def init_guess_by_wolfsberg_helmholtz(mol):
"""Diagonal will be taken from core hamiltonian, the off diagonal elements
are interpolated by wolfsberg helmholtz scheme.
H_ji = k_ji (H_ii + H_ij) S_ij / 2, with k_ij =1.75
(Generalized Wolfsberg Helmholtz GWH). See here:
http://www.q-chem.com/qchem-website/manual/qchem50_manual/sect-initialguess.html
M. Wolfsberg and L. Helmholz, J. Chem. Phys. 20, 837 (1952).
"""
from pyscf.scf.hf import eig, get_hcore, get_ovlp, get_occ, make_rdm1, SCF
import numpy
H = numpy.diag(get_hcore(mol))
k = numpy.ones((len(H), len(H))) * 1.75 - \
numpy.diag(numpy.ones(H.shape)) * 0.75
S = get_ovlp(mol)
H = k * numpy.add.outer(H, H) * S / 2
mo_energy, mo_coeff = eig(H, S)
mo_occ = get_occ(SCF(mol), mo_energy, mo_coeff)
return make_rdm1(mo_coeff, mo_occ)
def test_band_ase_kpts():
from ase.lattice import bulk
from ase.dft.kpoints import ibz_points, get_bandpath
c = bulk('C', 'diamond', a=3.5668)
print c.get_volume()
points = ibz_points['fcc']
G = points['Gamma']
X = points['X']
W = points['W']
K = points['K']
L = points['L']
band_kpts, x, X = get_bandpath([L, G, X, W, K, G], c.cell, npoints=30)
cell = pbcgto.Cell()
cell.atom = pyscf_ase.ase_atoms_to_pyscf(c)
cell.h = c.cell.T
cell.basis = 'gth-szv'
cell.pseudo = 'gth-pade'
cell.gs = np.array([5, 5, 5])
cell.verbose = 7
cell.build(None, None)
scaled_kpts = ase.dft.kpoints.monkhorst_pack((1, 1, 1))
abs_kpts = cell.get_abs_kpts(scaled_kpts)
kmf = pbckscf.KRKS(cell, abs_kpts)
kmf.analytic_int = False
kmf.xc = 'lda,vwn'
print kmf.scf()
e_kn = []
for kpt in band_kpts:
fb, sb = kmf.get_band_fock_ovlp(kmf.get_hcore() + kmf.get_veff(),
kmf.get_ovlp(), kpt)
e, c = hf.eig(fb, sb)
print kpt, e
e_kn.append(e)
emin = -1
emax = 2
plt.figure(figsize=(5, 6))
nbands = cell.nao_nr()
for n in range(nbands):
plt.plot(x, [e_kn[i][n] for i in range(len(x))])
for p in X:
plt.plot([p, p], [emin, emax], 'k-')
plt.plot([0, X[-1]], [0, 0], 'k-')
plt.xticks(X, ['$%s$' % n for n in ['L', 'G', 'X', 'W', 'K', r'\Gamma']])
plt.axis(xmin=0, xmax=X[-1], ymin=emin, ymax=emax)
plt.xlabel('k-vector')
plt.show()
def eig(mf, h, s):
'''Solve generalized eigenvalue problem, for each irrep. The
eigenvalues and eigenvectors are not sorted to ascending order.
Instead, they are grouped based on irreps.
'''
if not mf.mol.symmetry:
return hf.eig(h, s)
nirrep = mf.mol.symm_orb.__len__()
h = symm.symmetrize_matrix(h, mf.mol.symm_orb)
s = symm.symmetrize_matrix(s, mf.mol.symm_orb)
cs = []
es = []
for ir in range(nirrep):
e, c = hf.eig(h[ir], s[ir])
cs.append(c)
es.append(e)
e = numpy.hstack(es)
c = so2ao_mo_coeff(mf.mol.symm_orb, cs)
return e, c
def eig(mf, h, s):
'''Solve generalized eigenvalue problem, for each irrep. The
eigenvalues and eigenvectors are not sorted to ascending order.
Instead, they are grouped based on irreps.
'''
if not mf.mol.symmetry:
return hf.eig(h, s)
nirrep = mf.mol.symm_orb.__len__()
h = symm.symmetrize_matrix(h, mf.mol.symm_orb)
s = symm.symmetrize_matrix(s, mf.mol.symm_orb)
cs = []
es = []
for ir in range(nirrep):
e, c = hf.eig(h[ir], s[ir])
cs.append(c)
es.append(e)
e = numpy.hstack(es)
c = so2ao_mo_coeff(mf.mol.symm_orb, cs)
return e, c
def test_band_ase_kpts():
from ase.lattice import bulk
from ase.dft.kpoints import ibz_points, get_bandpath
c = bulk('C', 'diamond', a=3.5668)
print c.get_volume()
points = ibz_points['fcc']
G = points['Gamma']
X = points['X']
W = points['W']
K = points['K']
L = points['L']
band_kpts, x, X = get_bandpath([L, G, X, W, K, G], c.cell, npoints=30)
cell = pbcgto.Cell()
cell.atom=pyscf_ase.ase_atoms_to_pyscf(c)
cell.a=c.cell
cell.basis = 'gth-szv'
cell.pseudo = 'gth-pade'
cell.gs=np.array([5,5,5])
cell.verbose=7
cell.build(None,None)
scaled_kpts=ase.dft.kpoints.monkhorst_pack((1,1,1))
abs_kpts=cell.get_abs_kpts(scaled_kpts)
kmf = pbckscf.KRKS(cell, abs_kpts)
kmf.analytic_int=False
kmf.xc = 'lda,vwn'
print kmf.scf()
e_kn = []
for kpt in band_kpts:
fb, sb=kmf.get_band_fock_ovlp(kmf.get_hcore()+kmf.get_veff(),
kmf.get_ovlp(), kpt)
e, c=hf.eig(fb, sb)
print kpt, e
e_kn.append(e)
emin = -1
emax = 2
plt.figure(figsize=(5, 6))
nbands = cell.nao_nr()
for n in range(nbands):
plt.plot(x, [e_kn[i][n] for i in range(len(x))])
for p in X:
plt.plot([p, p], [emin, emax], 'k-')
plt.plot([0, X[-1]], [0, 0], 'k-')
plt.xticks(X, ['$%s$' % n for n in ['L', 'G', 'X', 'W', 'K', r'\Gamma']])
plt.axis(xmin=0, xmax=X[-1], ymin=emin, ymax=emax)
plt.xlabel('k-vector')
plt.show()
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 = self.get_hcore(cell, kpt_band)
fock = fock + self.get_veff(cell, dm_kpts, kpts=kpts, kpt_band=kpt_band)
s1e = self.get_ovlp(cell, kpt_band)
mo_energy, mo_coeff = hf.eig(fock, s1e)
return mo_energy, mo_coeff
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 = self.get_hcore(cell, kpt_band)
fock = fock + self.get_veff(
cell, dm_kpts, kpts=kpts, kpt_band=kpt_band)
s1e = self.get_ovlp(cell, kpt_band)
mo_energy, mo_coeff = hf.eig(fock, s1e)
return mo_energy, mo_coeff