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_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_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_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_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_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() -> 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_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 calculate_uhf( dalton_tmpdir: Path, hamiltonian: str, spin: str, operator_label: str, operator: str, source_moenergies: str, source_mocoeffs: str, source_operator: str, ): 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 = solvers.ExactInv(C, E, occupations) solver.tei_mo = AO2MOpyscf(mol, C).perform_uhf_partial() solver.tei_mo_type = AO2MOTransformationType.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(hamiltonian=Hamiltonian[hamiltonian.upper()], spin=Spin[spin]) return driver.results[0]
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
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_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