def test_reference_energy():
gos_system = construct_pyscf_system_rhf("li 0.0 0.0 0.0; h 0.0 0.0 3.08",
basis="cc-pvdz")
spas_system = construct_pyscf_system_rhf("li 0.0 0.0 0.0; h 0.0 0.0 3.08",
basis="cc-pvdz",
add_spin=False)
# This energy is found from PySCF's RHF solver
lih_energy = -7.98367215457454
assert abs(gos_system.compute_reference_energy() - lih_energy) < 1e-8
assert abs(spas_system.compute_reference_energy() - lih_energy) < 1e-8
def test_reference_energy():
system = construct_pyscf_system_rhf("he", basis="cc-pvdz")
# This energy is found from PySCF's RHF solver
he_energy = -2.85516047724274
assert abs(system.compute_reference_energy() - he_energy) < 1e-8
def test_spin_squared_constructions():
# TODO: Try to make this test applicable for non-orthonomal basis sets.
# n = 2
# l = 10
# system = GeneralOrbitalSystem(n, RandomBasisSet(l, 3))
# system = GeneralOrbitalSystem(
# n, ODQD(l, 10, 1001, potential=ODQD.HOPotential(1))
# )
# system = construct_pyscf_system_ao("he")
system = construct_pyscf_system_rhf("he", basis="cc-pVTZ")
spin_dir_tb_orig = []
spin_dir_tb_pm = []
spin_p = system.spin_x + 1j * system.spin_y
spin_m = system.spin_x - 1j * system.spin_y
spin_z = system.spin_z
s = system.s
np.testing.assert_allclose(spin_p @ s @ spin_m - spin_m @ s @ spin_p,
2 * spin_z,
atol=1e-10)
# S^2 = S_- * S_+ + S_z + S_z^2
spin_2_mp = spin_m @ spin_p + spin_z + spin_z @ spin_z
spin_2_tb_mp = (0.5 * np.einsum("pr, qs -> pqrs", spin_m, spin_p) +
0.5 * np.einsum("pr, qs -> pqrs", spin_p, spin_m) +
np.einsum("pr, qs -> pqrs", spin_z, spin_z))
spin_2_tb_mp = system._basis_set.anti_symmetrize_u(spin_2_tb_mp)
# S^2 = S_+ * S_- - S_z + S_z^2
spin_2_pm = spin_p @ spin_m - spin_z + spin_z @ spin_z
spin_2_tb_pm = (0.5 * np.einsum("pr, qs -> pqrs", spin_m, spin_p) +
0.5 * np.einsum("pr, qs -> pqrs", spin_p, spin_m) +
np.einsum("pr, qs -> pqrs", spin_z, spin_z))
spin_2_tb_pm = system._basis_set.anti_symmetrize_u(spin_2_tb_pm)
np.testing.assert_allclose(spin_2_mp, spin_2_pm, atol=1e-10)
np.testing.assert_allclose(spin_2_tb_mp, spin_2_tb_pm)
np.testing.assert_allclose(spin_2_mp, system.spin_2, atol=1e-10)
np.testing.assert_allclose(spin_2_tb_mp, system.spin_2_tb)
np.testing.assert_allclose(spin_2_pm, system.spin_2, atol=1e-10)
np.testing.assert_allclose(spin_2_tb_pm, system.spin_2_tb)