()
driver.run(solver_type="exact", hamiltonian=hamiltonian, spin=spin)
return driver.results[0]
def test_explicit_uhf() -> None:
mol = molecules.molecule_water_sto3g()
mol.charge = 1
mol.spin = 1
mol.build()
mf = pyscf.scf.UHF(mol)
mf.kernel()
C = np.stack(mf.mo_coeff, axis=0)
C_a = C[0, ...]
C_b = C[1, ...]
E_a = np.diag(mf.mo_energy[0])
E_b = np.diag(mf.mo_energy[1])
assert C_a.shape == C_b.shape
assert E_a.shape == E_b.shape
E = np.stack((E_a, E_b), axis=0)
norb = C_a.shape[1]
nocc_a, nocc_b = mol.nelec
nvirt_a, nvirt_b = norb - nocc_a, norb - nocc_b
occupations = [nocc_a, nvirt_a, nocc_b, nvirt_b]
C_occ_alph = C_a[:, :nocc_a]
C_virt_alph = C_a[:, nocc_a:]
C_occ_beta = C_b[:, :nocc_b]
C_virt_beta = C_b[:, nocc_b:]
C_ovov_aaaa = (C_occ_alph, C_virt_alph, C_occ_alph, C_virt_alph)
C_ovov_aabb = (C_occ_alph, C_virt_alph, C_occ_beta, C_virt_beta)
C_ovov_bbaa = (C_occ_beta, C_virt_beta, C_occ_alph, C_virt_alph)
C_ovov_bbbb = (C_occ_beta, C_virt_beta, C_occ_beta, C_virt_beta)
C_oovv_aaaa = (C_occ_alph, C_occ_alph, C_virt_alph, C_virt_alph)
C_oovv_bbbb = (C_occ_beta, C_occ_beta, C_virt_beta, C_virt_beta)
tei_mo_ovov_aaaa = pyscf.ao2mo.general(mol,
C_ovov_aaaa,
aosym="s4",
compact=False,
verbose=5).reshape(
nocc_a, nvirt_a, nocc_a,
nvirt_a)
tei_mo_ovov_aabb = pyscf.ao2mo.general(mol,
C_ovov_aabb,
aosym="s4",
compact=False,
verbose=5).reshape(
nocc_a, nvirt_a, nocc_b,
nvirt_b)
tei_mo_ovov_bbaa = pyscf.ao2mo.general(mol,
C_ovov_bbaa,
aosym="s4",
compact=False,
verbose=5).reshape(
nocc_b, nvirt_b, nocc_a,
nvirt_a)
tei_mo_ovov_bbbb = pyscf.ao2mo.general(mol,
C_ovov_bbbb,
aosym="s4",
compact=False,
verbose=5).reshape(
nocc_b, nvirt_b, nocc_b,
nvirt_b)
tei_mo_oovv_aaaa = pyscf.ao2mo.general(mol,
C_oovv_aaaa,
aosym="s4",
compact=False,
verbose=5).reshape(
nocc_a, nocc_a, nvirt_a,
nvirt_a)
tei_mo_oovv_bbbb = pyscf.ao2mo.general(mol,
C_oovv_bbbb,
aosym="s4",
compact=False,
verbose=5).reshape(
nocc_b, nocc_b, nvirt_b,
nvirt_b)
integrals_dipole_ao = mol.intor("cint1e_r_sph", comp=3)
solver = solvers.ExactInv(C, E, occupations)
solver.tei_mo = (
tei_mo_ovov_aaaa,
tei_mo_ovov_aabb,
tei_mo_ovov_bbaa,
tei_mo_ovov_bbbb,
tei_mo_oovv_aaaa,
tei_mo_oovv_bbbb,
)
solver.tei_mo_type = AO2MOTransformationType.partial
driver = cphf.CPHF(solver)
operator_dipole = operators.Operator(label="dipole",
is_imaginary=False,
is_spin_dependent=False)
operator_dipole.ao_integrals = integrals_dipole_ao
driver.add_operator(operator_dipole)
driver.set_frequencies()
driver.run(
hamiltonian=Hamiltonian.RPA,
spin=Spin.singlet,
program=Program.PySCF,
program_obj=mol,
)
assert len(driver.frequencies) == len(driver.results) == 1
res = driver.results[0]
print(res)
atol = 1.0e-5
rtol = 0.0
np.testing.assert_allclose(res,
ref_water_cation_UHF_HF_STO3G,
rtol=rtol,
atol=atol)
def test_final_result_rhf_h2o_sto3g_tda_triplet():
hamiltonian = "tda"
spin = "triplet"
C = utils.fix_mocoeffs_shape(utils.np_load(REFDIR / "C.npz"))
E = utils.fix_moenergies_shape(utils.np_load(REFDIR / "F_MO.npz"))
TEI_MO = utils.np_load(REFDIR / "TEI_MO.npz")
# nocc_alph, nvirt_alph, nocc_beta, nvirt_beta
occupations = [5, 2, 5, 2]
stub = "h2o_sto3g_"
dim = occupations[0] + occupations[1]
mat_dipole_x = utils.parse_int_file_2(REFDIR / f"{stub}mux.dat", dim)
mat_dipole_y = utils.parse_int_file_2(REFDIR / f"{stub}muy.dat", dim)
mat_dipole_z = utils.parse_int_file_2(REFDIR / f"{stub}muz.dat", dim)
solver = iterators.ExactInv(C, E, occupations)
solver.tei_mo = (TEI_MO, )
solver.tei_mo_type = "full"
driver = cphf.CPHF(solver)
ao_integrals_dipole = np.stack((mat_dipole_x, mat_dipole_y, mat_dipole_z),
axis=0)
operator_dipole = operators.Operator(label="dipole",
is_imaginary=False,
is_spin_dependent=False)
operator_dipole.ao_integrals = ao_integrals_dipole
driver.add_operator(operator_dipole)
frequencies = (0.0, 0.02, 0.06, 0.1)
driver.set_frequencies(frequencies)
driver.run(solver_type="exact", hamiltonian=hamiltonian, spin=spin)
assert len(driver.results) == len(frequencies)
result__0_00 = np.array([[14.64430714, 0.0, 0.0], [0.0, 8.80921432, 0.0],
[0.0, 0.0, 0.06859496]])
result__0_02 = np.array([[14.68168443, 0.0, 0.0], [0.0, 8.83562647, 0.0],
[0.0, 0.0, 0.0689291]])
result__0_06 = np.array([[14.98774296, 0.0, 0.0], [0.0, 9.0532224, 0.0],
[0.0, 0.0, 0.07172414]])
result__0_10 = np.array([[15.63997724, 0.0, 0.0], [0.0, 9.52504267, 0.0],
[0.0, 0.0, 0.07805428]])
atol = 1.0e-8
rtol = 0.0
np.testing.assert_allclose(driver.results[0],
result__0_00,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(driver.results[1],
result__0_02,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(driver.results[2],
result__0_06,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(driver.results[3],
result__0_10,
rtol=rtol,
atol=atol)
mol = molecules.molecule_water_sto3g()
mol.build()
polarizability = electric.Polarizability(Program.PySCF, mol, C, E,
occupations, frequencies)
polarizability.form_operators()
polarizability.run(hamiltonian=hamiltonian, spin=spin)
polarizability.form_results()
np.testing.assert_allclose(polarizability.polarizabilities[0],
result__0_00,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(polarizability.polarizabilities[1],
result__0_02,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(polarizability.polarizabilities[2],
result__0_06,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(polarizability.polarizabilities[3],
result__0_10,
rtol=rtol,
atol=atol)
return
def test_final_result_rhf_h2o_sto3g_rpa_triplet():
hamiltonian = "rpa"
spin = "triplet"
C = utils.fix_mocoeffs_shape(utils.np_load(REFDIR / "C.npz"))
E = utils.fix_moenergies_shape(utils.np_load(REFDIR / "F_MO.npz"))
TEI_MO = utils.np_load(REFDIR / "TEI_MO.npz")
# nocc_alph, nvirt_alph, nocc_beta, nvirt_beta
occupations = [5, 2, 5, 2]
stub = "h2o_sto3g_"
dim = occupations[0] + occupations[1]
mat_dipole_x = utils.parse_int_file_2(REFDIR / f"{stub}mux.dat", dim)
mat_dipole_y = utils.parse_int_file_2(REFDIR / f"{stub}muy.dat", dim)
mat_dipole_z = utils.parse_int_file_2(REFDIR / f"{stub}muz.dat", dim)
solver = iterators.ExactInv(C, E, occupations)
solver.tei_mo = (TEI_MO, )
solver.tei_mo_type = "full"
driver = cphf.CPHF(solver)
ao_integrals_dipole = np.stack((mat_dipole_x, mat_dipole_y, mat_dipole_z),
axis=0)
operator_dipole = operators.Operator(label="dipole",
is_imaginary=False,
is_spin_dependent=False)
operator_dipole.ao_integrals = ao_integrals_dipole
driver.add_operator(operator_dipole)
frequencies = (0.0, 0.02, 0.06, 0.1)
driver.set_frequencies(frequencies)
driver.run(solver_type="exact", hamiltonian=hamiltonian, spin=spin)
assert len(driver.results) == len(frequencies)
result__0_00 = np.array([[26.59744305, 0.0, 0.0], [0.0, 18.11879557, 0.0],
[0.0, 0.0, 0.07798969]])
result__0_02 = np.array([[26.68282287, 0.0, 0.0], [0.0, 18.19390051, 0.0],
[0.0, 0.0, 0.07837521]])
result__0_06 = np.array([[27.38617401, 0.0, 0.0], [0.0, 18.81922578, 0.0],
[0.0, 0.0, 0.08160226]])
result__0_10 = np.array([[28.91067234, 0.0, 0.0], [0.0, 20.21670386, 0.0],
[0.0, 0.0, 0.08892512]])
atol = 1.0e-8
rtol = 0.0
np.testing.assert_allclose(driver.results[0],
result__0_00,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(driver.results[1],
result__0_02,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(driver.results[2],
result__0_06,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(driver.results[3],
result__0_10,
rtol=rtol,
atol=atol)
mol = molecules.molecule_water_sto3g()
mol.build()
polarizability = electric.Polarizability(Program.PySCF, mol, C, E,
occupations, frequencies)
polarizability.form_operators()
polarizability.run(hamiltonian=hamiltonian, spin=spin)
polarizability.form_results()
np.testing.assert_allclose(polarizability.polarizabilities[0],
result__0_00,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(polarizability.polarizabilities[1],
result__0_02,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(polarizability.polarizabilities[2],
result__0_06,
rtol=rtol,
atol=atol)
np.testing.assert_allclose(polarizability.polarizabilities[3],
result__0_10,
rtol=rtol,
atol=atol)
return
def calculate_disk_rhf(
testcasedir: Path,
hamiltonian: str,
spin: str,
frequency: str,
label_1: str,
label_2: str,
) -> float:
occupations = utils.read_file_occupations(testcasedir / "occupations")
nocc_alph, nvirt_alph, nocc_beta, nvirt_beta = occupations
assert nocc_alph == nocc_beta
assert nvirt_alph == nvirt_beta
norb = nocc_alph + nvirt_alph
C = utils.read_file_3(testcasedir / "C")
assert C.shape[0] == 1
assert C.shape[2] == norb
nbasis = C.shape[1]
moene = utils.read_file_2(testcasedir / "moene")
assert moene.shape == (norb, 1)
moints_iajb_aaaa = utils.read_file_4(testcasedir / "moints_iajb_aaaa")
moints_ijab_aaaa = utils.read_file_4(testcasedir / "moints_ijab_aaaa")
assert moints_iajb_aaaa.shape == (nocc_alph, nvirt_alph, nocc_alph,
nvirt_alph)
assert moints_ijab_aaaa.shape == (nocc_alph, nocc_alph, nvirt_alph,
nvirt_alph)
operator_1 = dalton_label_to_operator(label_1)
operator_2 = dalton_label_to_operator(label_2)
operator_1_integrals_mn = utils.read_file_3(
testcasedir / f"operator_mn_{operator_1.label}")
operator_2_integrals_mn = utils.read_file_3(
testcasedir / f"operator_mn_{operator_2.label}")
# The first dimension can"t be checked since there may be multiple
# components.
assert operator_1_integrals_mn.shape[1:] == (nbasis, nbasis)
assert operator_2_integrals_mn.shape[1:] == (nbasis, nbasis)
# Only take the component/slice from the integral as determined
# from the DALTON operator label.
operator_1_integrals_mn = operator_1_integrals_mn[operator_1.slice_idx]
operator_2_integrals_mn = operator_2_integrals_mn[operator_2.slice_idx]
# However, this eliminates an axis, which needs to be added back.
operator_1_integrals_mn = operator_1_integrals_mn[np.newaxis, ...]
operator_2_integrals_mn = operator_2_integrals_mn[np.newaxis, ...]
operator_1.ao_integrals = operator_1_integrals_mn
operator_2.ao_integrals = operator_2_integrals_mn
moene = np.diag(moene[:, 0])[np.newaxis, ...]
assert moene.shape == (1, norb, norb)
solver = solvers.ExactInv(C, moene, occupations)
solver.tei_mo = (moints_iajb_aaaa, moints_ijab_aaaa)
solver.tei_mo_type = AO2MOTransformationType.partial
driver = cphf.CPHF(solver)
driver.add_operator(operator_1)
driver.add_operator(operator_2)
driver.set_frequencies([float(frequency)])
driver.run(
hamiltonian=Hamiltonian[hamiltonian.upper()],
spin=Spin[spin],
program=None,
program_obj=None,
)
assert len(driver.frequencies) == len(driver.results) == 1
res = driver.results[0]
assert res.shape == (2, 2)
bl = res[1, 0]
tr = res[0, 1]
diff = abs(abs(bl) - abs(tr))
# Results should be symmetric w.r.t. interchange between operators
# in the LR equations.
thresh = 1.0e-13
assert diff < thresh
return bl
