def get_veff(ks_grad, mol=None, dm=None):
'''Coulomb + XC functional
'''
if mol is None: mol = ks_grad.mol
if dm is None: dm = ks_grad.base.make_rdm1()
t0 = (time.clock(), time.time())
mf = ks_grad.base
ni = mf._numint
if ks_grad.grids is not None:
grids = ks_grad.grids
else:
grids = mf.grids
if grids.coords is None:
grids.build(with_non0tab=True)
if mf.nlc != '':
raise NotImplementedError
#enabling range-separated hybrids
omega, alpha, hyb = ni.rsh_and_hybrid_coeff(mf.xc, spin=mol.spin)
mem_now = lib.current_memory()[0]
max_memory = max(2000, ks_grad.max_memory*.9-mem_now)
if ks_grad.grid_response:
exc, vxc = rks_grad.get_vxc_full_response(
ni, mol, grids, mf.xc, dm,
max_memory=max_memory, verbose=ks_grad.verbose)
logger.debug1(ks_grad, 'sum(grids response) %s', exc.sum(axis=0))
else:
exc, vxc = rks_grad.get_vxc(
ni, mol, grids, mf.xc, dm,
max_memory=max_memory, verbose=ks_grad.verbose)
t0 = logger.timer(ks_grad, 'vxc', *t0)
if abs(hyb) < 1e-10 and abs(alpha) < 1e-10:
vj = ks_grad.get_j(mol, dm)
vxc += vj
if ks_grad.auxbasis_response:
e1_aux = vj.aux
else:
vj, vk = ks_grad.get_jk(mol, dm)
if ks_grad.auxbasis_response:
vk_aux = vk.aux * hyb
vk *= hyb
if abs(omega) > 1e-10: # For range separated Coulomb operator
raise NotImplementedError
vk_lr = ks_grad.get_k(mol, dm, omega=omega)
vk += vk_lr * (alpha - hyb)
if ks_grad.auxbasis_response:
vk_aux += vk_lr.aux * (alpha - hyb)
vxc += vj - vk * .5
if ks_grad.auxbasis_response:
e1_aux = vj.aux - vk_aux * .5
if ks_grad.auxbasis_response:
logger.debug1(ks_grad, 'sum(auxbasis response) %s', e1_aux.sum(axis=0))
vxc = lib.tag_array(vxc, exc1_grid=exc, aux=e1_aux)
else:
vxc = lib.tag_array(vxc, exc1_grid=exc)
return vxc
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)
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)