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 __init__(self,
C: np.ndarray,
verbose: int = 1,
pyscfmol: Optional[Any] = None) -> None:
self.pyscfmol = pyscfmol
occupations = occupations_from_pyscf_mol(self.pyscfmol, C)
super().__init__(C, occupations, verbose, I=None)
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_explicit_rhf_outside_solver_off_diagonal_blocks():
mol = molecules.molecule_water_sto3g()
mol.build()
mf = pyscf.scf.RHF(mol)
mf.kernel()
mocoeffs = mf.mo_coeff
moenergies = mf.mo_energy
ao2mo = AO2MOpyscf(mocoeffs, mol.verbose, mol)
ao2mo.perform_rhf_full()
tei_mo = ao2mo.tei_mo[0]
C = mocoeffs
E = np.diag(moenergies)
occupations = utils.occupations_from_pyscf_mol(mol, mocoeffs)
nocc, nvirt, _, _ = occupations
A = eqns.form_rpa_a_matrix_mo_singlet_full(E, tei_mo, nocc)
B = eqns.form_rpa_b_matrix_mo_singlet_full(tei_mo, nocc)
G = np.block([[A, B], [B, A]])
assert G.shape == (2 * nocc * nvirt, 2 * nocc * nvirt)
G_inv = np.linalg.inv(G)
components = 3
integrals_dipole_ao = mol.intor("cint1e_r_sph", comp=components)
integrals_dipole_mo_ai = []
for component in range(components):
integrals_dipole_mo_ai_component = np.dot(
C[:, nocc:].T,
np.dot(integrals_dipole_ao[component, ...],
C[:, :nocc])).reshape(-1, order="F")
integrals_dipole_mo_ai.append(integrals_dipole_mo_ai_component)
integrals_dipole_mo_ai = np.stack(integrals_dipole_mo_ai, axis=0).T
integrals_dipole_mo_ai_super = np.concatenate(
(integrals_dipole_mo_ai, -integrals_dipole_mo_ai), axis=0)
rhsvecs = integrals_dipole_mo_ai_super
rspvecs = np.dot(G_inv, rhsvecs)
polarizability = 4 * np.dot(rhsvecs.T, rspvecs) / 2
# pylint: disable=bad-whitespace
result__0_00 = np.array([[7.93556221, 0.0, 0.0], [0.0, 3.06821077, 0.0],
[0.0, 0.0, 0.05038621]])
atol = 1.0e-8
rtol = 0.0
np.testing.assert_allclose(polarizability,
result__0_00,
rtol=rtol,
atol=atol)
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_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_ao2mo_hand_against_pyscf_rhf_partial() -> None:
mol = molecules_pyscf.molecule_physicists_water_sto3g()
mol.build()
mf = pyscf.scf.RHF(mol)
mf.kernel()
C = fix_mocoeffs_shape(mf.mo_coeff)
occupations = occupations_from_pyscf_mol(mol, C)
nocc, nvirt, _, _ = occupations
nmo = nocc + nvirt
ntransforms = 2
o = slice(0, nocc)
v = slice(nocc, nmo)
ao2mo = AO2MOpyscf(C, verbose=mol.verbose, pyscfmol=mol)
ao2mo.perform_rhf_partial()
assert len(ao2mo.tei_mo) == ntransforms
tei_mo_ovov_pyscf = ao2mo.tei_mo[0]
tei_mo_oovv_pyscf = ao2mo.tei_mo[1]
tei_ao = mol.intor("int2e_sph", aosym="s1")
print("1. Use the class method explicitly.")
tei_mo_ovov_hand = AO2MO.transform(tei_ao, C[0, :, o], C[0, :, v], C[0, :, o], C[0, :, v])
tei_mo_oovv_hand = AO2MO.transform(tei_ao, C[0, :, o], C[0, :, o], C[0, :, v], C[0, :, v])
assert tei_mo_ovov_pyscf.shape == tei_mo_ovov_hand.shape == (nocc, nvirt, nocc, nvirt)
assert tei_mo_oovv_pyscf.shape == tei_mo_oovv_hand.shape == (nocc, nocc, nvirt, nvirt)
np.testing.assert_allclose(tei_mo_ovov_hand, tei_mo_ovov_pyscf, rtol=0, atol=1.0e-15)
np.testing.assert_allclose(tei_mo_oovv_hand, tei_mo_oovv_pyscf, rtol=0, atol=1.0e-15)
print("2. Use the class method normally.")
ao2mo_method = AO2MO(C, occupations, verbose=mol.verbose, I=tei_ao)
ao2mo_method.perform_rhf_partial()
assert len(ao2mo_method.tei_mo) == ntransforms
tei_mo_ovov_method = ao2mo_method.tei_mo[0]
tei_mo_oovv_method = ao2mo_method.tei_mo[1]
assert tei_mo_ovov_pyscf.shape == tei_mo_ovov_method.shape == (nocc, nvirt, nocc, nvirt)
assert tei_mo_oovv_pyscf.shape == tei_mo_oovv_method.shape == (nocc, nocc, nvirt, nvirt)
np.testing.assert_allclose(tei_mo_ovov_method, tei_mo_ovov_pyscf, rtol=0, atol=1.0e-15)
np.testing.assert_allclose(tei_mo_oovv_method, tei_mo_oovv_pyscf, rtol=0, atol=1.0e-15)
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 = solvers.ExactInv(C, E, occupations)
ao2mo = AO2MOpyscf(C, mol.verbose, mol)
ao2mo.perform_uhf_full()
solver.tei_mo = ao2mo.tei_mo
solver.tei_mo_type = AO2MOTransformationType.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(hamiltonian=Hamiltonian.RPA, spin=Spin.singlet, program=None, program_obj=None)
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_explicit_uhf_outside_solver():
mol = molecules.molecule_water_sto3g()
mol.charge = 1
mol.spin = 1
mol.build()
mf = pyscf.scf.UHF(mol)
mf.kernel()
C_a = mf.mo_coeff[0]
C_b = mf.mo_coeff[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
ao2mo = AO2MOpyscf(mf.mo_coeff, 5, mol)
ao2mo.perform_uhf_full()
tei_mo_aaaa, tei_mo_aabb, tei_mo_bbaa, tei_mo_bbbb = ao2mo.tei_mo
occupations = utils.occupations_from_pyscf_mol(mol, mf.mo_coeff)
nocc_a, nvirt_a, nocc_b, nvirt_b = occupations
A_s_ss_a = eqns.form_rpa_a_matrix_mo_singlet_ss_full(E_a, tei_mo_aaaa, nocc_a)
A_s_os_a = eqns.form_rpa_a_matrix_mo_singlet_os_full(tei_mo_aabb, nocc_a, nocc_b)
B_s_ss_a = eqns.form_rpa_b_matrix_mo_singlet_ss_full(tei_mo_aaaa, nocc_a)
B_s_os_a = eqns.form_rpa_b_matrix_mo_singlet_os_full(tei_mo_aabb, nocc_a, nocc_b)
A_s_ss_b = eqns.form_rpa_a_matrix_mo_singlet_ss_full(E_b, tei_mo_bbbb, nocc_b)
A_s_os_b = eqns.form_rpa_a_matrix_mo_singlet_os_full(tei_mo_bbaa, nocc_b, nocc_a)
B_s_ss_b = eqns.form_rpa_b_matrix_mo_singlet_ss_full(tei_mo_bbbb, nocc_b)
B_s_os_b = eqns.form_rpa_b_matrix_mo_singlet_os_full(tei_mo_bbaa, nocc_b, nocc_a)
# Since the "triplet" part contains no Coulomb contribution, and
# (xx|yy) is only in the Coulomb part, there is no ss/os
# separation for the triplet part.
G_aa = np.block([[A_s_ss_a, B_s_ss_a], [B_s_ss_a, A_s_ss_a]])
G_bb = np.block([[A_s_ss_b, B_s_ss_b], [B_s_ss_b, A_s_ss_b]])
G_ab = np.block([[A_s_os_a, B_s_os_a], [B_s_os_a, A_s_os_a]])
G_ba = np.block([[A_s_os_b, B_s_os_b], [B_s_os_b, A_s_os_b]])
G_aa_inv = np.linalg.inv(G_aa)
G_bb_inv = np.linalg.inv(G_bb)
nov_aa = nocc_a * nvirt_a
nov_bb = nocc_b * nvirt_b
assert G_aa_inv.shape == (2 * nov_aa, 2 * nov_aa)
assert G_bb_inv.shape == (2 * nov_bb, 2 * nov_bb)
# Form the operator-independent part of the response vectors.
left_a = np.linalg.inv(G_aa - np.dot(G_ab, np.dot(G_bb_inv, G_ba)))
left_b = np.linalg.inv(G_bb - np.dot(G_ba, np.dot(G_aa_inv, G_ab)))
integrals_dipole_ao = mol.intor("cint1e_r_sph", comp=3)
integrals_dipole_mo_ai_a = []
integrals_dipole_mo_ai_b = []
for comp in range(3):
integrals_dipole_mo_ai_comp_a = np.dot(
C_a[:, nocc_a:].T, np.dot(integrals_dipole_ao[comp, ...], C_a[:, :nocc_a])
)
integrals_dipole_mo_ai_comp_b = np.dot(
C_b[:, nocc_b:].T, np.dot(integrals_dipole_ao[comp, ...], C_b[:, :nocc_b])
)
integrals_dipole_mo_ai_comp_a = np.reshape(integrals_dipole_mo_ai_comp_a, -1, order="F")
integrals_dipole_mo_ai_comp_b = np.reshape(integrals_dipole_mo_ai_comp_b, -1, order="F")
integrals_dipole_mo_ai_a.append(integrals_dipole_mo_ai_comp_a)
integrals_dipole_mo_ai_b.append(integrals_dipole_mo_ai_comp_b)
integrals_dipole_mo_ai_a = np.stack(integrals_dipole_mo_ai_a, axis=0).T
integrals_dipole_mo_ai_b = np.stack(integrals_dipole_mo_ai_b, axis=0).T
integrals_dipole_mo_ai_a_super = np.concatenate(
(integrals_dipole_mo_ai_a, -integrals_dipole_mo_ai_a), axis=0
)
integrals_dipole_mo_ai_b_super = np.concatenate(
(integrals_dipole_mo_ai_b, -integrals_dipole_mo_ai_b), axis=0
)
# Form the operator-dependent part of the response vectors.
right_a = integrals_dipole_mo_ai_a_super - (
np.dot(G_ab, np.dot(G_bb_inv, integrals_dipole_mo_ai_b_super))
)
right_b = integrals_dipole_mo_ai_b_super - (
np.dot(G_ba, np.dot(G_aa_inv, integrals_dipole_mo_ai_a_super))
)
# The total response vector for each spin is the product of the
# operator-independent (left) and operator-dependent (right)
# parts.
rspvec_a = np.dot(left_a, right_a)
rspvec_b = np.dot(left_b, right_b)
res_a = np.dot(integrals_dipole_mo_ai_a_super.T, rspvec_a) / 2
res_b = np.dot(integrals_dipole_mo_ai_b_super.T, rspvec_b) / 2
res_u = 2 * (res_a + res_b)
print(res_u)
atol = 1.0e-5
rtol = 0.0
np.testing.assert_allclose(res_u, ref_water_cation_UHF_HF_STO3G, rtol=rtol, atol=atol)
def test_explicit_uhf_from_rhf_outside_solver():
mol = molecules.molecule_water_sto3g()
mol.build()
mf = pyscf.scf.RHF(mol)
mf.kernel()
mocoeffs = mf.mo_coeff
moenergies = mf.mo_energy
ao2mo = AO2MOpyscf(mocoeffs, mol.verbose, mol)
ao2mo.perform_rhf_full()
tei_mo = ao2mo.tei_mo[0]
C_a = mocoeffs
C_b = C_a.copy()
E_a = np.diag(moenergies)
# E_b = E_a.copy()
occupations = utils.occupations_from_pyscf_mol(mol, mocoeffs)
nocc_a, nvirt_a, nocc_b, nvirt_b = occupations
# Same-spin and opposite-spin contributions should add together
# properly for restricted wavefunction.
A_s = eqns.form_rpa_a_matrix_mo_singlet_full(E_a, tei_mo, nocc_a)
A_s_ss = eqns.form_rpa_a_matrix_mo_singlet_ss_full(E_a, tei_mo, nocc_a)
A_s_os = eqns.form_rpa_a_matrix_mo_singlet_os_full(tei_mo, nocc_a, nocc_b)
np.testing.assert_allclose(A_s, A_s_ss + A_s_os)
B_s = eqns.form_rpa_b_matrix_mo_singlet_full(tei_mo, nocc_a)
B_s_ss = eqns.form_rpa_b_matrix_mo_singlet_ss_full(tei_mo, nocc_a)
B_s_os = eqns.form_rpa_b_matrix_mo_singlet_os_full(tei_mo, nocc_a, nocc_b)
np.testing.assert_allclose(B_s, B_s_ss + B_s_os)
# Since the "triplet" part contains no Coulomb contribution, and
# (xx|yy) is only in the Coulomb part, there is no ss/os
# separation for the triplet part.
G_r = np.block([[A_s, B_s], [B_s, A_s]])
G_aa = np.block([[A_s_ss, B_s_ss], [B_s_ss, A_s_ss]])
G_bb = G_aa.copy()
G_ab = np.block([[A_s_os, B_s_os], [B_s_os, A_s_os]])
G_ba = G_ab.copy()
np.testing.assert_allclose(G_r, (G_aa + G_ab))
G_r_inv = np.linalg.inv(G_r)
G_aa_inv = np.linalg.inv(G_aa)
G_bb_inv = np.linalg.inv(G_bb)
assert G_r_inv.shape == (2 * nocc_a * nvirt_a, 2 * nocc_a * nvirt_a)
assert G_aa_inv.shape == (2 * nocc_a * nvirt_a, 2 * nocc_a * nvirt_a)
assert G_bb_inv.shape == (2 * nocc_b * nvirt_b, 2 * nocc_b * nvirt_b)
# Form the operator-independent part of the response vectors.
left_alph = np.linalg.inv(G_aa - np.dot(G_ab, np.dot(G_bb_inv, G_ba)))
left_beta = np.linalg.inv(G_bb - np.dot(G_ba, np.dot(G_aa_inv, G_ab)))
integrals_dipole_ao = mol.intor("cint1e_r_sph", comp=3)
integrals_dipole_mo_ai_r = []
integrals_dipole_mo_ai_a = []
integrals_dipole_mo_ai_b = []
for comp in range(3):
integrals_dipole_mo_ai_comp_r = np.dot(
C_a[:, nocc_a:].T, np.dot(integrals_dipole_ao[comp, ...], C_a[:, :nocc_a])
)
integrals_dipole_mo_ai_comp_a = np.dot(
C_a[:, nocc_a:].T, np.dot(integrals_dipole_ao[comp, ...], C_a[:, :nocc_a])
)
integrals_dipole_mo_ai_comp_b = np.dot(
C_b[:, nocc_b:].T, np.dot(integrals_dipole_ao[comp, ...], C_b[:, :nocc_b])
)
integrals_dipole_mo_ai_comp_r = np.reshape(integrals_dipole_mo_ai_comp_r, -1, order="F")
integrals_dipole_mo_ai_comp_a = np.reshape(integrals_dipole_mo_ai_comp_a, -1, order="F")
integrals_dipole_mo_ai_comp_b = np.reshape(integrals_dipole_mo_ai_comp_b, -1, order="F")
integrals_dipole_mo_ai_r.append(integrals_dipole_mo_ai_comp_r)
integrals_dipole_mo_ai_a.append(integrals_dipole_mo_ai_comp_a)
integrals_dipole_mo_ai_b.append(integrals_dipole_mo_ai_comp_b)
integrals_dipole_mo_ai_r = np.stack(integrals_dipole_mo_ai_r, axis=0).T
integrals_dipole_mo_ai_a = np.stack(integrals_dipole_mo_ai_a, axis=0).T
integrals_dipole_mo_ai_b = np.stack(integrals_dipole_mo_ai_b, axis=0).T
integrals_dipole_mo_ai_r_super = np.concatenate(
(integrals_dipole_mo_ai_r, -integrals_dipole_mo_ai_r), axis=0
)
integrals_dipole_mo_ai_a_super = np.concatenate(
(integrals_dipole_mo_ai_a, -integrals_dipole_mo_ai_a), axis=0
)
integrals_dipole_mo_ai_b_super = np.concatenate(
(integrals_dipole_mo_ai_b, -integrals_dipole_mo_ai_b), axis=0
)
# Form the operator-dependent part of the response vectors.
right_alph = integrals_dipole_mo_ai_a_super - (
np.dot(G_ab, np.dot(G_bb_inv, integrals_dipole_mo_ai_b_super))
)
right_beta = integrals_dipole_mo_ai_b_super - (
np.dot(G_ba, np.dot(G_aa_inv, integrals_dipole_mo_ai_a_super))
)
rspvec_r = np.dot(G_r_inv, integrals_dipole_mo_ai_r_super)
# The total response vector for each spin is the product of the
# operator-independent (left) and operator-dependent (right)
# parts.
rspvec_a = np.dot(left_alph, right_alph)
rspvec_b = np.dot(left_beta, right_beta)
res_r = 4 * np.dot(integrals_dipole_mo_ai_r_super.T, rspvec_r) / 2
res_a = np.dot(integrals_dipole_mo_ai_a_super.T, rspvec_a) / 2
res_b = np.dot(integrals_dipole_mo_ai_b_super.T, rspvec_b) / 2
res_u = 2 * (res_a + res_b)
atol = 1.0e-8
rtol = 0.0
np.testing.assert_allclose(res_u, res_r, rtol=rtol, atol=atol)
print(res_r)
print(res_u)
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_ECD_RPA_singlet_BC2H4_cation_HF_STO3G() -> None:
ref = BC2H4_cation_HF_STO3G_RPA_singlet_nwchem
nroots = ref["nroots"]
mol = molecules.molecule_bc2h4_cation_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)
ecd_dipvel_rpa = ecd.ECD(
Program.PySCF,
mol,
td.TDHF(solvers.ExactDiagonalizationSolver(C, E, occupations)),
C,
E,
occupations,
do_dipvel=True,
)
ecd_dipvel_rpa.form_operators()
ecd_dipvel_rpa.run(hamiltonian=Hamiltonian.RPA, spin=Spin.singlet)
ecd_dipvel_rpa.form_results()
print("excitation energies")
ref_etenergies = np.array(ref["etenergies"])
res_etenergies = ecd_dipvel_rpa.driver.solver.eigvals.real[:nroots]
print("ref, res")
for refval, resval in zip(ref_etenergies, res_etenergies):
print(refval, resval)
thresh = 2.5e-7
for i in range(nroots):
abs_diff = abs(ref_etenergies[i] - res_etenergies[i])
assert abs_diff < thresh
print("dipole (length) oscillator strengths")
ref_etoscslen = np.array(ref["etoscslen"])
res_etoscslen = ecd_dipvel_rpa.driver.solver.operators[
1].total_oscillator_strengths[:nroots]
print("ref, res")
for refval, resval in zip(ref_etoscslen, res_etoscslen):
print(refval, resval)
thresh = 1.0e-5
for i in range(nroots):
abs_diff = abs(ref_etoscslen[i] - res_etoscslen[i])
assert abs_diff < thresh
# TODO
print("TODO dipole (mixed length/velocity) oscillator strengths")
# TODO
print("TODO dipole (velocity) oscillator strengths")
ref_etoscsvel = np.array(ref["etoscsvel"])
res_etoscsvel = ecd_dipvel_rpa.driver.solver.operators[
2].total_oscillator_strengths[:nroots]
# print('ref, res')
# for refval, resval in zip(ref_etoscsvel, res_etoscsvel):
# print(refval, resval)
# print(ref_etoscsvel / res_etoscsvel)
# print(res_etoscsvel / ref_etoscsvel)
print("rotatory strengths (length)")
ref_etrotstrlen = np.array(ref["etrotstrlen"])
res_etrotstrlen = ecd_dipvel_rpa.rotational_strengths_diplen[:nroots]
print("ref, res")
for refval, resval in zip(ref_etrotstrlen, res_etrotstrlen):
print(refval, resval)
# TODO unlike other quantities, the error isn't uniformly
# distributed among the roots; how should this be handled?
thresh = 1.5e1
for i in range(nroots):
abs_diff = abs(ref_etrotstrlen[i] - res_etrotstrlen[i])
assert abs_diff < thresh
print("rotatory strengths (velocity)")
ref_etrotstrvel = np.array(ref["etrotstrvel"])
res_etrotstrvel = ecd_dipvel_rpa.rotational_strengths_dipvel[:nroots]
print("ref, res")
for refval, resval in zip(ref_etrotstrvel, res_etrotstrvel):
print(refval, resval)
thresh = 1.0e-2
for i in range(nroots):
abs_diff = abs(ref_etrotstrvel[i] - res_etrotstrvel[i])
assert abs_diff < thresh
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_HF_both_singlet_HF_STO3G():
mol = pyscf.gto.Mole()
mol.verbose = 0
mol.output = None
# pylint: disable=bad-whitespace
mol.atom = [["H", (0.0, 0.0, 0.917)], ["F", (0.0, 0.0, 0.0)]]
mol.basis = "sto-3g"
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_tda = solvers.ExactDiagonalizationSolverTDA(C, E, occupations)
solver_tdhf = solvers.ExactDiagonalizationSolver(C, E, occupations)
ao2mo = AO2MOpyscf(C, mol.verbose, mol)
ao2mo.perform_rhf_partial()
tei_mo = ao2mo.tei_mo
solver_tda.tei_mo = tei_mo
solver_tda.tei_mo_type = AO2MOTransformationType.partial
solver_tdhf.tei_mo = tei_mo
solver_tdhf.tei_mo_type = AO2MOTransformationType.partial
driver_tda = td.TDA(solver_tda)
driver_tdhf = td.TDHF(solver_tdhf)
nroots = 5
print("TDA using TDA()")
driver_tda.run(
hamiltonian=Hamiltonian.TDA,
spin=Spin.singlet,
program=Program.PySCF,
program_obj=mol,
)
excitation_energies_tda_using_tda = driver_tda.solver.eigvals[:nroots].real
print("TDA using TDHF()")
driver_tdhf.run(
hamiltonian=Hamiltonian.TDA,
spin=Spin.singlet,
program=Program.PySCF,
program_obj=mol,
)
excitation_energies_tda_using_tdhf = driver_tdhf.solver.eigvals[:
nroots].real
print("RPA using TDHF()")
driver_tdhf.run(
hamiltonian=Hamiltonian.RPA,
spin=Spin.singlet,
program=Program.PySCF,
program_obj=mol,
)
excitation_energies_rpa = driver_tdhf.solver.eigvals[:nroots].real
assert excitation_energies_tda_using_tda.shape == excitation_energies_tda_using_tdhf.shape
assert excitation_energies_tda_using_tdhf.shape == excitation_energies_rpa.shape
# There should be no difference in the TDA results regardless of
# which implementation used.
assert (excitation_energies_tda_using_tda -
excitation_energies_tda_using_tdhf).all() == 0
# Now compare against reference_data
ref_tda = HF_neutral_singlet_HF_STO3G_CIS_qchem
ref_rpa = HF_neutral_singlet_HF_STO3G_RPA_qchem
thresh = 1.0e-7
for i in range(nroots):
abs_diff = abs(ref_tda["etenergies"][i] -
excitation_energies_tda_using_tda[i])
assert abs_diff < thresh
thresh = 1.0e-7
for i in range(nroots):
abs_diff = abs(ref_rpa["etenergies"][i] - excitation_energies_rpa[i])
assert abs_diff < thresh
