def test_gto_nuclear(self):
"""
Test nuclear attraction integral for GTOs
V^{(c)}_ij = <gto_i | -1 / |r-Rc| | gto_j>
"""
# construct integrator object
integrator = PyQInt()
# test GTO
gto1 = gto(0.154329, [0.0, 0.0, 0.0], 3.425251, 0, 0, 0)
gto2 = gto(0.535328, [0.0, 0.0, 0.0], 0.623914, 0, 0, 0)
gto3 = gto(0.444635, [0.0, 0.0, 0.0], 0.168855, 0, 0, 0)
nuclear = integrator.nuclear_gto(gto1, gto1, [0.0, 0.0, 1.0])
result = -0.31049036979675293
np.testing.assert_almost_equal(nuclear, result, 4)
def test_gto_repulsion(self):
"""
Test two-electron integrals for primitive GTOs
(ij|kl) = <gto_i gto_j | r_ij | gto_k gto_l>
"""
# construct integrator object
integrator = PyQInt()
# test GTO
gto1 = gto(0.154329, [0.0, 0.0, 0.0], 3.425251, 0, 0, 0)
gto2 = gto(0.535328, [0.0, 0.0, 0.0], 0.623914, 0, 0, 0)
gto3 = gto(0.444635, [0.0, 0.0, 0.0], 0.168855, 0, 0, 0)
repulsion = integrator.repulsion_gto(gto1, gto1, gto1, gto1)
result = 0.20141123130697272
np.testing.assert_almost_equal(repulsion, result, 4)
def calculate_fy_bf_finite_difference(_gto, nucleus):
"""
Calculate the basis function derivative in the y-direction using
a finite difference method
"""
# build integrator object
integrator = PyQInt()
diff = 0.01
gto1 = gto(0.154329, [_gto.p[0], _gto.p[1] - diff / 2, _gto.p[2]],
3.425251, _gto.l, _gto.m, _gto.n)
gto2 = gto(0.154329, [_gto.p[0], _gto.p[1] + diff / 2, _gto.p[2]],
3.425251, _gto.l, _gto.m, _gto.n)
left = integrator.nuclear_gto(gto1, gto1, nucleus)
right = integrator.nuclear_gto(gto2, gto2, nucleus)
return (right - left) / diff
def testDerivRepulsionGTO(self):
# construct integrator object
integrator = PyQInt()
# build gtos
gto1 = gto(0.154329, [-0.50, 0.0, 0.0], 3.425251, 0, 0, 0)
gto2 = gto(0.154329, [-0.50, 0.0, 0.0], 3.425251, 0, 0, 0)
gto3 = gto(0.154329, [0.50, 0.0, 0.0], 3.425251, 0, 0, 0)
gto4 = gto(0.154329, [0.50, 0.0, 0.0], 3.425251, 0, 0, 0)
# perform integration
rep1 = integrator.repulsion_gto_deriv(gto1, gto2, gto3, gto4, 0)
rep2 = integrator.repulsion_gto_deriv(gto2, gto1, gto3, gto4, 0)
# perform finite difference
ans1 = calculate_deriv_gto(gto1, gto2, gto3, gto4, 0)
np.testing.assert_almost_equal(rep1, ans1, 4)
def calculate_deriv_gto(gto1, gto2, gto3, gto4, coord):
# build integrator object
integrator = PyQInt()
# distance
diff = 0.00001
p = np.zeros(3)
p[coord] = diff
gto1_new1 = gto(gto1.c, gto1.p - 0.5 * p, gto1.alpha, gto1.l, gto1.m,
gto1.n)
gto1_new2 = gto(gto1.c, gto1.p + 0.5 * p, gto1.alpha, gto1.l, gto1.m,
gto1.n)
# build hydrogen molecule
left = integrator.repulsion_gto(gto1_new1, gto2, gto3, gto4)
right = integrator.repulsion_gto(gto1_new2, gto2, gto3, gto4)
return (right - left) / diff