Source code for pyscf.mcscf.addons

#!/usr/bin/env python
# Copyright 2014-2018 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
import copy
from functools import reduce
import numpy
from pyscf import lib
from pyscf import gto
from pyscf.lib import logger
from pyscf import fci
from pyscf import scf
from pyscf import symm
from pyscf import __config__

BASE = getattr(__config__, 'mcscf_addons_sort_mo_base', 1)
MAP2HF_TOL = getattr(__config__, 'mcscf_addons_map2hf_tol', 0.4)


[docs]def sort_mo(casscf, mo_coeff, caslst, base=BASE): '''Pick orbitals for CAS space Args: casscf : an :class:`CASSCF` or :class:`CASCI` object mo_coeff : ndarray or a list of ndarray Orbitals for CASSCF initial guess. In the UHF-CASSCF, it's a list of two orbitals, for alpha and beta spin. caslst : list of int or nested list of int A list of orbital indices to represent the CAS space. In the UHF-CASSCF, it's consist of two lists, for alpha and beta spin. Kwargs: base : int 0-based (C-style) or 1-based (Fortran-style) caslst Returns: An reoreded mo_coeff, which put the orbitals given by caslst in the CAS space 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.CASSCF(mf, 4, 4) >>> cas_list = [5,6,8,9] # pi orbitals >>> mo = mc.sort_mo(cas_list) >>> mc.kernel(mo)[0] -109.007378939813691 ''' ncore = casscf.ncore def ext_list(nmo, caslst): mask = numpy.ones(nmo, dtype=bool) mask[caslst] = False idx = numpy.where(mask)[0] if len(idx) + casscf.ncas != nmo: raise ValueError('Active space size is incompatible with caslist. ' 'ncas = %d. caslist %s' % (casscf.ncas, caslst)) return idx if isinstance(ncore, (int, numpy.integer)): nmo = mo_coeff.shape[1] if base != 0: caslst = [i-base for i in caslst] idx = ext_list(nmo, caslst) mo = numpy.hstack((mo_coeff[:,idx[:ncore]], mo_coeff[:,caslst], mo_coeff[:,idx[ncore:]])) if hasattr(mo_coeff, 'orbsym'): orbsym = mo_coeff.orbsym orbsym = numpy.hstack((orbsym[idx[:ncore]], orbsym[caslst], orbsym[idx[ncore:]])) mo = lib.tag_array(mo, orbsym=orbsym) return mo else: # UHF-based CASSCF if isinstance(caslst[0], (int, numpy.integer)): if base != 0: caslsta = [i-1 for i in caslst] caslst = (caslsta, caslsta) else: # two casspace lists, for alpha and beta if base != 0: caslst = ([i-base for i in caslst[0]], [i-base for i in caslst[1]]) nmo = mo_coeff[0].shape[1] idxa = ext_list(nmo, caslst[0]) mo_a = numpy.hstack((mo_coeff[0][:,idxa[:ncore[0]]], mo_coeff[0][:,caslst[0]], mo_coeff[0][:,idxa[ncore[0]:]])) idxb = ext_list(nmo, caslst[1]) mo_b = numpy.hstack((mo_coeff[1][:,idxb[:ncore[1]]], mo_coeff[1][:,caslst[1]], mo_coeff[1][:,idxb[ncore[1]:]])) if hasattr(mo_coeff[0], 'orbsym'): orbsyma, orbsymb = mo_coeff[0].orbsym, mo_coeff[1].orbsym orbsyma = numpy.hstack((orbsyma[idxa[:ncore[0]]], orbsyma[caslst[0]], orbsyma[idxa[ncore[0]:]])) orbsymb = numpy.hstack((orbsymb[idxb[:ncore[1]]], orbsymb[caslst[1]], orbsymb[idxb[ncore[1]:]])) mo_a = lib.tag_array(mo_a, orbsym=orbsyma) mo_b = lib.tag_array(mo_b, orbsym=orbsymb) return (mo_a, mo_b)
def select_mo_by_irrep(casscf, cas_occ_num, mo = None, base=BASE): raise RuntimeError('This function has been replaced by function caslst_by_irrep')
[docs]def caslst_by_irrep(casscf, mo_coeff, cas_irrep_nocc, cas_irrep_ncore=None, s=None, base=BASE): '''Given number of active orbitals for each irrep, return the orbital indices of active space Args: casscf : an :class:`CASSCF` or :class:`CASCI` object cas_irrep_nocc : list or dict Number of active orbitals for each irrep. It can be a dict, eg {'A1': 2, 'B2': 4} to indicate the active space size based on irrep names, or {0: 2, 3: 4} for irrep Id, or a list [2, 0, 0, 4] (identical to {0: 2, 3: 4}) in which the list index is served as the irrep Id. Kwargs: cas_irrep_ncore : list or dict Number of closed shells for each irrep. It can be a dict, eg {'A1': 6, 'B2': 4} to indicate the closed shells based on irrep names, or {0: 6, 3: 4} for irrep Id, or a list [6, 0, 0, 4] (identical to {0: 6, 3: 4}) in which the list index is served as the irrep Id. If cas_irrep_ncore is not given, the program will generate a guess based on the lowest :attr:`CASCI.ncore` orbitals. s : ndarray overlap matrix base : int 0-based (C-like) or 1-based (Fortran-like) caslst Returns: A list of orbital indices Examples: >>> from pyscf import gto, scf, mcscf >>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvtz', symmetry=True, verbose=0) >>> mf = scf.RHF(mol) >>> mf.kernel() >>> mc = mcscf.CASSCF(mf, 12, 4) >>> mcscf.caslst_by_irrep(mc, mf.mo_coeff, {'E1gx':4, 'E1gy':4, 'E1ux':2, 'E1uy':2}) [5, 7, 8, 10, 11, 14, 15, 20, 25, 26, 31, 32] ''' mol = casscf.mol log = logger.Logger(casscf.stdout, casscf.verbose) orbsym = numpy.asarray(scf.hf_symm.get_orbsym(mol, mo_coeff)) ncore = casscf.ncore irreps = set(orbsym) if cas_irrep_ncore is not None: irrep_ncore = {} for k, v in cas_irrep_ncore.items(): if isinstance(k, str): irrep_ncore[symm.irrep_name2id(mol.groupname, k)] = v else: irrep_ncore[k] = v ncore_rest = casscf.ncore - sum(irrep_ncore.values()) if ncore_rest > 0: # guess core configuration mask = numpy.ones(len(orbsym), dtype=bool) for ir in irrep_ncore: mask[orbsym == ir] = False core_rest = orbsym[mask][:ncore_rest] core_rest = dict([(ir, numpy.count_nonzero(core_rest==ir)) for ir in set(core_rest)]) log.info('Given core space %s < casscf core size %d', cas_irrep_ncore, casscf.ncore) log.info('Add %s to core configuration', core_rest) irrep_ncore.update(core_rest) elif ncore_rest < 0: raise ValueError('Given core space %s > casscf core size %d' % (cas_irrep_ncore, casscf.ncore)) else: irrep_ncore = dict([(ir, sum(orbsym[:ncore]==ir)) for ir in irreps]) if not isinstance(cas_irrep_nocc, dict): # list => dict cas_irrep_nocc = dict([(ir, n) for ir,n in enumerate(cas_irrep_nocc) if n > 0]) irrep_ncas = {} for k, v in cas_irrep_nocc.items(): if isinstance(k, str): irrep_ncas[symm.irrep_name2id(mol.groupname, k)] = v else: irrep_ncas[k] = v ncas_rest = casscf.ncas - sum(irrep_ncas.values()) if ncas_rest > 0: mask = numpy.ones(len(orbsym), dtype=bool) # remove core and specified active space for ir in irrep_ncas: mask[orbsym == ir] = False for ir, ncore in irrep_ncore.items(): idx = numpy.where(orbsym == ir)[0] mask[idx[:ncore]] = False cas_rest = orbsym[mask][:ncas_rest] cas_rest = dict([(ir, numpy.count_nonzero(cas_rest==ir)) for ir in set(cas_rest)]) log.info('Given active space %s < casscf active space size %d', cas_irrep_nocc, casscf.ncas) log.info('Add %s to active space', cas_rest) irrep_ncas.update(cas_rest) elif ncas_rest < 0: raise ValueError('Given active space %s > casscf active space size %d' % (cas_irrep_nocc, casscf.ncas)) caslst = [] for ir, ncas in irrep_ncas.items(): if ncas > 0: if ir in irrep_ncore: nc = irrep_ncore[ir] else: nc = 0 no = nc + ncas idx = numpy.where(orbsym == ir)[0] caslst.extend(idx[nc:no]) caslst = numpy.sort(numpy.asarray(caslst)) + base if len(caslst) < casscf.ncas: raise ValueError('Not enough orbitals found for core %s, cas %s' % (cas_irrep_ncore, cas_irrep_nocc)) if log.verbose >= logger.INFO: log.info('ncore for each irreps %s', dict([(symm.irrep_id2name(mol.groupname, k), v) for k,v in irrep_ncore.items()])) log.info('ncas for each irreps %s', dict([(symm.irrep_id2name(mol.groupname, k), v) for k,v in irrep_ncas.items()])) log.info('(%d-based) caslst = %s', base, caslst) return caslst
[docs]def sort_mo_by_irrep(casscf, mo_coeff, cas_irrep_nocc, cas_irrep_ncore=None, s=None): '''Given number of active orbitals for each irrep, construct the mo initial guess for CASSCF Args: casscf : an :class:`CASSCF` or :class:`CASCI` object cas_irrep_nocc : list or dict Number of active orbitals for each irrep. It can be a dict, eg {'A1': 2, 'B2': 4} to indicate the active space size based on irrep names, or {0: 2, 3: 4} for irrep Id, or a list [2, 0, 0, 4] (identical to {0: 2, 3: 4}) in which the list index is served as the irrep Id. Kwargs: cas_irrep_ncore : list or dict Number of closed shells for each irrep. It can be a dict, eg {'A1': 6, 'B2': 4} to indicate the closed shells based on irrep names, or {0: 6, 3: 4} for irrep Id, or a list [6, 0, 0, 4] (identical to {0: 6, 3: 4}) in which the list index is served as the irrep Id. If cas_irrep_ncore is not given, the program will generate a guess based on the lowest :attr:`CASCI.ncore` orbitals. s : ndarray overlap matrix Returns: sorted orbitals, ordered as [c,..,c,a,..,a,v,..,v] Examples: >>> from pyscf import gto, scf, mcscf >>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvtz', symmetry=True, verbose=0) >>> mf = scf.RHF(mol) >>> mf.kernel() >>> mc = mcscf.CASSCF(mf, 12, 4) >>> mo = mc.sort_mo_by_irrep({'E1gx':4, 'E1gy':4, 'E1ux':2, 'E1uy':2}) >>> # Same to mo = sort_mo_by_irrep(mc, mf.mo_coeff, {2: 4, 3: 4, 6: 2, 7: 2}) >>> # Same to mo = sort_mo_by_irrep(mc, mf.mo_coeff, [0, 0, 4, 4, 0, 0, 2, 2]) >>> mc.kernel(mo)[0] -108.162863845084 ''' caslst = caslst_by_irrep(casscf, mo_coeff, cas_irrep_nocc, cas_irrep_ncore, s, base=0) return sort_mo(casscf, mo_coeff, caslst, base=0)
[docs]def project_init_guess(casscf, init_mo, prev_mol=None): '''Project the given initial guess to the current CASSCF problem. The projected initial guess has two parts. The core orbitals are directly taken from the Hartree-Fock orbitals, and the active orbitals are projected from the given initial guess. Args: casscf : an :class:`CASSCF` or :class:`CASCI` object init_mo : ndarray or list of ndarray Initial guess orbitals which are not orth-normal for the current molecule. When the casscf is UHF-CASSCF, the init_mo needs to be a list of two ndarrays, for alpha and beta orbitals Kwargs: prev_mol : an instance of :class:`Mole` If given, the inital guess orbitals are associated to the geometry and basis of prev_mol. Otherwise, the orbitals are based of the geometry and basis of casscf.mol Returns: New orthogonal initial guess orbitals with the core taken from Hartree-Fock orbitals and projected active space from original initial guess orbitals Examples: .. code:: python import numpy from pyscf import gto, scf, mcscf mol = gto.Mole() mol.build(atom='H 0 0 0; F 0 0 0.8', basis='ccpvdz', verbose=0) mf = scf.RHF(mol) mf.scf() mc = mcscf.CASSCF(mf, 6, 6) mo = mcscf.sort_mo(mc, mf.mo_coeff, [3,4,5,6,8,9]) print('E(0.8) = %.12f' % mc.kernel(mo)[0]) init_mo = mc.mo_coeff for b in numpy.arange(1.0, 3., .2): mol.atom = [['H', (0, 0, 0)], ['F', (0, 0, b)]] mol.build(0, 0) mf = scf.RHF(mol) mf.scf() mc = mcscf.CASSCF(mf, 6, 6) mo = mcscf.project_init_guess(mc, init_mo) print('E(%2.1f) = %.12f' % (b, mc.kernel(mo)[0])) init_mo = mc.mo_coeff ''' from pyscf import lo def project(mfmo, init_mo, ncore, s): s_init_mo = numpy.einsum('pi,pi->i', init_mo.conj(), s.dot(init_mo)) if abs(s_init_mo - 1).max() < 1e-7: # Initial guess orbitals are orthonormal return init_mo # TODO: test whether the canonicalized orbitals are better than the projected orbitals # Be careful that the ordering of the canonicalized orbitals may be very different # to the CASSCF orbitals. # else: # fock = casscf.get_fock(mc, init_mo, casscf.ci) # return casscf._scf.eig(fock, s)[1] nocc = ncore + casscf.ncas if ncore > 0: mo0core = init_mo[:,:ncore] s1 = reduce(numpy.dot, (mfmo.T, s, mo0core)) s1core = reduce(numpy.dot, (mo0core.T, s, mo0core)) coreocc = numpy.einsum('ij,ji->i', s1, lib.cho_solve(s1core, s1.T)) coreidx = numpy.sort(numpy.argsort(-coreocc)[:ncore]) logger.debug(casscf, 'Core indices %s', coreidx) logger.debug(casscf, 'Core components %s', coreocc[coreidx]) # take HF core mocore = mfmo[:,coreidx] # take projected CAS space mocas = init_mo[:,ncore:nocc] \ - reduce(numpy.dot, (mocore, mocore.T, s, init_mo[:,ncore:nocc])) mocc = lo.orth.vec_lowdin(numpy.hstack((mocore, mocas)), s) else: mocc = lo.orth.vec_lowdin(init_mo[:,:nocc], s) # remove core and active space from rest if mocc.shape[1] < mfmo.shape[1]: if casscf.mol.symmetry: restorb = [] orbsym = scf.hf_symm.get_orbsym(casscf.mol, mfmo, s) for ir in set(orbsym): mo_ir = mfmo[:,orbsym==ir] rest = mo_ir - reduce(numpy.dot, (mocc, mocc.T, s, mo_ir)) e, u = numpy.linalg.eigh(reduce(numpy.dot, (rest.T, s, rest))) restorb.append(numpy.dot(rest, u[:,e>1e-7])) restorb = numpy.hstack(restorb) else: rest = mfmo - reduce(numpy.dot, (mocc, mocc.T, s, mfmo)) e, u = numpy.linalg.eigh(reduce(numpy.dot, (rest.T, s, rest))) restorb = numpy.dot(rest, u[:,e>1e-7]) mo = numpy.hstack((mocc, restorb)) else: mo = mocc if casscf.verbose >= logger.DEBUG: s1 = reduce(numpy.dot, (mo[:,ncore:nocc].T, s, mfmo)) idx = numpy.argwhere(abs(s1) > 0.4) for i,j in idx: logger.debug(casscf, 'Init guess <mo-CAS|mo-hf> %d %d %12.8f', ncore+i+1, j+1, s1[i,j]) return mo ncore = casscf.ncore mfmo = casscf._scf.mo_coeff s = casscf._scf.get_ovlp() if prev_mol is None: if init_mo.shape[0] != mfmo.shape[0]: raise RuntimeError('Initial guess orbitals has wrong dimension') elif gto.same_mol(prev_mol, casscf.mol, cmp_basis=False): if isinstance(ncore, (int, numpy.integer)): # RHF init_mo = scf.addons.project_mo_nr2nr(prev_mol, init_mo, casscf.mol) else: init_mo = (scf.addons.project_mo_nr2nr(prev_mol, init_mo[0], casscf.mol), scf.addons.project_mo_nr2nr(prev_mol, init_mo[1], casscf.mol)) elif gto.same_basis_set(prev_mol, casscf.mol): if isinstance(ncore, (int, numpy.integer)): # RHF fock = casscf.get_fock(init_mo, casscf.ci) return casscf._scf.eig(fock, s)[1] else: raise NotImplementedError('Project initial for UHF orbitals.') else: raise NotImplementedError('Project initial guess from different system.') # Be careful with the orbital projection. The projection may lead to bad # initial guess orbitals if the geometry is dramatically changed. if isinstance(ncore, (int, numpy.integer)): mo = project(mfmo, init_mo, ncore, s) else: # UHF-based CASSCF mo = (project(mfmo[0], init_mo[0], ncore[0], s), project(mfmo[1], init_mo[1], ncore[1], s)) return mo
# on AO representation
[docs]def make_rdm1(casscf, mo_coeff=None, ci=None, **kwargs): '''One-particle densit matrix in AO representation Args: casscf : an :class:`CASSCF` or :class:`CASCI` object Kwargs: ci : ndarray CAS space FCI coefficients. If not given, take casscf.ci. mo_coeff : ndarray Orbital coefficients. If not given, take casscf.mo_coeff. Examples: >>> import scipy.linalg >>> from pyscf import gto, scf, mcscf >>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='sto-3g', verbose=0) >>> mf = scf.RHF(mol) >>> res = mf.scf() >>> mc = mcscf.CASSCF(mf, 6, 6) >>> res = mc.kernel() >>> natocc = numpy.linalg.eigh(mcscf.make_rdm1(mc), mf.get_ovlp(), type=2)[0] >>> print(natocc) [ 0.0121563 0.0494735 0.0494735 1.95040395 1.95040395 1.98808879 2. 2. 2. 2. ] ''' return casscf.make_rdm1(mo_coeff, ci, **kwargs)
# make both alpha and beta density matrices
[docs]def make_rdm1s(casscf, mo_coeff=None, ci=None, **kwargs): '''Alpha and beta one-particle densit matrices in AO representation ''' return casscf.make_rdm1s(mo_coeff, ci, **kwargs)
def _is_uhf_mo(mo_coeff): return not (isinstance(mo_coeff, numpy.ndarray) and mo_coeff.ndim == 2) def _make_rdm12_on_mo(casdm1, casdm2, ncore, ncas, nmo): nocc = ncas + ncore dm1 = numpy.zeros((nmo,nmo)) idx = numpy.arange(ncore) dm1[idx,idx] = 2 dm1[ncore:nocc,ncore:nocc] = casdm1 dm2 = numpy.zeros((nmo,nmo,nmo,nmo)) dm2[ncore:nocc,ncore:nocc,ncore:nocc,ncore:nocc] = casdm2 for i in range(ncore): for j in range(ncore): dm2[i,i,j,j] += 4 dm2[i,j,j,i] += -2 dm2[i,i,ncore:nocc,ncore:nocc] = dm2[ncore:nocc,ncore:nocc,i,i] =2*casdm1 dm2[i,ncore:nocc,ncore:nocc,i] = dm2[ncore:nocc,i,i,ncore:nocc] = -casdm1 return dm1, dm2 # on AO representation def make_rdm12(casscf, mo_coeff=None, ci=None): if ci is None: ci = casscf.ci if mo_coeff is None: mo_coeff = casscf.mo_coeff assert(not _is_uhf_mo(mo_coeff)) nelecas = casscf.nelecas ncas = casscf.ncas ncore = casscf.ncore nmo = mo_coeff.shape[1] casdm1, casdm2 = casscf.fcisolver.make_rdm12(ci, ncas, nelecas) rdm1, rdm2 = _make_rdm12_on_mo(casdm1, casdm2, ncore, ncas, nmo) rdm1 = reduce(numpy.dot, (mo_coeff, rdm1, mo_coeff.T)) rdm2 = numpy.dot(mo_coeff, rdm2.reshape(nmo,-1)) rdm2 = numpy.dot(rdm2.reshape(-1,nmo), mo_coeff.T) rdm2 = rdm2.reshape(nmo,nmo,nmo,nmo).transpose(2,3,0,1) rdm2 = numpy.dot(mo_coeff, rdm2.reshape(nmo,-1)) rdm2 = numpy.dot(rdm2.reshape(-1,nmo), mo_coeff.T) return rdm1, rdm2.reshape(nmo,nmo,nmo,nmo)
[docs]def get_fock(casscf, mo_coeff=None, ci=None): '''Generalized Fock matrix in AO representation ''' if mo_coeff is None: mo_coeff = casscf.mo_coeff if _is_uhf_mo(mo_coeff): raise RuntimeError('TODO: UCAS general fock') else: return casscf.get_fock(mo_coeff, ci)
[docs]def cas_natorb(casscf, mo_coeff=None, ci=None, sort=False): '''Natrual orbitals in CAS space ''' if mo_coeff is None: mo_coeff = casscf.mo_coeff if _is_uhf_mo(mo_coeff): raise RuntimeError('TODO: UCAS natrual orbitals') else: return casscf.cas_natorb(mo_coeff, ci, sort=sort)
[docs]def map2hf(casscf, mf_mo=None, base=BASE, tol=MAP2HF_TOL): '''The overlap between the CASSCF optimized orbitals and the canonical HF orbitals. ''' if mf_mo is None: mf_mo = casscf._scf.mo_coeff s = casscf.mol.intor_symmetric('int1e_ovlp') s = reduce(numpy.dot, (casscf.mo_coeff.T, s, mf_mo)) idx = numpy.argwhere(abs(s) > tol) for i,j in idx: logger.info(casscf, '<mo_coeff-mcscf|mo_coeff-hf> %d %d %12.8f', i+base, j+base, s[i,j]) return idx
[docs]def spin_square(casscf, mo_coeff=None, ci=None, ovlp=None): '''Spin square of the UHF-CASSCF wavefunction Returns: A list of two floats. The first is the expectation value of S^2. The second is the corresponding 2S+1 Examples: >>> from pyscf import gto, scf, mcscf >>> mol = gto.M(atom='O 0 0 0; O 0 0 1', basis='sto-3g', spin=2, verbose=0) >>> mf = scf.UHF(mol) >>> res = mf.scf() >>> mc = mcscf.CASSCF(mf, 4, 6) >>> res = mc.kernel() >>> print('S^2 = %.7f, 2S+1 = %.7f' % mcscf.spin_square(mc)) S^2 = 3.9831589, 2S+1 = 4.1149284 ''' if ci is None: ci = casscf.ci ncore = casscf.ncore ncas = casscf.ncas nelecas = casscf.nelecas if isinstance(ncore, (int, numpy.integer)): return fci.spin_op.spin_square0(ci, ncas, nelecas) else: if mo_coeff is None: mo_coeff = casscf.mo_coeff if ovlp is None: ovlp = casscf._scf.get_ovlp() nocc = (ncore[0] + ncas, ncore[1] + ncas) mocas = (mo_coeff[0][:,ncore[0]:nocc[0]], mo_coeff[1][:,ncore[1]:nocc[1]]) if isinstance(ci, (list, tuple)): sscas = numpy.array([fci.spin_op.spin_square(c, ncas, nelecas, mocas, ovlp)[0] for c in ci]) else: sscas = fci.spin_op.spin_square(ci, ncas, nelecas, mocas, ovlp)[0] mocore = (mo_coeff[0][:,:ncore[0]], mo_coeff[1][:,:ncore[1]]) sscore = casscf._scf.spin_square(mocore, ovlp)[0] logger.debug(casscf, 'S^2 of core %s S^2 of cas %s', sscore, sscas) ss = sscas+sscore s = numpy.sqrt(ss+.25) - .5 return ss, s*2+1
# A tag to label the derived FCI class class StateAverageFCISolver: pass
[docs]def state_average_(casscf, weights=(0.5,0.5)): ''' State average over the energy. The energy funcitonal is E = w1<psi1|H|psi1> + w2<psi2|H|psi2> + ... Note we may need change the FCI solver to mc.fcisolver = fci.solver(mol, False) before calling state_average_(mc), to mix the singlet and triplet states ''' assert(abs(sum(weights)-1) < 1e-3) fcibase_class = casscf.fcisolver.__class__ if fcibase_class.__name__ == 'FakeCISolver': raise TypeError('mc.fcisolver is not base FCI solver\n' 'state_average function cannot work with decorated ' 'fcisolver %s.\nYou can restore the base fcisolver ' 'then call state_average function, eg\n' ' mc.fcisolver = %s.%s(mc.mol)\n' ' mc.state_average_()\n' % (casscf.fcisolver, fcibase_class.__base__.__module__, fcibase_class.__base__.__name__)) has_spin_square = hasattr(casscf.fcisolver, 'spin_square') e_states = [None] class FakeCISolver(fcibase_class, StateAverageFCISolver): def __init__(self, mol=None): self.nroots = len(weights) def kernel(self, h1, h2, norb, nelec, ci0=None, **kwargs): # pass self to fcibase_class.kernel function because orbsym argument is stored in self # but undefined in fcibase object e, c = fcibase_class.kernel(self, h1, h2, norb, nelec, ci0, nroots=self.nroots, **kwargs) e_states[0] = e if casscf.verbose >= logger.DEBUG: if has_spin_square: for i, ei in enumerate(e): ss = fcibase_class.spin_square(self, c[i], norb, nelec) logger.debug(casscf, 'state %d E = %.15g S^2 = %.7f', i, ei, ss[0]) else: for i, ei in enumerate(e): logger.debug(casscf, 'state %d E = %.15g', i, ei) return numpy.einsum('i,i->', e, weights), c def approx_kernel(self, h1, h2, norb, nelec, ci0=None, **kwargs): e, c = fcibase_class.kernel(self, h1, h2, norb, nelec, ci0, max_cycle=casscf.ci_response_space, nroots=self.nroots, **kwargs) return numpy.einsum('i,i->', e, weights), c def make_rdm1(self, ci0, norb, nelec): dm1 = 0 for i, wi in enumerate(weights): dm1 += wi * fcibase_class.make_rdm1(self, ci0[i], norb, nelec) return dm1 def make_rdm1s(self, ci0, norb, nelec): dm1a, dm1b = 0, 0 for i, wi in enumerate(weights): dm1s = fcibase_class.make_rdm1s(self, ci0[i], norb, nelec) dm1a += wi * dm1s[0] dm1b += wi * dm1s[1] return dm1a, dm1b def make_rdm12(self, ci0, norb, nelec): rdm1 = 0 rdm2 = 0 for i, wi in enumerate(weights): dm1, dm2 = fcibase_class.make_rdm12(self, ci0[i], norb, nelec) rdm1 += wi * dm1 rdm2 += wi * dm2 return rdm1, rdm2 if has_spin_square: def spin_square(self, ci0, norb, nelec): ss = 0 multip = 0 for i, wi in enumerate(weights): res = fcibase_class.spin_square(self, ci0[i], norb, nelec) ss += wi * res[0] multip += wi * res[1] return ss, multip fcisolver = FakeCISolver(casscf.mol) fcisolver.__dict__.update(casscf.fcisolver.__dict__) fcisolver.nroots = len(weights) casscf.fcisolver = fcisolver old_finalize = casscf._finalize def _finalize(): old_finalize() casscf.e_tot = e_states[0] logger.note(casscf, 'CASCI energy for each state') if has_spin_square: ncas = casscf.ncas nelecas = casscf.nelecas for i, ei in enumerate(casscf.e_tot): ss = fcibase_class.spin_square(casscf.fcisolver, casscf.ci[i], ncas, nelecas)[0] logger.note(casscf, ' State %d weight %g E = %.15g S^2 = %.7f', i, weights[i], ei, ss) else: for i, ei in enumerate(casscf.e_tot): logger.note(casscf, ' State %d weight %g E = %.15g', i, weights[i], ei) return casscf casscf._finalize = _finalize return casscf
state_average = state_average_
[docs]def state_specific_(casscf, state=1): '''For excited state Kwargs: state : int 0 for ground state; 1 for first excited state. ''' fcibase_class = casscf.fcisolver.__class__ if fcibase_class.__name__ == 'FakeCISolver': raise TypeError('mc.fcisolver is not base FCI solver\n' 'state_specific function cannot work with decorated ' 'fcisolver %s.\nYou can restore the base fcisolver ' 'then call state_specific function, eg\n' ' mc.fcisolver = %s.%s(mc.mol)\n' ' mc.state_specific_()\n' % (casscf.fcisolver, fcibase_class.__base__.__module__, fcibase_class.__base__.__name__)) class FakeCISolver(fcibase_class, StateAverageFCISolver): def __init__(self): self.nroots = state+1 self._civec = None def kernel(self, h1, h2, norb, nelec, ci0=None, **kwargs): if self._civec is not None: ci0 = self._civec e, c = fcibase_class.kernel(self, h1, h2, norb, nelec, ci0, nroots=self.nroots, **kwargs) if state == 0: e = [e] c = [c] self._civec = c if casscf.verbose >= logger.DEBUG: if hasattr(fcibase_class, 'spin_square'): ss = fcibase_class.spin_square(self, c[state], norb, nelec) logger.debug(casscf, 'state %d E = %.15g S^2 = %.7f', state, e[state], ss[0]) else: logger.debug(casscf, 'state %d E = %.15g', state, e[state]) return e[state], c[state] def approx_kernel(self, h1, h2, norb, nelec, ci0=None, **kwargs): if self._civec is not None: ci0 = self._civec e, c = fcibase_class.kernel(self, h1, h2, norb, nelec, ci0, max_cycle=casscf.ci_response_space, nroots=self.nroots, **kwargs) if state == 0: self._civec = [c] return e, c else: self._civec = c return e[state], c[state] fcisolver = FakeCISolver() fcisolver.__dict__.update(casscf.fcisolver.__dict__) fcisolver.nroots = state+1 casscf.fcisolver = fcisolver return casscf
state_specific = state_specific_
[docs]def state_average_mix_(casscf, fcisolvers, weights=(0.5,0.5)): '''State-average CASSCF over multiple FCI solvers. ''' fcibase_class = fcisolvers[0].__class__ # if fcibase_class.__name__ == 'FakeCISolver': # logger.warn(casscf, 'casscf.fcisolver %s is a decorated FCI solver. ' # 'state_average_mix_ function rolls back to the base solver %s', # fcibase_class, fcibase_class.__base__) # fcibase_class = fcibase_class.__base__ nroots = sum(solver.nroots for solver in fcisolvers) assert(nroots == len(weights)) has_spin_square = all(hasattr(solver, 'spin_square') for solver in fcisolvers) e_states = [None] def collect(items): items = list(items) cols = [[item[i] for item in items] for i in range(len(items[0]))] return cols def loop_solver(solvers, ci0): p0 = 0 for solver in solvers: if ci0 is None: yield solver, None elif solver.nroots == 1: yield solver, ci0[p0] else: yield solver, ci0[p0:p0+solver.nroots] p0 += solver.nroots def loop_civecs(solvers, ci0): p0 = 0 for solver in solvers: for i in range(p0, p0+solver.nroots): yield solver, ci0[i] p0 += solver.nroots def get_nelec(solver, nelec): # FCISolver does not need this function. Some external solver may not # have the function to handle nelec and spin if solver.spin is not None: nelec = numpy.sum(nelec) nelec = (nelec+solver.spin)//2, (nelec-solver.spin)//2 return nelec class FakeCISolver(fcibase_class, StateAverageFCISolver): def kernel(self, h1, h2, norb, nelec, ci0=None, verbose=0, **kwargs): # Note self.orbsym is initialized lazily in mc1step_symm.kernel function log = logger.new_logger(self, verbose) es = [] cs = [] for solver, c0 in loop_solver(fcisolvers, ci0): e, c = solver.kernel(h1, h2, norb, get_nelec(solver, nelec), c0, orbsym=self.orbsym, verbose=log, **kwargs) if solver.nroots == 1: es.append(e) cs.append(c) else: es.extend(e) cs.extend(c) e_states[0] = es if log.verbose >= logger.DEBUG: if has_spin_square: ss, multip = collect(solver.spin_square(c0, norb, get_nelec(solver, nelec)) for solver, c0 in loop_civecs(fcisolvers, cs)) for i, ei in enumerate(es): log.debug('state %d E = %.15g S^2 = %.7f', i, ei, ss[i]) else: for i, ei in enumerate(es): log.debug('state %d E = %.15g', i, ei) return numpy.einsum('i,i', numpy.array(es), weights), cs def approx_kernel(self, h1, h2, norb, nelec, ci0=None, **kwargs): es = [] cs = [] for solver, c0 in loop_solver(fcisolvers, ci0): e, c = solver.kernel(h1, h2, norb, get_nelec(solver, nelec), c0, orbsym=self.orbsym, **kwargs) if solver.nroots == 1: es.append(e) cs.append(c) else: es.extend(e) cs.extend(c) return numpy.einsum('i,i->', es, weights), cs def make_rdm1(self, ci0, norb, nelec, **kwargs): dm1 = 0 for i, (solver, c) in enumerate(loop_civecs(fcisolvers, ci0)): dm1 += weights[i]*solver.make_rdm1(c, norb, get_nelec(solver, nelec), **kwargs) return dm1 def make_rdm1s(self, ci0, norb, nelec, **kwargs): dm1a, dm1b = 0, 0 for i, (solver, c) in enumerate(loop_civecs(fcisolvers, ci0)): dm1s = solver.make_rdm1s(c, norb, get_nelec(solver, nelec), **kwargs) dm1a += weights[i] * dm1s[0] dm1b += weights[i] * dm1s[1] return dm1a, dm1b def make_rdm12(self, ci0, norb, nelec, **kwargs): rdm1 = 0 rdm2 = 0 for i, (solver, c) in enumerate(loop_civecs(fcisolvers, ci0)): dm1, dm2 = solver.make_rdm12(c, norb, get_nelec(solver, nelec), **kwargs) rdm1 += weights[i] * dm1 rdm2 += weights[i] * dm2 return rdm1, rdm2 if has_spin_square: def spin_square(self, ci0, norb, nelec): ss = 0 multip = 0 for i, (solver, c) in enumerate(loop_civecs(fcisolvers, ci0)): res = solver.spin_square(c, norb, nelec) ss += weights[i] * res[0] multip += weights[i] * res[1] return ss, multip fcisolver = FakeCISolver(casscf.mol) fcisolver.__dict__.update(casscf.fcisolver.__dict__) fcisolver.fcisolvers = fcisolvers casscf.fcisolver = fcisolver old_finalize = casscf._finalize def _finalize(): old_finalize() casscf.e_tot = e_states[0] logger.note(casscf, 'CASCI energy for each state') if has_spin_square: ncas = casscf.ncas nelecas = casscf.nelecas ss, multip = collect(solver.spin_square(c0, ncas, get_nelec(solver, nelecas)) for solver, c0 in loop_civecs(fcisolvers, casscf.ci)) for i, ei in enumerate(casscf.e_tot): logger.note(casscf, ' State %d weight %g E = %.15g S^2 = %.7f', i, weights[i], ei, ss[i]) else: for i, ei in enumerate(casscf.e_tot): logger.note(casscf, ' State %d weight %g E = %.15g', i, weights[i], ei) return casscf casscf._finalize = _finalize return casscf
state_average_mix = state_average_mix_ del(BASE, MAP2HF_TOL) if __name__ == '__main__': from pyscf import gto from pyscf import mcscf from pyscf.tools import ring mol = gto.Mole() mol.verbose = 0 mol.output = None mol.atom = [['H', c] for c in ring.make(6, 1.2)] mol.basis = '6-31g' mol.build() m = scf.RHF(mol) ehf = m.scf() mc = mcscf.CASSCF(m, 6, 6) mc.verbose = 4 emc, e_ci, fcivec, mo, mo_energy = mc.mc1step() print(ehf, emc, emc-ehf) print(emc - -3.272089958) rdm1 = make_rdm1(mc, mo, fcivec) rdm1, rdm2 = make_rdm12(mc, mo, fcivec) print(rdm1) mo1 = cas_natorb(mc)[0] numpy.set_printoptions(2) print(reduce(numpy.dot, (mo1[:,:6].T, mol.intor('int1e_ovlp_sph'), mo[:,:6]))) # state average mol.atom = [ ['O', ( 0., 0. , 0. )], ['H', ( 0., -0.757, 0.587)], ['H', ( 0., 0.757 , 0.587)],] mol.basis = '6-31g' mol.symmetry = 1 mol.build() m = scf.RHF(mol) ehf = m.scf() mc = mcscf.CASSCF(m, 4, 4) mc.verbose = 4 mc.fcisolver = fci.solver(mol, False) # to mix the singlet and triplet mc = state_average_(mc, (.64,.36)) emc, e_ci, fcivec, mo, mo_energy = mc.mc1step()[:5] mc = mcscf.CASCI(m, 4, 4) emc = mc.casci(mo)[0] print(ehf, emc, emc-ehf) print(emc - -76.003352190262532) mc = mcscf.CASSCF(m, 4, 4) mc.verbose = 4 mc = state_average_(mc, (.64,.36)) emc, e_ci, fcivec, mo, mo_energy = mc.mc1step()[:5] mc = mcscf.CASCI(m, 4, 4) emc = mc.casci(mo)[0] print(ehf, emc, emc-ehf) print(emc - -75.982520334896776) mc = mcscf.CASSCF(m, 4, 4) mc.verbose = 4 mc = state_specific_(mc, 2) emc = mc.kernel()[0] mc = mcscf.CASSCF(m, 4, 4) mc.verbose = 4 hot_tuning_(mc, 'config1') mc.kernel() mc = None # release for gc