#!/usr/bin/env python
'''
Gamma point Hartree-Fock/DFT
The 2-electron integrals are computed using Poisson solver with FFT by default.
In most scenario, it should be used with pseudo potential.
'''
# Note import path which is different to molecule code
from pyscf.pbc import gto, scf, dft
import numpy
cell = gto.Cell()
# .a is a matrix for lattice vectors.
cell.a = '''
3.5668 0 0
0 3.5668 0
0 0 3.5668'''
cell.atom = '''C 0. 0. 0.
C 0.8917 0.8917 0.8917
C 1.7834 1.7834 0.
C 2.6751 2.6751 0.8917
C 1.7834 0. 1.7834
C 2.6751 0.8917 2.6751
C 0. 1.7834 1.7834
C 0.8917 2.6751 2.6751'''
cell.basis = 'gth-szv'
cell.pseudo = 'gth-pade'
cell.verbose = 4
cell.build()
-1, 1)
Lpq = numpy.empty((self.blockdim, ao_pairs_G.shape[1]))
for p0, p1 in lib.prange(0, ngrids, blksize):
Lpq[:p1 - p0] = ao_pairs_G[p0:p1].real
yield Lpq[:p1 - p0]
Lpq[:p1 - p0] = ao_pairs_G[p0:p1].imag
yield Lpq[:p1 - p0]
def get_naoaux(self):
mesh = numpy.asarray(self.mesh)
ngrids = numpy.prod(mesh)
return ngrids * 2
if __name__ == '__main__':
from pyscf.pbc import gto as pbcgto
cell = pbcgto.Cell()
cell.verbose = 0
cell.atom = 'C 0 0 0; C 1 1 1; C 0 2 2; C 2 0 2'
cell.a = numpy.diag([4, 4, 4])
cell.basis = 'gth-szv'
cell.pseudo = 'gth-pade'
cell.mesh = [20] * 3
cell.build()
k = numpy.ones(3) * .25
df = FFTDF(cell)
v1 = get_pp(df, k)
print(lib.finger(v1) - (1.8428463642697195 - 0.10478381725330854j))
v1 = get_nuc(df, k)
print(lib.finger(v1) - (2.3454744614944714 - 0.12528407127454744j))
vk = vkR + vkI * 1j
if cell.dimension != 3 and exxdiv:
assert (exxdiv.lower() == 'ewald')
_ewald_exxdiv_for_G0(cell, kpt, dms, vk)
vk = vk.reshape(dm.shape)
return vj, vk
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
#!/usr/bin/env python
from pyscf.pbc import df, scf
### generated system text ###
from numpy import array
from pyscf.pbc import gto as gto_loc
cell = gto_loc.Cell()
cell.a = '''
1.78500000 1.78500000 0.00000000
0.00000000 1.78500000 1.78500000
1.78500000 0.00000000 1.78500000
'''
cell.basis = 'bfd-vdz'
cell.dimension = 3
cell.ecp = 'bfd'
cell.unit = 'A'
cell.atom = '''
C 0.00000000 0.00000000 0.00000000
C 0.89250000 0.89250000 0.89250000
'''
cell.drop_exponent = 0.1
cell.verbose = 5
cell.charge = 0
cell.spin = 0
cell.build()
kpts = array([
[0.0, 0.0, 0.0]])
### end generated system text ###
def setUpClass(cls):
k_grid = [2, 1, 1]
# Unit cell
cls.cell = gto.Cell()
cls.cell.atom = '''
C 0.000000000000 0.000000000000 0.000000000000
C 1.685068664391 1.685068664391 1.685068664391
'''
cls.cell.basis = 'gth-szv'
cls.cell.pseudo = 'gth-pade'
cls.cell.a = '''
0.000000000, 3.370137329, 3.370137329
3.370137329, 0.000000000, 3.370137329
3.370137329, 3.370137329, 0.000000000
'''
cls.cell.unit = 'B'
cls.cell.verbose = 7
cls.cell.mesh = [24] * 3
cls.cell.build()
# MF
cls.mf = scf.KRHF(cls.cell, kpts=cls.cell.make_kpts(k_grid), exxdiv=None)
cls.mf.chkfile = 'test_kgf_proper_rhf_chk.dat'
if os.path.exists(cls.mf.chkfile):
cls.mf.update()
else:
cls.mf.kernel()
# Supercell
cls.cell2 = super_cell(cls.cell, k_grid)
cls.mf2 = scf.KRHF(cls.cell2, exxdiv=None)
cls.order = numpy.argsort(numpy.hstack(cls.mf.mo_energy))
c1 = cls.mf.mo_coeff[0]
c2 = cls.mf.mo_coeff[1]
c1, c2 = numpy.concatenate((c1, c1), axis=0) / 2.**.5, numpy.concatenate((c2, -c2), axis=0) / 2.**.5
cls.mf2.mo_coeff = [numpy.concatenate((c1, c2), axis=1)[:, cls.order]]
cls.mf2.mo_energy = [numpy.concatenate(cls.mf.mo_energy)[cls.order]]
cls.mf2.mo_occ = [numpy.concatenate(cls.mf.mo_occ)[cls.order]]
cls.mf2.make_rdm1()
# CCSD
cls.ccsd = cc.KRCCSD(cls.mf)
cls.ccsd.conv_tol_normt = 1e-8
cls.ccsd.kernel()
cls.ccsd2 = cc.KRCCSD(cls.mf2)
cls.ccsd2.conv_tol_normt = 1e-8
cls.ccsd2.kernel()
# TODO: lambda iterations
cls.ccsd.l1 = cls.ccsd.t1
cls.ccsd.l2 = cls.ccsd.t2
# cls.ccsd.ipccsd(nroots=2)
# cls.ccsd.eaccsd(nroots=2)
# cls.ip_samples = [-0.71, -1]
cls.ip_samples = [-0.71]
cls.ea_samples = [1.13, 0.3]
cls.eta = 0.01
# =====
cls.nocc, cls.nvirt = cls.ccsd.t1[0].shape
cls.nmo = cls.nocc + cls.nvirt
cls.o1 = cls.order[:2*cls.nocc] < cls.nmo
cls.o2 = cls.order[:2*cls.nocc] >= cls.nmo
cls.v1 = cls.order[2*cls.nocc:] < cls.nmo
cls.v2 = cls.order[2*cls.nocc:] >= cls.nmo
cls.a1 = cls.order < cls.nmo
cls.a2 = cls.order >= cls.nmo
# =====
cls.ccsd2.l1 = cls.ccsd2.t1
cls.ccsd2.l2 = cls.ccsd2.t2
def test_h4_fcc_k2_frozen(self):
'''Metallic hydrogen fcc lattice with frozen lowest lying occupied
and highest lying virtual orbitals. Checks versus a corresponding
supercell calculation.
NOTE: different versions of the davidson may converge to a different
solution for the k-point IP/EA eom. If you're getting the wrong
root, check to see if it's contained in the supercell set of
eigenvalues.'''
cell = pbcgto.Cell()
cell.atom = [['H', (0.000000000, 0.000000000, 0.000000000)],
['H', (0.000000000, 0.500000000, 0.250000000)],
['H', (0.500000000, 0.500000000, 0.500000000)],
['H', (0.500000000, 0.000000000, 0.750000000)]]
cell.unit = 'Bohr'
cell.a = [[1., 0., 0.], [0., 1., 0], [0, 0, 2.2]]
cell.verbose = 7
cell.spin = 0
cell.charge = 0
cell.basis = [
[0, [1.0, 1]],
]
cell.pseudo = 'gth-pade'
cell.output = '/dev/null'
#cell.max_memory = 1000
for i in range(len(cell.atom)):
cell.atom[i][1] = tuple(
np.dot(np.array(cell.atom[i][1]), np.array(cell.a)))
cell.build()
nmp = [2, 1, 1]
kmf = pbcscf.KRHF(cell)
kmf.kpts = cell.make_kpts(nmp, scaled_center=[0.0, 0.0, 0.0])
e = kmf.kernel()
frozen = [[0, 3], []]
mycc = pbcc.KCCSD(kmf, frozen=frozen)
ekccsd, _, _ = mycc.kernel()
self.assertAlmostEqual(ekccsd, -0.04683399814247455, 6)
# Getting more roots than 1 is difficult
e = mycc.eaccsd(nroots=1, koopmans=False, kptlist=(0, ))[0]
self.assertAlmostEqual(e[0][0], 5.060562738181741, 6)
e = mycc.eaccsd(nroots=1, koopmans=False, kptlist=(1, ))[0]
self.assertAlmostEqual(e[0][0], 4.188511644938458, 6)
e = mycc.ipccsd(nroots=1, koopmans=False, kptlist=(0, ))[0]
self.assertAlmostEqual(e[0][0], -3.477663551987023, 6)
e = mycc.ipccsd(nroots=1, koopmans=False, kptlist=(1, ))[0]
self.assertAlmostEqual(e[0][0], -4.23523412155825, 6)
# Start of supercell calculations
from pyscf.pbc.tools.pbc import super_cell
supcell = super_cell(cell, nmp)
supcell.build()
mf = pbcscf.KRHF(supcell)
e = mf.kernel()
myscc = pbcc.KCCSD(mf, frozen=[0, 7])
eccsd, _, _ = myscc.kernel()
eccsd /= np.prod(nmp)
self.assertAlmostEqual(eccsd, -0.04683401678904569, 6)
e = myscc.eaccsd(nroots=4, koopmans=False, kptlist=(0, ))[0]
self.assertAlmostEqual(e[0][0], 4.188511680212755, 6)
self.assertAlmostEqual(e[0][1], 4.205924087610756, 6)
self.assertAlmostEqual(e[0][2], 5.060562771978923, 6)
self.assertAlmostEqual(e[0][3], 5.077249823137741, 6)
e = myscc.ipccsd(nroots=4, koopmans=False, kptlist=(0, ))[0]
self.assertAlmostEqual(e[0][0], -4.261818242746091, 6)
self.assertAlmostEqual(e[0][1], -4.235233956876479, 6)
self.assertAlmostEqual(e[0][2], -3.477663568390151, 6)
self.assertAlmostEqual(e[0][3], -3.459133332687474, 6)
def test_h4_fcc_k2(self):
'''Metallic hydrogen fcc lattice. Checks versus a corresponding
supercell calculation.
NOTE: different versions of the davidson may converge to a different
solution for the k-point IP/EA eom. If you're getting the wrong
root, check to see if it's contained in the supercell set of
eigenvalues.'''
cell = pbcgto.Cell()
cell.atom = [['H', (0.000000000, 0.000000000, 0.000000000)],
['H', (0.000000000, 0.500000000, 0.250000000)],
['H', (0.500000000, 0.500000000, 0.500000000)],
['H', (0.500000000, 0.000000000, 0.750000000)]]
cell.unit = 'Bohr'
cell.a = [[1., 0., 0.], [0., 1., 0], [0, 0, 2.2]]
cell.verbose = 7
cell.spin = 0
cell.charge = 0
cell.basis = [
[0, [1.0, 1]],
]
cell.pseudo = 'gth-pade'
cell.output = '/dev/null'
#cell.max_memory = 1000
for i in range(len(cell.atom)):
cell.atom[i][1] = tuple(
np.dot(np.array(cell.atom[i][1]), np.array(cell.a)))
cell.build()
nmp = [2, 1, 1]
kmf = pbcscf.KRHF(cell)
kmf.kpts = cell.make_kpts(nmp, scaled_center=[0.0, 0.0, 0.0])
e = kmf.kernel()
mycc = pbcc.KCCSD(kmf)
ekccsd, _, _ = mycc.kernel()
self.assertAlmostEqual(ekccsd, -0.06146759560406628, 6)
# Getting more roots than 1 is difficult
e = mycc.eaccsd(nroots=1, koopmans=False, kptlist=(0, ))[0]
self.assertAlmostEqual(e[0][0], 5.079427283440857, 6)
e = mycc.eaccsd(nroots=1, koopmans=False, kptlist=(1, ))[0]
self.assertAlmostEqual(e[0][0], 4.183328878177331, 6)
e = mycc.ipccsd(nroots=1, koopmans=False, kptlist=(0, ))[0]
self.assertAlmostEqual(e[0][0], -3.471710821544506, 6)
e = mycc.ipccsd(nroots=1, koopmans=False, kptlist=(1, ))[0]
self.assertAlmostEqual(e[0][0], -4.272015727359054, 6)
# Start of supercell calculations
from pyscf.pbc.tools.pbc import super_cell
supcell = super_cell(cell, nmp)
supcell.build()
mf = pbcscf.KRHF(supcell)
e = mf.kernel()
myscc = pbcc.KCCSD(mf)
eccsd, _, _ = myscc.kernel()
eccsd /= np.prod(nmp)
self.assertAlmostEqual(eccsd, -0.06146759560406628, 6)
e = myscc.eaccsd(nroots=4, koopmans=False, kptlist=(0, ))[0]
self.assertAlmostEqual(e[0][0], 4.183328873793568, 6)
self.assertAlmostEqual(e[0][1], 4.225034294249784, 6)
self.assertAlmostEqual(e[0][2], 5.068962665511664, 6)
self.assertAlmostEqual(e[0][3], 5.07942727935064, 6)
e = myscc.ipccsd(nroots=4, koopmans=False, kptlist=(0, ))[0]
self.assertAlmostEqual(e[0][0], -4.272015724869052, 6)
self.assertAlmostEqual(e[0][1], -4.254298274388934, 6)
self.assertAlmostEqual(e[0][2], -3.471710821688812, 6)
self.assertAlmostEqual(e[0][3], -3.462817764320668, 6)
# limitations under the License.
#
# Author: Qiming Sun <*****@*****.**>
#
import unittest
import ctypes
import numpy
import numpy as np
from pyscf import gto
from pyscf import lib
from pyscf.pbc import gto as pgto
L = 1.5
n = 41
cl = pgto.Cell()
cl.build(a=[[L, 0, 0], [0, L, 0], [0, 0, L]],
mesh=[n, n, n],
atom='He %f %f %f' % ((L / 2., ) * 3),
basis='ccpvdz')
numpy.random.seed(1)
cl1 = pgto.Cell()
cl1.build(a=numpy.random.random((3, 3)).T,
precision=1e-9,
mesh=[n, n, n],
atom='''He .1 .0 .0
He .5 .1 .0
He .0 .5 .0
He .1 .3 .2''',
basis='ccpvdz')
def test_k_kpts_2(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.h = numpy.eye(3) * 2.5
cell.gs = [5] * 3
cell.build()
kpts = cell.make_kpts((2, 2, 2))
numpy.random.seed(1)
nao = cell.nao_nr()
dm = numpy.random.random((8, nao, nao))
mydf = mdf.MDF(cell)
mydf.kpts = kpts
mydf.auxbasis = 'weigend'
mydf.exxdiv = None
vk = mdf_jk.get_k_kpts(mydf, dm, 0, mydf.kpts)
self.assertAlmostEqual(finger(vk[0]),
(0.54167993564799133 - 0.0078722013632614562j),
9)
self.assertAlmostEqual(finger(vk[1]),
(0.3593714867663208 + 0.0036054974436528706j),
9)
self.assertAlmostEqual(finger(vk[2]),
(0.46234927585203783 - 0.0065043520189423856j),
9)
self.assertAlmostEqual(finger(vk[3]),
(0.63626519337979948 + 0.0075118282426430818j),
9)
self.assertAlmostEqual(finger(vk[4]),
(0.53630228285345427 - 0.0076423773076679524j),
9)
self.assertAlmostEqual(finger(vk[5]),
(0.4956577130753681 + 0.0060590034846796439j),
9)
self.assertAlmostEqual(finger(vk[6]),
(0.45380714659933519 - 0.0068616367194157396j),
9)
self.assertAlmostEqual(finger(vk[7]),
(0.41808297427780505 + 0.0051096506509061114j),
9)
numpy.random.seed(1)
dm = numpy.random.random((8, nao, nao))
dm = dm + dm.transpose(0, 2, 1)
vk = mdf_jk.get_k_kpts(mydf, dm, 1, mydf.kpts)
self.assertAlmostEqual(finger(vk[0]),
(1.0929902110020242 - 0.014742288503285355j), 9)
self.assertAlmostEqual(finger(vk[1]),
(0.72006803096300986 + 0.0086853082996361259j),
9)
self.assertAlmostEqual(finger(vk[2]),
(0.89763598759314234 - 0.011090943227218j), 9)
self.assertAlmostEqual(finger(vk[3]),
(1.2594746237554506 + 0.015976836949610319j), 9)
self.assertAlmostEqual(finger(vk[4]),
(1.0482108645807622 - 0.012426406003793576j), 9)
self.assertAlmostEqual(finger(vk[5]),
(0.99174830962018801 + 0.012694552375379626j),
9)
self.assertAlmostEqual(finger(vk[6]),
(0.9208432538335829 - 0.01203638564702492j), 9)
self.assertAlmostEqual(finger(vk[7]),
(0.8508739289672812 + 0.010089099047683993j), 9)
def test_eomea_matvec(self):
cell = gto.Cell()
cell.atom = '''
He 0.000000000000 0.000000000000 0.000000000000
He 1.685068664391 1.685068664391 1.685068664391
'''
cell.basis = [[0, (1., 1.)], [0, (.5, 1.)]]
cell.a = '''
0.000000000, 3.370137329, 3.370137329
3.370137329, 0.000000000, 3.370137329
3.370137329, 3.370137329, 0.000000000'''
cell.unit = 'B'
cell.mesh = [13] * 3
cell.build()
np.random.seed(2)
kmf = pbcscf.KUHF(cell, kpts=cell.make_kpts([1, 1, 3]), exxdiv=None)
nmo = cell.nao_nr()
kmf.mo_occ = np.zeros((2, 3, nmo))
kmf.mo_occ[0, :, :3] = 1
kmf.mo_occ[1, :, :1] = 1
kmf.mo_energy = np.arange(nmo) + np.random.random((2, 3, nmo)) * .3
kmf.mo_energy[kmf.mo_occ == 0] += 2
mo = (np.random.random((2, 3, nmo, nmo)) + np.random.random(
(2, 3, nmo, nmo)) * 1j - .5 - .5j)
s = kmf.get_ovlp()
kmf.mo_coeff = np.empty_like(mo)
nkpts = len(kmf.kpts)
for k in range(nkpts):
kmf.mo_coeff[0, k] = lo.orth.vec_lowdin(mo[0, k], s[k])
kmf.mo_coeff[1, k] = lo.orth.vec_lowdin(mo[1, k], s[k])
def rand_t1_t2(mycc):
nkpts = mycc.nkpts
nocca, noccb = mycc.nocc
nmoa, nmob = mycc.nmo
nvira, nvirb = nmoa - nocca, nmob - noccb
np.random.seed(1)
t1a = (np.random.random((nkpts, nocca, nvira)) + np.random.random(
(nkpts, nocca, nvira)) * 1j - .5 - .5j)
t1b = (np.random.random((nkpts, noccb, nvirb)) + np.random.random(
(nkpts, noccb, nvirb)) * 1j - .5 - .5j)
t2aa = (
np.random.random(
(nkpts, nkpts, nkpts, nocca, nocca, nvira, nvira)) +
np.random.random(
(nkpts, nkpts, nkpts, nocca, nocca, nvira, nvira)) * 1j -
.5 - .5j)
kconserv = kpts_helper.get_kconserv(kmf.cell, kmf.kpts)
t2aa = t2aa - t2aa.transpose(1, 0, 2, 4, 3, 5, 6)
tmp = t2aa.copy()
for ki, kj, kk in kpts_helper.loop_kkk(nkpts):
kl = kconserv[ki, kk, kj]
t2aa[ki, kj,
kk] = t2aa[ki, kj, kk] - tmp[ki, kj, kl].transpose(
0, 1, 3, 2)
t2ab = (
np.random.random(
(nkpts, nkpts, nkpts, nocca, noccb, nvira, nvirb)) +
np.random.random(
(nkpts, nkpts, nkpts, nocca, noccb, nvira, nvirb)) * 1j -
.5 - .5j)
t2bb = (
np.random.random(
(nkpts, nkpts, nkpts, noccb, noccb, nvirb, nvirb)) +
np.random.random(
(nkpts, nkpts, nkpts, noccb, noccb, nvirb, nvirb)) * 1j -
.5 - .5j)
t2bb = t2bb - t2bb.transpose(1, 0, 2, 4, 3, 5, 6)
tmp = t2bb.copy()
for ki, kj, kk in kpts_helper.loop_kkk(nkpts):
kl = kconserv[ki, kk, kj]
t2bb[ki, kj,
kk] = t2bb[ki, kj, kk] - tmp[ki, kj, kl].transpose(
0, 1, 3, 2)
t1 = (t1a, t1b)
t2 = (t2aa, t2ab, t2bb)
return t1, t2
mycc = pbcc.KUCCSD(kmf)
t1, t2 = rand_t1_t2(mycc)
mycc.t1 = t1
mycc.t2 = t2
eris = mycc.ao2mo()
eom = EOMEA(mycc)
imds = eom.make_imds(eris)
np.random.seed(9)
vector = np.random.random(eom.vector_size())
hc = eom.matvec(vector, 0, imds)
self.assertAlmostEqual(lib.finger(hc),
(4.126336947439054 + 0.5931985341760211j), 9)
hc = eom.matvec(vector, 1, imds)
self.assertAlmostEqual(lib.finger(hc),
(1.248516714348047 + 2.310336141756983j), 9)
hc = eom.matvec(vector, 2, imds)
self.assertAlmostEqual(lib.finger(hc),
(-3.4529892564020126 - 5.093287166283228j), 9)
kmf = kmf.density_fit(auxbasis=[[0, (2.,
1.)], [0, (1.,
1.)], [0, (.5, 1.)]])
mycc._scf = kmf
mycc.max_memory = 0
eris = mycc.ao2mo()
imds = eom.make_imds(eris)
hc = eom.matvec(vector, 0, imds)
self.assertAlmostEqual(lib.finger(hc),
(4.045928342346641 + 0.5861843966140339j), 9)
hc = eom.matvec(vector, 1, imds)
self.assertAlmostEqual(lib.finger(hc),
(1.2695743252320795 + 2.28060203958305j), 9)
hc = eom.matvec(vector, 2, imds)
self.assertAlmostEqual(lib.finger(hc),
(-3.435385905375094 - 5.0991524119952505j), 9)
mycc.max_memory = 4000
eris = mycc.ao2mo()
imds = eom.make_imds(eris)
hc = eom.matvec(vector, 0, imds)
self.assertAlmostEqual(lib.finger(hc),
(4.045928342346641 + 0.5861843966140339j), 9)
hc = eom.matvec(vector, 1, imds)
self.assertAlmostEqual(lib.finger(hc),
(1.2695743252320795 + 2.28060203958305j), 9)
hc = eom.matvec(vector, 2, imds)
self.assertAlmostEqual(lib.finger(hc),
(-3.435385905375094 - 5.0991524119952505j), 9)
