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)