def test_polarizability_with_freq(self):
mol = gto.M(atom='''O 0. 0. 0.
H 0. -0.757 0.587
H 0. 0.757 0.587''',
basis='6-31g')
mf = scf.RHF(mol).run(conv_tol=1e-14)
mo_coeff = mf.mo_coeff
occidx = mf.mo_occ > 0
orbo = mo_coeff[:, occidx]
orbv = mo_coeff[:,~occidx]
nocc = orbo.shape[1]
nvir = orbv.shape[1]
nov = nocc*nvir
charges = mol.atom_charges()
coords = mol.atom_coords()
charge_center = numpy.einsum('i,ix->x', charges, coords) / charges.sum()
with mol.with_common_orig(charge_center):
int_r = mol.intor_symmetric('int1e_r', comp=3)
h1 = lib.einsum('xpq,pi,qj->xij', int_r, mo_coeff.conj(), orbo)
v1 = h1[:,nocc:].transpose(2,1,0).reshape(nov,-1)
v = numpy.vstack((v1,v1))
a, b = get_ab(mf)
a = a.reshape(nov,nov)
b = b.reshape(nov,nov)
mat = numpy.bmat(((a,b),(b,a)))
freq = 0.1
mat[:nov,:nov] -= numpy.eye(nov)*freq
mat[nov:,nov:] += numpy.eye(nov)*freq
# frequency-dependent property
u1 = numpy.linalg.solve(mat, v)
ref = numpy.einsum('px,py->xy', v, u1)*2
val = rhf.Polarizability(mf).polarizability_with_freq(freq)
# errors mainly due to krylov solver
self.assertAlmostEqual(abs(ref-val).max(), 0, 2)
# static property
ref = numpy.einsum('px,py->xy', v1, numpy.linalg.solve(a+b, v1))*4
val = rhf.Polarizability(mf).polarizability()
self.assertAlmostEqual(abs(ref-val).max(), 0, 7)
val = rhf.Polarizability(mf).polarizability_with_freq(freq=0)
# errors mainly due to krylov solver
self.assertAlmostEqual(abs(ref-val).max(), 0, 3)
def test_ab_lda(self):
mf = mf_lda
a, b = rhf.get_ab(mf)
ftda = rhf.gen_tda_operation(mf, singlet=True)[0]
ftdhf = rhf.gen_tdhf_operation(mf, singlet=True)[0]
nocc = numpy.count_nonzero(mf.mo_occ == 2)
nvir = numpy.count_nonzero(mf.mo_occ == 0)
numpy.random.seed(2)
x, y = xy = numpy.random.random((2,nocc,nvir))
ax = numpy.einsum('iajb,jb->ia', a, x)
self.assertAlmostEqual(abs(ax - ftda([x]).reshape(nocc,nvir)).max(), 0, 9)
ab1 = ax + numpy.einsum('iajb,jb->ia', b, y)
ab2 =-numpy.einsum('iajb,jb->ia', b, x)
ab2-= numpy.einsum('iajb,jb->ia', a, y)
abxy_ref = ftdhf([xy]).reshape(2,nocc,nvir)
self.assertAlmostEqual(abs(ab1 - abxy_ref[0]).max(), 0, 9)
self.assertAlmostEqual(abs(ab2 - abxy_ref[1]).max(), 0, 9)
def test_ab_lda(self):
mf = mf_lda
a, b = rhf.get_ab(mf)
ftda = rhf.gen_tda_operation(mf, singlet=True)[0]
ftdhf = rhf.gen_tdhf_operation(mf, singlet=True)[0]
nocc = numpy.count_nonzero(mf.mo_occ == 2)
nvir = numpy.count_nonzero(mf.mo_occ == 0)
numpy.random.seed(2)
x, y = xy = numpy.random.random((2,nocc,nvir))
ax = numpy.einsum('iajb,jb->ia', a, x)
self.assertAlmostEqual(abs(ax - ftda([x]).reshape(nocc,nvir)).max(), 0, 9)
ab1 = ax + numpy.einsum('iajb,jb->ia', b, y)
ab2 =-numpy.einsum('iajb,jb->ia', b, x)
ab2-= numpy.einsum('iajb,jb->ia', a, y)
abxy_ref = ftdhf([xy]).reshape(2,nocc,nvir)
self.assertAlmostEqual(abs(ab1 - abxy_ref[0]).max(), 0, 9)
self.assertAlmostEqual(abs(ab2 - abxy_ref[1]).max(), 0, 9)
