Source code for pyscf.mcscf.casci

#!/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>
#

import sys

from functools import reduce
import warnings
import numpy
from pyscf import lib
from pyscf.lib import logger
from pyscf import gto
from pyscf import scf
from pyscf import ao2mo
from pyscf import fci
from pyscf.mcscf import addons
from pyscf import __config__

WITH_META_LOWDIN = getattr(__config__, 'mcscf_analyze_with_meta_lowdin', True)
LARGE_CI_TOL = getattr(__config__, 'mcscf_analyze_large_ci_tol', 0.1)
PENALTY = getattr(__config__, 'mcscf_casci_CASCI_fix_spin_shift', 0.2)
FRAC_OCC_THRESHOLD = 1e-6

if sys.version_info < (3,):
    RANGE_TYPE = list
else:
    RANGE_TYPE = range


[docs] def h1e_for_cas(casci, mo_coeff=None, ncas=None, ncore=None): '''CAS sapce one-electron hamiltonian Args: casci : a CASSCF/CASCI object or RHF object Returns: A tuple, the first is the effective one-electron hamiltonian defined in CAS space, the second is the electronic energy from core. ''' if mo_coeff is None: mo_coeff = casci.mo_coeff if ncas is None: ncas = casci.ncas if ncore is None: ncore = casci.ncore mo_core = mo_coeff[:,:ncore] mo_cas = mo_coeff[:,ncore:ncore+ncas] hcore = casci.get_hcore() energy_core = casci.energy_nuc() if mo_core.size == 0: corevhf = 0 else: core_dm = numpy.dot(mo_core, mo_core.conj().T) * 2 corevhf = casci.get_veff(casci.mol, core_dm) energy_core += numpy.einsum('ij,ji', core_dm, hcore).real energy_core += numpy.einsum('ij,ji', core_dm, corevhf).real * .5 h1eff = reduce(numpy.dot, (mo_cas.conj().T, hcore+corevhf, mo_cas)) return h1eff, energy_core
[docs] def analyze(casscf, mo_coeff=None, ci=None, verbose=None, large_ci_tol=LARGE_CI_TOL, with_meta_lowdin=WITH_META_LOWDIN, **kwargs): from pyscf.lo import orth from pyscf.tools import dump_mat from pyscf.mcscf import addons log = logger.new_logger(casscf, verbose) if mo_coeff is None: mo_coeff = casscf.mo_coeff if ci is None: ci = casscf.ci nelecas = casscf.nelecas ncas = casscf.ncas ncore = casscf.ncore nocc = ncore + ncas mocore = mo_coeff[:,:ncore] mocas = mo_coeff[:,ncore:nocc] label = casscf.mol.ao_labels() if (isinstance(ci, (list, tuple, RANGE_TYPE)) and not isinstance(casscf.fcisolver, addons.StateAverageFCISolver)): log.warn('Mulitple states found in CASCI/CASSCF solver. Density ' 'matrix of the first state is generated in .analyze() function.') civec = ci[0] else: civec = ci if getattr(casscf.fcisolver, 'make_rdm1s', None): casdm1a, casdm1b = casscf.fcisolver.make_rdm1s(civec, ncas, nelecas) casdm1 = casdm1a + casdm1b dm1b = numpy.dot(mocore, mocore.conj().T) dm1a = dm1b + reduce(numpy.dot, (mocas, casdm1a, mocas.conj().T)) dm1b += reduce(numpy.dot, (mocas, casdm1b, mocas.conj().T)) dm1 = dm1a + dm1b spin_dm1 = dm1a - dm1b if log.verbose >= logger.DEBUG2: log.info('alpha density matrix (on AO)') dump_mat.dump_tri(log.stdout, dm1a, label, **kwargs) log.info('beta density matrix (on AO)') dump_mat.dump_tri(log.stdout, dm1b, label, **kwargs) else: casdm1 = casscf.fcisolver.make_rdm1(civec, ncas, nelecas) dm1a = (numpy.dot(mocore, mocore.conj().T) * 2 + reduce(numpy.dot, (mocas, casdm1, mocas.conj().T))) dm1b = None dm1 = dm1a spin_dm1 = None if log.verbose >= logger.INFO: ovlp_ao = casscf._scf.get_ovlp() # note the last two args of ._eig for mc1step_symm occ, ucas = casscf._eig(-casdm1, ncore, nocc) log.info('Natural occ %s', str(-occ)) mocas = numpy.dot(mocas, ucas) if with_meta_lowdin: log.info('Natural orbital (expansion on meta-Lowdin AOs) in CAS space') orth_coeff = orth.orth_ao(casscf.mol, 'meta_lowdin', s=ovlp_ao) mocas = reduce(numpy.dot, (orth_coeff.conj().T, ovlp_ao, mocas)) else: log.info('Natural orbital (expansion on AOs) in CAS space') dump_mat.dump_rec(log.stdout, mocas, label, start=1, **kwargs) if log.verbose >= logger.DEBUG2: if not casscf.natorb: log.debug2('NOTE: mc.mo_coeff in active space is different to ' 'the natural orbital coefficients printed in above.') if with_meta_lowdin: c = reduce(numpy.dot, (orth_coeff.conj().T, ovlp_ao, mo_coeff)) log.debug2('MCSCF orbital (expansion on meta-Lowdin AOs)') else: c = mo_coeff log.debug2('MCSCF orbital (expansion on AOs)') dump_mat.dump_rec(log.stdout, c, label, start=1, **kwargs) if casscf._scf.mo_coeff is not None: addons.map2hf(casscf, casscf._scf.mo_coeff) if (ci is not None and (getattr(casscf.fcisolver, 'large_ci', None) or getattr(casscf.fcisolver, 'states_large_ci', None))): log.info('** Largest CI components **') if isinstance(ci, (list, tuple, RANGE_TYPE)): if hasattr(casscf.fcisolver, 'states_large_ci'): # defined in state_average_mix_ mcscf object res = casscf.fcisolver.states_large_ci(ci, casscf.ncas, casscf.nelecas, large_ci_tol, return_strs=False) else: res = [casscf.fcisolver.large_ci(civec, casscf.ncas, casscf.nelecas, large_ci_tol, return_strs=False) for civec in ci] for i, civec in enumerate(ci): log.info(' [alpha occ-orbitals] [beta occ-orbitals] state %-3d CI coefficient', i) for c,ia,ib in res[i]: log.info(' %-20s %-30s % .12f', ia, ib, c) else: log.info(' [alpha occ-orbitals] [beta occ-orbitals] CI coefficient') res = casscf.fcisolver.large_ci(ci, casscf.ncas, casscf.nelecas, large_ci_tol, return_strs=False) for c,ia,ib in res: log.info(' %-20s %-30s % .12f', ia, ib, c) if with_meta_lowdin: casscf._scf.mulliken_meta(casscf.mol, dm1, s=ovlp_ao, verbose=log) else: casscf._scf.mulliken_pop(casscf.mol, dm1, s=ovlp_ao, verbose=log) if spin_dm1 is not None: if with_meta_lowdin: log.info('Mulliken spin population analysis on meta-Lowdin AOs:') spin_pop, spin_chg = casscf._scf.mulliken_meta(casscf.mol, spin_dm1, s=ovlp_ao, verbose=log) else: log.info('Mulliken spin population analysis on AOs:') spin_pop, spin_chg = casscf._scf.mulliken_pop(casscf.mol, spin_dm1, s=ovlp_ao, verbose=log) for i, s in enumerate(label): log.info('spop of %-12s %10.5f', s, spin_pop[i]) spin_chg = casscf.mol.atom_charges() - spin_chg log.note('Mulliken atomic spins:') for ia in range(casscf.mol.natm): symb = casscf.mol.atom_symbol(ia) log.note('spin of %d%s = %10.5f', ia, symb, spin_chg[ia]) return dm1a, dm1b
[docs] def get_fock(mc, mo_coeff=None, ci=None, eris=None, casdm1=None, verbose=None): r''' Effective one-electron Fock matrix in AO representation f = \sum_{pq} E_{pq} F_{pq} F_{pq} = h_{pq} + \sum_{rs} [(pq|rs)-(ps|rq)] DM_{sr} Ref. Theor. Chim. Acta., 91, 31 Chem. Phys. 48, 157 For state-average CASCI/CASSCF object, the effective fock matrix is based on the state-average density matrix. To obtain Fock matrix of a specific state in the state-average calculations, you can pass "casdm1" of the specific state to this function. Args: mc: a CASSCF/CASCI object or RHF object Kwargs: mo_coeff (ndarray): orbitals that span the core, active and external space. ci (ndarray): CI coefficients (or objects to represent the CI wavefunctions in DMRG/QMC-MCSCF calculations). eris: Integrals for the MCSCF object. Input this object to reduce the overhead of computing integrals. It can be generated by :func:`mc.ao2mo` method. casdm1 (ndarray): 1-particle density matrix in active space. Without input casdm1, the density matrix is computed with the input ci coefficients/object. If neither ci nor casdm1 were given, density matrix is computed by :func:`mc.fcisolver.make_rdm1` method. For state-average CASCI/CASCF calculation, this results in the effective Fock matrix based on the state-average density matrix. To obtain the effective Fock matrix for one particular state, you can assign the density matrix of that state to the kwarg casdm1. Returns: Fock matrix ''' if ci is None: ci = mc.ci if mo_coeff is None: mo_coeff = mc.mo_coeff nmo = mo_coeff.shape[1] ncore = mc.ncore ncas = mc.ncas nocc = ncore + ncas nelecas = mc.nelecas if casdm1 is None: casdm1 = mc.fcisolver.make_rdm1(ci, ncas, nelecas) if getattr(eris, 'ppaa', None) is not None: vj = numpy.empty((nmo,nmo)) vk = numpy.empty((nmo,nmo)) for i in range(nmo): vj[i] = numpy.einsum('ij,qij->q', casdm1, eris.ppaa[i]) vk[i] = numpy.einsum('ij,iqj->q', casdm1, eris.papa[i]) mo_inv = numpy.dot(mo_coeff.conj().T, mc._scf.get_ovlp()) fock = (mc.get_hcore() + reduce(numpy.dot, (mo_inv.conj().T, eris.vhf_c+vj-vk*.5, mo_inv))) else: dm_core = numpy.dot(mo_coeff[:,:ncore]*2, mo_coeff[:,:ncore].conj().T) mocas = mo_coeff[:,ncore:nocc] dm = dm_core + reduce(numpy.dot, (mocas, casdm1, mocas.conj().T)) vj, vk = mc._scf.get_jk(mc.mol, dm) fock = mc.get_hcore() + vj-vk*.5 return fock
[docs] def cas_natorb(mc, mo_coeff=None, ci=None, eris=None, sort=False, casdm1=None, verbose=None, with_meta_lowdin=WITH_META_LOWDIN): '''Transform active orbitals to natural orbitals, and update the CI wfn accordingly Args: mc : a CASSCF/CASCI object or RHF object Kwargs: sort : bool Sort natural orbitals wrt the occupancy. Returns: A tuple, the first item is natural orbitals, the second is updated CI coefficients, the third is the natural occupancy associated to the natural orbitals. ''' from pyscf.lo import orth from pyscf.tools import dump_mat from pyscf.tools.mo_mapping import mo_1to1map if mo_coeff is None: mo_coeff = mc.mo_coeff if ci is None: ci = mc.ci log = logger.new_logger(mc, verbose) ncore = mc.ncore ncas = mc.ncas nocc = ncore + ncas nelecas = mc.nelecas nmo = mo_coeff.shape[1] if casdm1 is None: casdm1 = mc.fcisolver.make_rdm1(ci, ncas, nelecas) if getattr(mo_coeff, 'orbsym', None) is not None: orbsym = numpy.copy(mo_coeff.orbsym) else: orbsym = numpy.zeros(mo_coeff.shape[1], dtype=int) if getattr(mc, 'extrasym', None) is not None: orbsym_extra = numpy.asarray([str(i1) + str(i2) for i1, i2 in zip(orbsym, mc.extrasym)]) else: orbsym_extra = orbsym # orbital symmetry is reserved in this _eig call cas_occ, ucas = mc._eig(-casdm1, ncore, nocc, orbsym_extra[ncore:nocc]) if sort: casorb_idx = numpy.argsort(cas_occ.round(9), kind='mergesort') cas_occ = cas_occ[casorb_idx] ucas = ucas[:,casorb_idx] cas_occ = -cas_occ mo_occ = numpy.zeros(mo_coeff.shape[1]) mo_occ[:ncore] = 2 mo_occ[ncore:nocc] = cas_occ mo_coeff1 = mo_coeff.copy() mo_coeff1[:,ncore:nocc] = numpy.dot(mo_coeff[:,ncore:nocc], ucas) if getattr(mo_coeff, 'orbsym', None) is not None: if sort: orbsym[ncore:nocc] = orbsym[ncore:nocc][casorb_idx] mo_coeff1 = lib.tag_array(mo_coeff1, orbsym=orbsym) else: orbsym = numpy.zeros(nmo, dtype=int) # When occupancies of active orbitals equal to 2 or 0, these orbitals # need to be canonicalized along with inactive(core or virtual) orbitals # using general Fock matrix. Because they are strongly coupled with # inactive orbitals, the 0th order Hamiltonian of MRPT methods can be # strongly affected. Numerical uncertainty may be found in the perturbed # correlation energy. # See issue https://github.com/pyscf/pyscf/issues/1041 occ2_idx = numpy.where(2 - cas_occ < FRAC_OCC_THRESHOLD)[0] occ0_idx = numpy.where(cas_occ < FRAC_OCC_THRESHOLD)[0] if occ2_idx.size > 0 or occ0_idx.size > 0: fock_ao = mc.get_fock(mo_coeff, ci, eris, casdm1, verbose) def _diag_subfock_(idx): c = mo_coeff1[:,idx] fock = reduce(numpy.dot, (c.conj().T, fock_ao, c)) w, c = mc._eig(fock, None, None, orbsym[idx]) mo_coeff1[:,idx] = mo_coeff1[:,idx].dot(c) if occ2_idx.size > 0: log.warn('Active orbitals %s (occs = %s) are canonicalized with core orbitals', occ2_idx, cas_occ[occ2_idx]) full_occ2_idx = numpy.append(numpy.arange(ncore), ncore + occ2_idx) _diag_subfock_(full_occ2_idx) if occ0_idx.size > 0: log.warn('Active orbitals %s (occs = %s) are canonicalized with external orbitals', occ0_idx, cas_occ[occ0_idx]) full_occ0_idx = numpy.append(ncore + occ0_idx, numpy.arange(nocc, nmo)) _diag_subfock_(full_occ0_idx) # Rotate CI according to the unitary coefficients ucas if applicable fcivec = None if getattr(mc.fcisolver, 'transform_ci_for_orbital_rotation', None): if isinstance(ci, (fci.FCIvector, fci.SCIvector, numpy.ndarray)): fcivec = mc.fcisolver.transform_ci_for_orbital_rotation(ci, ncas, nelecas, ucas) elif (isinstance(ci, (list, tuple)) and all(isinstance(x[0], (fci.FCIvector, fci.SCIvector, numpy.ndarray)) for x in ci)): fcivec = [mc.fcisolver.transform_ci_for_orbital_rotation(x, ncas, nelecas, ucas) for x in ci] elif getattr(mc.fcisolver, 'states_transform_ci_for_orbital_rotation', None): fcivec = mc.fcisolver.states_transform_ci_for_orbital_rotation(ci, ncas, nelecas, ucas) # Rerun fcisolver to get wavefunction if it cannot be transformed from # existed one. if fcivec is None: log.info('FCI vector not available, call CASCI to update wavefunction') mocas = mo_coeff1[:,ncore:nocc] hcore = mc.get_hcore() dm_core = numpy.dot(mo_coeff1[:,:ncore]*2, mo_coeff1[:,:ncore].conj().T) ecore = mc.energy_nuc() ecore+= numpy.einsum('ij,ji', hcore, dm_core) h1eff = reduce(numpy.dot, (mocas.conj().T, hcore, mocas)) if getattr(eris, 'ppaa', None) is not None: ecore += eris.vhf_c[:ncore,:ncore].trace() h1eff += reduce(numpy.dot, (ucas.conj().T, eris.vhf_c[ncore:nocc,ncore:nocc], ucas)) aaaa = ao2mo.restore(4, eris.ppaa[ncore:nocc,ncore:nocc,:,:], ncas) aaaa = ao2mo.incore.full(aaaa, ucas) else: if getattr(mc, 'with_df', None): aaaa = mc.with_df.ao2mo(mocas) else: aaaa = ao2mo.kernel(mc.mol, mocas) corevhf = mc.get_veff(mc.mol, dm_core) ecore += numpy.einsum('ij,ji', dm_core, corevhf) * .5 h1eff += reduce(numpy.dot, (mocas.conj().T, corevhf, mocas)) # See label_symmetry_ function in casci_symm.py which initialize the # orbital symmetry information in fcisolver. This orbital symmetry # labels should be reordered to match the sorted active space orbitals. if sort and getattr(mo_coeff1, 'orbsym', None) is not None: mc.fcisolver.orbsym = mo_coeff1.orbsym[ncore:nocc] max_memory = max(400, mc.max_memory-lib.current_memory()[0]) e, fcivec = mc.fcisolver.kernel(h1eff, aaaa, ncas, nelecas, ecore=ecore, max_memory=max_memory, verbose=log) log.debug('In Natural orbital, CASCI energy = %s', e) if log.verbose >= logger.INFO: ovlp_ao = mc._scf.get_ovlp() # where_natorb gives the new locations of the natural orbitals where_natorb = mo_1to1map(ucas) log.debug('where_natorb %s', str(where_natorb)) log.info('Natural occ %s', str(cas_occ)) if with_meta_lowdin: log.info('Natural orbital (expansion on meta-Lowdin AOs) in CAS space') label = mc.mol.ao_labels() orth_coeff = orth.orth_ao(mc.mol, 'meta_lowdin', s=ovlp_ao) mo_cas = reduce(numpy.dot, (orth_coeff.conj().T, ovlp_ao, mo_coeff1[:,ncore:nocc])) else: log.info('Natural orbital (expansion on AOs) in CAS space') label = mc.mol.ao_labels() mo_cas = mo_coeff1[:,ncore:nocc] dump_mat.dump_rec(log.stdout, mo_cas, label, start=1) if mc._scf.mo_coeff is not None: s = reduce(numpy.dot, (mo_coeff1[:,ncore:nocc].conj().T, mc._scf.get_ovlp(), mc._scf.mo_coeff)) idx = numpy.argwhere(abs(s)>.4) for i,j in idx: log.info('<CAS-nat-orb|mo-hf> %-5d %-5d % 12.8f', ncore+i+1, j+1, s[i,j]) return mo_coeff1, fcivec, mo_occ
[docs] def canonicalize(mc, mo_coeff=None, ci=None, eris=None, sort=False, cas_natorb=False, casdm1=None, verbose=logger.NOTE, with_meta_lowdin=WITH_META_LOWDIN, stav_dm1=False): '''Canonicalized CASCI/CASSCF orbitals of effecitive Fock matrix and update CI coefficients accordingly. Effective Fock matrix is built with one-particle density matrix (see also :func:`mcscf.casci.get_fock`). For state-average CASCI/CASSCF object, the canonicalized orbitals are based on the state-average density matrix. To obtain canonicalized orbitals for an individual state, you need to pass "casdm1" of the specific state to this function. Args: mc: a CASSCF/CASCI object or RHF object Kwargs: mo_coeff (ndarray): orbitals that span the core, active and external space. ci (ndarray): CI coefficients (or objects to represent the CI wavefunctions in DMRG/QMC-MCSCF calculations). eris: Integrals for the MCSCF object. Input this object to reduce the overhead of computing integrals. It can be generated by :func:`mc.ao2mo` method. sort (bool): Whether the canonicalized orbitals are sorted based on the orbital energy (diagonal part of the effective Fock matrix) within each subspace (core, active, external). If point group symmetry is not available in the system, orbitals are always sorted. When point group symmetry is available, sort=False will preserve the symmetry label of input orbitals and only sort the orbitals in each symmetry sector. sort=True will reorder all orbitals over all symmetry sectors in each subspace and the symmetry labels may be changed. cas_natorb (bool): Whether to transform active orbitals to natual orbitals. If enabled, the output orbitals in active space are transformed to natural orbitals and CI coefficients are updated accordingly. casdm1 (ndarray): 1-particle density matrix in active space. This density matrix is used to build effective fock matrix. Without input casdm1, the density matrix is computed with the input ci coefficients/object. If neither ci nor casdm1 were given, density matrix is computed by :func:`mc.fcisolver.make_rdm1` method. For state-average CASCI/CASCF calculation, this results in a set of canonicalized orbitals of state-average effective Fock matrix. To canonicalize the orbitals for one particular state, you can assign the density matrix of that state to the kwarg casdm1. stav_dm1 (bool): Use state-average 1-particle density matrix for computing Fock matrices and natural orbitals Returns: A tuple, (natural orbitals, CI coefficients, orbital energies) The orbital energies are the diagonal terms of effective Fock matrix. ''' from pyscf.mcscf import addons log = logger.new_logger(mc, verbose) if mo_coeff is None: mo_coeff = mc.mo_coeff if ci is None: ci = mc.ci if casdm1 is None: if (isinstance(ci, (list, tuple, RANGE_TYPE)) and not isinstance(mc.fcisolver, addons.StateAverageFCISolver)): if stav_dm1: log.warn('Mulitple states found in CASCI solver. ' 'Use state-average 1RDM to compute the Fock matrix' ' and natural orbitals in the active space.') casdm1 = mc.fcisolver.make_rdm1(ci[0], mc.ncas, mc.nelecas) for root in range(1, len(ci)): casdm1 += mc.fcisolver.make_rdm1(ci[root], mc.ncas, mc.nelecas) casdm1 /= len(ci) else: log.warn('Mulitple states found in CASCI solver. ' 'First state is used to compute the Fock matrix' ' and natural orbitals in active space.') casdm1 = mc.fcisolver.make_rdm1(ci[0], mc.ncas, mc.nelecas) else: casdm1 = mc.fcisolver.make_rdm1(ci, mc.ncas, mc.nelecas) ncore = mc.ncore nocc = ncore + mc.ncas nmo = mo_coeff.shape[1] fock_ao = mc.get_fock(mo_coeff, ci, eris, casdm1, verbose) if cas_natorb: mo_coeff1, ci, mc.mo_occ = mc.cas_natorb(mo_coeff, ci, eris, sort, casdm1, verbose, with_meta_lowdin) else: # Keep the active space unchanged by default. The rotation in active space # may cause problem for external CI solver eg DMRG. mo_coeff1 = mo_coeff.copy() log.info('Density matrix diagonal elements %s', casdm1.diagonal()) mo_energy = numpy.einsum('pi,pi->i', mo_coeff1.conj(), fock_ao.dot(mo_coeff1)) if getattr(mo_coeff, 'orbsym', None) is not None: orbsym = mo_coeff.orbsym else: orbsym = numpy.zeros(nmo, dtype=int) extrasym = getattr(mc, 'extrasym', None) if extrasym is not None: orbsym_extra = numpy.asarray([str(i1) + str(i2) for i1, i2 in zip(orbsym, extrasym)]) else: orbsym_extra = orbsym def _diag_subfock_(idx): if idx.size > 1: c = mo_coeff1[:,idx] fock = reduce(numpy.dot, (c.conj().T, fock_ao, c)) # note the last argument orbysm is needed by mc1step_symm._eig w, c = mc._eig(fock, None, None, orbsym_extra[idx]) if sort: sub_order = numpy.argsort(w.round(9), kind='mergesort') w = w[sub_order] c = c[:,sub_order] orbsym[idx] = orbsym[idx][sub_order] mo_coeff1[:,idx] = mo_coeff1[:,idx].dot(c) mo_energy[idx] = w mask = numpy.ones(nmo, dtype=bool) frozen = getattr(mc, 'frozen', None) if frozen is not None: if isinstance(frozen, (int, numpy.integer)): mask[:frozen] = False else: mask[frozen] = False core_idx = numpy.where(mask[:ncore])[0] vir_idx = numpy.where(mask[nocc:])[0] + nocc _diag_subfock_(core_idx) _diag_subfock_(vir_idx) # orbsym is required only for symmetry-adapted methods. Here to use # mo_coeff.orbsym to test if a symmetry-adapted calculation. if getattr(mo_coeff, 'orbsym', None) is not None: mo_coeff1 = lib.tag_array(mo_coeff1, orbsym=orbsym) if log.verbose >= logger.DEBUG: for i in range(nmo): log.debug('i = %d <i|F|i> = %12.8f', i+1, mo_energy[i]) # still return ci coefficients, in case the canonicalization funciton changed # cas orbitals, the ci coefficients should also be updated. return mo_coeff1, ci, mo_energy
[docs] def kernel(casci, mo_coeff=None, ci0=None, verbose=logger.NOTE, envs=None): '''CASCI solver Args: casci: CASCI or CASSCF object mo_coeff : ndarray orbitals to construct active space Hamiltonian ci0 : ndarray or custom types FCI sovler initial guess. For external FCI-like solvers, it can be overloaded different data type. For example, in the state-average FCI solver, ci0 is a list of ndarray. In other solvers such as DMRGCI solver, SHCI solver, ci0 are custom types. kwargs: envs: dict The variable envs is created (for PR 807) to passes MCSCF runtime environment variables to SHCI solver. For solvers which do not need this parameter, a kwargs should be created in kernel method and "envs" pop in kernel function ''' if mo_coeff is None: mo_coeff = casci.mo_coeff log = logger.new_logger(casci, verbose) t0 = (logger.process_clock(), logger.perf_counter()) log.debug('Start CASCI') ncas = casci.ncas nelecas = casci.nelecas # 2e eri_cas = casci.get_h2eff(mo_coeff) t1 = log.timer('integral transformation to CAS space', *t0) # 1e h1eff, energy_core = casci.get_h1eff(mo_coeff) log.debug('core energy = %.15g', energy_core) t1 = log.timer('effective h1e in CAS space', *t1) if h1eff.shape[0] != ncas: raise RuntimeError('Active space size error. nmo=%d ncore=%d ncas=%d' % (mo_coeff.shape[1], casci.ncore, ncas)) # FCI max_memory = max(400, casci.max_memory-lib.current_memory()[0]) e_tot, fcivec = casci.fcisolver.kernel(h1eff, eri_cas, ncas, nelecas, ci0=ci0, verbose=log, max_memory=max_memory, ecore=energy_core) t1 = log.timer('FCI solver', *t1) e_cas = e_tot - energy_core return e_tot, e_cas, fcivec
[docs] def as_scanner(mc): '''Generating a scanner for CASCI PES. The returned solver is a function. This function requires one argument "mol" as input and returns total CASCI energy. The solver will automatically use the results of last calculation as the initial guess of the new calculation. All parameters of MCSCF object are automatically applied in the solver. Note scanner has side effects. It may change many underlying objects (_scf, with_df, with_x2c, ...) during calculation. Examples: >>> from pyscf import gto, scf, mcscf >>> mf = scf.RHF(gto.Mole().set(verbose=0)) >>> mc_scanner = mcscf.CASCI(mf, 4, 4).as_scanner() >>> mc_scanner(gto.M(atom='N 0 0 0; N 0 0 1.1')) >>> mc_scanner(gto.M(atom='N 0 0 0; N 0 0 1.5')) ''' if isinstance(mc, lib.SinglePointScanner): return mc logger.info(mc, 'Create scanner for %s', mc.__class__) name = mc.__class__.__name__ + CASCI_Scanner.__name_mixin__ return lib.set_class(CASCI_Scanner(mc), (CASCI_Scanner, mc.__class__), name)
[docs] class CASCI_Scanner(lib.SinglePointScanner): def __init__(self, mc): self.__dict__.update(mc.__dict__) self._scf = mc._scf.as_scanner() def __call__(self, mol_or_geom, mo_coeff=None, ci0=None): if isinstance(mol_or_geom, gto.MoleBase): mol = mol_or_geom else: mol = self.mol.set_geom_(mol_or_geom, inplace=False) self.reset (mol) if mo_coeff is None: mf_scanner = self._scf mf_scanner(mol) mo_coeff = mf_scanner.mo_coeff if ci0 is None: ci0 = self.ci self.mol = mol e_tot = self.kernel(mo_coeff, ci0)[0] return e_tot
[docs] class CASBase(lib.StreamObject): '''CASCI/CASSCF Args: mf_or_mol : SCF object or Mole object SCF or Mole to define the problem size. ncas : int Number of active orbitals. nelecas : int or a pair of int Number of electrons in active space. Kwargs: ncore : int Number of doubly occupied core orbitals. If not presented, this parameter can be automatically determined. Attributes: verbose : int Print level. Default value equals to :class:`Mole.verbose`. max_memory : float or int Allowed memory in MB. Default value equals to :class:`Mole.max_memory`. ncas : int Active space size. nelecas : tuple of int Active (nelec_alpha, nelec_beta) ncore : int or tuple of int Core electron number. In UHF-CASSCF, it's a tuple to indicate the different core eletron numbers. natorb : bool Whether to transform natural orbitals in active space. Note: when CASCI/CASSCF are combined with DMRG solver or selected CI solver, enabling this parameter may slightly change the total energy. False by default. canonicalization : bool Whether to canonicalize orbitals in core and external space against the general Fock matrix. The orbitals in active space are NOT transformed by default. To get the natural orbitals in active space, the attribute .natorb needs to be enabled. True by default. sorting_mo_energy : bool Whether to sort the orbitals based on the diagonal elements of the general Fock matrix. Default is False. fcisolver : an instance of :class:`FCISolver` The pyscf.fci module provides several FCISolver for different scenario. Generally, fci.direct_spin1.FCISolver can be used for all RHF-CASSCF. However, a proper FCISolver can provide better performance and better numerical stability. One can either use :func:`fci.solver` function to pick the FCISolver by the program or manually assigen the FCISolver to this attribute, e.g. >>> from pyscf import fci >>> mc = mcscf.CASSCF(mf, 4, 4) >>> mc.fcisolver = fci.solver(mol, singlet=True) >>> mc.fcisolver = fci.direct_spin1.FCISolver(mol) You can control FCISolver by setting e.g.:: >>> mc.fcisolver.max_cycle = 30 >>> mc.fcisolver.conv_tol = 1e-7 For more details of the parameter for FCISolver, See :mod:`fci`. Saved results e_tot : float Total MCSCF energy (electronic energy plus nuclear repulsion) e_cas : float CAS space FCI energy ci : ndarray CAS space FCI coefficients mo_coeff : ndarray When canonicalization is specified, the orbitals are canonical orbitals which make the general Fock matrix (Fock operator on top of MCSCF 1-particle density matrix) diagonalized within each subspace (core, active, external). If natorb (natural orbitals in active space) is specified, the active segment of the mo_coeff is natural orbitls. mo_energy : ndarray Diagonal elements of general Fock matrix (in mo_coeff representation). mo_occ : ndarray Occupation numbers of natural orbitals if natorb is specified. Examples: >>> from pyscf import gto, scf, mcscf >>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvdz', verbose=0) >>> mf = scf.RHF(mol) >>> mf.scf() >>> mc = mcscf.CASCI(mf, 6, 6) >>> mc.kernel()[0] -108.980200816243354 ''' natorb = getattr(__config__, 'mcscf_casci_CASCI_natorb', False) canonicalization = getattr(__config__, 'mcscf_casci_CASCI_canonicalization', True) sorting_mo_energy = getattr(__config__, 'mcscf_casci_CASCI_sorting_mo_energy', False) _keys = set(( 'natorb', 'canonicalization', 'sorting_mo_energy', 'mol', 'max_memory', 'ncas', 'nelecas', 'ncore', 'fcisolver', 'frozen', 'extrasym', 'e_tot', 'e_cas', 'ci', 'mo_coeff', 'mo_energy', 'mo_occ', 'converged', )) def __init__(self, mf_or_mol, ncas, nelecas, ncore=None): if isinstance(mf_or_mol, gto.Mole): mf = scf.RHF(mf_or_mol) else: mf = mf_or_mol mol = mf.mol self.mol = mol self._scf = mf self.verbose = mol.verbose self.stdout = mol.stdout self.max_memory = mf.max_memory self.ncas = ncas if isinstance(nelecas, (int, numpy.integer)): nelecb = (nelecas-mol.spin)//2 neleca = nelecas - nelecb self.nelecas = (neleca, nelecb) else: self.nelecas = (nelecas[0],nelecas[1]) self.ncore = ncore singlet = (getattr(__config__, 'mcscf_casci_CASCI_fcisolver_direct_spin0', False) and self.nelecas[0] == self.nelecas[1]) # leads to direct_spin1 self.fcisolver = fci.solver(mol, singlet, symm=False) # CI solver parameters are set in fcisolver object self.fcisolver.lindep = getattr(__config__, 'mcscf_casci_CASCI_fcisolver_lindep', 1e-12) self.fcisolver.max_cycle = getattr(__config__, 'mcscf_casci_CASCI_fcisolver_max_cycle', 200) self.fcisolver.conv_tol = getattr(__config__, 'mcscf_casci_CASCI_fcisolver_conv_tol', 1e-8) self.frozen = None self.extrasym = None ################################################## # don't modify the following attributes, they are not input options self.e_tot = 0 self.e_cas = None self.ci = None self.mo_coeff = mf.mo_coeff self.mo_energy = mf.mo_energy self.mo_occ = None self.converged = False @property def ncore(self): if self._ncore is None: ncorelec = self.mol.nelectron - sum(self.nelecas) assert ncorelec % 2 == 0 assert ncorelec >= 0 return ncorelec // 2 else: return self._ncore @ncore.setter def ncore(self, x): assert x is None or isinstance(x, (int, numpy.integer)) assert x is None or x >= 0 self._ncore = x
[docs] def dump_flags(self, verbose=None): log = logger.new_logger(self, verbose) log.info('') log.info('******** CASCI flags ********') ncore = self.ncore ncas = self.ncas nvir = self.mo_coeff.shape[1] - ncore - ncas log.info('CAS (%de+%de, %do), ncore = %d, nvir = %d', self.nelecas[0], self.nelecas[1], ncas, ncore, nvir) if self.frozen is not None: log.info('frozen orbitals %s', str(self.frozen)) if self.extrasym is not None: log.info('extra symmetry labels:\n%s', str(self.extrasym)) log.info('natorb = %s', self.natorb) log.info('canonicalization = %s', self.canonicalization) log.info('sorting_mo_energy = %s', self.sorting_mo_energy) log.info('max_memory %d (MB)', self.max_memory) if getattr(self.fcisolver, 'dump_flags', None): self.fcisolver.dump_flags(log.verbose) if self.mo_coeff is None: log.error('Orbitals for CASCI are not specified. The relevant SCF ' 'object may not be initialized.') if (getattr(self._scf, 'with_solvent', None) and not getattr(self, 'with_solvent', None)): log.warn('''Solvent model %s was found at SCF level but not applied to the CASCI object. The SCF solvent model will not be applied to the current CASCI calculation. To enable the solvent model for CASCI, the following code needs to be called from pyscf import solvent mc = mcscf.CASCI(...) mc = solvent.ddCOSMO(mc) ''', self._scf.with_solvent.__class__) return self
[docs] def check_sanity(self): super().check_sanity() assert self.ncas > 0 ncore = self.ncore nvir = self.mo_coeff.shape[1] - ncore - self.ncas assert ncore >= 0 assert nvir >= 0 assert ncore * 2 + sum(self.nelecas) == self.mol.nelectron assert 0 <= self.nelecas[0] <= self.ncas assert 0 <= self.nelecas[1] <= self.ncas return self
[docs] def reset(self, mol=None): if mol is not None: self.mol = mol self.fcisolver.mol = mol self._scf.reset(mol) return self
[docs] def energy_nuc(self): return self._scf.energy_nuc()
[docs] def get_hcore(self, mol=None): return self._scf.get_hcore(mol)
[docs] @lib.with_doc(scf.hf.get_jk.__doc__) def get_jk(self, mol, dm, hermi=1, with_j=True, with_k=True, omega=None): return self._scf.get_jk(mol, dm, hermi, with_j=with_j, with_k=with_k, omega=omega)
[docs] @lib.with_doc(scf.hf.get_veff.__doc__) def get_veff(self, mol=None, dm=None, hermi=1): if mol is None: mol = self.mol if dm is None: mocore = self.mo_coeff[:,:self.ncore] dm = numpy.dot(mocore, mocore.conj().T) * 2 # don't call self._scf.get_veff because _scf might be DFT object vj, vk = self.get_jk(mol, dm, hermi) return vj - vk * .5
def _eig(self, h, *args): return scf.hf.eig(h, None)
[docs] def get_h2cas(self, mo_coeff=None): '''An alias of get_h2eff method''' return self.get_h2eff(mo_coeff)
[docs] def get_h2eff(self, mo_coeff=None): '''Compute the active space two-particle Hamiltonian. ''' raise NotImplementedError
[docs] def ao2mo(self, mo_coeff=None): '''Compute the active space two-particle Hamiltonian. ''' raise NotImplementedError
[docs] def get_h1cas(self, mo_coeff=None, ncas=None, ncore=None): '''An alias of get_h1eff method''' return self.get_h1eff(mo_coeff, ncas, ncore)
get_h1eff = h1e_for_cas = h1e_for_cas
[docs] def casci(self, mo_coeff=None, ci0=None, verbose=None): raise NotImplementedError
[docs] def kernel(self, mo_coeff=None, ci0=None, verbose=None): ''' Returns: Five elements, they are total energy, active space CI energy, the active space FCI wavefunction coefficients or DMRG wavefunction ID, the MCSCF canonical orbital coefficients, the MCSCF canonical orbital coefficients. They are attributes of mcscf object, which can be accessed by .e_tot, .e_cas, .ci, .mo_coeff, .mo_energy ''' raise NotImplementedError
def _finalize(self): log = logger.Logger(self.stdout, self.verbose) if log.verbose >= logger.NOTE and getattr(self.fcisolver, 'spin_square', None): if isinstance(self.e_cas, (float, numpy.number)): try: ss = self.fcisolver.spin_square(self.ci, self.ncas, self.nelecas) log.note('CASCI E = %#.15g E(CI) = %#.15g S^2 = %.7f', self.e_tot, self.e_cas, ss[0]) except NotImplementedError: log.note('CASCI E = %#.15g E(CI) = %#.15g', self.e_tot, self.e_cas) else: for i, e in enumerate(self.e_cas): try: ss = self.fcisolver.spin_square(self.ci[i], self.ncas, self.nelecas) log.note('CASCI state %3d E = %#.15g E(CI) = %#.15g S^2 = %.7f', i, self.e_tot[i], e, ss[0]) except NotImplementedError: log.note('CASCI state %3d E = %#.15g E(CI) = %#.15g', i, self.e_tot[i], e) else: if isinstance(self.e_cas, (float, numpy.number)): log.note('CASCI E = %#.15g E(CI) = %#.15g', self.e_tot, self.e_cas) else: for i, e in enumerate(self.e_cas): log.note('CASCI state %3d E = %#.15g E(CI) = %#.15g', i, self.e_tot[i], e) return self
[docs] @lib.with_doc(cas_natorb.__doc__) def cas_natorb(self, mo_coeff=None, ci=None, eris=None, sort=False, casdm1=None, verbose=None, with_meta_lowdin=WITH_META_LOWDIN): return cas_natorb(self, mo_coeff, ci, eris, sort, casdm1, verbose, with_meta_lowdin)
[docs] @lib.with_doc(cas_natorb.__doc__) def cas_natorb_(self, mo_coeff=None, ci=None, eris=None, sort=False, casdm1=None, verbose=None, with_meta_lowdin=WITH_META_LOWDIN): self.mo_coeff, self.ci, self.mo_occ = cas_natorb(self, mo_coeff, ci, eris, sort, casdm1, verbose) return self.mo_coeff, self.ci, self.mo_occ
[docs] def get_fock(self, mo_coeff=None, ci=None, eris=None, casdm1=None, verbose=None): return get_fock(self, mo_coeff, ci, eris, casdm1, verbose)
canonicalize = canonicalize
[docs] @lib.with_doc(canonicalize.__doc__) def canonicalize_(self, mo_coeff=None, ci=None, eris=None, sort=False, cas_natorb=False, casdm1=None, verbose=None, with_meta_lowdin=WITH_META_LOWDIN): self.mo_coeff, ci, self.mo_energy = \ canonicalize(self, mo_coeff, ci, eris, sort, cas_natorb, casdm1, verbose, with_meta_lowdin) if cas_natorb: # When active space is changed, the ci solution needs to be updated self.ci = ci return self.mo_coeff, ci, self.mo_energy
analyze = analyze
[docs] @lib.with_doc(addons.sort_mo.__doc__) def sort_mo(self, caslst, mo_coeff=None, base=1): if mo_coeff is None: mo_coeff = self.mo_coeff return addons.sort_mo(self, mo_coeff, caslst, base)
[docs] @lib.with_doc(addons.state_average.__doc__) def state_average_(self, weights=(0.5,0.5), wfnsym=None): addons.state_average_(self, weights, wfnsym) return self
[docs] @lib.with_doc(addons.state_average.__doc__) def state_average(self, weights=(0.5,0.5), wfnsym=None): return addons.state_average(self, weights, wfnsym)
[docs] @lib.with_doc(addons.state_specific_.__doc__) def state_specific_(self, state=1): addons.state_specific(self, state) return self
[docs] def make_rdm1s(self, mo_coeff=None, ci=None, ncas=None, nelecas=None, ncore=None, **kwargs): '''One-particle density matrices for alpha and beta spin on AO basis ''' if mo_coeff is None: mo_coeff = self.mo_coeff if ci is None: ci = self.ci if ncas is None: ncas = self.ncas if nelecas is None: nelecas = self.nelecas if ncore is None: ncore = self.ncore casdm1a, casdm1b = self.fcisolver.make_rdm1s(ci, ncas, nelecas) mocore = mo_coeff[:,:ncore] mocas = mo_coeff[:,ncore:ncore+ncas] dm1b = numpy.dot(mocore, mocore.conj().T) dm1a = dm1b + reduce(numpy.dot, (mocas, casdm1a, mocas.conj().T)) dm1b += reduce(numpy.dot, (mocas, casdm1b, mocas.conj().T)) return dm1a, dm1b
[docs] def make_rdm1(self, mo_coeff=None, ci=None, ncas=None, nelecas=None, ncore=None, **kwargs): '''One-particle density matrix in AO representation ''' if mo_coeff is None: mo_coeff = self.mo_coeff if ci is None: ci = self.ci if ncas is None: ncas = self.ncas if nelecas is None: nelecas = self.nelecas if ncore is None: ncore = self.ncore casdm1 = self.fcisolver.make_rdm1(ci, ncas, nelecas) mocore = mo_coeff[:,:ncore] mocas = mo_coeff[:,ncore:ncore+ncas] dm1 = numpy.dot(mocore, mocore.conj().T) * 2 dm1 = dm1 + reduce(numpy.dot, (mocas, casdm1, mocas.conj().T)) return dm1
[docs] def fix_spin_(self, shift=PENALTY, ss=None): r'''Use level shift to control FCI solver spin. .. math:: (H + shift*S^2) |\Psi\rangle = E |\Psi\rangle Kwargs: shift : float Energy penalty for states which have wrong spin ss : number S^2 expection value == s*(s+1) ''' fci.addons.fix_spin_(self.fcisolver, shift, ss) return self
fix_spin = fix_spin_
[docs] def density_fit(self, auxbasis=None, with_df=None): from pyscf.mcscf import df return df.density_fit(self, auxbasis, with_df)
[docs] def sfx2c1e(self): from pyscf.x2c import sfx2c1e self._scf = sfx2c1e.sfx2c1e(self._scf).run() self.mo_coeff = self._scf.mo_coeff self.mo_energy = self._scf.mo_energy return self
x2c = x2c1e = sfx2c1e
[docs] def nuc_grad_method(self): raise NotImplementedError
[docs] class CASCI(CASBase):
[docs] def get_h2eff(self, mo_coeff=None): '''Compute the active space two-particle Hamiltonian. ''' ncore = self.ncore ncas = self.ncas nocc = ncore + ncas if mo_coeff is None: ncore = self.ncore mo_coeff = self.mo_coeff[:,ncore:nocc] elif mo_coeff.shape[1] != ncas: mo_coeff = mo_coeff[:,ncore:nocc] if hasattr(self._scf, '_eri') and self._scf._eri is not None: eri = ao2mo.full(self._scf._eri, mo_coeff, max_memory=self.max_memory) else: eri = ao2mo.full(self.mol, mo_coeff, verbose=self.verbose, max_memory=self.max_memory) return eri
[docs] def casci(self, mo_coeff=None, ci0=None, verbose=None): return self.kernel(mo_coeff, ci0, verbose)
[docs] def kernel(self, mo_coeff=None, ci0=None, verbose=None): ''' Returns: Five elements, they are total energy, active space CI energy, the active space FCI wavefunction coefficients or DMRG wavefunction ID, the MCSCF canonical orbital coefficients, the MCSCF canonical orbital coefficients. They are attributes of mcscf object, which can be accessed by .e_tot, .e_cas, .ci, .mo_coeff, .mo_energy ''' if mo_coeff is None: mo_coeff = self.mo_coeff else: self.mo_coeff = mo_coeff if ci0 is None: ci0 = self.ci log = logger.new_logger(self, verbose) self.check_sanity() self.dump_flags(log) self.e_tot, self.e_cas, self.ci = \ kernel(self, mo_coeff, ci0=ci0, verbose=log) if self.canonicalization: self.canonicalize_(mo_coeff, self.ci, sort=self.sorting_mo_energy, cas_natorb=self.natorb, verbose=log) elif self.natorb: # FIXME (pyscf-2.0): Whether to transform natural orbitals in # active space when this flag is enabled? log.warn('The attribute .natorb of mcscf object affects only the ' 'orbital canonicalization.\n' 'If you would like to get natural orbitals in active space ' 'without touching core and external orbitals, an explicit ' 'call to mc.cas_natorb_() is required') if getattr(self.fcisolver, 'converged', None) is not None: self.converged = numpy.all(self.fcisolver.converged) if self.converged: log.info('CASCI converged') else: log.info('CASCI not converged') else: self.converged = True self._finalize() return self.e_tot, self.e_cas, self.ci, self.mo_coeff, self.mo_energy
as_scanner = as_scanner
[docs] def nuc_grad_method(self): from pyscf.grad import casci return casci.Gradients(self)
scf.hf.RHF.CASCI = scf.rohf.ROHF.CASCI = lib.class_as_method(CASCI) scf.uhf.UHF.CASCI = None del (WITH_META_LOWDIN, LARGE_CI_TOL, PENALTY)