#!/usr/bin/env python
# Copyright 2014-2020 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>
#
from functools import reduce
import numpy
import scipy.linalg
from pyscf.lib import logger
from pyscf.tools import dump_mat
from pyscf import scf, gto
from pyscf import __config__
THRESHOLD = getattr(__config__, 'mcscf_dmet_cas_threshold', 0.05)
OCC_CUTOFF = getattr(__config__, 'mcscf_dmet_cas_occ_cutoff', 1e-6)
BASE = getattr(__config__, 'BASE', 0)
ORTH_METHOD = getattr(__config__, 'mcscf_dmet_cas_orth_method', 'meta_lowdin')
CANONICALIZE = getattr(__config__, 'mcscf_dmet_cas_canonicalize', True)
FREEZE_IMP = getattr(__config__, 'mcscf_dmet_cas_freeze_imp', False)
[docs]
def kernel(mf, dm, aolabels_or_baslst, threshold=THRESHOLD,
occ_cutoff=OCC_CUTOFF, base=BASE,
orth_method=ORTH_METHOD, s=None, canonicalize=CANONICALIZE,
freeze_imp=FREEZE_IMP, verbose=None):
'''DMET method to generate CASSCF initial guess.
Ref. arXiv:1701.07862 [physics.chem-ph]
Args:
mf : an :class:`SCF` object
dm : 2D np.array or a list of 2D array
Density matrix
aolabels_or_baslst : string or a list of strings or a list of index
AO labels or indices
Kwargs:
threshold : float
Entanglement threshold of DMET bath. If the occupancy of an
orbital is less than threshold, the orbital is considered as bath
orbital. If occ is greater than (1-threshold), the orbitals are
taken for core determinant.
base : int
0-based (C-style) or 1-based (Fortran-style) for baslst if baslst
is index list
orth_method : str
It can be one of 'lowdin' and 'meta_lowdin'
s : 2D array
AO overlap matrix. This option is mainly used for custom Hamiltonian.
canonicalize : bool
Orbitals defined in AVAS method are local orbitals. Symmetrizing
the core, active and virtual space.
Returns:
active-space-size, #-active-electrons, orbital-initial-guess-for-CASCI/CASSCF
Examples:
>>> from pyscf import gto, scf, mcscf
>>> from pyscf.mcscf import dmet_cas
>>> mol = gto.M(atom='Cr 0 0 0; Cr 0 0 1.6', basis='ccpvtz')
>>> mf = scf.RHF(mol).run()
>>> ncas, nelecas, mo = dmet_cas.dmet_cas(mf, ['Cr 3d', 'Cr 4s'])
>>> mc = mcscf.CASSCF(mf, ncas, nelecas).run(mo)
'''
from pyscf import lo
if isinstance(verbose, logger.Logger):
log = verbose
elif verbose is not None:
log = logger.Logger(mf.stdout, verbose)
else:
log = logger.Logger(mf.stdout, mf.verbose)
if not (isinstance(dm, numpy.ndarray) and dm.ndim == 2): # ROHF/UHF DM
dm = sum(dm)
mol = mf.mol
if s is None:
s = mf.get_ovlp()
if (not isinstance(mf, scf.hf.SCF)) and getattr(mf, '_scf', None):
mf = mf._scf
baslst = gto.mole._aolabels2baslst(mol, aolabels_or_baslst, base)
nao = dm.shape[0]
nimp = len(baslst)
log.debug('*** decompose density matrix')
log.debug('orth AO method = %s', orth_method)
log.debug('embedding AO list = %s', str(baslst))
if orth_method is not None:
corth = lo.orth.orth_ao(mol, method=orth_method, s=s)
cinv = numpy.dot(corth.T, s)
dm = reduce(numpy.dot, (cinv, dm, cinv.T))
else:
corth = numpy.eye(nao)
notimp = numpy.asarray([i for i in range(nao) if i not in baslst])
occi, ui = scipy.linalg.eigh(-dm[baslst[:,None],baslst])
occi *= -1
idxi = numpy.argsort(abs(occi-1))
log.debug('entanglement weight occ = %s', str(occi[idxi]))
occb, ub = scipy.linalg.eigh(dm[notimp[:,None],notimp])
idxb = numpy.argsort(abs(occb-1)) # sort by entanglement
occb = occb[idxb]
ub = ub[:,idxb]
# guess ncas and nelecas
nb = ((occb > occ_cutoff) & (occb < 2-occ_cutoff)).sum()
log.debug('bath weight occ = %s', occb[:nb])
cum_nelec = numpy.cumsum(occb[:nb]) + occi.sum()
cum_nelec = numpy.append(occi.sum(), cum_nelec)
log.debug('Active space cum nelec imp|[baths] = %f |%s',
cum_nelec[0], cum_nelec[1:])
ne_error = abs(cum_nelec.round() - cum_nelec)
nb4cas = nb
for i in range(nb):
if (ne_error[i] < threshold and
# whether all baths next to ith bath are less important
(occb[i] < threshold or occb[i] > 2-threshold)):
nb4cas = i
break
ncas = nb4cas + nimp
nelecas = int(cum_nelec[nb4cas].round())
ncore = (mol.nelectron - nelecas) // 2
log.info('From DMET guess, ncas = %d nelecas = %d ncore = %d',
ncas, nelecas, ncore)
log.debug('DMET impurity and bath orbitals on orthogonal AOs')
log.debug('DMET %d impurity sites/occ', nimp)
if log.verbose >= logger.DEBUG1:
label = mol.ao_labels()
occ_label = ['#%d/%.5f'%(i+1,x) for i,x in enumerate(occi)]
#dump_mat.dump_rec(mol.stdout, numpy.dot(corth[:,baslst], ui),
# label=label, label2=occ_label, start=1)
dump_mat.dump_rec(mol.stdout, ui, label=[label[i] for i in baslst],
label2=occ_label, start=1)
log.debug('DMET %d entangled baths/occ', nb)
if log.verbose >= logger.DEBUG1:
occ_label = ['#%d/%.5f'%(i+1,occb[i]) for i in range(nb)]
#dump_mat.dump_rec(mol.stdout, numpy.dot(corth[:,notimp], ub[:,:nb]),
# label=label, label2=occ_label, start=1)
dump_mat.dump_rec(mol.stdout, ub[:,:nb], label=[label[i] for i in notimp],
label2=occ_label, start=1)
mob = numpy.dot(corth[:,notimp], ub[:,:nb4cas])
idxenv = numpy.argsort(-occb[nb4cas:]) + nb4cas
mo_env = numpy.dot(corth[:,notimp], ub[:,idxenv])
mocore = mo_env[:,:ncore]
mocas = numpy.hstack((numpy.dot(corth[:,baslst],ui), mob))
movir = mo_env[:,ncore:]
if canonicalize or freeze_imp:
if mf.mo_energy is None or mf.mo_coeff is None:
fock = mf.get_hcore()
else:
if isinstance(mf.mo_coeff, numpy.ndarray) and mf.mo_coeff.ndim == 2:
sc = numpy.dot(s, mf.mo_coeff)
fock = numpy.dot(sc*mf.mo_energy, sc.T)
else:
sc = numpy.dot(s, mf.mo_coeff[0])
fock = numpy.dot(sc*mf.mo_energy[0], sc.T)
def trans(c):
if c.shape[1] == 0:
return c
else:
f1 = reduce(numpy.dot, (c.T, fock, c))
e, u = scipy.linalg.eigh(f1)
log.debug1('Fock eig %s', e)
return symmetrize(mol, e, numpy.dot(c, u), s, log)
if freeze_imp:
# freeze_imp to avoid canonicalization for impurity orbitals. It
# reserves the locality of the impurity orbitals even the rest
# orbitals are diffused due to the canonicalization.
log.debug('Semi-canonicalization for freeze_imp=True')
mo = numpy.hstack([trans(mocore), trans(mocas[:,:nimp]),
trans(mocas[:,nimp:]), trans(movir)])
else:
mo = numpy.hstack([trans(mocore), trans(mocas), trans(movir)])
else:
mo = numpy.hstack((mocore, mocas, movir))
return ncas, nelecas, mo
dmet_cas = guess_cas = kernel
[docs]
def search_for_degeneracy(e):
idx = numpy.where(abs(e[1:] - e[:-1]) < 1e-3)[0]
return numpy.unique(numpy.hstack((idx, idx+1)))
[docs]
def symmetrize(mol, e, c, s, log):
if mol.symmetry:
degidx = search_for_degeneracy(e)
log.debug1('degidx %s', degidx)
if degidx.size > 0:
esub = e[degidx]
csub = c[:,degidx]
scsub = numpy.dot(s, csub)
emin = abs(esub).min() * .5
es = []
cs = []
for i,ir in enumerate(mol.irrep_id):
so = mol.symm_orb[i]
sosc = numpy.dot(so.T, scsub)
s_ir = reduce(numpy.dot, (so.T, s, so))
fock_ir = numpy.dot(sosc*esub, sosc.T)
e, u = scipy.linalg.eigh(fock_ir, s_ir)
idx = abs(e) > emin
es.append(e[idx])
cs.append(numpy.dot(mol.symm_orb[i], u[:,idx]))
es = numpy.hstack(es)
idx = numpy.argsort(es, kind='mergesort')
assert (numpy.allclose(es[idx], esub, rtol=1e-3, atol=1e-4))
c[:,degidx] = numpy.hstack(cs)[:,idx]
return c
del (THRESHOLD, OCC_CUTOFF, BASE, ORTH_METHOD, CANONICALIZE, FREEZE_IMP)
if __name__ == '__main__':
from pyscf import mcscf
mol = gto.M(
verbose = 0,
atom = '''
H 0.000000, 0.500000, 1.5
O 0.000000, 0.000000, 1.
O 0.000000, 0.000000, -1.
H 0.000000, -0.500000, -1.5''',
basis = 'ccpvdz',
)
mf = scf.RHF(mol)
mf.scf()
aolst = [i for i,s in enumerate(mol.ao_labels()) if 'H 1s' in s]
dm = mf.make_rdm1()
ncas, nelecas, mo = guess_cas(mf, dm, aolst, verbose=4)
mc = mcscf.CASSCF(mf, ncas, nelecas).set(verbose=4)
emc = mc.kernel(mo)[0]
print(emc,)
