def eig(self, h, s):
mol = self.mol
if not mol.symmetry:
return self._eigh(h, s)
nirrep = mol.symm_orb.__len__()
s = symm.symmetrize_matrix(s, mol.symm_orb)
ha = symm.symmetrize_matrix(h[0], mol.symm_orb)
cs = []
es = []
orbsym = []
for ir in range(nirrep):
e, c = self._eigh(ha[ir], s[ir])
cs.append(c)
es.append(e)
orbsym.append([mol.irrep_id[ir]] * e.size)
ea = numpy.hstack(es)
ca = hf_symm.so2ao_mo_coeff(mol.symm_orb, cs)
ca = hf_symm.attach_orbsym(ca, numpy.hstack(orbsym))
hb = symm.symmetrize_matrix(h[1], mol.symm_orb)
cs = []
es = []
orbsym = []
for ir in range(nirrep):
e, c = self._eigh(hb[ir], s[ir])
cs.append(c)
es.append(e)
orbsym.append([mol.irrep_id[ir]] * e.size)
eb = numpy.hstack(es)
cb = hf_symm.so2ao_mo_coeff(mol.symm_orb, cs)
cb = hf_symm.attach_orbsym(cb, numpy.hstack(orbsym))
return numpy.array((ea, eb)), (ca, cb)
def eig(self, 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.
'''
mol = self.mol
if not mol.symmetry:
return self._eigh(h, s)
nirrep = mol.symm_orb.__len__()
h = symm.symmetrize_matrix(h, mol.symm_orb)
s = symm.symmetrize_matrix(s, mol.symm_orb)
partner_ir = [self.partner_irrep(ir, mol.groupname) for ir in mol.irrep_id]
for ir in range(nirrep):
if ir > 0 and mol.irrep_id[ir-1] == partner_ir[ir]:
h_av = (h[ir] + h[ir-1])/2
h[ir] = h[ir-1] = h_av
cs = []
es = []
orbsym = []
for ir in range(nirrep):
e, c = self._eigh(h[ir], s[ir])
cs.append(c)
es.append(e)
orbsym.append([mol.irrep_id[ir]] * e.size)
e = numpy.hstack(es)
c = hf_symm.so2ao_mo_coeff(mol.symm_orb, cs)
c = lib.tag_array(c, orbsym=numpy.hstack(orbsym))
return e, c
def eig(self, h, s):
if not self.mol.symmetry:
return uhf.UHF.eig(self, h, s)
nirrep = self.mol.symm_orb.__len__()
s = symm.symmetrize_matrix(s, self.mol.symm_orb)
ha = symm.symmetrize_matrix(h[0], self.mol.symm_orb)
cs = []
es = []
for ir in range(nirrep):
e, c = hf.SCF.eig(self, ha[ir], s[ir])
cs.append(c)
es.append(e)
ea = numpy.hstack(es)
ca = hf_symm.so2ao_mo_coeff(self.mol.symm_orb, cs)
hb = symm.symmetrize_matrix(h[1], self.mol.symm_orb)
cs = []
es = []
for ir in range(nirrep):
e, c = scipy.linalg.eigh(hb[ir], s[ir])
cs.append(c)
es.append(e)
eb = numpy.hstack(es)
cb = hf_symm.so2ao_mo_coeff(self.mol.symm_orb, cs)
return numpy.array((ea,eb)), (ca,cb)
def eig(self, h, s):
mol = self.mol
if not mol.symmetry:
return self._eigh(h, s)
nirrep = mol.symm_orb.__len__()
s = symm.symmetrize_matrix(s, mol.symm_orb)
ha = symm.symmetrize_matrix(h[0], mol.symm_orb)
cs = []
es = []
orbsym = []
for ir in range(nirrep):
e, c = self._eigh(ha[ir], s[ir])
cs.append(c)
es.append(e)
orbsym.append([mol.irrep_id[ir]] * e.size)
ea = numpy.hstack(es)
ca = hf_symm.so2ao_mo_coeff(mol.symm_orb, cs)
ca = lib.tag_array(ca, orbsym=numpy.hstack(orbsym))
hb = symm.symmetrize_matrix(h[1], mol.symm_orb)
cs = []
es = []
orbsym = []
for ir in range(nirrep):
e, c = self._eigh(hb[ir], s[ir])
cs.append(c)
es.append(e)
orbsym.append([mol.irrep_id[ir]] * e.size)
eb = numpy.hstack(es)
cb = hf_symm.so2ao_mo_coeff(mol.symm_orb, cs)
cb = lib.tag_array(cb, orbsym=numpy.hstack(orbsym))
return (ea,eb), (ca,cb)
def eig(self, h, s):
if not self.mol.symmetry:
return uhf.UHF.eig(self, h, s)
nirrep = self.mol.symm_orb.__len__()
s = symm.symmetrize_matrix(s, self.mol.symm_orb)
ha = symm.symmetrize_matrix(h[0], self.mol.symm_orb)
cs = []
es = []
for ir in range(nirrep):
e, c = hf.SCF.eig(self, ha[ir], s[ir])
cs.append(c)
es.append(e)
ea = numpy.hstack(es)
ca = hf_symm.so2ao_mo_coeff(self.mol.symm_orb, cs)
hb = symm.symmetrize_matrix(h[1], self.mol.symm_orb)
cs = []
es = []
for ir in range(nirrep):
e, c = scipy.linalg.eigh(hb[ir], s[ir])
cs.append(c)
es.append(e)
eb = numpy.hstack(es)
cb = hf_symm.so2ao_mo_coeff(self.mol.symm_orb, cs)
return numpy.array((ea,eb)), (ca,cb)
def eig(self, h, s):
nirrep = self.mol.symm_orb.__len__()
h = symm.symmetrize_matrix(h, self.mol.symm_orb)
s = symm.symmetrize_matrix(s, self.mol.symm_orb)
cs = []
es = []
for ir in range(nirrep):
e, c = hf.SCF.eig(self, h[ir], s[ir])
cs.append(c)
es.append(e)
e = numpy.hstack(es)
c = so2ao_mo_coeff(self.mol.symm_orb, cs)
return e, c
def eig(self, h, s):
nirrep = self.mol.symm_orb.__len__()
h = symm.symmetrize_matrix(h, self.mol.symm_orb)
s = symm.symmetrize_matrix(s, self.mol.symm_orb)
cs = []
es = []
for ir in range(nirrep):
e, c = hf.SCF.eig(self, h[ir], s[ir])
cs.append(c)
es.append(e)
e = numpy.hstack(es)
c = so2ao_mo_coeff(self.mol.symm_orb, cs)
return e, c
def eig_symm(h, s):
nirrep = mol.symm_orb.__len__()
h = symm.symmetrize_matrix(h, mol.symm_orb)
s = symm.symmetrize_matrix(s, mol.symm_orb)
cs = []
es = []
for ir in range(nirrep):
d, t = numpy.linalg.eigh(s[ir])
x = t[:, d > 1e-8] / numpy.sqrt(d[d > 1e-8])
xhx = reduce(numpy.dot, (x.T, h[ir], x))
e, c = numpy.linalg.eigh(xhx)
cs.append(reduce(numpy.dot, (mol.symm_orb[ir], x, c)))
es.append(e)
e = numpy.hstack(es)
c = numpy.hstack(cs)
return e, c
def eig_symm(h, s):
nirrep = mol.symm_orb.__len__()
h = symm.symmetrize_matrix(h, mol.symm_orb)
s = symm.symmetrize_matrix(s, mol.symm_orb)
cs = []
es = []
for ir in range(nirrep):
d, t = numpy.linalg.eigh(s[ir])
x = t[:,d>1e-8] / numpy.sqrt(d[d>1e-8])
xhx = reduce(numpy.dot, (x.T, h[ir], x))
e, c = numpy.linalg.eigh(xhx)
cs.append(reduce(numpy.dot, (mol.symm_orb[ir], x, c)))
es.append(e)
e = numpy.hstack(es)
c = numpy.hstack(cs)
return e, c
def eig(self, 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.
'''
nirrep = self.mol.symm_orb.__len__()
h = symm.symmetrize_matrix(h, self.mol.symm_orb)
s = symm.symmetrize_matrix(s, self.mol.symm_orb)
cs = []
es = []
for ir in range(nirrep):
e, c = hf.SCF.eig(self, h[ir], s[ir])
cs.append(c)
es.append(e)
e = numpy.hstack(es)
c = so2ao_mo_coeff(self.mol.symm_orb, cs)
return e, c
def eig(self, 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.
'''
nirrep = self.mol.symm_orb.__len__()
h = symm.symmetrize_matrix(h, self.mol.symm_orb)
s = symm.symmetrize_matrix(s, self.mol.symm_orb)
cs = []
es = []
for ir in range(nirrep):
e, c = hf.SCF.eig(self, h[ir], s[ir])
cs.append(c)
es.append(e)
e = numpy.hstack(es)
c = so2ao_mo_coeff(self.mol.symm_orb, cs)
return e, c
def eig(h, s):
from pyscf import symm
nirrep = len(mol.symm_orb)
h = symm.symmetrize_matrix(h, mol.symm_orb)
s = symm.symmetrize_matrix(s, mol.symm_orb)
cs = []
es = []
#
# Linear dependency are removed by looping over different symmetry irreps.
#
for ir in range(nirrep):
d, t = numpy.linalg.eigh(s[ir])
x = t[:,d>1e-8] / numpy.sqrt(d[d>1e-8])
xhx = reduce(numpy.dot, (x.T, h[ir], x))
e, c = numpy.linalg.eigh(xhx)
cs.append(reduce(numpy.dot, (mol.symm_orb[ir], x, c)))
es.append(e)
e = numpy.hstack(es)
c = numpy.hstack(cs)
return e, c
def eig(h, s):
from pyscf import symm
nirrep = len(mol.symm_orb)
h = symm.symmetrize_matrix(h, mol.symm_orb)
s = symm.symmetrize_matrix(s, mol.symm_orb)
cs = []
es = []
#
# Linear dependency are removed by looping over different symmetry irreps.
#
for ir in range(nirrep):
d, t = numpy.linalg.eigh(s[ir])
x = t[:, d > 1e-8] / numpy.sqrt(d[d > 1e-8])
xhx = reduce(numpy.dot, (x.T, h[ir], x))
e, c = numpy.linalg.eigh(xhx)
cs.append(reduce(numpy.dot, (mol.symm_orb[ir], x, c)))
es.append(e)
e = numpy.hstack(es)
c = numpy.hstack(cs)
return e, c
def scf(self, *args):
logger.info(self, '\n')
logger.info(self, '******** 1 electron system ********')
self.converged = True
h1e = self.get_hcore(self.mol)
s1e = self.get_ovlp(self.mol)
nirrep = self.mol.symm_orb.__len__()
h1e = symm.symmetrize_matrix(h1e, self.mol.symm_orb)
s1e = symm.symmetrize_matrix(s1e, self.mol.symm_orb)
cs = []
es = []
for ir in range(nirrep):
e, c = hf.SCF.eig(self, h1e[ir], s1e[ir])
cs.append(c)
es.append(e)
e = numpy.hstack(es).round(9)
idx = numpy.argsort(e)
self.mo_energy = e[idx]
self.mo_coeff = so2ao_mo_coeff(self.mol.symm_orb, cs)[:,idx]
self.mo_occ = numpy.zeros_like(self.mo_energy)
self.mo_occ[0] = 1
self.e_tot = self.mo_energy[0] + self.mol.energy_nuc()
return self.e_tot
def scf(self, *args):
logger.info(self, '\n')
logger.info(self, '******** 1 electron system ********')
self.converged = True
h1e = self.get_hcore(self.mol)
s1e = self.get_ovlp(self.mol)
nirrep = self.mol.symm_orb.__len__()
h1e = symm.symmetrize_matrix(h1e, self.mol.symm_orb)
s1e = symm.symmetrize_matrix(s1e, self.mol.symm_orb)
cs = []
es = []
for ir in range(nirrep):
e, c = hf.SCF.eig(self, h1e[ir], s1e[ir])
cs.append(c)
es.append(e)
e = numpy.hstack(es).round(9)
idx = numpy.argsort(e)
self.mo_energy = e[idx]
self.mo_coeff = so2ao_mo_coeff(self.mol.symm_orb, cs)[:, idx]
self.mo_occ = numpy.zeros_like(self.mo_energy)
self.mo_occ[0] = 1
self.e_tot = self.mo_energy[0] + self.mol.energy_nuc()
return self.e_tot
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.
'''
mol = mf.mol
if not mol.symmetry:
return mf._eigh(h, s)
nirrep = mol.symm_orb.__len__()
h = symm.symmetrize_matrix(h, mol.symm_orb)
s = symm.symmetrize_matrix(s, mol.symm_orb)
cs = []
es = []
orbsym = []
for ir in range(nirrep):
e, c = mf._eigh(h[ir], s[ir])
cs.append(c)
es.append(e)
orbsym.append([mol.irrep_id[ir]] * e.size)
e = numpy.hstack(es)
c = so2ao_mo_coeff(mol.symm_orb, cs)
c = lib.tag_array(c, orbsym=numpy.hstack(orbsym))
return e, c
