def test_detect_symm_c2h(self):
atoms = [['H' , (1., 0., 2.)],
['He', (0., 1., 0.)],
['H' , (1., 0., 0.)],
['H' , (-1.,0., 0.)],
['H' , (-1.,0.,-2.)],
['He', (0.,-1., 0.)]]
l, orig, axes = geom.detect_symm(atoms)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(l, 'C2h')
self.assertEqual(geom.symm_identical_atoms(l,atoms), [[0,4],[1,5],[2,3]])
self.assertTrue(geom.check_given_symm('C2h', atoms))
atoms = [['H' , (1., 0., 1.)],
['H' , (1., 0.,-1.)],
['He', (0., 0., 2.)],
['He', (2., 0.,-2.)],
['Li', (1., 1., 0.)],
['Li', (1.,-1., 0.)]]
l, orig, axes = geom.detect_symm(atoms)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(l, 'C2h')
self.assertEqual(geom.symm_identical_atoms(l,atoms),
[[0, 1], [2, 3], [4, 5]])
self.assertTrue(geom.check_given_symm('C2h', atoms))
def test_d5h(self):
atoms = ringhat(5, u)
atoms = atoms[5:]
gpname, orig, axes = geom.detect_symm(atoms)
self.assertEqual(gpname, 'D5h')
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(gpname, 'C2v')
self.assertTrue(geom.check_given_symm('C2v', atoms))
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0], [1, 4], [2, 3], [5, 6]])
atoms = ringhat(5, u)
atoms = atoms[5:]
atoms[1][0] = 'C1'
gpname, orig, axes = geom.detect_symm(atoms, {
'C': 'ccpvdz',
'C1': 'sto3g',
'N': '631g'
})
self.assertEqual(gpname, 'C2v')
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(gpname, 'C2v')
self.assertTrue(geom.check_given_symm('C2v', atoms))
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0, 2], [1], [3, 4], [5, 6]])
def test_d5h(self):
atoms = ringhat(5, u)
atoms = atoms[5:]
gpname, orig, axes = geom.detect_symm(atoms)
self.assertEqual(gpname, 'D5h')
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(gpname, 'C2v')
self.assertTrue(geom.check_given_symm('C2v', atoms))
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0], [1, 4], [2, 3], [5, 6]])
atoms = ringhat(5, u)
atoms = atoms[5:]
atoms[1][0] = 'C1'
gpname, orig, axes = geom.detect_symm(atoms, {'C':'ccpvdz','C1':'sto3g','N':'631g'})
self.assertEqual(gpname, 'C2v')
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(gpname, 'C2v')
self.assertTrue(geom.check_given_symm('C2v', atoms))
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0,2],[1],[3,4],[5,6]])
def test_detect_symm_c2h(self):
atoms = [['H' , (1., 0., 2.)],
['He', (0., 1., 0.)],
['H' , (1., 0., 0.)],
['H' , (-1.,0., 0.)],
['H' , (-1.,0.,-2.)],
['He', (0.,-1., 0.)]]
l, orig, axes = geom.detect_symm(atoms)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(l, 'C2h')
self.assertEqual(geom.symm_identical_atoms(l,atoms), [[0,4],[1,5],[2,3]])
self.assertTrue(geom.check_given_symm('C2h', atoms))
atoms = [['H' , (1., 0., 1.)],
['H' , (1., 0.,-1.)],
['He', (0., 0., 2.)],
['He', (2., 0.,-2.)],
['Li', (1., 1., 0.)],
['Li', (1.,-1., 0.)]]
l, orig, axes = geom.detect_symm(atoms)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(l, 'C2h')
self.assertEqual(geom.symm_identical_atoms(l,atoms),
[[0, 1], [2, 3], [4, 5]])
self.assertTrue(geom.check_given_symm('C2h', atoms))
def test_Coov(self):
atoms = [['H', (0,0,0)], ['H', (0,0,-1)], ['H1', (0,0,1)]]
basis = {'H':'sto3g', 'H1':'6-31g'}
gpname, orig, axes = geom.detect_symm(atoms, basis)
self.assertEqual(gpname, 'Coov')
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0], [1] ,[2]])
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(gpname, 'Coov')
self.assertTrue(geom.check_given_symm('Coov', atoms, basis))
self.assertTrue(geom.check_given_symm('C2v', atoms, basis))
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0], [1], [2]])
def test_Coov(self):
atoms = [['H', (0, 0, 0)], ['H', (0, 0, -1)], ['H1', (0, 0, 1)]]
basis = {'H': 'sto3g', 'H1': '6-31g'}
gpname, orig, axes = geom.detect_symm(atoms, basis)
self.assertEqual(gpname, 'Coov')
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0], [1], [2]])
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(gpname, 'Coov')
self.assertTrue(geom.check_given_symm('Coov', atoms, basis))
self.assertTrue(geom.check_given_symm('C2v', atoms, basis))
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0], [1], [2]])
def test_t(self):
atoms = [['C', ( 1.0 ,-1.0 , 1.0 )],
['O', ( 1.0-.1,-1.0+.2, 1.0 )],
['O', ( 1.0 ,-1.0+.1, 1.0-.2)],
['O', ( 1.0-.2,-1.0 , 1.0-.1)],
['C', (-1.0 , 1.0 , 1.0 )],
['O', (-1.0+.1, 1.0-.2, 1.0 )],
['O', (-1.0 , 1.0-.1, 1.0-.2)],
['O', (-1.0+.2, 1.0 , 1.0-.1)],
['C', ( 1.0 , 1.0 ,-1.0 )],
['O', ( 1.0-.2, 1.0 ,-1.0+.1)],
['O', ( 1.0 , 1.0-.1,-1.0+.2)],
['O', ( 1.0-.1, 1.0-.2,-1.0 )],
['C', (-1.0 ,-1.0 ,-1.0 )],
['O', (-1.0 ,-1.0+.1,-1.0+.2)],
['O', (-1.0+.2,-1.0 ,-1.0+.1)],
['O', (-1.0+.1,-1.0+.2,-1.0 )]]
gpname, orig, axes = geom.detect_symm(atoms)
self.assertEqual(gpname, 'T')
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(gpname, 'D2')
self.assertTrue(geom.check_given_symm('D2', atoms))
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0, 4, 8, 12], [1, 5, 11, 15],
[2, 6, 10, 13], [3, 7, 9, 14]])
def test_t(self):
atoms = [['C', ( 1.0 ,-1.0 , 1.0 )],
['O', ( 1.0-.1,-1.0+.2, 1.0 )],
['O', ( 1.0 ,-1.0+.1, 1.0-.2)],
['O', ( 1.0-.2,-1.0 , 1.0-.1)],
['C', (-1.0 , 1.0 , 1.0 )],
['O', (-1.0+.1, 1.0-.2, 1.0 )],
['O', (-1.0 , 1.0-.1, 1.0-.2)],
['O', (-1.0+.2, 1.0 , 1.0-.1)],
['C', ( 1.0 , 1.0 ,-1.0 )],
['O', ( 1.0-.2, 1.0 ,-1.0+.1)],
['O', ( 1.0 , 1.0-.1,-1.0+.2)],
['O', ( 1.0-.1, 1.0-.2,-1.0 )],
['C', (-1.0 ,-1.0 ,-1.0 )],
['O', (-1.0 ,-1.0+.1,-1.0+.2)],
['O', (-1.0+.2,-1.0 ,-1.0+.1)],
['O', (-1.0+.1,-1.0+.2,-1.0 )]]
gpname, orig, axes = geom.detect_symm(atoms)
self.assertEqual(gpname, 'T')
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(gpname, 'D2')
self.assertTrue(geom.check_given_symm('D2', atoms))
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0, 4, 8, 12], [1, 5, 11, 15],
[2, 6, 10, 13], [3, 7, 9, 14]])
def test_detect_symm_c2(self):
atoms = [['H', (1., 0., 1.)], ['H', (1., 0., -1.)],
['He', (0., -3., 2.)], ['He', (0., 3., -2.)]]
l, orig, axes = geom.detect_symm(atoms)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(l, 'C2')
self.assertTrue(geom.check_symm('C2', atoms))
self.assertEqual(geom.symm_identical_atoms(l, atoms), [[0, 1], [2, 3]])
def test_detect_symm_d2h_b(self):
atoms = [['H', (1., 0., 2.)], ['He', (0., 1., 0.)],
['H', (-1., 0., -2.)], ['He', (0., -1., 0.)]]
l, orig, axes = geom.detect_symm(atoms)
self.assertEqual(l, 'D2h')
atoms = geom.shift_atom(atoms, orig, axes)
self.assertTrue(geom.check_given_symm('D2h', atoms))
self.assertEqual(geom.symm_identical_atoms(l, atoms), [[0, 2], [1, 3]])
def test_Dooh(self):
atoms = [['H', (0, 0, 0)], ['H', (0, 0, -1)], ['H1', (0, 0, 1)]]
basis = {'H': 'sto3g'}
gpname, orig, axes = geom.detect_symm(atoms, basis)
self.assertEqual(gpname, 'Dooh')
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0], [1, 2]])
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(gpname, 'Dooh')
self.assertTrue(geom.check_symm('Dooh', atoms, basis))
self.assertTrue(geom.check_symm('D2h', atoms, basis))
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0], [1, 2]])
atoms = [['H', (0, 0, 0)], ['H', (1, 0, 0)]]
self.assertFalse(geom.check_symm('Dooh', atoms))
def test_detect_symm_c1(self):
atoms = [['H', (1., 0., 0.)], ['He', (0., 1., 0.)],
['Li', (0., 0., 1.)], ['Be', (.5, .5, .5)]]
l, orig, axes = geom.detect_symm(atoms)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(l, 'C1')
self.assertTrue(geom.check_given_symm('C1', atoms))
self.assertEqual(geom.symm_identical_atoms(l, atoms),
[[0], [1], [2], [3]])
def test_detect_symm_d2_a(self):
atoms = [['H', (1., 0., 1.)], ['H', (1., 0., -1.)],
['He', (0., 0., 2.)], ['He', (2., 0., 2.)],
['He', (1., 1., -2.)], ['He', (1., -1., -2.)]]
l, orig, axes = geom.detect_symm(atoms)
self.assertEqual(l, 'D2d')
atoms = geom.shift_atom(atoms, orig, axes)
self.assertTrue(geom.check_given_symm('D2', atoms))
self.assertEqual(geom.symm_identical_atoms('D2', atoms),
[[0, 1], [2, 3, 4, 5]])
def test_d6h(self):
atoms = ringhat(6, u)
atoms = atoms[6:]
gpname, orig, axes = geom.detect_symm(atoms)
self.assertEqual(gpname, 'D6h')
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0,3],[1,2,4,5],[6,7]])
self.assertTrue(geom.check_given_symm('D2h', atoms))
def test_d6h(self):
atoms = ringhat(6, u)
atoms = atoms[6:]
gpname, orig, axes = geom.detect_symm(atoms)
self.assertEqual(gpname, 'D6h')
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0, 3], [1, 2, 4, 5], [6, 7]])
self.assertTrue(geom.check_given_symm('D2h', atoms))
def test_detect_symm_d2h_b(self):
atoms = [['H' , (1., 0., 2.)],
['He', (0., 1., 0.)],
['H' , (-1.,0.,-2.)],
['He', (0.,-1., 0.)]]
l, orig, axes = geom.detect_symm(atoms)
self.assertEqual(l, 'D2h')
atoms = geom.shift_atom(atoms, orig, axes)
self.assertTrue(geom.check_given_symm('D2h', atoms))
self.assertEqual(geom.symm_identical_atoms(l,atoms), [[0,2],[1,3]])
def test_td1(self):
coords1 = numpy.dot(make4(1.5), u)
atoms = [['C', c] for c in coords1]
gpname, orig, axes = geom.detect_symm(atoms)
self.assertEqual(gpname, 'Td')
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(gpname, 'D2')
self.assertTrue(geom.check_given_symm('D2', atoms))
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0, 1, 2, 3]])
def test_detect_symm_ci(self):
atoms = [['H', (1., 0., 0.)], ['He', (0., 1., 0.)],
['Li', (0., 0., 1.)], ['Be', (.5, .5, .5)],
['H', (-1., 0., 0.)], ['He', (0., -1., 0.)],
['Li', (0., 0., -1.)], ['Be', (-.5, -.5, -.5)]]
l, orig, axes = geom.detect_symm(atoms)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(l, 'Ci')
self.assertTrue(geom.check_given_symm('Ci', atoms))
self.assertEqual(geom.symm_identical_atoms(l, atoms),
[[0, 4], [1, 5], [2, 6], [3, 7]])
def test_c5v(self):
atoms = ringhat(5, u)[5:-1]
gpname, orig, axes = geom.detect_symm(atoms)
self.assertEqual(gpname, 'C5v')
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(gpname, 'Cs')
self.assertTrue(geom.check_given_symm('Cs', atoms))
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0, 1], [2, 4], [3], [5]])
def test_c5h(self):
atoms = ringhat(5, u)
gpname, orig, axes = geom.detect_symm(atoms)
self.assertEqual(gpname, 'C5h')
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(gpname, 'Cs')
self.assertTrue(geom.check_given_symm('Cs', atoms))
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0], [1], [2], [3], [4], [5], [6], [7], [8], [9], [10,11]])
def test_detect_symm_d2_b(self):
s2 = numpy.sqrt(.5)
atoms = [['C', (0., 0., 1.)], ['C', (0., 0., -1.)], ['H', (1, 0., 2.)],
['H', (-1, 0., 2.)], ['H', (s2, s2, -2.)],
['H', (-s2, -s2, -2.)]]
l, orig, axes = geom.detect_symm(atoms)
self.assertEqual(l, 'D2')
atoms = geom.shift_atom(atoms, orig, axes)
self.assertTrue(geom.check_given_symm('D2', atoms))
self.assertEqual(geom.symm_identical_atoms(l, atoms),
[[0, 1], [2, 3, 4, 5]])
def test_c5h(self):
atoms = ringhat(5, u)
gpname, orig, axes = geom.detect_symm(atoms)
self.assertEqual(gpname, 'C5h')
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(gpname, 'Cs')
self.assertTrue(geom.check_given_symm('Cs', atoms))
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0], [1], [2], [3], [4], [5], [6], [7], [8], [9], [10,11]])
def test_c5v(self):
atoms = ringhat(5, u)[5:-1]
gpname, orig, axes = geom.detect_symm(atoms)
self.assertEqual(gpname, 'C5v')
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(gpname, 'Cs')
self.assertTrue(geom.check_given_symm('Cs', atoms))
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0, 4], [1, 3], [2], [5]])
def test_detect_symm_c1(self):
atoms = [['H' , ( 1., 0., 0.)],
['He', ( 0., 1., 0.)],
['Li', ( 0., 0., 1.)],
['Be', ( .5, .5, .5)]]
l, orig, axes = geom.detect_symm(atoms)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(l, 'C1')
self.assertTrue(geom.check_given_symm('C1', atoms))
self.assertEqual(geom.symm_identical_atoms(l,atoms),
[[0], [1], [2], [3]])
def test_td1(self):
coords1 = numpy.dot(make4(1.5), u)
atoms = [['C', c] for c in coords1]
gpname, orig, axes = geom.detect_symm(atoms)
self.assertEqual(gpname, 'Td')
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(gpname, 'D2')
self.assertTrue(geom.check_given_symm('D2', atoms))
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0, 1, 2, 3]])
def test_detect_symm_cs3(self):
atoms = [['H', (2., 1., 0.)], ['He', (0., 1., 0.)],
['Li', (-1., 2., 0.)], ['Be', (1., 0., 0.)],
['S', (.5, 1., -3)], ['S', (.5, 1., 3)]]
coord = numpy.dot([a[1] for a in atoms], u)
atoms = [[atoms[i][0], c] for i, c in enumerate(coord)]
l, orig, axes = geom.detect_symm(atoms)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(l, 'Cs')
self.assertTrue(geom.check_given_symm('Cs', atoms))
self.assertEqual(geom.symm_identical_atoms(l, atoms),
[[0], [1], [2], [3], [4, 5]])
def test_s4(self):
atoms = [['C', (0.5, 0, 1)], ['O', (0.4, 0.2, 1)], ['C', (-0.5, 0, 1)],
['O', (-0.4, -0.2, 1)], ['C', (0, 0.5, -1)],
['O', (-0.2, 0.4, -1)], ['C', (0, -0.5, -1)],
['O', (0.2, -0.4, -1)]]
gpname, orig, axes = geom.detect_symm(atoms)
self.assertEqual(gpname, 'S4')
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0, 2], [1, 3], [4, 6], [5, 7]])
self.assertTrue(geom.check_given_symm('C2', atoms))
def test_td2(self):
coords1 = make4(1.5)
coords2 = make4(1.9)
atoms = [['C', c] for c in coords1] + [['C', c] for c in coords2]
gpname, orig, axes = geom.detect_symm(atoms)
self.assertEqual(gpname, 'Td')
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(gpname, 'C2v')
self.assertTrue(geom.check_given_symm('C2v', atoms))
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0, 1], [2, 3], [4, 5], [6, 7]])
def test_c2v(self):
atoms = ringhat(6, u)
atoms = atoms[6:]
atoms[1][0] = 'C1'
atoms[2][0] = 'C1'
basis = {'C': 'sto3g', 'N':'sto3g', 'C1':'ccpvdz'}
gpname, orig, axes = geom.detect_symm(atoms, basis)
self.assertEqual(gpname, 'C2v')
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0, 3], [1, 2], [4, 5], [6, 7]])
self.assertTrue(geom.check_given_symm('C2', atoms, basis))
def test_detect_symm_d2_a(self):
atoms = [['H' , (1., 0., 1.)],
['H' , (1., 0.,-1.)],
['He', (0., 0., 2.)],
['He', (2., 0., 2.)],
['He', (1., 1.,-2.)],
['He', (1.,-1.,-2.)]]
l, orig, axes = geom.detect_symm(atoms)
self.assertEqual(l, 'D2')
atoms = geom.shift_atom(atoms, orig, axes)
self.assertTrue(geom.check_given_symm('D2', atoms))
self.assertEqual(geom.symm_identical_atoms(l,atoms),
[[0, 1], [2, 3, 4, 5]])
def test_td2(self):
coords1 = make4(1.5)
coords2 = make4(1.9)
atoms = [['C', c] for c in coords1] + [['C', c] for c in coords2]
gpname, orig, axes = geom.detect_symm(atoms)
self.assertEqual(gpname, 'Td')
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(gpname, 'D2')
self.assertTrue(geom.check_given_symm('D2', atoms))
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0, 1, 2, 3], [4, 5, 6, 7]])
def test_c2v(self):
atoms = ringhat(6, u)
atoms = atoms[6:]
atoms[1][0] = 'C1'
atoms[2][0] = 'C1'
basis = {'C': 'sto3g', 'N': 'sto3g', 'C1': 'ccpvdz'}
gpname, orig, axes = geom.detect_symm(atoms, basis)
self.assertEqual(gpname, 'C2v')
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0, 3], [1, 2], [4, 5], [6, 7]])
self.assertTrue(geom.check_given_symm('C2', atoms, basis))
def test_detect_symm_d2_b(self):
s2 = numpy.sqrt(.5)
atoms = [['C', (0., 0., 1.)],
['C', (0., 0.,-1.)],
['H', ( 1, 0., 2.)],
['H', (-1, 0., 2.)],
['H', ( s2, s2,-2.)],
['H', (-s2,-s2,-2.)]]
l, orig, axes = geom.detect_symm(atoms)
self.assertEqual(l, 'D2')
atoms = geom.shift_atom(atoms, orig, axes)
self.assertTrue(geom.check_given_symm('D2', atoms))
self.assertEqual(geom.symm_identical_atoms(l,atoms),
[[0, 1], [2, 3, 4, 5]])
def test_td3(self):
coords1 = make4(1.5)
coords2 = make4(1.9)
atoms = [['C', c] for c in coords1] + [['C', c] for c in coords2]
atoms[2][0] = 'C1'
gpname, orig, axes = geom.detect_symm(atoms)
self.assertEqual(gpname, 'C3v')
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(gpname, 'Cs')
self.assertTrue(geom.check_given_symm('Cs', atoms))
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0], [1, 3], [2], [4], [5, 7], [6]])
def test_c3v(self):
coords1 = numpy.dot(make4(1.5), u)
coords2 = numpy.dot(make4(1.9), u)
atoms = [['C', c] for c in coords1] + [['C', c] for c in coords2]
atoms[2][0] = 'C1'
gpname, orig, axes = geom.detect_symm(atoms)
self.assertEqual(gpname, 'C3v')
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(gpname, 'Cs')
self.assertTrue(geom.check_given_symm('Cs', atoms))
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0, 3], [1], [2], [4, 7], [5], [6]])
def test_c3v(self):
coords1 = numpy.dot(make4(1.5), u)
coords2 = numpy.dot(make4(1.9), u)
atoms = [['C', c] for c in coords1] + [['C', c] for c in coords2]
atoms[2][0] = 'C1'
gpname, orig, axes = geom.detect_symm(atoms)
self.assertEqual(gpname, 'C3v')
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(gpname, 'Cs')
self.assertTrue(geom.check_given_symm('Cs', atoms))
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0, 1], [2], [3], [4, 5], [6], [7]])
def test_detect_symm_s4(self):
atoms = [['H', (-1,-1.,-2.)],
['H', ( 1, 1.,-2.)],
['C', (-.9,-1.,-2.)],
['C', (.9, 1.,-2.)],
['H', ( 1,-1., 2.)],
['H', (-1, 1., 2.)],
['C', ( 1,-.9, 2.)],
['C', (-1, .9, 2.)],]
l, orig, axes = geom.detect_symm(atoms)
self.assertEqual(l, 'S4')
atoms = geom.shift_atom(atoms, orig, axes)
self.assertTrue(geom.check_given_symm('C2', atoms))
self.assertEqual(geom.symm_identical_atoms('C2',atoms),
[[0, 1], [2, 3], [4, 5], [6, 7]])
def test_d5d(self):
coord1 = ring(5)
coord2 = ring(5, numpy.pi/5)
coord1[:,2] = 1
coord2[:,2] =-1
atoms = [['H', c] for c in numpy.vstack((coord1,coord2))]
gpname, orig, axes = geom.detect_symm(atoms)
self.assertEqual(gpname, 'D5d')
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(gpname, 'C2h')
self.assertTrue(geom.check_given_symm('C2h', atoms))
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0, 3, 5, 7], [1, 2, 8, 9], [4, 6]])
def test_detect_symm_s4(self):
atoms = [['H', (-1,-1.,-2.)],
['H', ( 1, 1.,-2.)],
['C', (-.9,-1.,-2.)],
['C', (.9, 1.,-2.)],
['H', ( 1,-1., 2.)],
['H', (-1, 1., 2.)],
['C', ( 1,-.9, 2.)],
['C', (-1, .9, 2.)],]
l, orig, axes = geom.detect_symm(atoms)
self.assertEqual(l, 'S4')
atoms = geom.shift_atom(atoms, orig, axes)
self.assertTrue(geom.check_given_symm('C2', atoms))
self.assertEqual(geom.symm_identical_atoms('C2',atoms),
[[0, 1], [2, 3], [4, 5], [6, 7]])
def test_detect_symm_ci(self):
atoms = [['H' , ( 1., 0., 0.)],
['He', ( 0., 1., 0.)],
['Li', ( 0., 0., 1.)],
['Be', ( .5, .5, .5)],
['H' , (-1., 0., 0.)],
['He', ( 0.,-1., 0.)],
['Li', ( 0., 0.,-1.)],
['Be', (-.5,-.5,-.5)]]
l, orig, axes = geom.detect_symm(atoms)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(l, 'Ci')
self.assertTrue(geom.check_given_symm('Ci', atoms))
self.assertEqual(geom.symm_identical_atoms(l,atoms),
[[0, 4], [1, 5], [2, 6], [3, 7]])
def test_detect_symm_cs3(self):
atoms = [['H' , ( 2.,1., 0.)],
['He', ( 0.,1., 0.)],
['Li', (-1.,2., 0.)],
['Be', ( 1.,0., 0.)],
['S' , ( .5,1., -3)],
['S' , ( .5,1., 3)]]
coord = numpy.dot([a[1] for a in atoms], u)
atoms = [[atoms[i][0], c] for i,c in enumerate(coord)]
l, orig, axes = geom.detect_symm(atoms)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(l, 'Cs')
self.assertTrue(geom.check_given_symm('Cs', atoms))
self.assertEqual(geom.symm_identical_atoms(l,atoms),
[[0], [1], [2], [3], [4, 5]])
def test_d5d(self):
coord1 = ring(5)
coord2 = ring(5, numpy.pi / 5)
coord1[:, 2] = 1
coord2[:, 2] = -1
atoms = [['H', c] for c in numpy.vstack((coord1, coord2))]
gpname, orig, axes = geom.detect_symm(atoms)
self.assertEqual(gpname, 'D5d')
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(gpname, 'C2h')
self.assertTrue(geom.check_given_symm('C2h', atoms))
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0, 3, 5, 7], [1, 2, 8, 9], [4, 6]])
def test_s4(self):
atoms = [['C', ( 0.5, 0 , 1)],
['O', ( 0.4, 0.2 , 1)],
['C', ( -0.5, 0 , 1)],
['O', ( -0.4, -0.2 , 1)],
['C', ( 0 , 0.5 , -1)],
['O', ( -0.2, 0.4 , -1)],
['C', ( 0 , -0.5 , -1)],
['O', ( 0.2, -0.4 , -1)]]
gpname, orig, axes = geom.detect_symm(atoms)
self.assertEqual(gpname, 'S4')
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0, 2], [1, 3], [4, 6], [5, 7]])
self.assertTrue(geom.check_given_symm('C2', atoms))
def test_ih1(self):
coords = numpy.dot(make60(1.5, 1), u)
atoms = [['C', c] for c in coords]
gpname, orig, axes = geom.detect_symm(atoms)
self.assertEqual(gpname, 'Ih')
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(gpname, 'Ci')
self.assertTrue(geom.check_given_symm('Ci', atoms))
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0, 55], [1, 56], [2, 57], [3, 58], [4, 59],
[5, 30], [6, 31], [7, 32], [8, 33], [9, 34],
[10, 35], [11, 36], [12, 37], [13, 38], [14, 39],
[15, 40], [16, 41], [17, 42], [18, 43], [19, 44],
[20, 45], [21, 46], [22, 47], [23, 48], [24, 49],
[25, 50], [26, 51], [27, 52], [28, 53], [29, 54]])
def test_ih1(self):
coords = make60(1.5, 1)
atoms = [['C', c] for c in coords]
gpname, orig, axes = geom.detect_symm(atoms)
self.assertEqual(gpname, 'Ih')
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(gpname, 'Cs')
self.assertTrue(geom.check_given_symm('Cs', atoms))
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0], [1, 4], [2, 3], [5], [6, 9], [7, 8], [10, 25],
[11, 29], [12, 28], [13, 27], [14, 26], [15, 20],
[16, 24], [17, 23], [18, 22], [19, 21], [30],
[31, 34], [32, 33], [35, 50], [36, 54], [37, 53],
[38, 52], [39, 51], [40, 45], [41, 49], [42, 48],
[43, 47], [44, 46], [55], [56, 59], [57, 58]])
def test_ih1(self):
coords = numpy.dot(make60(1.5, 1), u)
atoms = [['C', c] for c in coords]
gpname, orig, axes = geom.detect_symm(atoms)
self.assertEqual(gpname, 'Ih')
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(gpname, 'Ci')
self.assertTrue(geom.check_given_symm('Ci', atoms))
self.assertEqual(
geom.symm_identical_atoms(gpname, atoms),
[[0, 55], [1, 56], [2, 57], [3, 58], [4, 59], [5, 30], [6, 31],
[7, 32], [8, 33], [9, 34], [10, 35], [11, 36], [12, 37], [13, 38],
[14, 39], [15, 40], [16, 41], [17, 42], [18, 43], [19, 44],
[20, 45], [21, 46], [22, 47], [23, 48], [24, 49], [25, 50],
[26, 51], [27, 52], [28, 53], [29, 54]])
def test_th(self):
atoms = [['C', ( 1.0 ,-1.0 , 1.0 )],
['O', ( 1.0-.1,-1.0+.2, 1.0 )],
['O', ( 1.0 ,-1.0+.1, 1.0-.2)],
['O', ( 1.0-.2,-1.0 , 1.0-.1)],
['C', ( 1.0 , 1.0 , 1.0 )],
['O', ( 1.0-.1, 1.0-.2, 1.0 )],
['O', ( 1.0 , 1.0-.1, 1.0-.2)],
['O', ( 1.0-.2, 1.0 , 1.0-.1)],
['C', (-1.0 , 1.0 , 1.0 )],
['O', (-1.0+.1, 1.0-.2, 1.0 )],
['O', (-1.0 , 1.0-.1, 1.0-.2)],
['O', (-1.0+.2, 1.0 , 1.0-.1)],
['C', (-1.0 ,-1.0 , 1.0 )],
['O', (-1.0+.1,-1.0+.2, 1.0 )],
['O', (-1.0 ,-1.0+.1, 1.0-.2)],
['O', (-1.0+.2,-1.0 , 1.0-.1)],
['C', ( 1.0 ,-1.0 ,-1.0 )],
['O', ( 1.0-.2,-1.0 ,-1.0+.1)],
['O', ( 1.0 ,-1.0+.1,-1.0+.2)],
['O', ( 1.0-.1,-1.0+.2,-1.0 )],
['C', ( 1.0 , 1.0 ,-1.0 )],
['O', ( 1.0-.2, 1.0 ,-1.0+.1)],
['O', ( 1.0 , 1.0-.1,-1.0+.2)],
['O', ( 1.0-.1, 1.0-.2,-1.0 )],
['C', (-1.0 , 1.0 ,-1.0 )],
['O', (-1.0+.2, 1.0 ,-1.0+.1)],
['O', (-1.0 , 1.0-.1,-1.0+.2)],
['O', (-1.0+.1, 1.0-.2,-1.0 )],
['C', (-1.0 ,-1.0 ,-1.0 )],
['O', (-1.0 ,-1.0+.1,-1.0+.2)],
['O', (-1.0+.2,-1.0 ,-1.0+.1)],
['O', (-1.0+.1,-1.0+.2,-1.0 )]]
gpname, orig, axes = geom.detect_symm(atoms)
self.assertEqual(gpname, 'Th')
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(gpname, 'D2')
self.assertTrue(geom.check_given_symm('D2', atoms))
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0, 8, 20, 28], [1, 9, 23, 31],
[2, 10, 22, 29], [3, 11, 21, 30],
[4, 12, 16, 24], [5, 13, 19, 27],
[6, 14, 18, 26], [7, 15, 17, 25]])
def test_th(self):
atoms = [['C', ( 1.0 ,-1.0 , 1.0 )],
['O', ( 1.0-.1,-1.0+.2, 1.0 )],
['O', ( 1.0 ,-1.0+.1, 1.0-.2)],
['O', ( 1.0-.2,-1.0 , 1.0-.1)],
['C', ( 1.0 , 1.0 , 1.0 )],
['O', ( 1.0-.1, 1.0-.2, 1.0 )],
['O', ( 1.0 , 1.0-.1, 1.0-.2)],
['O', ( 1.0-.2, 1.0 , 1.0-.1)],
['C', (-1.0 , 1.0 , 1.0 )],
['O', (-1.0+.1, 1.0-.2, 1.0 )],
['O', (-1.0 , 1.0-.1, 1.0-.2)],
['O', (-1.0+.2, 1.0 , 1.0-.1)],
['C', (-1.0 ,-1.0 , 1.0 )],
['O', (-1.0+.1,-1.0+.2, 1.0 )],
['O', (-1.0 ,-1.0+.1, 1.0-.2)],
['O', (-1.0+.2,-1.0 , 1.0-.1)],
['C', ( 1.0 ,-1.0 ,-1.0 )],
['O', ( 1.0-.2,-1.0 ,-1.0+.1)],
['O', ( 1.0 ,-1.0+.1,-1.0+.2)],
['O', ( 1.0-.1,-1.0+.2,-1.0 )],
['C', ( 1.0 , 1.0 ,-1.0 )],
['O', ( 1.0-.2, 1.0 ,-1.0+.1)],
['O', ( 1.0 , 1.0-.1,-1.0+.2)],
['O', ( 1.0-.1, 1.0-.2,-1.0 )],
['C', (-1.0 , 1.0 ,-1.0 )],
['O', (-1.0+.2, 1.0 ,-1.0+.1)],
['O', (-1.0 , 1.0-.1,-1.0+.2)],
['O', (-1.0+.1, 1.0-.2,-1.0 )],
['C', (-1.0 ,-1.0 ,-1.0 )],
['O', (-1.0 ,-1.0+.1,-1.0+.2)],
['O', (-1.0+.2,-1.0 ,-1.0+.1)],
['O', (-1.0+.1,-1.0+.2,-1.0 )]]
gpname, orig, axes = geom.detect_symm(atoms)
self.assertEqual(gpname, 'Th')
gpname, axes = geom.subgroup(gpname, axes)
atoms = geom.shift_atom(atoms, orig, axes)
self.assertEqual(gpname, 'D2')
self.assertTrue(geom.check_given_symm('D2', atoms))
self.assertEqual(geom.symm_identical_atoms(gpname, atoms),
[[0, 8, 20, 28], [1, 9, 23, 31],
[2, 10, 22, 29], [3, 11, 21, 30],
[4, 12, 16, 24], [5, 13, 19, 27],
[6, 14, 18, 26], [7, 15, 17, 25]])
def linearmole_symm_adapted_basis(mol, gpname, eql_atom_ids=None):
assert(gpname in ('Dooh', 'Coov'))
assert(not mol.cart)
if eql_atom_ids is None:
eql_atom_ids = geom.symm_identical_atoms(gpname, mol._atom)
aoslice = mol.aoslice_by_atom()
basoff = aoslice[:,2]
nao = mol.nao_nr()
sodic = {}
shalf = numpy.sqrt(.5)
def plus(i0, i1):
c = numpy.zeros(nao)
c[i0] = c[i1] = shalf
return c
def minus(i0, i1):
c = numpy.zeros(nao)
c[i0] = shalf
c[i1] =-shalf
return c
def identity(i0):
c = numpy.zeros(nao)
c[i0] = 1
return c
def add_so(irrep_name, c):
if irrep_name in sodic:
sodic[irrep_name].append(c)
else:
sodic[irrep_name] = [c]
if gpname == 'Dooh':
for atom_ids in eql_atom_ids:
if len(atom_ids) == 2:
at0 = atom_ids[0]
at1 = atom_ids[1]
ip = 0
b0, b1, p0, p1 = aoslice[at0]
for ib in range(b0, b1):
angl = mol.bas_angular(ib)
nc = mol.bas_nctr(ib)
degen = angl * 2 + 1
if angl == 1:
for i in range(nc):
aoff = ip + i*degen + angl
# m = 0
idx0 = basoff[at0] + aoff + 1
idx1 = basoff[at1] + aoff + 1
add_so('A1g', minus(idx0, idx1))
add_so('A1u', plus (idx0, idx1))
# m = +/- 1
idx0 = basoff[at0] + aoff - 1
idy0 = basoff[at0] + aoff
idx1 = basoff[at1] + aoff - 1
idy1 = basoff[at1] + aoff
add_so('E1ux', plus (idx0, idx1))
add_so('E1uy', plus (idy0, idy1))
add_so('E1gx', minus(idx0, idx1))
add_so('E1gy', minus(idy0, idy1))
else:
for i in range(nc):
aoff = ip + i*degen + angl
# m = 0
idx0 = basoff[at0] + aoff
idx1 = basoff[at1] + aoff
if angl % 2: # p-sigma, f-sigma
add_so('A1g', minus(idx0, idx1))
add_so('A1u', plus (idx0, idx1))
else: # s-sigma, d-sigma
add_so('A1g', plus (idx0, idx1))
add_so('A1u', minus(idx0, idx1))
# +/-m
for m in range(1,angl+1):
idx0 = basoff[at0] + aoff + m
idy0 = basoff[at0] + aoff - m
idx1 = basoff[at1] + aoff + m
idy1 = basoff[at1] + aoff - m
if angl % 2: # odd parity
add_so('E%dux'%m, plus (idx0, idx1))
add_so('E%duy'%m, plus (idy0, idy1))
add_so('E%dgx'%m, minus(idx0, idx1))
add_so('E%dgy'%m, minus(idy0, idy1))
else:
add_so('E%dgy'%m, plus (idy0, idy1))
add_so('E%dgx'%m, plus (idx0, idx1))
add_so('E%duy'%m, minus(idy0, idy1))
add_so('E%dux'%m, minus(idx0, idx1))
ip += nc * degen
elif len(atom_ids) == 1:
at0 = atom_ids[0]
ip = 0
b0, b1, p0, p1 = aoslice[at0]
for ib in range(b0, b1):
angl = mol.bas_angular(ib)
nc = mol.bas_nctr(ib)
degen = angl * 2 + 1
if angl == 1:
for i in range(nc):
aoff = ip + i*degen + angl
# m = 0
idx0 = basoff[at0] + aoff + 1
add_so('A1u', identity(idx0))
# m = +/- 1
idx0 = basoff[at0] + aoff - 1
idy0 = basoff[at0] + aoff
add_so('E1uy', identity(idy0))
add_so('E1ux', identity(idx0))
else:
for i in range(nc):
aoff = ip + i*degen + angl
idx0 = basoff[at0] + aoff
# m = 0
if angl % 2:
add_so('A1u', identity(idx0))
else:
add_so('A1g', identity(idx0))
# +/-m
for m in range(1,angl+1):
idx0 = basoff[at0] + aoff + m
idy0 = basoff[at0] + aoff - m
if angl % 2: # p, f functions
add_so('E%dux'%m, identity(idx0))
add_so('E%duy'%m, identity(idy0))
else: # d, g functions
add_so('E%dgy'%m, identity(idy0))
add_so('E%dgx'%m, identity(idx0))
ip += nc * degen
elif gpname == 'Coov':
for atom_ids in eql_atom_ids:
at0 = atom_ids[0]
ip = 0
b0, b1, p0, p1 = aoslice[at0]
for ib in range(b0, b1):
angl = mol.bas_angular(ib)
nc = mol.bas_nctr(ib)
degen = angl * 2 + 1
if angl == 1:
for i in range(nc):
aoff = ip + i*degen + angl
# m = 0
idx0 = basoff[at0] + aoff + 1
add_so('A1', identity(idx0))
# m = +/- 1
idx0 = basoff[at0] + aoff - 1
idy0 = basoff[at0] + aoff
add_so('E1x', identity(idx0))
add_so('E1y', identity(idy0))
else:
for i in range(nc):
aoff = ip + i*degen + angl
idx0 = basoff[at0] + aoff
# m = 0
add_so('A1', identity(idx0))
# +/-m
for m in range(1,angl+1):
idx0 = basoff[at0] + aoff + m
idy0 = basoff[at0] + aoff - m
add_so('E%dx'%m, identity(idx0))
add_so('E%dy'%m, identity(idy0))
ip += nc * degen
so = []
irrep_ids = []
irrep_names = list(sodic.keys())
for irname in irrep_names:
irrep_ids.append(linearmole_irrep_symb2id(gpname, irname))
idx = numpy.argsort(irrep_ids)
for i in idx:
so.append(numpy.vstack(sodic[irrep_names[i]]).T)
irrep_ids = [irrep_ids[i] for i in idx]
return so, irrep_ids
def linearmole_symm_adapted_basis(mol, gpname, eql_atom_ids=None):
assert (gpname in ('Dooh', 'Coov'))
assert (not mol.cart)
if eql_atom_ids is None:
eql_atom_ids = geom.symm_identical_atoms(gpname, mol._atom)
aoslice = mol.aoslice_by_atom()
basoff = aoslice[:, 2]
nao = mol.nao_nr()
sodic = {}
shalf = numpy.sqrt(.5)
def plus(i0, i1):
c = numpy.zeros(nao)
c[i0] = c[i1] = shalf
return c
def minus(i0, i1):
c = numpy.zeros(nao)
c[i0] = shalf
c[i1] = -shalf
return c
def identity(i0):
c = numpy.zeros(nao)
c[i0] = 1
return c
def add_so(irrep_name, c):
if irrep_name in sodic:
sodic[irrep_name].append(c)
else:
sodic[irrep_name] = [c]
if gpname == 'Dooh':
for atom_ids in eql_atom_ids:
if len(atom_ids) == 2:
at0 = atom_ids[0]
at1 = atom_ids[1]
ip = 0
b0, b1, p0, p1 = aoslice[at0]
for ib in range(b0, b1):
angl = mol.bas_angular(ib)
nc = mol.bas_nctr(ib)
degen = angl * 2 + 1
if angl == 1:
for i in range(nc):
aoff = ip + i * degen + angl
# m = 0
idx0 = basoff[at0] + aoff + 1
idx1 = basoff[at1] + aoff + 1
add_so('A1g', minus(idx0, idx1))
add_so('A1u', plus(idx0, idx1))
# m = +/- 1
idx0 = basoff[at0] + aoff - 1
idy0 = basoff[at0] + aoff
idx1 = basoff[at1] + aoff - 1
idy1 = basoff[at1] + aoff
add_so('E1ux', plus(idx0, idx1))
add_so('E1uy', plus(idy0, idy1))
add_so('E1gx', minus(idx0, idx1))
add_so('E1gy', minus(idy0, idy1))
else:
for i in range(nc):
aoff = ip + i * degen + angl
# m = 0
idx0 = basoff[at0] + aoff
idx1 = basoff[at1] + aoff
if angl % 2: # p-sigma, f-sigma
add_so('A1g', minus(idx0, idx1))
add_so('A1u', plus(idx0, idx1))
else: # s-sigma, d-sigma
add_so('A1g', plus(idx0, idx1))
add_so('A1u', minus(idx0, idx1))
# +/-m
for m in range(1, angl + 1):
idx0 = basoff[at0] + aoff + m
idy0 = basoff[at0] + aoff - m
idx1 = basoff[at1] + aoff + m
idy1 = basoff[at1] + aoff - m
if angl % 2: # odd parity
add_so('E%dux' % m, plus(idx0, idx1))
add_so('E%duy' % m, plus(idy0, idy1))
add_so('E%dgx' % m, minus(idx0, idx1))
add_so('E%dgy' % m, minus(idy0, idy1))
else:
add_so('E%dgy' % m, plus(idy0, idy1))
add_so('E%dgx' % m, plus(idx0, idx1))
add_so('E%duy' % m, minus(idy0, idy1))
add_so('E%dux' % m, minus(idx0, idx1))
ip += nc * degen
elif len(atom_ids) == 1:
at0 = atom_ids[0]
ip = 0
b0, b1, p0, p1 = aoslice[at0]
for ib in range(b0, b1):
angl = mol.bas_angular(ib)
nc = mol.bas_nctr(ib)
degen = angl * 2 + 1
if angl == 1:
for i in range(nc):
aoff = ip + i * degen + angl
# m = 0
idx0 = basoff[at0] + aoff + 1
add_so('A1u', identity(idx0))
# m = +/- 1
idx0 = basoff[at0] + aoff - 1
idy0 = basoff[at0] + aoff
add_so('E1uy', identity(idy0))
add_so('E1ux', identity(idx0))
else:
for i in range(nc):
aoff = ip + i * degen + angl
idx0 = basoff[at0] + aoff
# m = 0
if angl % 2:
add_so('A1u', identity(idx0))
else:
add_so('A1g', identity(idx0))
# +/-m
for m in range(1, angl + 1):
idx0 = basoff[at0] + aoff + m
idy0 = basoff[at0] + aoff - m
if angl % 2: # p, f functions
add_so('E%dux' % m, identity(idx0))
add_so('E%duy' % m, identity(idy0))
else: # d, g functions
add_so('E%dgy' % m, identity(idy0))
add_so('E%dgx' % m, identity(idx0))
ip += nc * degen
elif gpname == 'Coov':
for atom_ids in eql_atom_ids:
at0 = atom_ids[0]
ip = 0
b0, b1, p0, p1 = aoslice[at0]
for ib in range(b0, b1):
angl = mol.bas_angular(ib)
nc = mol.bas_nctr(ib)
degen = angl * 2 + 1
if angl == 1:
for i in range(nc):
aoff = ip + i * degen + angl
# m = 0
idx0 = basoff[at0] + aoff + 1
add_so('A1', identity(idx0))
# m = +/- 1
idx0 = basoff[at0] + aoff - 1
idy0 = basoff[at0] + aoff
add_so('E1x', identity(idx0))
add_so('E1y', identity(idy0))
else:
for i in range(nc):
aoff = ip + i * degen + angl
idx0 = basoff[at0] + aoff
# m = 0
add_so('A1', identity(idx0))
# +/-m
for m in range(1, angl + 1):
idx0 = basoff[at0] + aoff + m
idy0 = basoff[at0] + aoff - m
add_so('E%dx' % m, identity(idx0))
add_so('E%dy' % m, identity(idy0))
ip += nc * degen
so = []
irrep_ids = []
irrep_names = list(sodic.keys())
for irname in irrep_names:
irrep_ids.append(linearmole_irrep_symb2id(gpname, irname))
idx = numpy.argsort(irrep_ids)
for i in idx:
so.append(numpy.vstack(sodic[irrep_names[i]]).T)
irrep_ids = [irrep_ids[i] for i in idx]
return so, irrep_ids
def symm_adapted_basis(mol, gpname, eql_atom_ids=None):
if eql_atom_ids is None:
eql_atom_ids = geom.symm_identical_atoms(gpname, mol._atom)
if gpname in ('Dooh', 'Coov'):
return linearmole_symm_adapted_basis(mol, gpname, eql_atom_ids)
ops = numpy.asarray(
[param.D2H_OPS[op] for op in param.OPERATOR_TABLE[gpname]])
chartab = numpy.array([x[1:] for x in param.CHARACTER_TABLE[gpname]])
nirrep = chartab.__len__()
aoslice = mol.aoslice_by_atom()
nao = mol.nao_nr()
atom_coords = mol.atom_coords()
sodic = [[] for i in range(8)]
for atom_ids in eql_atom_ids:
r0 = mol.atom_coord(atom_ids[0])
op_coords = numpy.einsum('x,nxy->ny', r0, ops)
# Using ops to generate other atoms from atom_ids[0]
coords0 = atom_coords[atom_ids]
natm = len(atom_ids)
dc = abs(op_coords.reshape(-1, 1, 3) - coords0).sum(axis=2)
op_relate_idx = numpy.argwhere(dc < geom.TOLERANCE)[:, 1]
ao_loc = numpy.array([aoslice[atom_ids[i], 2] for i in op_relate_idx])
b0, b1 = aoslice[atom_ids[0], :2]
ip = 0
for ib in range(b0, b1):
l = mol.bas_angular(ib)
if mol.cart:
degen = (l + 1) * (l + 2) // 2
cbase = numpy.zeros((degen, nirrep, nao))
for op_id, op in enumerate(ops):
n = 0
for x in range(l, -1, -1):
for y in range(l - x, -1, -1):
z = l - x - y
idx = ao_loc[op_id] + n
sign = op[0, 0]**x * op[1, 1]**y * op[2, 2]**z
cbase[n, :, idx] += sign * chartab[:, op_id]
n += 1
else:
degen = l * 2 + 1
cbase = numpy.zeros((degen, nirrep, nao))
for op_id, op in enumerate(param.OPERATOR_TABLE[gpname]):
for n, m in enumerate(range(-l, l + 1)):
idx = ao_loc[op_id] + n
if tot_parity_odd(op, l, m):
cbase[n, :, idx] -= chartab[:, op_id]
else:
cbase[n, :, idx] += chartab[:, op_id]
norms = numpy.sqrt(numpy.einsum('mij,mij->mi', cbase, cbase))
for i in range(mol.bas_nctr(ib)):
for n, ir in numpy.argwhere(norms > 1e-12):
c = numpy.zeros(nao)
c[ip:] = cbase[n, ir, :nao - ip] / norms[n, ir]
sodic[ir].append(c)
ip += degen
so = []
irrep_ids = []
for ir, c in enumerate(sodic):
if len(c) > 0:
irrep_ids.append(ir)
so.append(numpy.vstack(c).T)
return so, irrep_ids
if __name__ == "__main__":
h2o = pyscf.gto.Mole()
h2o.verbose = 0
h2o.output = None
h2o.atom = [['O' , (1. , 0. , 0. ,)],
[1 , (0. , -.757 , 0.587,)],
[1 , (0. , 0.757 , 0.587,)] ]
h2o.basis = {'H': 'cc-pvdz',
'O': 'cc-pvdz',}
h2o.build()
gpname, origin, axes = geom.detect_symm(h2o.atom)
atoms = pyscf.gto.mole.format_atom(h2o.atom, origin, axes)
print(gpname)
eql_atoms = geom.symm_identical_atoms(gpname, atoms)
print(symm_adapted_basis(gpname, eql_atoms, atoms, h2o._basis))
mol = pyscf.gto.M(
atom = [['H', (0,0,0)], ['H', (0,0,-1)], ['H', (0,0,1)]],
basis = 'ccpvtz')
gpname, orig, axes = geom.detect_symm(mol.atom)
atoms = pyscf.gto.mole.format_atom(mol.atom, orig, axes)
print(gpname)
eql_atoms = geom.symm_identical_atoms(gpname, atoms)
print(symm_adapted_basis(gpname, eql_atoms, atoms, mol._basis)[1])
mol = pyscf.gto.M(
atom = [['H', (0,0,0)], ['H', (0,0,-1)], ['He', (0,0,1)]],
basis = 'ccpvtz')
gpname, orig, axes = geom.detect_symm(mol.atom)
def symm_adapted_basis(mol, gpname, eql_atom_ids=None):
if eql_atom_ids is None:
eql_atom_ids = geom.symm_identical_atoms(gpname, mol._atom)
if gpname in ('Dooh', 'Coov'):
return linearmole_symm_adapted_basis(mol, gpname, eql_atom_ids)
ops = numpy.asarray([param.D2H_OPS[op] for op in param.OPERATOR_TABLE[gpname]])
chartab = numpy.array([x[1:] for x in param.CHARACTER_TABLE[gpname]])
nirrep = chartab.__len__()
aoslice = mol.aoslice_by_atom()
nao = mol.nao_nr()
atom_coords = mol.atom_coords()
sodic = [[] for i in range(8)]
for atom_ids in eql_atom_ids:
r0 = mol.atom_coord(atom_ids[0])
op_coords = numpy.einsum('x,nxy->ny', r0, ops)
# Using ops to generate other atoms from atom_ids[0]
coords0 = atom_coords[atom_ids]
natm = len(atom_ids)
dc = abs(op_coords.reshape(-1,1,3) - coords0).sum(axis=2)
op_relate_idx = numpy.argwhere(dc < geom.TOLERANCE)[:,1]
ao_loc = numpy.array([aoslice[atom_ids[i],2] for i in op_relate_idx])
b0, b1 = aoslice[atom_ids[0],:2]
ip = 0
for ib in range(b0, b1):
l = mol.bas_angular(ib)
if mol.cart:
degen = (l + 1) * (l + 2) // 2
cbase = numpy.zeros((degen,nirrep,nao))
for op_id, op in enumerate(ops):
n = 0
for x in range(l, -1, -1):
for y in range(l-x, -1, -1):
z = l-x-y
idx = ao_loc[op_id] + n
sign = op[0,0]**x * op[1,1]**y * op[2,2]**z
cbase[n,:,idx] += sign * chartab[:,op_id]
n += 1
else:
degen = l * 2 + 1
cbase = numpy.zeros((degen,nirrep,nao))
for op_id, op in enumerate(param.OPERATOR_TABLE[gpname]):
for n, m in enumerate(range(-l, l+1)):
idx = ao_loc[op_id] + n
if tot_parity_odd(op, l, m):
cbase[n,:,idx] -= chartab[:,op_id]
else:
cbase[n,:,idx] += chartab[:,op_id]
norms = numpy.sqrt(numpy.einsum('mij,mij->mi', cbase, cbase))
for i in range(mol.bas_nctr(ib)):
for n, ir in numpy.argwhere(norms > 1e-12):
c = numpy.zeros(nao)
c[ip:] = cbase[n,ir,:nao-ip] / norms[n,ir]
sodic[ir].append(c)
ip += degen
so = []
irrep_ids = []
for ir, c in enumerate(sodic):
if len(c) > 0:
irrep_ids.append(ir)
so.append(numpy.vstack(c).T)
return so, irrep_ids
0.587,
)], [1, (
0.,
0.757,
0.587,
)]]
h2o.basis = {
'H': 'cc-pvdz',
'O': 'cc-pvdz',
}
h2o.build()
gpname, origin, axes = geom.detect_symm(h2o._atom)
atoms = gto.format_atom(h2o._atom, origin, axes)
h2o.build(False, False, atom=atoms)
print(gpname)
eql_atoms = geom.symm_identical_atoms(gpname, atoms)
print(symm_adapted_basis(h2o, gpname, eql_atoms)[1])
mol = gto.M(atom=[['H', (0, 0, 0)], ['H', (0, 0, -1)], ['H', (0, 0, 1)]],
basis='ccpvtz',
charge=1)
gpname, orig, axes = geom.detect_symm(mol._atom)
atoms = gto.format_atom(mol._atom, orig, axes)
mol.build(False, False, atom=atoms)
print(gpname)
eql_atoms = geom.symm_identical_atoms(gpname, atoms)
print(symm_adapted_basis(mol, gpname, eql_atoms)[1])
mol = gto.M(atom=[['H', (0, 0, 0)], ['H', (0, 0, -1)], ['He', (0, 0, 1)]],
basis='ccpvtz')
gpname, orig, axes = geom.detect_symm(mol._atom)
def linearmole_symm_adapted_basis(mol, gpname, orig=0, coordinates=None):
assert (gpname in ('Dooh', 'Coov'))
assert (not mol.cart)
if coordinates is None:
coordinates = numpy.eye(3)
prop_atoms = mol.format_atom(mol._atom, orig, coordinates, 'Bohr')
eql_atom_ids = geom.symm_identical_atoms(gpname, prop_atoms)
aoslice = mol.aoslice_by_atom()
basoff = aoslice[:, 2]
nao = mol.nao_nr()
sodic = {}
shalf = numpy.sqrt(.5)
def plus(i0, i1):
c = numpy.zeros(nao)
c[i0] = c[i1] = shalf
return c
def minus(i0, i1):
c = numpy.zeros(nao)
c[i0] = shalf
c[i1] = -shalf
return c
def identity(i0):
c = numpy.zeros(nao)
c[i0] = 1
return c
def add_so(irrep_name, c):
if irrep_name in sodic:
sodic[irrep_name].append(c)
else:
sodic[irrep_name] = [c]
if gpname == 'Dooh':
for atom_ids in eql_atom_ids:
if len(atom_ids) == 2:
at0 = atom_ids[0]
at1 = atom_ids[1]
ip = 0
b0, b1, p0, p1 = aoslice[at0]
for ib in range(b0, b1):
angl = mol.bas_angular(ib)
nc = mol.bas_nctr(ib)
degen = angl * 2 + 1
if angl == 1:
for i in range(nc):
aoff = ip + i * degen + angl
# m = 0
idx0 = basoff[at0] + aoff + 1
idx1 = basoff[at1] + aoff + 1
add_so('A1g', minus(idx0, idx1))
add_so('A1u', plus(idx0, idx1))
# m = +/- 1
idx0 = basoff[at0] + aoff - 1
idy0 = basoff[at0] + aoff
idx1 = basoff[at1] + aoff - 1
idy1 = basoff[at1] + aoff
add_so('E1ux', plus(idx0, idx1))
add_so('E1uy', plus(idy0, idy1))
add_so('E1gx', minus(idx0, idx1))
add_so('E1gy', minus(idy0, idy1))
else:
for i in range(nc):
aoff = ip + i * degen + angl
# m = 0
idx0 = basoff[at0] + aoff
idx1 = basoff[at1] + aoff
if angl % 2: # p-sigma, f-sigma
add_so('A1g', minus(idx0, idx1))
add_so('A1u', plus(idx0, idx1))
else: # s-sigma, d-sigma
add_so('A1g', plus(idx0, idx1))
add_so('A1u', minus(idx0, idx1))
# +/-m
for m in range(1, angl + 1):
idx0 = basoff[at0] + aoff + m
idy0 = basoff[at0] + aoff - m
idx1 = basoff[at1] + aoff + m
idy1 = basoff[at1] + aoff - m
if angl % 2: # odd parity
add_so('E%dux' % m, plus(idx0, idx1))
add_so('E%duy' % m, plus(idy0, idy1))
add_so('E%dgx' % m, minus(idx0, idx1))
add_so('E%dgy' % m, minus(idy0, idy1))
else:
add_so('E%dgy' % m, plus(idy0, idy1))
add_so('E%dgx' % m, plus(idx0, idx1))
add_so('E%duy' % m, minus(idy0, idy1))
add_so('E%dux' % m, minus(idx0, idx1))
ip += nc * degen
elif len(atom_ids) == 1:
at0 = atom_ids[0]
ip = 0
b0, b1, p0, p1 = aoslice[at0]
for ib in range(b0, b1):
angl = mol.bas_angular(ib)
nc = mol.bas_nctr(ib)
degen = angl * 2 + 1
if angl == 1:
for i in range(nc):
aoff = ip + i * degen + angl
# m = 0
idx0 = basoff[at0] + aoff + 1
add_so('A1u', identity(idx0))
# m = +/- 1
idx0 = basoff[at0] + aoff - 1
idy0 = basoff[at0] + aoff
add_so('E1uy', identity(idy0))
add_so('E1ux', identity(idx0))
else:
for i in range(nc):
aoff = ip + i * degen + angl
idx0 = basoff[at0] + aoff
# m = 0
if angl % 2:
add_so('A1u', identity(idx0))
else:
add_so('A1g', identity(idx0))
# +/-m
for m in range(1, angl + 1):
idx0 = basoff[at0] + aoff + m
idy0 = basoff[at0] + aoff - m
if angl % 2: # p, f functions
add_so('E%dux' % m, identity(idx0))
add_so('E%duy' % m, identity(idy0))
else: # d, g functions
add_so('E%dgy' % m, identity(idy0))
add_so('E%dgx' % m, identity(idx0))
ip += nc * degen
elif gpname == 'Coov':
for atom_ids in eql_atom_ids:
at0 = atom_ids[0]
ip = 0
b0, b1, p0, p1 = aoslice[at0]
for ib in range(b0, b1):
angl = mol.bas_angular(ib)
nc = mol.bas_nctr(ib)
degen = angl * 2 + 1
if angl == 1:
for i in range(nc):
aoff = ip + i * degen + angl
# m = 0
idx0 = basoff[at0] + aoff + 1
add_so('A1', identity(idx0))
# m = +/- 1
idx0 = basoff[at0] + aoff - 1
idy0 = basoff[at0] + aoff
add_so('E1x', identity(idx0))
add_so('E1y', identity(idy0))
else:
for i in range(nc):
aoff = ip + i * degen + angl
idx0 = basoff[at0] + aoff
# m = 0
add_so('A1', identity(idx0))
# +/-m
for m in range(1, angl + 1):
idx0 = basoff[at0] + aoff + m
idy0 = basoff[at0] + aoff - m
add_so('E%dx' % m, identity(idx0))
add_so('E%dy' % m, identity(idy0))
ip += nc * degen
irrep_ids = []
irrep_names = list(sodic.keys())
for irname in irrep_names:
irrep_ids.append(linearmole_irrep_symb2id(gpname, irname))
irrep_idx = numpy.argsort(irrep_ids)
irrep_ids = [irrep_ids[i] for i in irrep_idx]
ao_loc = mol.ao_loc_nr()
l_idx = {}
ANG_OF = 1
for l in range(mol._bas[:, ANG_OF].max() + 1):
idx = [
numpy.arange(ao_loc[ib], ao_loc[ib + 1])
for ib in numpy.where(mol._bas[:, ANG_OF] == l)[0]
]
if idx:
l_idx[l] = numpy.hstack(idx)
Ds = _ao_rotation_matrices(mol, coordinates)
so = []
for i in irrep_idx:
c_ir = numpy.vstack(sodic[irrep_names[i]]).T
nso = c_ir.shape[1]
for l, idx in l_idx.items():
c = c_ir[idx].reshape(-1, Ds[l].shape[1], nso)
c_ir[idx] = numpy.einsum('nm,smp->snp', Ds[l], c).reshape(-1, nso)
so.append(c_ir)
return so, irrep_ids
def symm_adapted_basis(mol, gpname, orig=0, coordinates=None):
if gpname == 'SO3':
return so3_symm_adapted_basis(mol, gpname, orig, coordinates)
elif gpname in ('Dooh', 'Coov'):
return linearmole_symm_adapted_basis(mol, gpname, orig, coordinates)
# prop_atoms are the atoms relocated wrt the charge center with proper
# orientation
if coordinates is None:
coordinates = numpy.eye(3)
prop_atoms = mol.format_atom(mol._atom, orig, coordinates, 'Bohr')
eql_atom_ids = geom.symm_identical_atoms(gpname, prop_atoms)
ops = numpy.asarray(
[param.D2H_OPS[op] for op in param.OPERATOR_TABLE[gpname]])
chartab = numpy.array([x[1:] for x in param.CHARACTER_TABLE[gpname]])
nirrep = chartab.__len__()
aoslice = mol.aoslice_by_atom()
nao = mol.nao_nr()
atom_coords = numpy.array([a[1] for a in prop_atoms])
sodic = [[] for i in range(8)]
for atom_ids in eql_atom_ids:
r0 = atom_coords[atom_ids[0]]
op_coords = numpy.einsum('x,nxy->ny', r0, ops)
# Using ops to generate other atoms from atom_ids[0]
coords0 = atom_coords[atom_ids]
dc = abs(op_coords.reshape(-1, 1, 3) - coords0).max(axis=2)
op_relate_idx = numpy.argwhere(dc < geom.TOLERANCE)[:, 1]
ao_loc = numpy.array([aoslice[atom_ids[i], 2] for i in op_relate_idx])
b0, b1 = aoslice[atom_ids[0], :2]
ip = 0
for ib in range(b0, b1):
l = mol.bas_angular(ib)
if mol.cart:
degen = (l + 1) * (l + 2) // 2
cbase = numpy.zeros((degen, nirrep, nao))
for op_id, op in enumerate(ops):
n = 0
for x in range(l, -1, -1):
for y in range(l - x, -1, -1):
z = l - x - y
idx = ao_loc[op_id] + n
sign = op[0, 0]**x * op[1, 1]**y * op[2, 2]**z
cbase[n, :, idx] += sign * chartab[:, op_id]
n += 1
else:
degen = l * 2 + 1
cbase = numpy.zeros((degen, nirrep, nao))
for op_id, op in enumerate(param.OPERATOR_TABLE[gpname]):
for n, m in enumerate(range(-l, l + 1)):
idx = ao_loc[op_id] + n
if tot_parity_odd(op, l, m):
cbase[n, :, idx] -= chartab[:, op_id]
else:
cbase[n, :, idx] += chartab[:, op_id]
norms = numpy.sqrt(numpy.einsum('mij,mij->mi', cbase, cbase))
for i in range(mol.bas_nctr(ib)):
for n, ir in numpy.argwhere(norms > 1e-12):
c = numpy.zeros(nao)
c[ip:] = cbase[n, ir, :nao - ip] / norms[n, ir]
sodic[ir].append(c)
ip += degen
ao_loc = mol.ao_loc_nr()
l_idx = {}
ANG_OF = 1
for l in range(mol._bas[:, ANG_OF].max() + 1):
idx = [
numpy.arange(ao_loc[ib], ao_loc[ib + 1])
for ib in numpy.where(mol._bas[:, ANG_OF] == l)[0]
]
if idx:
l_idx[l] = numpy.hstack(idx)
Ds = _ao_rotation_matrices(mol, coordinates)
so = []
irrep_ids = []
for ir, c in enumerate(sodic):
if len(c) > 0:
irrep_ids.append(ir)
c_ir = numpy.vstack(c).T
nso = c_ir.shape[1]
for l, idx in l_idx.items():
c = c_ir[idx].reshape(-1, Ds[l].shape[1], nso)
c_ir[idx] = numpy.einsum('nm,smp->snp', Ds[l],
c).reshape(-1, nso)
so.append(c_ir)
return so, irrep_ids
