def test_aux_e2_becke(self):
cell = pgto.Cell()
cell.unit = 'B'
cell.h = np.eye(3) * 3.
cell.gs = np.array([20,20,20])
cell.atom = 'He 0 1 1; He 1 1 0'
cell.basis = { 'He': [[0, (10.8, 1.0)],
[0, (300.2, 1.0)]] }
cell.verbose = 0
cell.build(0, 0)
auxcell = df.format_aux_basis(cell)
auxcell.nimgs = [3,3,3]
a1 = df.aux_e2(cell, auxcell, 'cint3c1e_sph')
grids = pdft.gen_grid.BeckeGrids(cell)
grids.level = 3
#grids = pdft.gen_grid.UniformGrids(cell)
grids.build_()
a2 = df.aux_e2_grid(cell, auxcell, grids)
self.assertAlmostEqual(np.linalg.norm(a1-a2), 0, 4)
def get_j_gaussian_mod(cell, dm, auxcell, modcell, kpt=None, grids=None):
ovlp = pscf.scfint.get_ovlp(cell)
nao = ovlp.shape[0]
if grids is None:
c3 = df.aux_e2(cell, auxcell, 'cint3c1e_sph').reshape(nao,nao,-1)
else:
c3 = df.aux_e2_grid(cell, auxcell, grids).reshape(nao,nao,-1)
rho = np.einsum('ijk,ij->k', c3, dm)
modchg = np.asarray([cell.atom_charge(ia) for ia in range(cell.natm)])
modchg = modchg / auxnorm(modcell)
s1 = pscf.scfint.get_int1e_cross('cint1e_ovlp_sph', auxcell, modcell)
rho -= np.einsum('ij,j->i', s1, modchg)
v1 = np.linalg.solve(pscf.scfint.get_t(auxcell), 2*np.pi*rho)
vj = np.einsum('ijk,k->ij', c3, v1)
# remove the constant in potential
intdf = auxnorm(auxcell)
vj -= np.dot(v1, intdf) / cell.vol * ovlp
return vj
def get_j_uniform_mod(cell, dm, auxcell, kpt=None, grids=None):
ovlp = pscf.scfint.get_ovlp(cell)
nao = ovlp.shape[0]
if grids is None:
c3 = df.aux_e2(cell, auxcell, 'cint3c1e_sph').reshape(nao,nao,-1)
else:
c3 = df.aux_e2_grid(cell, auxcell, grids).reshape(nao,nao,-1)
rho = np.einsum('ijk,ij->k', c3, dm)
nelec = np.einsum('ij,ij', ovlp, dm)
intdf = auxnorm(auxcell)
rho -= nelec / cell.vol * intdf
v1 = np.linalg.solve(pscf.scfint.get_t(auxcell), 2*np.pi*rho)
vj = np.einsum('ijk,k->ij', c3, v1)
# remove the constant in potential
# vj += (np.dot(v1, rho) - (vj*dm).sum())/nelec * ovlp
# v1[idx].sum()/cell.vol == (np.dot(v1, rho) - (vj*dm).sum())/nelec
vj -= np.dot(v1, intdf) / cell.vol * ovlp
return vj
def get_nuc_gaussian_mod(cell, auxcell, modcell, kpt=None, grids=None):
coords = np.asarray([cell.atom_coord(ia) for ia in range(cell.natm)])
chargs = np.asarray([cell.atom_charge(ia) for ia in range(cell.natm)])
rho = np.dot(-chargs, pdft.numint.eval_ao(auxcell, coords))
modchg = chargs / auxnorm(modcell)
s1 = pscf.scfint.get_int1e_cross('cint1e_ovlp_sph', auxcell, modcell)
rho += np.einsum('ij,j->i', s1, modchg)
ovlp = pscf.scfint.get_ovlp(cell)
nao = ovlp.shape[0]
if grids is None:
c3 = df.aux_e2(cell, auxcell, 'cint3c1e_sph').reshape(nao,nao,-1)
else:
c3 = df.aux_e2_grid(cell, auxcell, grids).reshape(nao,nao,-1)
v1 = np.linalg.solve(pscf.scfint.get_t(auxcell), 2*np.pi*rho)
vnuc = np.einsum('ijk,k->ij', c3, v1)
# remove constant from potential. The constant contributes to V(G=0)
intdf = auxnorm(auxcell)
vnuc -= np.dot(v1, intdf) / cell.vol * ovlp
return vnuc
def get_nuc_uniform_mod(cell, auxcell, kpt=None, grids=None):
r'''Solving Poisson equation for Nuclear attraction
\nabla^2|g>V_g = rho_nuc - C
V_pq = \sum_g <pq|g> V_g
'''
intdf = auxnorm(auxcell)
coords = np.asarray([cell.atom_coord(ia) for ia in range(cell.natm)])
chargs =-np.asarray([cell.atom_charge(ia) for ia in range(cell.natm)])
rho = np.dot(chargs, pdft.numint.eval_ao(auxcell, coords))
rho += cell.nelectron / cell.vol * intdf
ovlp = pscf.scfint.get_ovlp(cell)
nao = ovlp.shape[0]
if grids is None:
c3 = df.aux_e2(cell, auxcell, 'cint3c1e_sph').reshape(nao,nao,-1)
else:
c3 = df.aux_e2_grid(cell, auxcell, grids).reshape(nao,nao,-1)
v1 = np.linalg.solve(pscf.scfint.get_t(auxcell), 2*np.pi*rho)
vnuc = np.einsum('ijk,k->ij', c3, v1)
# remove constant from potential. The constant contributes to V(G=0)
vnuc -= np.dot(v1, intdf) / cell.vol * ovlp
return vnuc