#!/usr/bin/env python
# Copyright 2014-2019 The PySCF Developers. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#
# Author: Qiming Sun <osirpt.sun@gmail.com>
#
'''
Restricted Open-shell Hartree-Fock
'''
from functools import reduce
import numpy
import pyscf.gto
from pyscf import lib
from pyscf.lib import logger
from pyscf.scf import hf
from pyscf.scf import uhf
from pyscf import __config__
WITH_META_LOWDIN = getattr(__config__, 'scf_analyze_with_meta_lowdin', True)
MO_BASE = getattr(__config__, 'MO_BASE', 1)
[docs]
def init_guess_by_minao(mol):
dm = hf.init_guess_by_minao(mol)
dm = numpy.array((dm*.5, dm*.5))
if hasattr(dm, 'mo_coeff'):
dm = lib.tag_array(dm, mo_coeff=dm.mo_coeff, mo_occ=dm.mo_occ)
return dm
[docs]
def init_guess_by_atom(mol):
dm = hf.init_guess_by_atom(mol)
dm = numpy.array((dm*.5, dm*.5))
if hasattr(dm, 'mo_coeff'):
dm = lib.tag_array(dm, mo_coeff=dm.mo_coeff, mo_occ=dm.mo_occ)
return dm
init_guess_by_huckel = uhf.init_guess_by_huckel
init_guess_by_mod_huckel = uhf.init_guess_by_mod_huckel
init_guess_by_chkfile = uhf.init_guess_by_chkfile
[docs]
def get_fock(mf, h1e=None, s1e=None, vhf=None, dm=None, cycle=-1, diis=None,
diis_start_cycle=None, level_shift_factor=None, damp_factor=None):
'''Build fock matrix based on Roothaan's effective fock.
See also :func:`get_roothaan_fock`
'''
if h1e is None: h1e = mf.get_hcore()
if s1e is None: s1e = mf.get_ovlp()
if vhf is None: vhf = mf.get_veff(mf.mol, dm)
if dm is None: dm = mf.make_rdm1()
if isinstance(dm, numpy.ndarray) and dm.ndim == 2:
dm = numpy.array((dm*.5, dm*.5))
# To Get orbital energy in get_occ, we saved alpha and beta fock, because
# Roothaan effective Fock cannot provide correct orbital energy with `eig`
# TODO, check other treatment J. Chem. Phys. 133, 141102
focka = h1e + vhf[0]
fockb = h1e + vhf[1]
f = get_roothaan_fock((focka,fockb), dm, s1e)
if cycle < 0 and diis is None: # Not inside the SCF iteration
return f
if diis_start_cycle is None:
diis_start_cycle = mf.diis_start_cycle
if level_shift_factor is None:
level_shift_factor = mf.level_shift
if damp_factor is None:
damp_factor = mf.damp
dm_tot = dm[0] + dm[1]
if 0 <= cycle < diis_start_cycle-1 and abs(damp_factor) > 1e-4:
raise NotImplementedError('ROHF Fock-damping')
if diis and cycle >= diis_start_cycle:
f = diis.update(s1e, dm_tot, f, mf, h1e, vhf)
if abs(level_shift_factor) > 1e-4:
f = hf.level_shift(s1e, dm_tot*.5, f, level_shift_factor)
f = lib.tag_array(f, focka=focka, fockb=fockb)
return f
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def get_roothaan_fock(focka_fockb, dma_dmb, s):
'''Roothaan's effective fock.
Ref. http://www-theor.ch.cam.ac.uk/people/ross/thesis/node15.html
======== ======== ====== =========
space closed open virtual
======== ======== ====== =========
closed Fc Fb Fc
open Fb Fc Fa
virtual Fc Fa Fc
======== ======== ====== =========
where Fc = (Fa + Fb) / 2
Returns:
Roothaan effective Fock matrix
'''
nao = s.shape[0]
focka, fockb = focka_fockb
dma, dmb = dma_dmb
fc = (focka + fockb) * .5
# Projector for core, open-shell, and virtual
pc = numpy.dot(dmb, s)
po = numpy.dot(dma-dmb, s)
pv = numpy.eye(nao) - numpy.dot(dma, s)
fock = reduce(numpy.dot, (pc.conj().T, fc, pc)) * .5
fock += reduce(numpy.dot, (po.conj().T, fc, po)) * .5
fock += reduce(numpy.dot, (pv.conj().T, fc, pv)) * .5
fock += reduce(numpy.dot, (po.conj().T, fockb, pc))
fock += reduce(numpy.dot, (po.conj().T, focka, pv))
fock += reduce(numpy.dot, (pv.conj().T, fc, pc))
fock = fock + fock.conj().T
fock = lib.tag_array(fock, focka=focka, fockb=fockb)
return fock
[docs]
def get_occ(mf, mo_energy=None, mo_coeff=None):
'''Label the occupancies for each orbital.
NOTE the occupancies are not assigned based on the orbital energy ordering.
The first N orbitals are assigned to be occupied orbitals.
Examples:
>>> mol = gto.M(atom='H 0 0 0; O 0 0 1.1', spin=1)
>>> mf = scf.hf.SCF(mol)
>>> energy = numpy.array([-10., -1., 1, -2., 0, -3])
>>> mf.get_occ(energy)
array([2, 2, 2, 2, 1, 0])
'''
if mo_energy is None: mo_energy = mf.mo_energy
if getattr(mo_energy, 'mo_ea', None) is not None:
mo_ea = mo_energy.mo_ea
mo_eb = mo_energy.mo_eb
else:
mo_ea = mo_eb = mo_energy
nmo = mo_ea.size
mo_occ = numpy.zeros(nmo)
if getattr(mf, 'nelec', None) is None:
nelec = mf.mol.nelec
else:
nelec = mf.nelec
if nelec[0] > nelec[1]:
nocc, ncore = nelec
else:
ncore, nocc = nelec
nopen = nocc - ncore
mo_occ = _fill_rohf_occ(mo_energy, mo_ea, mo_eb, ncore, nopen)
if mf.verbose >= logger.INFO and nocc < nmo and ncore > 0:
ehomo = max(mo_energy[mo_occ> 0])
elumo = min(mo_energy[mo_occ==0])
if ehomo+1e-3 > elumo:
logger.warn(mf, 'HOMO %.15g >= LUMO %.15g', ehomo, elumo)
else:
logger.info(mf, ' HOMO = %.15g LUMO = %.15g', ehomo, elumo)
if nopen > 0 and mf.verbose >= logger.DEBUG:
core_idx = mo_occ == 2
open_idx = mo_occ == 1
vir_idx = mo_occ == 0
logger.debug(mf, ' Roothaan | alpha | beta')
logger.debug(mf, ' Highest 2-occ = %18.15g | %18.15g | %18.15g',
max(mo_energy[core_idx]),
max(mo_ea[core_idx]), max(mo_eb[core_idx]))
logger.debug(mf, ' Lowest 0-occ = %18.15g | %18.15g | %18.15g',
min(mo_energy[vir_idx]),
min(mo_ea[vir_idx]), min(mo_eb[vir_idx]))
for i in numpy.where(open_idx)[0]:
logger.debug(mf, ' 1-occ = %18.15g | %18.15g | %18.15g',
mo_energy[i], mo_ea[i], mo_eb[i])
if mf.verbose >= logger.DEBUG:
numpy.set_printoptions(threshold=nmo)
logger.debug(mf, ' Roothaan mo_energy =\n%s', mo_energy)
logger.debug1(mf, ' alpha mo_energy =\n%s', mo_ea)
logger.debug1(mf, ' beta mo_energy =\n%s', mo_eb)
numpy.set_printoptions(threshold=1000)
return mo_occ
def _fill_rohf_occ(mo_energy, mo_energy_a, mo_energy_b, ncore, nopen):
mo_occ = numpy.zeros_like(mo_energy)
open_idx = []
core_sort = numpy.argsort(mo_energy)
core_idx = core_sort[:ncore]
if nopen > 0:
open_idx = core_sort[ncore:]
open_sort = numpy.argsort(mo_energy_a[open_idx])
open_idx = open_idx[open_sort[:nopen]]
mo_occ[core_idx] = 2
mo_occ[open_idx] = 1
return mo_occ
[docs]
def get_grad(mo_coeff, mo_occ, fock):
'''ROHF gradients is the off-diagonal block [co + cv + ov], where
[ cc co cv ]
[ oc oo ov ]
[ vc vo vv ]
'''
occidxa = mo_occ > 0
occidxb = mo_occ == 2
viridxa = ~occidxa
viridxb = ~occidxb
uniq_var_a = viridxa.reshape(-1,1) & occidxa
uniq_var_b = viridxb.reshape(-1,1) & occidxb
if getattr(fock, 'focka', None) is not None:
focka = fock.focka
fockb = fock.fockb
elif isinstance(fock, (tuple, list)) or getattr(fock, 'ndim', None) == 3:
focka, fockb = fock
else:
focka = fockb = fock
focka = reduce(numpy.dot, (mo_coeff.conj().T, focka, mo_coeff))
fockb = reduce(numpy.dot, (mo_coeff.conj().T, fockb, mo_coeff))
g = numpy.zeros_like(focka)
g[uniq_var_a] = focka[uniq_var_a]
g[uniq_var_b] += fockb[uniq_var_b]
return g[uniq_var_a | uniq_var_b]
[docs]
def make_rdm1(mo_coeff, mo_occ, **kwargs):
'''One-particle density matrix. mo_occ is a 1D array, with occupancy 1 or 2.
'''
if isinstance(mo_occ, numpy.ndarray) and mo_occ.ndim == 1:
mo_occa = (mo_occ > 0).astype(numpy.double)
mo_occb = (mo_occ ==2).astype(numpy.double)
else:
mo_occa, mo_occb = mo_occ
dm_a = numpy.dot(mo_coeff*mo_occa, mo_coeff.conj().T)
dm_b = numpy.dot(mo_coeff*mo_occb, mo_coeff.conj().T)
return lib.tag_array((dm_a, dm_b), mo_coeff=mo_coeff, mo_occ=mo_occ)
[docs]
def energy_elec(mf, dm=None, h1e=None, vhf=None):
if dm is None: dm = mf.make_rdm1()
elif isinstance(dm, numpy.ndarray) and dm.ndim == 2:
dm = numpy.array((dm*.5, dm*.5))
return uhf.energy_elec(mf, dm, h1e, vhf)
get_veff = uhf.get_veff
[docs]
def analyze(mf, verbose=logger.DEBUG, with_meta_lowdin=WITH_META_LOWDIN,
**kwargs):
'''Analyze the given SCF object: print orbital energies, occupancies;
print orbital coefficients; Mulliken population analysis
'''
from pyscf.lo import orth
from pyscf.tools import dump_mat
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
mo_coeff = mf.mo_coeff
log = logger.new_logger(mf, verbose)
if log.verbose >= logger.NOTE:
mf.dump_scf_summary(log)
log.note('**** MO energy ****')
if getattr(mo_energy, 'mo_ea', None) is not None:
mo_ea = mo_energy.mo_ea
mo_eb = mo_energy.mo_eb
log.note(' Roothaan | alpha | beta')
for i,c in enumerate(mo_occ):
log.note('MO #%-3d energy= %-18.15g | %-18.15g | %-18.15g occ= %g',
i+MO_BASE, mo_energy[i], mo_ea[i], mo_eb[i], c)
else:
for i,c in enumerate(mo_occ):
log.note('MO #%-3d energy= %-18.15g occ= %g',
i+MO_BASE, mo_energy[i], c)
ovlp_ao = mf.get_ovlp()
if log.verbose >= logger.DEBUG:
label = mf.mol.ao_labels()
if with_meta_lowdin:
log.debug(' ** MO coefficients (expansion on meta-Lowdin AOs) **')
orth_coeff = orth.orth_ao(mf.mol, 'meta_lowdin', s=ovlp_ao)
c = reduce(numpy.dot, (orth_coeff.conj().T, ovlp_ao, mo_coeff))
else:
log.debug(' ** MO coefficients (expansion on AOs) **')
c = mo_coeff
dump_mat.dump_rec(mf.stdout, c, label, start=MO_BASE, **kwargs)
dm = mf.make_rdm1(mo_coeff, mo_occ)
if with_meta_lowdin:
pop_and_charge = mf.mulliken_meta(mf.mol, dm, s=ovlp_ao, verbose=log)
else:
pop_and_charge = mf.mulliken_pop(mf.mol, dm, s=ovlp_ao, verbose=log)
dip = mf.dip_moment(mf.mol, dm, verbose=log)
return pop_and_charge, dip
mulliken_pop = hf.mulliken_pop
mulliken_meta = hf.mulliken_meta
[docs]
def canonicalize(mf, mo_coeff, mo_occ, fock=None):
'''Canonicalization diagonalizes the Fock matrix within occupied, open,
virtual subspaces separatedly (without change occupancy).
'''
if getattr(fock, 'focka', None) is None:
dm = mf.make_rdm1(mo_coeff, mo_occ)
fock = mf.get_fock(dm=dm)
mo_e, mo_coeff = hf.canonicalize(mf, mo_coeff, mo_occ, fock)
fa, fb = fock.focka, fock.fockb
mo_ea = numpy.einsum('pi,pi->i', mo_coeff.conj(), fa.dot(mo_coeff)).real
mo_eb = numpy.einsum('pi,pi->i', mo_coeff.conj(), fb.dot(mo_coeff)).real
mo_e = lib.tag_array(mo_e, mo_ea=mo_ea, mo_eb=mo_eb)
return mo_e, mo_coeff
dip_moment = hf.dip_moment
# use UHF init_guess, get_veff, diis, and intermediates such as fock, vhf, dm
# keep mo_energy, mo_coeff, mo_occ as RHF structure
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class ROHF(hf.RHF):
__doc__ = hf.SCF.__doc__
def __init__(self, mol):
hf.SCF.__init__(self, mol)
self.nelec = None
@property
def nelec(self):
if getattr(self, '_nelec', None) is not None:
return self._nelec
else:
return self.mol.nelec
@nelec.setter
def nelec(self, x):
self._nelec = x
@property
def nelectron_alpha(self):
return self.nelec[0]
@nelectron_alpha.setter
def nelectron_alpha(self, x):
logger.warn(self, 'WARN: Attribute .nelectron_alpha is deprecated. '
'Set .nelec instead')
#raise RuntimeError('API updates')
self.nelec = (x, self.mol.nelectron-x)
check_sanity = hf.SCF.check_sanity
[docs]
def dump_flags(self, verbose=None):
hf.SCF.dump_flags(self, verbose)
nelec = self.nelec
logger.info(self, 'num. doubly occ = %d num. singly occ = %d',
nelec[1], nelec[0]-nelec[1])
get_init_guess = uhf.UHF.get_init_guess
[docs]
def init_guess_by_minao(self, mol=None):
if mol is None: mol = self.mol
return init_guess_by_minao(mol)
[docs]
def init_guess_by_atom(self, mol=None):
if mol is None: mol = self.mol
logger.info(self, 'Initial guess from the superpostion of atomic densties.')
return init_guess_by_atom(mol)
[docs]
def init_guess_by_huckel(self, mol=None):
if mol is None: mol = self.mol
logger.info(self, 'Initial guess from on-the-fly Huckel, doi:10.1021/acs.jctc.8b01089.')
return init_guess_by_huckel(mol)
[docs]
def init_guess_by_mod_huckel(self, mol=None):
if mol is None: mol = self.mol
logger.info(self, '''Initial guess from on-the-fly Huckel, doi:10.1021/acs.jctc.8b01089,
employing the updated GWH rule from doi:10.1021/ja00480a005.''')
return init_guess_by_mod_huckel(mol)
[docs]
def init_guess_by_1e(self, mol=None):
if mol is None: mol = self.mol
logger.info(self, 'Initial guess from hcore.')
h1e = self.get_hcore(mol)
s1e = self.get_ovlp(mol)
mo_energy, mo_coeff = self.eig(h1e, s1e)
mo_occ = self.get_occ(mo_energy, mo_coeff)
return self.make_rdm1(mo_coeff, mo_occ)
[docs]
def init_guess_by_chkfile(self, chkfile=None, project=None):
if chkfile is None: chkfile = self.chkfile
return init_guess_by_chkfile(self.mol, chkfile, project=project)
get_fock = get_fock
get_occ = get_occ
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@lib.with_doc(hf.eig.__doc__)
def eig(self, fock, s):
e, c = self._eigh(fock, s)
if getattr(fock, 'focka', None) is not None:
mo_ea = numpy.einsum('pi,pi->i', c.conj(), fock.focka.dot(c)).real
mo_eb = numpy.einsum('pi,pi->i', c.conj(), fock.fockb.dot(c)).real
e = lib.tag_array(e, mo_ea=mo_ea, mo_eb=mo_eb)
return e, c
[docs]
@lib.with_doc(get_grad.__doc__)
def get_grad(self, mo_coeff, mo_occ, fock=None):
if fock is None:
dm1 = self.make_rdm1(mo_coeff, mo_occ)
fock = self.get_hcore(self.mol) + self.get_veff(self.mol, dm1)
return get_grad(mo_coeff, mo_occ, fock)
[docs]
@lib.with_doc(make_rdm1.__doc__)
def make_rdm1(self, mo_coeff=None, mo_occ=None, **kwargs):
if mo_coeff is None: mo_coeff = self.mo_coeff
if mo_occ is None: mo_occ = self.mo_occ
if self.mol.spin < 0:
# Flip occupancies of alpha and beta orbitals
mo_occ = (numpy.asarray(mo_occ == 2, dtype=numpy.double),
numpy.asarray(mo_occ > 0, dtype=numpy.double))
return make_rdm1(mo_coeff, mo_occ, **kwargs)
energy_elec = energy_elec
[docs]
@lib.with_doc(uhf.get_veff.__doc__)
def get_veff(self, mol=None, dm=None, dm_last=0, vhf_last=0, hermi=1):
if mol is None: mol = self.mol
if dm is None: dm = self.make_rdm1()
if isinstance(dm, numpy.ndarray) and dm.ndim == 2:
dm = numpy.array((dm*.5, dm*.5))
if self._eri is not None or not self.direct_scf:
if hasattr(dm, 'mo_occ') and numpy.ndim(dm.mo_occ) == 1:
mo_occa = (dm.mo_occ > 0).astype(numpy.double)
mo_occb = (dm.mo_occ ==2).astype(numpy.double)
dm = lib.tag_array(dm, mo_coeff=(dm.mo_coeff,)*2,
mo_occ=(mo_occa,mo_occb))
vj, vk = self.get_jk(mol, dm, hermi)
vhf = vj[0] + vj[1] - vk
else:
ddm = dm - numpy.asarray(dm_last)
vj, vk = self.get_jk(mol, ddm, hermi)
vhf = vj[0] + vj[1] - vk
vhf += numpy.asarray(vhf_last)
return vhf
[docs]
@lib.with_doc(analyze.__doc__)
def analyze(self, verbose=None, with_meta_lowdin=WITH_META_LOWDIN,
**kwargs):
if verbose is None: verbose = self.verbose
return analyze(self, verbose, with_meta_lowdin, **kwargs)
canonicalize = canonicalize
[docs]
def spin_square(self, mo_coeff=None, s=None):
'''Spin square and multiplicity of RHF determinant'''
neleca, nelecb = self.nelec
ms = (neleca - nelecb) * .5
ss = ms * (ms + 1)
return ss, ms*2+1
[docs]
def stability(self,
internal=getattr(__config__, 'scf_stability_internal', True),
external=getattr(__config__, 'scf_stability_external', False),
verbose=None,
return_status=False):
'''
ROHF/ROKS stability analysis.
See also pyscf.scf.stability.rohf_stability function.
Kwargs:
internal : bool
Internal stability, within the RHF optimization space.
external : bool
External stability. It is not available in current version.
return_status: bool
Whether to return `stable_i` and `stable_e`
Returns:
If return_status is False (default), the return value includes
two set of orbitals, which are more close to the stable condition.
The first corresponds to the internal stability
and the second corresponds to the external stability.
Else, another two boolean variables (indicating current status:
stable or unstable) are returned.
The first corresponds to the internal stability
and the second corresponds to the external stability.
'''
from pyscf.scf.stability import rohf_stability
return rohf_stability(self, internal, external, verbose, return_status)
[docs]
def nuc_grad_method(self):
from pyscf.grad import rohf
return rohf.Gradients(self)
convert_from_ = hf.RHF.convert_from_
[docs]
def to_ks(self, xc='HF'):
'''Convert to ROKS object.
'''
from pyscf import dft
return self._transfer_attrs_(dft.ROKS(self.mol, xc=xc))
[docs]
class HF1e(ROHF):
scf = hf._hf1e_scf
del (WITH_META_LOWDIN)