def test_shls_slice1(self):
mol = gto.M(atom='H 0 -.5 0; H 0 .5 0', basis='cc-pvdz')
nao = mol.nao_nr()
dm = numpy.random.random((nao,nao))
mol1 = gto.M(atom='He 2 0 0', basis='6-31g')
nao1 = mol1.nao_nr()
dm1 = numpy.random.random((nao1,nao1))
eri0 = gto.conc_mol(mol, mol1).intor('int2e_sph').reshape([nao+nao1]*4)
j1part = jk.get_jk((mol1,mol1,mol,mol), dm1[:1,:1], scripts='ijkl,ji->kl', intor='int2e',
shls_slice=(0,1,0,1,0,mol.nbas,0,mol.nbas))
j1ref = numpy.einsum('ijkl,ji->kl', eri0[nao:nao+1,nao:nao+1,:nao,:nao], dm1[:1,:1])
self.assertAlmostEqual(abs(j1part - j1ref).max(), 0, 12)
k1part = jk.get_jk((mol1,mol,mol,mol1), dm1[:,:1], scripts='ijkl,li->kj', intor='int2e',
shls_slice=(0,1,0,1,0,mol.nbas,0,mol1.nbas))
k1ref = numpy.einsum('ijkl,li->kj', eri0[nao:nao+1,:1,:nao,nao:], dm1[:,:1])
self.assertAlmostEqual(abs(k1part - k1ref).max(), 0, 12)
j1part = jk.get_jk(mol, dm[:1,1:2], scripts='ijkl,ji->kl', intor='int2e',
shls_slice=(1,2,0,1,0,mol.nbas,0,mol.nbas))
j1ref = numpy.einsum('ijkl,ji->kl', eri0[1:2,:1,:nao,:nao], dm[:1,1:2])
self.assertAlmostEqual(abs(j1part - j1ref).max(), 0, 12)
k1part = jk.get_jk(mol, dm[:,1:2], scripts='ijkl,li->kj', intor='int2e',
shls_slice=(1,2,0,1,0,mol.nbas,0,mol.nbas))
k1ref = numpy.einsum('ijkl,li->kj', eri0[:1,1:2,:nao,:nao], dm[:,1:2])
self.assertAlmostEqual(abs(k1part - k1ref).max(), 0, 12)
def test_shls_slice1(self):
mol = gto.M(atom='H 0 -.5 0; H 0 .5 0', basis='cc-pvdz')
nao = mol.nao_nr()
dm = numpy.random.random((nao,nao))
mol1 = gto.M(atom='He 2 0 0', basis='6-31g')
nao1 = mol1.nao_nr()
dm1 = numpy.random.random((nao1,nao1))
eri0 = gto.conc_mol(mol, mol1).intor('int2e_sph').reshape([nao+nao1]*4)
j1part = jk.get_jk((mol1,mol1,mol,mol), dm1[:1,:1], scripts='ijkl,ji->kl', intor='int2e',
shls_slice=(0,1,0,1,0,mol.nbas,0,mol.nbas))
j1ref = numpy.einsum('ijkl,ji->kl', eri0[nao:nao+1,nao:nao+1,:nao,:nao], dm1[:1,:1])
self.assertAlmostEqual(abs(j1part - j1ref).max(), 0, 12)
k1part = jk.get_jk((mol1,mol,mol,mol1), dm1[:,:1], scripts='ijkl,li->kj', intor='int2e',
shls_slice=(0,1,0,1,0,mol.nbas,0,mol1.nbas))
k1ref = numpy.einsum('ijkl,li->kj', eri0[nao:nao+1,:1,:nao,nao:], dm1[:,:1])
self.assertAlmostEqual(abs(k1part - k1ref).max(), 0, 12)
j1part = jk.get_jk(mol, dm[:1,1:2], scripts='ijkl,ji->kl', intor='int2e',
shls_slice=(1,2,0,1,0,mol.nbas,0,mol.nbas))
j1ref = numpy.einsum('ijkl,ji->kl', eri0[1:2,:1,:nao,:nao], dm[:1,1:2])
self.assertAlmostEqual(abs(j1part - j1ref).max(), 0, 12)
k1part = jk.get_jk(mol, dm[:,1:2], scripts='ijkl,li->kj', intor='int2e',
shls_slice=(1,2,0,1,0,mol.nbas,0,mol.nbas))
k1ref = numpy.einsum('ijkl,li->kj', eri0[:1,1:2,:nao,:nao], dm[:,1:2])
self.assertAlmostEqual(abs(k1part - k1ref).max(), 0, 12)
def find_cabs(mol, auxmol, lindep=1e-8):
cabs_mol = gto.conc_mol(mol, auxmol)
nao = mol.nao_nr()
s = cabs_mol.intor_symmetric('int1e_ovlp')
ls12 = scipy.linalg.solve(s[:nao,:nao], s[:nao,nao:], sym_pos=True)
s[nao:,nao:] -= s[nao:,:nao].dot(ls12)
w, v = scipy.linalg.eigh(s[nao:,nao:])
c2 = v[:,w>lindep]/numpy.sqrt(w[w>lindep])
c1 = ls12.dot(c2)
return cabs_mol, numpy.vstack((-c1,c2))
def add_ghost_link(subsys_mols, sub_settings):
"""Adds linking ghost atoms to the subsystem mol objects.
Parameters
----------
subsys_mols : list
A list of mol objects for the different subsystems.
sub_settings : list
A list of subsystem settings
"""
max_dist = 3.8
ghost_basis = '3-21g'
#First get array of interatom distances
coord_array = np.asarray(np.vstack([x.atom_coords() for x in subsys_mols]))
inter_dist = gto.inter_distance(None, coords=coord_array)
close_indices = np.argwhere(inter_dist <= max_dist)
#Iterate through all close indices and add link atoms to the sub on one conditional line.
lowest_index = 0
for i, subsystem in enumerate(sub_settings):
num_atoms = len(subsys_mols[i].atom)
high_index = lowest_index + num_atoms
if subsystem.addlinkbasis:
ghost_mol = gto.M()
ghost_mol.atom = []
ghost_mol.basis = {}
for index in close_indices:
if ((index[0] >= lowest_index and index[0] < high_index) and
(index[1] < lowest_index or index[1] >= high_index)):
atm1_coord = coord_array[index[0]]
atm2_coord = coord_array[index[1]]
if subsystem.basis:
new_atom, new_basis = helpers.gen_link_basis(
atm1_coord, atm2_coord, subsystem.basis)
else:
new_atom, new_basis = helpers.gen_link_basis(
atm1_coord, atm2_coord, ghost_basis)
ghost_mol.atom.append(new_atom)
ghost_mol.basis.update(new_basis)
ghost_mol.build(unit='bohr')
subsys_mols[i] = gto.conc_mol(subsys_mols[i], ghost_mol)
lowest_index = high_index
eri0 = mol.intor('int2e_sph').reshape((nao,)*4)
vj = get_jk(mol, dm, 'ijkl,ji->kl')
print(numpy.allclose(vj, numpy.einsum('ijkl,ji->kl', eri0, dm)))
vj = get_jk(mol, dm, 'ijkl,ji->kl', aosym='s8')
print(numpy.allclose(vj, numpy.einsum('ijkl,ji->kl', eri0, dm)))
vk = get_jk(mol, dm, 'ijkl,jk->il', aosym='s8')
print(numpy.allclose(vk, numpy.einsum('ijkl,jk->il', eri0, dm)))
vj, vk = get_jk(mol, (dm,dm), ('ijkl,ji->kl','ijkl,li->kj'))
eri1 = mol.intor('int2e_ip1_sph', comp=3).reshape([3]+[nao]*4)
j1 = get_jk(mol, dm, 'ijkl,lk->ij', intor='int2e_ip1_sph', aosym='s2kl', comp=3)
print(numpy.allclose(j1, numpy.einsum('xijkl,lk->xij', eri1, dm)))
mol1 = gto.M(atom='He 2 0 0', basis='6-31g')
nao1 = mol1.nao_nr()
dm1 = numpy.random.random((nao1,nao1))
eri0 = gto.conc_mol(mol, mol1).intor('int2e_sph').reshape([nao+nao1]*4)
jcross = get_jk((mol1,mol1,mol,mol), dm, scripts='ijkl,lk->ij', aosym='s4')
ecoul = numpy.einsum('ij,ij', jcross, dm1)
print(numpy.allclose(jcross, numpy.einsum('ijkl,lk->ij', eri0[nao:,nao:,:nao,:nao], dm)))
print(ecoul-numpy.einsum('ijkl,lk,ij', eri0[nao:,nao:,:nao,:nao], dm, dm1))
kcross = get_jk((mol1,mol,mol,mol1), dm, scripts='ijkl,jk->il')
ex = numpy.einsum('ij,ji', kcross, dm1)
print(numpy.allclose(kcross, numpy.einsum('ijkl,jk->il', eri0[nao:,:nao,:nao,nao:], dm)))
print(ex-numpy.einsum('ijkl,jk,li', eri0[nao:,:nao,:nao,nao:], dm, dm1))
eri1 = gto.conc_mol(mol, mol1).intor('int2e_ip1_sph',comp=3).reshape([3]+[nao+nao1]*4)
j1cross = get_jk((mol1,mol1,mol,mol), dm, scripts='ijkl,lk->ij', intor='int2e_ip1_sph', comp=3)
print(numpy.allclose(j1cross, numpy.einsum('xijkl,lk->xij', eri1[:,nao:,nao:,:nao,:nao], dm)))
j1part = get_jk((mol1,mol1,mol,mol), dm, scripts='ijkl,lk->ij', intor='int2e_ip1_sph', comp=3,
shls_slice=(0,1,0,1,0,mol.nbas,0,mol.nbas))
print(numpy.allclose(j1part, numpy.einsum('xijkl,lk->xij', eri1[:,nao:nao+1,nao:nao+1,:nao,:nao], dm)))
eri0 = mol.intor('cint2e_sph').reshape((nao,)*4)
vj = get_jk(mol, dm, 'ijkl,ji->kl')
print(numpy.allclose(vj, numpy.einsum('ijkl,ji->kl', eri0, dm)))
vj = get_jk(mol, dm, 'ijkl,ji->kl', aosym='s8')
print(numpy.allclose(vj, numpy.einsum('ijkl,ji->kl', eri0, dm)))
vk = get_jk(mol, dm, 'ijkl,jk->il', aosym='s8')
print(numpy.allclose(vk, numpy.einsum('ijkl,jk->il', eri0, dm)))
vj, vk = get_jk(mol, (dm,dm), ('ijkl,ji->kl','ijkl,li->kj'))
eri1 = mol.intor('cint2e_ip1_sph', comp=3).reshape([3]+[nao]*4)
j1 = get_jk(mol, dm, 'ijkl,lk->ij', intor='cint2e_ip1_sph', aosym='s2kl', comp=3)
print(numpy.allclose(j1, numpy.einsum('xijkl,lk->xij', eri1, dm)))
mol1 = gto.M(atom='He 2 0 0', basis='6-31g')
nao1 = mol1.nao_nr()
dm1 = numpy.random.random((nao1,nao1))
eri0 = gto.conc_mol(mol, mol1).intor('cint2e_sph').reshape([nao+nao1]*4)
jcross = get_jk((mol1,mol1,mol,mol), dm, scripts='ijkl,lk->ij', aosym='s4')
ecoul = numpy.einsum('ij,ij', jcross, dm1)
print(numpy.allclose(jcross, numpy.einsum('ijkl,lk->ij', eri0[nao:,nao:,:nao,:nao], dm)))
print(ecoul-numpy.einsum('ijkl,lk,ij', eri0[nao:,nao:,:nao,:nao], dm, dm1))
kcross = get_jk((mol1,mol,mol,mol1), dm, scripts='ijkl,jk->il')
ex = numpy.einsum('ij,ji', kcross, dm1)
print(numpy.allclose(kcross, numpy.einsum('ijkl,jk->il', eri0[nao:,:nao,:nao,nao:], dm)))
print(ex-numpy.einsum('ijkl,jk,li', eri0[nao:,:nao,:nao,nao:], dm, dm1))
eri1 = gto.conc_mol(mol, mol1).intor('cint2e_ip1_sph',comp=3).reshape([3]+[nao+nao1]*4)
j1cross = get_jk((mol1,mol1,mol,mol), dm, scripts='ijkl,lk->ij', intor='cint2e_ip1_sph', comp=3)
print(numpy.allclose(j1cross, numpy.einsum('xijkl,lk->xij', eri1[:,nao:,nao:,:nao,:nao], dm)))
j1part = get_jk((mol1,mol1,mol,mol), dm, scripts='ijkl,lk->ij', intor='cint2e_ip1_sph', comp=3,
shls_slice=(0,1,0,1,0,mol.nbas,0,mol.nbas))
print(numpy.allclose(j1part, numpy.einsum('xijkl,lk->xij', eri1[:,nao:nao+1,nao:nao+1,:nao,:nao], dm)))