Source code for pyscf.mcscf.dmet_cas

#!/usr/bin/env python
# Copyright 2014-2020 The PySCF Developers. All Rights Reserved.
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# 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
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#     http://www.apache.org/licenses/LICENSE-2.0
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# 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.
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# limitations under the License.
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# 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 orbtial. 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 Hamilatonian. 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,)