def uhf_external(mf, with_symmetry=True, verbose=None):
log = logger.new_logger(mf, verbose)
hop1, hdiag1, hop2, hdiag2 = _gen_hop_uhf_external(mf, with_symmetry)
def precond(dx, e, x0):
hdiagd = hdiag1 - e
hdiagd[abs(hdiagd) < 1e-8] = 1e-8
return dx / hdiagd
x0 = numpy.zeros_like(hdiag1)
x0[hdiag1 > 1e-5] = 1. / hdiag1[hdiag1 > 1e-5]
if not with_symmetry: # allow to break point group symmetry
x0[numpy.argmin(hdiag1)] = 1
e1, v = lib.davidson(hop1, x0, precond, tol=1e-4, verbose=log)
if e1 < -1e-5:
log.note('UHF/UKS wavefunction has a real -> complex instability')
else:
log.note(
'UHF/UKS wavefunction is stable in the real -> complex stability analysis'
)
def precond(dx, e, x0):
hdiagd = hdiag2 - e
hdiagd[abs(hdiagd) < 1e-8] = 1e-8
return dx / hdiagd
x0 = numpy.zeros_like(hdiag2)
x0[hdiag2 > 1e-5] = 1. / hdiag2[hdiag2 > 1e-5]
if not with_symmetry: # allow to break point group symmetry
x0[numpy.argmin(hdiag2)] = 1
e3, v = lib.davidson(hop2, x0, precond, tol=1e-4, verbose=log)
log.debug('uhf_external: lowest eigs of H = %s', e3)
mo = scipy.linalg.block_diag(*mf.mo_coeff)
if e3 < -1e-5:
stable_e = False # added by qingchun 3/13 2018
log.note('UHF/UKS wavefunction has an UHF/UKS -> GHF/GKS instability.')
occidxa = numpy.where(mf.mo_occ[0] > 0)[0]
viridxa = numpy.where(mf.mo_occ[0] == 0)[0]
occidxb = numpy.where(mf.mo_occ[1] > 0)[0]
viridxb = numpy.where(mf.mo_occ[1] == 0)[0]
nocca = len(occidxa)
nvira = len(viridxa)
noccb = len(occidxb)
nvirb = len(viridxb)
nmo = nocca + nvira
dx = numpy.zeros((nmo * 2, nmo * 2))
dx[viridxa[:, None],
nmo + occidxb] = v[:nvira * noccb].reshape(nvira, noccb)
dx[nmo + viridxb[:, None],
occidxa] = v[nvira * noccb:].reshape(nvirb, nocca)
u = newton_ah.expmat(dx - dx.T)
mo = numpy.dot(mo, u)
else:
stable_e = True # added by qingchun 3/13 2018
log.note(
'UHF/UKS wavefunction is stable in the UHF/UKS -> GHF/GKS stability analysis'
)
return mo, stable_e
def update_rotate_matrix(self, dx, mo_occ, u0=1):
p0 = 0
u = []
for k, occ in enumerate(mo_occ):
occidx = occ > 0
viridx = ~occidx
nocc = occidx.sum()
nvir = viridx.sum()
nmo = nocc + nvir
dr = numpy.zeros((nmo, nmo), dtype=dx.dtype)
dr[viridx[:, None] & occidx] = dx[p0:p0 + nocc * nvir]
dr = dr - dr.T.conj()
p0 += nocc * nvir
u1 = newton_ah.expmat(dr)
if isinstance(u0, int) and u0 == 1:
u.append(u1)
else:
u.append(numpy.dot(u0[k], u1))
return lib.asarray(u)
def update_rotate_matrix(self, dx, mo_occ, u0=1):
nmo = mo_occ.shape[-1]
p0 = 0
u = []
for k, occ in enumerate(mo_occ):
occidx = occ > 0
viridx = ~occidx
nocc = occidx.sum()
nvir = nmo - nocc
dr = numpy.zeros((nmo,nmo), dtype=dx.dtype)
dr[viridx[:,None]&occidx] = dx[p0:p0+nocc*nvir]
dr = dr - dr.T.conj()
p0 += nocc * nvir
u1 = newton_ah.expmat(dr)
if isinstance(u0, int) and u0 == 1:
u.append(u1)
else:
u.append(numpy.dot(u0[k], u1))
return lib.asarray(u)
def update_rotate_matrix(self, dx, mo_occ, u0=1):
nkpts = len(mo_occ[0])
nmo = mo_occ[0].shape[-1]
p0 = 0
u = []
for occ in mo_occ:
ua = []
for k in range(nkpts):
occidx = occ[k] > 0
viridx = ~occidx
nocc = occidx.sum()
nvir = nmo - nocc
dr = numpy.zeros((nmo, nmo), dtype=dx.dtype)
dr[viridx[:, None] & occidx] = dx[p0:p0 + nocc * nvir]
dr = dr - dr.T.conj()
p0 += nocc * nvir
u1 = newton_ah.expmat(dr)
if isinstance(u0, int) and u0 == 1:
ua.append(u1)
else:
ua.append(numpy.dot(u0[k], u1))
u.append(ua)
return lib.asarray(u)
def _rotate_mo(mo_coeff, mo_occ, dx):
dr = hf.unpack_uniq_var(dx, mo_occ)
u = newton_ah.expmat(dr)
return numpy.dot(mo_coeff, u)