def test_jk(self):
mf0 = scf.RHF(cell)
dm = mf0.get_init_guess()
mydf = aft.AFTDF(cell)
mydf.mesh = [11] * 3
vj, vk = mydf.get_jk(dm, exxdiv='ewald')
ej1 = numpy.einsum('ij,ji->', vj, dm)
ek1 = numpy.einsum('ij,ji->', vk, dm)
self.assertAlmostEqual(ej1,
3.0455881073561235 * (4. / 3.66768353356587)**2,
9)
self.assertAlmostEqual(ek1,
7.7905480251964629 * (4. / 3.66768353356587)**2,
9)
numpy.random.seed(12)
nao = cell.nao_nr()
dm = numpy.random.random((nao, nao))
dm = dm + dm.T
vj1, vk1 = mydf.get_jk(dm, hermi=0, exxdiv='ewald')
ej1 = numpy.einsum('ij,ji->', vj1, dm)
ek1 = numpy.einsum('ij,ji->', vk1, dm)
self.assertAlmostEqual(ej1, 12.234106555081793, 9)
self.assertAlmostEqual(ek1, 43.988705494650802, 9)
numpy.random.seed(1)
kpt = numpy.random.random(3)
vj, vk = mydf.get_jk(dm, 1, kpt, exxdiv='ewald')
ej1 = numpy.einsum('ij,ji->', vj, dm)
ek1 = numpy.einsum('ij,ji->', vk, dm)
self.assertAlmostEqual(ej1, 12.233546641482697, 9)
self.assertAlmostEqual(ek1, 43.946958026023722, 9)
def test_aft_k1_high_cost(self):
kpts = cell.get_abs_kpts([[-.25, -.25, -.25], [-.25, -.25, .25],
[-.25, .25, -.25], [-.25, .25, .25],
[.25, -.25, -.25], [.25, -.25, .25],
[.25, .25, -.25], [.25, .25, .25]])
numpy.random.seed(1)
nao = cell.nao_nr()
dm = numpy.random.random((8, nao, nao))
mydf = aft.AFTDF(cell)
mydf.kpts = kpts
numpy.random.seed(1)
dm = numpy.random.random((8, nao, nao))
dm = dm + dm.transpose(0, 2, 1)
vk = aft_jk.get_k_kpts(mydf, dm, 1, mydf.kpts)
self.assertAlmostEqual(finger(vk[0]),
(8.7518173818250702 - 0.11793770445839372j) / 8,
9)
self.assertAlmostEqual(finger(
vk[1]), (5.7682393685317894 + 0.069482280306391239j) / 8, 9)
self.assertAlmostEqual(finger(
vk[2]), (7.1890462727492324 - 0.088727079644645671j) / 8, 9)
self.assertAlmostEqual(finger(vk[3]),
(10.08358152800003 + 0.1278144339422369j) / 8,
9)
self.assertAlmostEqual(finger(vk[4]),
(8.393281242945573 - 0.099410704957774876j) / 8,
9)
self.assertAlmostEqual(finger(vk[5]),
(7.9413682328898769 + 0.1015563120870652j) / 8,
9)
self.assertAlmostEqual(finger(
vk[6]), (7.3743790120272408 - 0.096290683129384574j) / 8, 9)
self.assertAlmostEqual(finger(vk[7]),
(6.8144379626901443 + 0.08071261392857812j) / 8,
9)
def test_aft_k(self):
kpts = cell.get_abs_kpts([[-.25, -.25, -.25], [-.25, -.25, .25],
[-.25, .25, -.25], [-.25, .25, .25],
[.25, -.25, -.25], [.25, -.25, .25],
[.25, .25, -.25], [.25, .25, .25]])
numpy.random.seed(1)
nao = cell.nao_nr()
dm = numpy.random.random((8, nao, nao))
mydf = aft.AFTDF(cell)
mydf.kpts = kpts
vk = aft_jk.get_k_kpts(mydf, dm, 0, mydf.kpts)
self.assertAlmostEqual(finger(
vk[0]), (4.3373802352168278 - 0.062977052131451577j) / 8, 9)
self.assertAlmostEqual(finger(vk[1]),
(2.878809181709983 + 0.028843869853690692j) / 8,
9)
self.assertAlmostEqual(finger(
vk[2]), (3.7027622609953061 - 0.052034330663180237j) / 8, 9)
self.assertAlmostEqual(finger(
vk[3]), (5.0939994842559422 + 0.060094478876149444j) / 8, 9)
self.assertAlmostEqual(finger(
vk[4]), (4.2942087551592651 - 0.061138484763336887j) / 8, 9)
self.assertAlmostEqual(finger(
vk[5]), (3.9689429688683679 + 0.048471952758750547j) / 8, 9)
self.assertAlmostEqual(finger(
vk[6]), (3.6342630872923456 - 0.054892635365850449j) / 8, 9)
self.assertAlmostEqual(finger(
vk[7]), (3.3483735224533548 + 0.040877095049528467j) / 8, 9)
def test_ao2mo_7d(self):
L = 3.
n = 6
cell = pgto.Cell()
cell.a = numpy.diag([L, L, L])
cell.mesh = [n, n, n]
cell.atom = '''He 2. 2.2 2.
He 1.2 1. 1.'''
cell.basis = {'He': [[0, (1.2, 1)], [1, (0.6, 1)]]}
cell.verbose = 0
cell.build(0, 0)
kpts = cell.make_kpts([1, 3, 1])
nkpts = len(kpts)
nao = cell.nao_nr()
numpy.random.seed(1)
mo = (numpy.random.random((nkpts, nao, nao)) + numpy.random.random(
(nkpts, nao, nao)) * 1j)
with_df = aft.AFTDF(cell, kpts)
out = with_df.ao2mo_7d(mo, kpts)
ref = numpy.empty_like(out)
kconserv = kpts_helper.get_kconserv(cell, kpts)
for ki, kj, kk in kpts_helper.loop_kkk(nkpts):
kl = kconserv[ki, kj, kk]
tmp = with_df.ao2mo((mo[ki], mo[kj], mo[kk], mo[kl]),
kpts[[ki, kj, kk, kl]])
ref[ki, kj, kk] = tmp.reshape([nao] * 4)
self.assertAlmostEqual(abs(out - ref).max(), 0, 12)
def test_get_eri_gamma(self):
odf0 = mdf.MDF(cell1)
odf = aft.AFTDF(cell1)
ref = odf0.get_eri()
eri0000 = odf.get_eri(compact=True)
self.assertTrue(eri0000.dtype == numpy.double)
self.assertTrue(np.allclose(eri0000, ref, atol=1e-6, rtol=1e-6))
self.assertAlmostEqual(finger(eri0000), 0.23714016293926865, 9)
def test_get_eri_0123(self):
odf = aft.AFTDF(cell1)
ref = kdf0.get_eri(kpts)
eri1111 = odf.get_eri(kpts)
self.assertAlmostEqual(abs(eri1111-ref).max(), 0, 9)
self.assertAlmostEqual(finger(eri1111), (1.2917759427391706-0.013340252488069412j), 9)
ref = fft.FFTDF(cell1).get_mo_eri([numpy.eye(cell1.nao_nr())]*4, kpts)
self.assertAlmostEqual(abs(eri1111-ref).max(), 0, 9)
def test_get_eri_0123(self):
odf = aft.AFTDF(cell1)
ref = kdf0.get_eri(kpts)
eri1111 = odf.get_eri(kpts)
self.assertTrue(np.allclose(eri1111, ref, atol=1e-8, rtol=1e-8))
self.assertAlmostEqual(finger(eri1111), (1.2917759427391706-0.013340252488069412j), 9)
ref = fft.FFTDF(cell1).get_mo_eri([numpy.eye(cell1.nao_nr())]*4, kpts)
self.assertTrue(np.allclose(eri1111, ref, atol=1e-8, rtol=1e-8))
def get_hcore(self, cell=None, kpts=None):
if cell is None: cell = self.cell
if kpts is None:
kpts_lst = numpy.zeros((1, 3))
else:
kpts_lst = numpy.reshape(kpts, (-1, 3))
xcell, contr_coeff = self.get_xmol(cell)
with_df = aft.AFTDF(xcell)
c = lib.param.LIGHT_SPEED
assert ('1E' in self.approx.upper())
if 'ATOM' in self.approx.upper():
atom_slices = xcell.offset_nr_by_atom()
nao = xcell.nao_nr()
x = numpy.zeros((nao, nao))
vloc = numpy.zeros((nao, nao))
wloc = numpy.zeros((nao, nao))
for ia in range(xcell.natm):
ish0, ish1, p0, p1 = atom_slices[ia]
shls_slice = (ish0, ish1, ish0, ish1)
t1 = xcell.intor('int1e_kin', shls_slice=shls_slice)
s1 = xcell.intor('int1e_ovlp', shls_slice=shls_slice)
with xcell.with_rinv_at_nucleus(ia):
z = -xcell.atom_charge(ia)
v1 = z * xcell.intor('int1e_rinv', shls_slice=shls_slice)
w1 = z * xcell.intor('int1e_prinvp', shls_slice=shls_slice)
vloc[p0:p1, p0:p1] = v1
wloc[p0:p1, p0:p1] = w1
x[p0:p1, p0:p1] = x2c._x2c1e_xmatrix(t1, v1, w1, s1, c)
else:
raise NotImplementedError
t = xcell.pbc_intor('int1e_kin', 1, lib.HERMITIAN, kpts_lst)
s = xcell.pbc_intor('int1e_ovlp', 1, lib.HERMITIAN, kpts_lst)
v = with_df.get_nuc(kpts_lst)
#w = get_pnucp(with_df, kpts_lst)
if self.basis is not None:
s22 = s
s21 = pbcgto.intor_cross('int1e_ovlp', xcell, cell, kpts=kpts_lst)
h1_kpts = []
for k in range(len(kpts_lst)):
# The treatment of pnucp local part has huge effects to hcore
#h1 = x2c._get_hcore_fw(t[k], vloc, wloc, s[k], x, c) - vloc + v[k]
#h1 = x2c._get_hcore_fw(t[k], v[k], w[k], s[k], x, c)
h1 = x2c._get_hcore_fw(t[k], v[k], wloc, s[k], x, c)
if self.basis is not None:
c = lib.cho_solve(s22[k], s21[k])
h1 = reduce(numpy.dot, (c.T, h1, c))
if self.xuncontract and contr_coeff is not None:
h1 = reduce(numpy.dot, (contr_coeff.T, h1, contr_coeff))
h1_kpts.append(h1)
if kpts is None or numpy.shape(kpts) == (3, ):
h1_kpts = h1_kpts[0]
return lib.asarray(h1_kpts)
def test_get_eri_gamma(self):
odf = aft.AFTDF(cell1)
ref = kdf0.get_eri((kpts[0],kpts[0],kpts[0],kpts[0]))
eri1111 = odf.get_eri((kpts[0],kpts[0],kpts[0],kpts[0]))
self.assertTrue(np.allclose(eri1111, ref, atol=1e-6, rtol=1e-6))
self.assertAlmostEqual(finger(eri1111), (1.2410388899583582-5.2370501878355006e-06j), 9)
eri1111 = odf.get_eri((kpts[0]+1e-8,kpts[0]+1e-8,kpts[0],kpts[0]))
self.assertTrue(np.allclose(eri1111, ref, atol=1e-6, rtol=1e-6))
self.assertAlmostEqual(finger(eri1111), (1.2410388899583582-5.2370501878355006e-06j), 9)
def test_get_eri_0011(self):
odf = aft.AFTDF(cell1)
ref = kdf0.get_eri((kpts[0],kpts[0],kpts[1],kpts[1]))
eri0011 = odf.get_eri((kpts[0],kpts[0],kpts[1],kpts[1]))
self.assertTrue(np.allclose(eri0011, ref, atol=1e-3, rtol=1e-3))
self.assertAlmostEqual(finger(eri0011), (1.2410162858084512+0.00074485383749912936j), 9)
ref = fft.FFTDF(cell1).get_mo_eri([numpy.eye(cell1.nao_nr())]*4, (kpts[0],kpts[0],kpts[1],kpts[1]))
eri0011 = odf.get_eri((kpts[0],kpts[0],kpts[1],kpts[1]))
self.assertTrue(np.allclose(eri0011, ref, atol=1e-9, rtol=1e-9))
self.assertAlmostEqual(finger(eri0011), (1.2410162860852818+0.00074485383748954838j), 9)
def test_aft_get_pp(self):
v0 = pgto.pseudo.get_pp(cell, kpts[0])
v1 = aft.AFTDF(cell).get_pp(kpts)
self.assertTrue(np.allclose(v0, v1[0], atol=1e-5, rtol=1e-5))
self.assertAlmostEqual(finger(v1[0]), (-5.6240305085898807+0.22094834207603817j), 8)
v0 = pgto.pseudo.get_pp(cell, kpts[1])
self.assertTrue(np.allclose(v0, v1[1], atol=1e-5, rtol=1e-5))
self.assertAlmostEqual(finger(v1[1]), (-5.53877585793+1.043933371359j) ,8)
self.assertAlmostEqual(finger(v1[2]), (-6.05309558678+0.281728966073j), 8)
self.assertAlmostEqual(finger(v1[3]), (-5.60115995450+0.275973062529j), 8)
def test_init_aft_1d(self):
cell = pgto.Cell()
cell.atom = 'He 1. .5 .5; He .1 1.3 2.1'
cell.basis = {'He': [(0, (2.5, 1)), (0, (1., 1))]}
cell.a = np.eye(3) * 2.5
cell.dimension = 1
cell.mesh = [3, 3, 3]
cell.build()
f = aft.AFTDF(cell)
np.random.seed(1)
f.kpts = np.random.random((4, 3))
f.check_sanity()
def get_jk(self,
dm,
hermi=1,
kpts=None,
kpts_band=None,
with_j=True,
with_k=True,
omega=None,
exxdiv=None):
if omega is not None: # J/K for RSH functionals
cell = self.cell
# * AFT is computationally more efficient than GDF if the Coulomb
# attenuation tends to the long-range role (i.e. small omega).
# * Note: changing to AFT integrator may cause small difference to
# the GDF integrator. If a very strict GDF result is desired,
# we can disable this trick by setting
# LONGRANGE_AFT_TURNOVER_THRESHOLD to 0.
# * The sparse mesh is not appropriate for low dimensional systems
# with infinity vacuum since the ERI may require large mesh to
# sample density in vacuum.
if (omega < LONGRANGE_AFT_TURNOVER_THRESHOLD
and cell.dimension >= 2
and cell.low_dim_ft_type != 'inf_vacuum'):
mydf = aft.AFTDF(cell, self.kpts)
mydf.ke_cutoff = aft.estimate_ke_cutoff_for_omega(cell, omega)
mydf.mesh = tools.cutoff_to_mesh(cell.lattice_vectors(),
mydf.ke_cutoff)
else:
mydf = self
return _sub_df_jk_(mydf, dm, hermi, kpts, kpts_band, with_j,
with_k, omega, exxdiv)
if kpts is None:
if numpy.all(self.kpts == 0):
# Gamma-point calculation by default
kpts = numpy.zeros(3)
else:
kpts = self.kpts
kpts = numpy.asarray(kpts)
if kpts.shape == (3, ):
return df_jk.get_jk(self, dm, hermi, kpts, kpts_band, with_j,
with_k, exxdiv)
vj = vk = None
if with_k:
vk = df_jk.get_k_kpts(self, dm, hermi, kpts, kpts_band, exxdiv)
if with_j:
vj = df_jk.get_j_kpts(self, dm, hermi, kpts, kpts_band)
return vj, vk
def test_aft_get_ao_eri(self):
df0 = fft.FFTDF(cell1)
df = aft.AFTDF(cell1)
eri0 = df0.get_ao_eri(compact=True)
eri1 = df.get_ao_eri(compact=True)
self.assertAlmostEqual(abs(eri0 - eri1).max(), 0, 9)
eri0 = df0.get_ao_eri(kpts[0])
eri1 = df.get_ao_eri(kpts[0])
self.assertAlmostEqual(abs(eri0 - eri1).max(), 0, 9)
eri0 = df0.get_ao_eri(kpts)
eri1 = df.get_ao_eri(kpts)
self.assertAlmostEqual(abs(eri0 - eri1).max(), 0, 9)
def test_eri1111(self):
kpts = numpy.random.random((4, 3)) * .25
kpts[3] = -numpy.einsum('ij->j', kpts[:3])
with_df = aft.AFTDF(cell)
with_df.kpts = kpts
mo = (numpy.random.random((nao, nao)) + numpy.random.random(
(nao, nao)) * 1j)
eri = with_df.get_eri(kpts).reshape((nao, ) * 4)
eri0 = numpy.einsum('pjkl,pi->ijkl', eri, mo.conj())
eri0 = numpy.einsum('ipkl,pj->ijkl', eri0, mo)
eri0 = numpy.einsum('ijpl,pk->ijkl', eri0, mo.conj())
eri0 = numpy.einsum('ijkp,pl->ijkl', eri0, mo)
eri1 = with_df.ao2mo(mo, kpts)
self.assertAlmostEqual(
abs(eri1.reshape(eri0.shape) - eri0).sum(), 0, 9)
def test_get_eri_0110(self):
odf = aft.AFTDF(cell1)
ref = kdf0.get_eri((kpts[0],kpts[1],kpts[1],kpts[0]))
eri0110 = odf.get_eri((kpts[0],kpts[1],kpts[1],kpts[0]))
self.assertTrue(np.allclose(eri0110, ref, atol=1e-6, rtol=1e-6))
eri0110 = odf.get_eri((kpts[0]+1e-8,kpts[1]+1e-8,kpts[1],kpts[0]))
self.assertTrue(np.allclose(eri0110, ref, atol=1e-6, rtol=1e-6))
self.assertAlmostEqual(finger(eri0110), (1.2928399254827956-0.011820590601969154j), 9)
ref = fft.FFTDF(cell1).get_mo_eri([numpy.eye(cell1.nao_nr())]*4, (kpts[0],kpts[1],kpts[1],kpts[0]))
eri0110 = odf.get_eri((kpts[0],kpts[1],kpts[1],kpts[0]))
self.assertTrue(np.allclose(eri0110, ref, atol=1e-9, rtol=1e-9))
self.assertAlmostEqual(finger(eri0110), (1.2928399254827956-0.011820590601969154j), 9)
eri0110 = odf.get_eri((kpts[0]+1e-8,kpts[1]+1e-8,kpts[1],kpts[0]))
self.assertTrue(np.allclose(eri0110, ref, atol=1e-9, rtol=1e-9))
self.assertAlmostEqual(finger(eri0110), (1.2928399254827956-0.011820590601969154j), 9)
def test_aft_get_ao_eri(self):
df0 = fft.FFTDF(cell)
df = aft.AFTDF(cell)
eri0 = df0.get_ao_eri(compact=True)
eri1 = df.get_ao_eri(compact=True)
self.assertTrue(np.allclose(eri0, eri1, atol=1e-5, rtol=1e-5))
self.assertAlmostEqual(finger(eri1), 0.80425361966560172, 8)
eri0 = df0.get_ao_eri(kpts[0])
eri1 = df.get_ao_eri(kpts[0])
self.assertTrue(np.allclose(eri0, eri1, atol=1e-5, rtol=1e-5))
self.assertAlmostEqual(finger(eri1), (2.9346374476387949-0.20479054936779137j), 8)
eri0 = df0.get_ao_eri(kpts)
eri1 = df.get_ao_eri(kpts)
self.assertTrue(np.allclose(eri0, eri1, atol=1e-5, rtol=1e-5))
self.assertAlmostEqual(finger(eri1), (0.33709287302019619-0.94185725020966538j), 8)
def test_aft_j(self):
numpy.random.seed(1)
nao = cell.nao_nr()
dm = numpy.random.random((4, nao, nao))
dm = dm + dm.transpose(0, 2, 1)
mydf = aft.AFTDF(cell)
mydf.kpts = numpy.random.random((4, 3))
mydf.mesh = numpy.asarray((11, ) * 3)
vj = aft_jk.get_j_kpts(mydf, dm, 1, mydf.kpts)
self.assertAlmostEqual(finger(
vj[0]), (0.93946193432413905 + 0.00010862804196223034j) / 4, 9)
self.assertAlmostEqual(finger(
vj[1]), (0.94866073525335626 + 0.005571199307452865j) / 4, 9)
self.assertAlmostEqual(finger(
vj[2]), (1.1492194255929766 + 0.0093705761598793739j) / 4, 9)
self.assertAlmostEqual(finger(
vj[3]), (1.1397493412770023 + 0.010731970529096637j) / 4, 9)
def test_get_eri_gamma(self):
odf = aft.AFTDF(cell1)
ref = odf.get_eri(compact=True)
df = fft.FFTDF(cell1)
eri0000 = df.get_eri(compact=True)
self.assertTrue(eri0000.dtype == numpy.double)
self.assertTrue(np.allclose(eri0000, ref, atol=1e-9, rtol=1e-9))
self.assertAlmostEqual(finger(eri0000), 0.23714016293926865, 9)
ref = odf.get_eri((kpts[0],kpts[0],kpts[0],kpts[0]))
eri1111 = df.get_eri((kpts[0],kpts[0],kpts[0],kpts[0]))
self.assertTrue(np.allclose(eri1111, ref, atol=1e-9, rtol=1e-9))
self.assertAlmostEqual(finger(eri1111), (1.2410388899583582-5.2370501878355006e-06j), 9)
eri1111 = df.get_eri((kpts[0]+1e-8,kpts[0]+1e-8,kpts[0],kpts[0]))
self.assertTrue(np.allclose(eri1111, ref, atol=1e-9, rtol=1e-9))
self.assertAlmostEqual(finger(eri1111), (1.2410388899583582-5.2370501878355006e-06j), 9)
def test_get_mo_eri(self):
df0 = fft.FFTDF(cell)
odf = aft.AFTDF(cell)
nao = cell.nao_nr()
numpy.random.seed(5)
mo =(numpy.random.random((nao,nao)) +
numpy.random.random((nao,nao))*1j)
eri_mo0 = df0.get_mo_eri((mo,)*4, kpts)
eri_mo1 = odf.get_mo_eri((mo,)*4, kpts)
self.assertTrue(np.allclose(eri_mo1, eri_mo0, atol=1e-7, rtol=1e-7))
kpts_t = (kpts[2],kpts[3],kpts[0],kpts[1])
eri_mo2 = df0.get_mo_eri((mo,)*4, kpts_t)
eri_mo2 = eri_mo2.reshape((nao,)*4).transpose(2,3,0,1).reshape(nao**2,-1)
self.assertTrue(np.allclose(eri_mo2, eri_mo0, atol=1e-7, rtol=1e-7))
eri_mo0 = df0.get_mo_eri((mo,)*4, (kpts[0],)*4)
eri_mo1 = odf.get_mo_eri((mo,)*4, (kpts[0],)*4)
self.assertTrue(np.allclose(eri_mo1, eri_mo0, atol=1e-7, rtol=1e-7))
eri_mo0 = df0.get_mo_eri((mo,)*4, (kpts[0],kpts[1],kpts[1],kpts[0],))
eri_mo1 = odf.get_mo_eri((mo,)*4, (kpts[0],kpts[1],kpts[1],kpts[0],))
self.assertTrue(np.allclose(eri_mo1, eri_mo0, atol=1e-7, rtol=1e-7))
eri_mo0 = df0.get_mo_eri((mo,)*4, (kpt0,kpt0,kpts[0],kpts[0],))
eri_mo1 = odf.get_mo_eri((mo,)*4, (kpt0,kpt0,kpts[0],kpts[0],))
self.assertTrue(np.allclose(eri_mo1, eri_mo0, atol=1e-7, rtol=1e-7))
eri_mo0 = df0.get_mo_eri((mo,)*4, (kpts[0],kpts[0],kpt0,kpt0,))
eri_mo1 = odf.get_mo_eri((mo,)*4, (kpts[0],kpts[0],kpt0,kpt0,))
self.assertTrue(np.allclose(eri_mo1, eri_mo0, atol=1e-7, rtol=1e-7))
mo1 = mo[:,:nao//2+1]
eri_mo0 = df0.get_mo_eri((mo1,mo,mo,mo1), (kpts[0],)*4)
eri_mo1 = odf.get_mo_eri((mo1,mo,mo,mo1), (kpts[0],)*4)
self.assertTrue(np.allclose(eri_mo1, eri_mo0, atol=1e-7, rtol=1e-7))
eri_mo0 = df0.get_mo_eri((mo1,mo,mo1,mo), (kpts[0],kpts[1],kpts[1],kpts[0],))
eri_mo1 = odf.get_mo_eri((mo1,mo,mo1,mo), (kpts[0],kpts[1],kpts[1],kpts[0],))
self.assertTrue(np.allclose(eri_mo1, eri_mo0, atol=1e-7, rtol=1e-7))
def test_eri0000(self):
with_df = aft.AFTDF(cell)
with_df.kpts = numpy.zeros((4, 3))
mo = (numpy.random.random((nao, nao)) + numpy.random.random(
(nao, nao)) * 1j)
eri = ao2mo.restore(1, with_df.get_eri(with_df.kpts), nao)
eri0 = numpy.einsum('pjkl,pi->ijkl', eri, mo.conj())
eri0 = numpy.einsum('ipkl,pj->ijkl', eri0, mo)
eri0 = numpy.einsum('ijpl,pk->ijkl', eri0, mo.conj())
eri0 = numpy.einsum('ijkp,pl->ijkl', eri0, mo)
eri1 = with_df.ao2mo(mo, with_df.kpts)
self.assertAlmostEqual(
abs(eri1.reshape(eri0.shape) - eri0).sum(), 0, 9)
mo = mo.real
eri0 = numpy.einsum('pjkl,pi->ijkl', eri, mo.conj())
eri0 = numpy.einsum('ipkl,pj->ijkl', eri0, mo)
eri0 = numpy.einsum('ijpl,pk->ijkl', eri0, mo.conj())
eri0 = numpy.einsum('ijkp,pl->ijkl', eri0, mo)
eri1 = with_df.ao2mo(mo, with_df.kpts, compact=False)
self.assertAlmostEqual(
abs(eri1.reshape(eri0.shape) - eri0).sum(), 0, 9)
def test_aft_get_nuc(self):
df = aft.AFTDF(cell)
v1 = df.get_nuc(kpts[0])
self.assertAlmostEqual(finger(v1),
(-5.764786312608102 + 0.19126292955145852j), 8)
def test_get_pp_loc_part1_high_cost(self):
df = aft.AFTDF(cell)
v1 = aft.get_pp_loc_part1(df, kpts[0])
self.assertAlmostEqual(finger(v1),
(-6.0893491060887159 + 0.19823828749533859j), 8)
def test_aft_get_nuc(self):
df = aft.AFTDF(cell)
v1 = df.get_nuc(kpts[0])
self.assertAlmostEqual(finger(v1),
(-6.0893491060887159 + 0.19823828749533859j), 8)
wj_kpts = wj_kpts[0]
return numpy.asarray(wj_kpts)
if __name__ == '__main__':
from pyscf.pbc import scf
cell = pbcgto.Cell()
cell.build(unit='B',
a=numpy.eye(3) * 4,
mesh=[11] * 3,
atom='H 0 0 0; H 0 0 1.8',
verbose=4,
basis='sto3g')
lib.param.LIGHT_SPEED = 2
mf = scf.RHF(cell)
mf.with_df = aft.AFTDF(cell)
enr = mf.kernel()
print('E(NR) = %.12g' % enr)
mf = sfx2c1e(mf)
esfx2c = mf.kernel()
print('E(SFX2C1E) = %.12g' % esfx2c)
mf = scf.KRHF(cell)
mf.with_df = aft.AFTDF(cell)
mf.kpts = cell.make_kpts([2, 2, 1])
enr = mf.kernel()
print('E(k-NR) = %.12g' % enr)
mf = sfx2c1e(mf)
esfx2c = mf.kernel()
if __name__ == '__main__':
from pyscf.pbc import gto as pgto
from pyscf.pbc import scf as pscf
from pyscf.pbc.df import aft
L = 5.
n = 5
cell = pgto.Cell()
cell.a = numpy.diag([L,L,L])
cell.gs = numpy.array([n,n,n])
cell.atom = '''He 3. 2. 3.
He 1. 1. 1.'''
#cell.basis = {'He': [[0, (1.0, 1.0)]]}
#cell.basis = '631g'
#cell.basis = {'He': [[0, (2.4, 1)], [1, (1.1, 1)]]}
cell.basis = 'ccpvdz'
cell.verbose = 0
cell.build(0,0)
cell.verbose = 5
df = aft.AFTDF(cell)
df.gs = (15,)*3
dm = pscf.RHF(cell).get_init_guess()
vj, vk = df.get_jk(dm)
print(numpy.einsum('ij,ji->', df.get_nuc(), dm), 'ref=-10.577490961074622')
print(numpy.einsum('ij,ji->', vj, dm), 'ref=5.3766911667862516')
print(numpy.einsum('ij,ji->', vk, dm), 'ref=8.2255177602309022')
def get_pbc_pvxp(cell, kpts=None):
import numpy
import copy
import time
from pyscf import lib
from pyscf.lib import logger
from pyscf.pbc import tools
from pyscf.gto import mole
from pyscf.pbc.df import ft_ao
from pyscf.pbc.df import aft_jk
from pyscf.pbc.df import aft
if kpts is None:
kpts_lst = numpy.zeros((1,3))
else:
kpts_lst = numpy.reshape(kpts, (-1,3))
log = logger.Logger(cell.stdout, cell.verbose)
t1 = t0 = (time.clock(), time.time())
mydf = aft.AFTDF(cell, kpts)
mydf.eta = 0.2
ke_guess = aft.estimate_ke_cutoff_for_eta(cell, mydf.eta, cell.precision)
mydf.mesh = tools.cutoff_to_mesh(cell.lattice_vectors(), ke_guess)
log.debug('mydf.mesh %s', mydf.mesh)
nkpts = len(kpts_lst)
nao = cell.nao_nr()
nao_pair = nao * (nao+1) // 2
Gv, Gvbase, kws = cell.get_Gv_weights(mydf.mesh)
charge = -cell.atom_charges() # Apply Koseki effective charge?
kpt_allow = numpy.zeros(3)
coulG = tools.get_coulG(cell, kpt_allow, mesh=mydf.mesh, Gv=Gv)
coulG *= kws
if mydf.eta == 0:
soc_mat = numpy.zeros((nkpts,3,nao*nao), dtype=numpy.complex128)
SI = cell.get_SI(Gv)
vG = numpy.einsum('i,ix->x', charge, SI) * coulG
else:
nuccell = copy.copy(cell)
half_sph_norm = .5/numpy.sqrt(numpy.pi)
norm = half_sph_norm/mole.gaussian_int(2, mydf.eta)
chg_env = [mydf.eta, norm]
ptr_eta = cell._env.size
ptr_norm = ptr_eta + 1
chg_bas = [[ia, 0, 1, 1, 0, ptr_eta, ptr_norm, 0] for ia in range(cell.natm)]
nuccell._atm = cell._atm
nuccell._bas = numpy.asarray(chg_bas, dtype=numpy.int32)
nuccell._env = numpy.hstack((cell._env, chg_env))
soc_mat = mydf._int_nuc_vloc(nuccell, kpts_lst, 'int3c2e_pvxp1_sph',
aosym='s1', comp=3)
soc_mat = numpy.asarray(soc_mat).reshape(nkpts,3,nao**2)
t1 = log.timer_debug1('pnucp pass1: analytic int', *t1)
aoaux = ft_ao.ft_ao(nuccell, Gv)
vG = numpy.einsum('i,xi->x', charge, aoaux) * coulG
max_memory = max(2000, mydf.max_memory-lib.current_memory()[0])
for aoaoks, p0, p1 in mydf.ft_loop(mydf.mesh, kpt_allow, kpts_lst,
max_memory=max_memory, aosym='s1',
intor='GTO_ft_pxp_sph', comp=3):
for k, aoao in enumerate(aoaoks):
aoao = aoao.reshape(3,-1,nao**2)
if aft_jk.gamma_point(kpts_lst[k]):
soc_mat[k] += numpy.einsum('k,ckx->cx', vG[p0:p1].real, aoao.real)
soc_mat[k] += numpy.einsum('k,ckx->cx', vG[p0:p1].imag, aoao.imag)
else:
soc_mat[k] += numpy.einsum('k,ckx->cx', vG[p0:p1].conj(), aoao)
t1 = log.timer_debug1('contracting pnucp', *t1)
soc_mat_kpts = []
for k, kpt in enumerate(kpts_lst):
if aft_jk.gamma_point(kpt):
soc_mat_kpts.append(soc_mat[k].real.reshape(3,nao,nao))
else:
soc_mat_kpts.append(soc_mat[k].reshape(3,nao,nao))
if kpts is None or numpy.shape(kpts) == (3,):
soc_mat_kpts = soc_mat_kpts[0]
return numpy.asarray(soc_mat_kpts)