def test_0069_vnucele_coulomb_water_ae(self):
""" This """
mol = gto.M(verbose=1,
atom='O 0 0 0; H 0 0.489 1.074; H 0 0.489 -1.074',
basis='cc-pvdz')
gto_mf = scf.RHF(mol)
gto_mf.kernel()
vne = mol.intor_symmetric('int1e_nuc')
dm_gto = gto_mf.make_rdm1()
E_ne_gto = (vne * dm_gto).sum() * 0.5
self.assertAlmostEqual(E_ne_gto, -97.67612964579993)
tk = mol.intor_symmetric('int1e_kin')
E_kin_gto = (tk * dm_gto).sum()
self.assertAlmostEqual(E_kin_gto, 75.37551418889902)
#print(__name__, E_ne_gto)
mf = mf_c(gto=mol, mf=gto_mf)
vne_nao = mf.vnucele_coo_coulomb().toarray()
dm_nao = mf.make_rdm1().reshape((mf.norbs, mf.norbs))
E_ne_nao = (vne_nao * dm_nao).sum() * 0.5
#print(__name__, E_ne_nao)
self.assertAlmostEqual(E_ne_nao, -97.67612893873279)
tk_nao = -0.5 * mf.laplace_coo().toarray()
E_kin_nao = (tk_nao * dm_nao).sum()
#print(__name__, E_ne_nao)
self.assertAlmostEqual(E_kin_nao, 75.37551418889902)
def test_vneutral_atom_matrix_elements(self):
""" reSCF then G0W0 """
dname = os.path.dirname(os.path.abspath(__file__))
mf = mf_c(label='lih', cd=dname)
vna = mf.vna_coo(level=1).toarray()
rdm = mf.make_rdm1()[0,0,:,:,0]
Ena = 27.2114*(-0.5)*(vna*rdm).sum()
#print('Ena = ', Ena)
self.assertAlmostEqual(Ena, 6.0251859727456596) # this does compares badly with lih.out
def test_vneutral_atom_matrix_elements(self):
""" reSCF then G0W0 """
dname = os.path.dirname(os.path.abspath(__file__))
mf = mf_c(label='n2', cd=dname)
vna = mf.vna_coo(level=1).toarray()
rdm = mf.make_rdm1()[0,0,:,:,0]
Ena = 27.2114*(-0.5)*(vna*rdm).sum()
#print('Ena = ', Ena)
self.assertAlmostEqual(Ena, 133.24203392039948)
def test_vneutral_atom_matrix_elements(self):
""" reSCF then G0W0 """
dname = os.path.dirname(os.path.abspath(__file__))
mf = mf_c(label='lih', cd=dname)
vna = mf.vna_coo(level=1).toarray()
rdm = mf.make_rdm1()[0, 0, :, :, 0]
Ena = 27.2114 * (-0.5) * (vna * rdm).sum()
#print('Ena = ', Ena)
self.assertAlmostEqual(
Ena, 6.0251859727456596) # this does compares badly with lih.out
def test_0073_vna_vnl_N2(self):
""" Test the Ena energy and indirectly VNA matrix elements """
dname = os.path.dirname(os.path.abspath(__file__))
mf = mf_c(label='n2', cd=dname)
vna = mf.vna_coo(level=3).toarray()
rdm = mf.make_rdm1()[0, 0, :, :, 0]
Ena = HARTREE2EV * (-0.5) * (vna * rdm).sum()
self.assertAlmostEqual(Ena, 133.24212864149359)
# siesta: Ena = 133.196299
vnl = mf.vnl_coo().toarray()
Enl = HARTREE2EV * (vnl * rdm).sum()
self.assertAlmostEqual(Enl, -61.604522776730128)
def test_double_sparse(self): """ This is a test of a double-sparse storage of the vertex """ dname = os.path.dirname(os.path.abspath(__file__)) mf = mf_c(label='water', cd=dname) pb = mf.pb v_dab_array = pb.get_dp_vertex_array() nnn = v_dab_array.size vds = pb.get_dp_vertex_doubly_sparse(axis=0) self.assertEqual(vds.shape, v_dab_array.shape) self.assertTrue(abs(vds.toarray()-v_dab_array).sum()/nnn<1e-14) vds = pb.get_dp_vertex_doubly_sparse(axis=1) self.assertTrue(abs(vds.toarray()-v_dab_array).sum()/nnn<1e-14) vds = pb.get_dp_vertex_doubly_sparse(axis=2) self.assertTrue(abs(vds.toarray()-v_dab_array).sum()/nnn<1e-14)
def test_double_sparse(self):
""" This is a test of a double-sparse storage of the vertex """
dname = os.path.dirname(os.path.abspath(__file__))
mf = mf_c(label='water', cd=dname)
pb = mf.pb
v_dab_array = pb.get_dp_vertex_array()
nnn = v_dab_array.size
vds = pb.get_dp_vertex_doubly_sparse(axis=0)
self.assertEqual(vds.shape, v_dab_array.shape)
self.assertTrue(abs(vds.toarray() - v_dab_array).sum() / nnn < 1e-14)
vds = pb.get_dp_vertex_doubly_sparse(axis=1)
self.assertTrue(abs(vds.toarray() - v_dab_array).sum() / nnn < 1e-14)
vds = pb.get_dp_vertex_doubly_sparse(axis=2)
self.assertTrue(abs(vds.toarray() - v_dab_array).sum() / nnn < 1e-14)
def test_0074_vna_vnl_LiH(self):
""" reSCF then G0W0 """
dname = os.path.dirname(os.path.abspath(__file__))
mf = mf_c(label='lih', cd=dname)
vna = mf.vna_coo(level=1).toarray()
rdm = mf.make_rdm1()[0, 0, :, :, 0]
Ena = HARTREE2EV * (-0.5) * (vna * rdm).sum()
self.assertAlmostEqual(
Ena, 6.0251828965429937) # This compares badly with lih.out
# siesta: Ena = 9.253767
vnl = mf.vnl_coo().toarray()
Enl = HARTREE2EV * (vnl * rdm).sum()
self.assertAlmostEqual(
Enl, -2.8533506650656162) # This compares ok with lih.out
def test_0078_vhartree_pbc_water(self):
""" Test Hartree potential on equidistant grid with Periodic Boundary Conditions """
import os
dname = os.path.dirname(os.path.abspath(__file__))
mf = mf_c(label='water', cd=dname, gen_pb=False, Ecut=100.0)
d = abs(np.dot(mf.ucell_mom(), mf.ucell) -
(2 * np.pi) * np.eye(3)).sum()
self.assertTrue(d < 1e-15)
g = mf.mesh3d.get_3dgrid()
dens = mf.dens_elec(g.coords, mf.make_rdm1()).reshape(mf.mesh3d.shape)
ts = timer()
vh = mf.vhartree_pbc(dens)
tf = timer()
#print(__name__, tf-ts)
E_Hartree = 0.5 * (vh * dens * g.weights).sum() * HARTREE2EV
self.assertAlmostEqual(E_Hartree, 382.8718239023864)
def test_matelem_speed(self):
""" Test the computation of atomic orbitals in coordinate space """
dname = os.path.dirname(os.path.abspath(__file__))
mf = mf_c(verbosity=0, label='water', cd=dname, gen_pb=False, force_gamma=True, Ecut=50)
g = mf.mesh3d.get_3dgrid()
t0 = timer()
vna = mf.vna(g.coords)
t1 = timer()
ab2v1 = mf.matelem_int3d_coo(g, vna)
t2 = timer()
ab2v2 = mf.matelem_int3d_coo_ref(g, vna)
t3 = timer()
#print(__name__, 't1 t2: ', t1-t0, t2-t1, t3-t2)
#print(abs(ab2v1.toarray()-ab2v2.toarray()).sum()/ab2v2.size, (abs(ab2v1.toarray()-ab2v2.toarray()).max()))
self.assertTrue(np.allclose(ab2v1.toarray(), ab2v2.toarray()))
def test_0079_recomp_hamilt_water(self):
""" Recomputing all parts of KS Hamiltonian a la SIESTA """
import os
dname = os.path.dirname(os.path.abspath(__file__))
mf = mf_c(label='water', cd=dname, gen_pb=False, Ecut=100.0)
dm = mf.make_rdm1().reshape((mf.norbs, mf.norbs))
hamilt1 = mf.get_hamiltonian()[0].toarray()
Ebs1 = (hamilt1*dm).sum()*HARTREE2EV
self.assertAlmostEqual(Ebs1, -103.13708410565928)
vh = mf.vhartree_pbc_coo().toarray()
Ehartree = (vh*dm).sum()*0.5*HARTREE2EV
self.assertAlmostEqual(Ehartree, 382.8718239023866)
tkin = -0.5*mf.laplace_coo().toarray()
Ekin = (tkin*dm).sum()*HARTREE2EV
self.assertAlmostEqual(Ekin, 351.7667746178386)
dvh = mf.vhartree_pbc_coo(density_factors=[1,1]).toarray()
Edvh = (dvh*dm).sum()*0.5*HARTREE2EV
self.assertAlmostEqual(Edvh, -120.65336476645524)
Exc = mf.exc()*HARTREE2EV
self.assertAlmostEqual(Exc, -112.71570171625233)
vxc_lil = mf.vxc_lil()
vxc = vxc_lil[0].toarray()
vna = mf.vna_coo().toarray()
Ena = (vna*dm).sum()*HARTREE2EV
self.assertAlmostEqual(Ena, -265.011709776208)
vnl = mf.vnl_coo().toarray()
Enl = (vnl*dm).sum()*HARTREE2EV
self.assertAlmostEqual(Enl, -62.17621375282889)
for f1 in [1.0]:
for f2 in [-2.0, -1.0, -0.5, 0.0, 0.5, 1.0, 2.0]:
for f3 in [1.0]:
for f4 in [1.0]:
for f5 in [1.0]:
hamilt2 = f1*tkin + f2*vna + f3*vnl + f4*dvh + f5*vxc
Ebs2 = (hamilt2*dm).sum()*HARTREE2EV
if abs(Ebs2+103.137894)<10.0:
print(f1,f2,f3,f4,f5, Ebs2, -103.137894, Ebs2+103.137894, abs(hamilt2-hamilt1).sum())
def test_0166_cn_uhf_spin_contamination(self):
""" Interacting case """
spin = 1
mol = gto.M(verbose=0,
atom='C 0 0 -0.6;N 0 0 0.52',
basis='cc-pvdz',
spin=spin)
gto_mf = scf.UHF(mol)
gto_mf.kernel()
#print( ' gto_mf.spin_square() ', gto_mf.spin_square(), spin*0.5*(spin*0.5+1), spin+1 )
ss_2sp1 = gto_mf.spin_square()
self.assertTrue(
np.allclose(ss_2sp1, (0.9768175623447295, 2.2152359353754889)))
nao_mf = mf_c(gto=mol, mf=gto_mf, verbosity=0, gen_pb=False)
ss_2sp1 = nao_mf.spin_square()
self.assertTrue(
np.allclose(ss_2sp1, (0.9767930087836918, 2.2152137673675574)))
def test_ao_eval_speed(self):
""" Test the computation of atomic orbitals in coordinate space """
dname = os.path.dirname(os.path.abspath(__file__))
mf = mf_c(verbosity=0,
label='water',
cd=dname,
gen_pb=False,
force_gamma=True,
Ecut=20)
g = mf.mesh3d.get_3dgrid()
t0 = timer()
oc2v1 = mf.comp_aos_den(g.coords)
t1 = timer()
oc2v2 = mf.comp_aos_py(g.coords)
t2 = timer()
print(__name__, 't1 t2: ', t1 - t0, t2 - t1)
print(
abs(oc2v1 - oc2v2).sum() / oc2v2.size, (abs(oc2v1 - oc2v2).max()))
self.assertTrue(np.allclose(oc2v1, oc2v2, atol=3.5e-5))
def test_0379_recomp_hamilt_oxygen(self):
""" Recomputing all parts of KS Hamiltonian a la SIESTA """
import os
dname = os.path.dirname(os.path.abspath(__file__))
F = -0.27012188215107336
mf = mf_c(verbosity=1,
label='oxygen',
cd=dname,
gen_pb=False,
fermi_energy=F,
Ecut=125.0)
mf.overlap_check()
mf.diag_check()
dm = mf.make_rdm1().reshape((mf.norbs, mf.norbs))
hamilt1 = mf.get_hamiltonian()[0].toarray()
Ebs1 = (hamilt1 * dm).sum() * HARTREE2EV
#self.assertAlmostEqual(Ebs1, -73.18443295100552)
g = mf.mesh3d.get_3dgrid()
dens = mf.dens_elec(g.coords,
dm=mf.make_rdm1()).reshape(mf.mesh3d.shape)
mf.mesh3d.write('0379_dens_elec.cube',
mol=mf,
field=dens,
comment='density')
vh3d = mf.vhartree_pbc(dens)
Ehartree = (vh3d * dens).sum() * 0.5 * HARTREE2EV * g.weights
#self.assertAlmostEqual(Ehartree, 225.386052971981)
vh = mf.vhartree_pbc_coo().toarray()
Ehartree = (vh * dm).sum() * 0.5 * HARTREE2EV
#self.assertAlmostEqual(Ehartree, 225.386052971981)
tkin = -0.5 * mf.laplace_coo().toarray()
Ekin = (tkin * dm).sum() * HARTREE2EV
#self.assertAlmostEqual(Ekin, 308.28672736957884)
dens_atom = mf.vna(g.coords,
sp2v=mf.ao_log.sp2chlocal,
sp2rcut=mf.ao_log.sp2rcut_chlocal).reshape(
mf.mesh3d.shape)
dvh3d = mf.vhartree_pbc(dens + dens_atom)
mf.mesh3d.write('0379_dvh.cube', mol=mf, field=dvh3d, comment='dVH')
dvh = mf.vhartree_pbc_coo(density_factors=[1, 1]).toarray()
Edvh = (dvh * dm).sum() * 0.5 * HARTREE2EV
#self.assertAlmostEqual(Edvh, -109.5022234053683) # ???
vhatom = mf.vhartree_pbc_coo(density_factors=[0, 1]).toarray()
Ena_atom = (vhatom * dm).sum() * 0.5 * HARTREE2EV
#self.assertAlmostEqual(Ena_atom, -334.88827637734926) # ???
Exc = mf.exc() * HARTREE2EV
#self.assertAlmostEqual(Exc, -87.78500822036436) # Exc = -87.785701
vxc_lil = mf.vxc_lil()
vxc = vxc_lil[0].toarray()
vna = mf.vna_coo().toarray()
Ena = (vna * dm).sum() * HARTREE2EV
#self.assertAlmostEqual(Ena, -217.77241233140285) # Enascf = -217.774110
vnl = mf.vnl_coo().toarray()
Enl = (vnl * dm).sum() * HARTREE2EV
#self.assertAlmostEqual(Enl, -43.272671826080604) # Enl = -43.273074
for f1 in [1.0]:
for f2 in [-2.0, -1.0, -0.5, 0.0, 0.5, 1.0, 2.0]:
for f3 in [1.0]:
for f4 in [1.0]:
for f5 in [1.0]:
hamilt2 = f1 * tkin + f2 * vna + f3 * vnl + f4 * dvh + f5 * vxc
Ebs2 = (hamilt2 * dm).sum() * HARTREE2EV
print(__name__, f2, Ebs2)
if abs(Ebs2 + 73.185007) < 10.0:
print(f1, f2, f3, f4, f5, Ebs2, -73.185007,
Ebs2 + 73.185007,
abs(hamilt2 - hamilt1).sum())
