def get_bands(self, kpt_band, cell=None, dm_kpts=None, kpts=None):
'''Get energy bands at a given (arbitrary) 'band' k-point.
Returns:
mo_energy : (nao,) ndarray
Bands energies E_n(k)
mo_coeff : (nao, nao) ndarray
Band orbitals psi_n(k)
'''
if cell is None: cell = self.cell
if dm_kpts is None: dm_kpts = self.make_rdm1()
if kpts is None: kpts = self.kpts
fock = pbchf.get_hcore(cell, kpt_band) \
+ self.get_veff(kpts=kpts, kpt_band=kpt_band)
s1e = pbchf.get_ovlp(cell, kpt_band)
mo_energy, mo_coeff = pyscf.scf.hf.eig(fock, s1e)
return mo_energy, mo_coeff
def get_ovlp(mf, cell, kpts):
'''Get the overlap AO matrices at sampled k-points.
Args:
kpts : (nkpts, 3) ndarray
Returns:
ovlp_kpts : (nkpts, nao, nao) ndarray
'''
nkpts = len(kpts)
nao = cell.nao_nr()
ovlp_kpts = np.zeros((nkpts,nao,nao), np.complex128)
for k in range(nkpts):
kpt = kpts[k,:]
if mf.analytic_int:
ovlp_kpts[k,:,:] = scfint.get_ovlp(cell, kpt)
else:
ovlp_kpts[k,:,:] = pbchf.get_ovlp(cell, kpt)
return ovlp_kpts
def test_components(pseudo=None):
# The molecular calculation
mol = gto.Mole()
mol.unit = 'B'
L = 60
mol.atom.extend([['He', (L/2.,L/2.,L/2.)], ])
mol.basis = 'sto-3g'
mol.build()
m = rks.RKS(mol)
m.xc = 'LDA,VWN_RPA'
print(m.scf()) # -2.90705411168
dm = m.make_rdm1()
# The periodic calculation
cell = pbcgto.Cell()
cell.unit = 'B'
cell.a = np.diag([L,L,L])
cell.gs = np.array([80,80,80])
cell.atom = mol.atom
cell.basis = mol.basis
cell.pseudo = pseudo
cell.build()
# These should match reasonably well (roughly with accuracy of normalization)
print "Kinetic energy"
tao = pbchf.get_t(cell)
tao2 = mol.intor_symmetric('cint1e_kin_sph')
print np.dot(np.ravel(tao), np.ravel(dm)) # 2.82793077196
print np.dot(np.ravel(tao2), np.ravel(dm)) # 2.82352636524
print "Overlap"
sao = pbchf.get_ovlp(cell)
print np.dot(np.ravel(sao), np.ravel(dm)) # 1.99981725342
print np.dot(np.ravel(m.get_ovlp()), np.ravel(dm)) # 2.0
# The next two entries should *not* match, since G=0 component is removed
print "Coulomb (G!=0)"
jao = pbchf.get_j(cell, dm)
print np.dot(np.ravel(dm),np.ravel(jao)) # 4.03425518427
print np.dot(np.ravel(dm),np.ravel(m.get_j(dm))) # 4.22285177049
# The next two entries should *not* match, since G=0 component is removed
print "Nuc-el (G!=0)"
if cell.pseudo:
vppao = pbchf.get_pp(cell)
print np.dot(np.ravel(dm), np.ravel(vppao))
else:
neao = pbchf.get_nuc(cell)
print np.dot(np.ravel(dm), np.ravel(neao)) # -6.50203360062
vne = mol.intor_symmetric('cint1e_nuc_sph')
print np.dot(np.ravel(dm), np.ravel(vne)) # -6.68702326551
print "Normalization"
coords = gen_uniform_grids(cell)
aoR = eval_ao(cell, coords)
rhoR = eval_rho(cell, aoR, dm)
print cell.vol/len(rhoR)*np.sum(rhoR) # 1.99981725342 (should be 2.0)
print "(Hartree + vne) * DM"
print np.dot(np.ravel(dm),np.ravel(m.get_j(dm)))+np.dot(np.ravel(dm), np.ravel(vne))
if cell.pseudo:
print np.einsum("ij,ij", dm, vppao + jao + pbchf.get_jvloc_G0(cell))
else:
print np.einsum("ij,ij", dm, neao + jao)
ew_cut = (40,40,40)
ew_eta = 0.05
for ew_eta in [0.1, 0.5, 1.]:
ew = pbchf.ewald(cell, ew_eta, ew_cut)
print "Ewald (eta, energy)", ew_eta, ew # should be same for all eta
print "Ewald divergent terms summation", ew
# These two should now match if the box is reasonably big to
# remove images, and ngs is big.
print "Total coulomb (analytic) ",
print (.5*np.dot(np.ravel(dm), np.ravel(m.get_j(dm)))
+ np.dot(np.ravel(dm), np.ravel(vne)) ) # -4.57559738004
if not cell.pseudo:
print "Total coulomb (fft coul + ewald)",
print np.einsum("ij,ij", dm, neao + .5*jao) + ew # -4.57948259115
# Exc
cell.ew_eta, cell.ew_cut = ew_eta, ew_cut
mf = pbcdft.RKS(cell)
mf.xc = 'LDA,VWN_RPA'
rks.get_veff(mf, cell, dm)
print "Exc", mf._exc # -1.05967570089
def test_components(pseudo=None):
# The molecular calculation
mol = gto.Mole()
mol.unit = 'B'
L = 60
mol.atom.extend([
['He', (L / 2., L / 2., L / 2.)],
])
mol.basis = 'sto-3g'
mol.build()
m = rks.RKS(mol)
m.xc = 'LDA,VWN_RPA'
print(m.scf()) # -2.90705411168
dm = m.make_rdm1()
# The periodic calculation
cell = pbcgto.Cell()
cell.unit = 'B'
cell.a = np.diag([L, L, L])
cell.gs = np.array([80, 80, 80])
cell.atom = mol.atom
cell.basis = mol.basis
cell.pseudo = pseudo
cell.build()
# These should match reasonably well (roughly with accuracy of normalization)
print "Kinetic energy"
tao = pbchf.get_t(cell)
tao2 = mol.intor_symmetric('cint1e_kin_sph')
print np.dot(np.ravel(tao), np.ravel(dm)) # 2.82793077196
print np.dot(np.ravel(tao2), np.ravel(dm)) # 2.82352636524
print "Overlap"
sao = pbchf.get_ovlp(cell)
print np.dot(np.ravel(sao), np.ravel(dm)) # 1.99981725342
print np.dot(np.ravel(m.get_ovlp()), np.ravel(dm)) # 2.0
# The next two entries should *not* match, since G=0 component is removed
print "Coulomb (G!=0)"
jao = pbchf.get_j(cell, dm)
print np.dot(np.ravel(dm), np.ravel(jao)) # 4.03425518427
print np.dot(np.ravel(dm), np.ravel(m.get_j(dm))) # 4.22285177049
# The next two entries should *not* match, since G=0 component is removed
print "Nuc-el (G!=0)"
if cell.pseudo:
vppao = pbchf.get_pp(cell)
print np.dot(np.ravel(dm), np.ravel(vppao))
else:
neao = pbchf.get_nuc(cell)
print np.dot(np.ravel(dm), np.ravel(neao)) # -6.50203360062
vne = mol.intor_symmetric('cint1e_nuc_sph')
print np.dot(np.ravel(dm), np.ravel(vne)) # -6.68702326551
print "Normalization"
coords = gen_uniform_grids(cell)
aoR = eval_ao(cell, coords)
rhoR = eval_rho(cell, aoR, dm)
print cell.vol / len(rhoR) * np.sum(rhoR) # 1.99981725342 (should be 2.0)
print "(Hartree + vne) * DM"
print np.dot(np.ravel(dm), np.ravel(m.get_j(dm))) + np.dot(
np.ravel(dm), np.ravel(vne))
if cell.pseudo:
print np.einsum("ij,ij", dm, vppao + jao + pbchf.get_jvloc_G0(cell))
else:
print np.einsum("ij,ij", dm, neao + jao)
ew_cut = (40, 40, 40)
ew_eta = 0.05
for ew_eta in [0.1, 0.5, 1.]:
ew = pbchf.ewald(cell, ew_eta, ew_cut)
print "Ewald (eta, energy)", ew_eta, ew # should be same for all eta
print "Ewald divergent terms summation", ew
# These two should now match if the box is reasonably big to
# remove images, and ngs is big.
print "Total coulomb (analytic) ",
print(.5 * np.dot(np.ravel(dm), np.ravel(m.get_j(dm))) +
np.dot(np.ravel(dm), np.ravel(vne))) # -4.57559738004
if not cell.pseudo:
print "Total coulomb (fft coul + ewald)",
print np.einsum("ij,ij", dm, neao + .5 * jao) + ew # -4.57948259115
# Exc
cell.ew_eta, cell.ew_cut = ew_eta, ew_cut
mf = pbcdft.RKS(cell)
mf.xc = 'LDA,VWN_RPA'
rks.get_veff(mf, cell, dm)
print "Exc", mf._exc # -1.05967570089
def test_overlap20(self):
mol, cell = make_cell2(20, 20)
sao = pbchf.get_ovlp(cell)
self.assertAlmostEqual(finger(sao), -0.8503588722723614, 9)
def test_ovlp_uniform(self):
mol, cell = make_cell2(4, 40)
sao = pbchf.get_ovlp(cell)
s0 = pscf.scfint.get_ovlp(cell)
self.assertAlmostEqual(np.linalg.norm(sao-s0), 0, 9)