def nuc_grad_method(self):
from pyscf.grad import rks as rks_grad
return rks_grad.Gradients(self)
def test_get_vxc(self):
mol = gto.Mole()
mol.verbose = 0
mol.atom = [['O', (0., 0., 0.)], [1, (0., -0.757, 0.587)],
[1, (0., 0.757, 0.587)]]
mol.basis = '631g'
mol.build()
mf = dft.RKS(mol)
mf.conv_tol = 1e-12
mf.grids.radii_adjust = radi.becke_atomic_radii_adjust
mf.scf()
g = rks.Gradients(mf)
g.grid_response = True
g0 = g.kernel()
dm0 = mf.make_rdm1()
mol0 = gto.Mole()
mol0.verbose = 0
mol0.atom = [['O', (0., 0., -0.00001)], [1, (0., -0.757, 0.587)],
[1, (0., 0.757, 0.587)]]
mol0.basis = '631g'
mol0.build()
mf0 = dft.RKS(mol0)
mf0.grids.radii_adjust = radi.becke_atomic_radii_adjust
mf0.conv_tol = 1e-12
e0 = mf0.scf()
denom = 1 / .00002 * lib.param.BOHR
mol1 = gto.Mole()
mol1.verbose = 0
mol1.atom = [['O', (0., 0., 0.00001)], [1, (0., -0.757, 0.587)],
[1, (0., 0.757, 0.587)]]
mol1.basis = '631g'
mol1.build()
mf1 = dft.RKS(mol1)
mf1.grids.radii_adjust = radi.becke_atomic_radii_adjust
mf1.conv_tol = 1e-12
e1 = mf1.scf()
self.assertAlmostEqual((e1 - e0) * denom, g0[0, 2], 6)
# grids response have non-negligible effects for small grids
grids = dft.gen_grid.Grids(mol)
grids.atom_grid = (20, 86)
grids.build(with_non0tab=False)
grids0 = dft.gen_grid.Grids(mol0)
grids0.atom_grid = (20, 86)
grids0.build(with_non0tab=False)
grids1 = dft.gen_grid.Grids(mol1)
grids1.atom_grid = (20, 86)
grids1.build(with_non0tab=False)
xc = 'lda,'
exc0 = dft.numint.nr_rks(mf0._numint, mol0, grids0, xc, dm0)[1]
exc1 = dft.numint.nr_rks(mf1._numint, mol1, grids1, xc, dm0)[1]
grids0_w = copy.copy(grids0)
grids0_w.weights = grids1.weights
grids0_c = copy.copy(grids0)
grids0_c.coords = grids1.coords
exc0_w = dft.numint.nr_rks(mf0._numint, mol0, grids0_w, xc, dm0)[1]
exc0_c = dft.numint.nr_rks(mf1._numint, mol1, grids0_c, xc, dm0)[1]
dexc_t = (exc1 - exc0) * denom
dexc_c = (exc0_c - exc0) * denom
dexc_w = (exc0_w - exc0) * denom
self.assertAlmostEqual(dexc_t, dexc_c + dexc_w, 4)
vxc = rks.get_vxc(mf._numint, mol, grids, xc, dm0)[1]
ev1, vxc1 = rks.get_vxc_full_response(mf._numint, mol, grids, xc, dm0)
p0, p1 = mol.aoslice_by_atom()[0][2:]
exc1_approx = numpy.einsum('xij,ij->x', vxc[:, p0:p1], dm0[p0:p1]) * 2
exc1_full = numpy.einsum('xij,ij->x', vxc1[:, p0:p1],
dm0[p0:p1]) * 2 + ev1[0]
self.assertAlmostEqual(dexc_t, exc1_approx[2], 2)
self.assertAlmostEqual(dexc_t, exc1_full[2], 5)
xc = 'pbe,'
exc0 = dft.numint.nr_rks(mf0._numint, mol0, grids0, xc, dm0)[1]
exc1 = dft.numint.nr_rks(mf1._numint, mol1, grids1, xc, dm0)[1]
grids0_w = copy.copy(grids0)
grids0_w.weights = grids1.weights
grids0_c = copy.copy(grids0)
grids0_c.coords = grids1.coords
exc0_w = dft.numint.nr_rks(mf0._numint, mol0, grids0_w, xc, dm0)[1]
exc0_c = dft.numint.nr_rks(mf1._numint, mol1, grids0_c, xc, dm0)[1]
dexc_t = (exc1 - exc0) * denom
dexc_c = (exc0_c - exc0) * denom
dexc_w = (exc0_w - exc0) * denom
self.assertAlmostEqual(dexc_t, dexc_c + dexc_w, 4)
vxc = rks.get_vxc(mf._numint, mol, grids, xc, dm0)[1]
ev1, vxc1 = rks.get_vxc_full_response(mf._numint, mol, grids, xc, dm0)
p0, p1 = mol.aoslice_by_atom()[0][2:]
exc1_approx = numpy.einsum('xij,ij->x', vxc[:, p0:p1], dm0[p0:p1]) * 2
exc1_full = numpy.einsum('xij,ij->x', vxc1[:, p0:p1],
dm0[p0:p1]) * 2 + ev1[0]
self.assertAlmostEqual(dexc_t, exc1_approx[2], 2)
self.assertAlmostEqual(dexc_t, exc1_full[2], 5)
xc = 'pbe0'
grids.radii_adjust = None
grids0.radii_adjust = None
grids1.radii_adjust = None
exc0 = dft.numint.nr_rks(mf0._numint, mol0, grids0, xc, dm0)[1]
exc1 = dft.numint.nr_rks(mf1._numint, mol1, grids1, xc, dm0)[1]
grids0_w = copy.copy(grids0)
grids0_w.weights = grids1.weights
grids0_c = copy.copy(grids0)
grids0_c.coords = grids1.coords
exc0_w = dft.numint.nr_rks(mf0._numint, mol0, grids0_w, xc, dm0)[1]
exc0_c = dft.numint.nr_rks(mf1._numint, mol1, grids0_c, xc, dm0)[1]
dexc_t = (exc1 - exc0) * denom
dexc_c = (exc0_c - exc0) * denom
dexc_w = (exc0_w - exc0) * denom
self.assertAlmostEqual(dexc_t, dexc_c + dexc_w, 4)
vxc = rks.get_vxc(mf._numint, mol, grids, xc, dm0)[1]
ev1, vxc1 = rks.get_vxc_full_response(mf._numint, mol, grids, xc, dm0)
p0, p1 = mol.aoslice_by_atom()[0][2:]
exc1_approx = numpy.einsum('xij,ij->x', vxc[:, p0:p1], dm0[p0:p1]) * 2
exc1_full = numpy.einsum('xij,ij->x', vxc1[:, p0:p1],
dm0[p0:p1]) * 2 + ev1[0]
self.assertAlmostEqual(dexc_t, exc1_approx[2], 1)
#FIXME: exc1_full is quite different to the finite difference results, why?
self.assertAlmostEqual(dexc_t, exc1_full[2], 2)
