Source code for pyscf.scf.rohf

#!/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>
#

'''
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
import pyscf.scf.chkfile
from pyscf import __config__

WITH_META_LOWDIN = getattr(__config__, 'scf_analyze_with_meta_lowdin', True)
MO_BASE = getattr(__config__, 'MO_BASE', 1)


def init_guess_by_minao(mol):
    dm = hf.init_guess_by_minao(mol)
    return numpy.array((dm*.5, dm*.5))

def init_guess_by_atom(mol):
    dm = hf.init_guess_by_atom(mol)
    return numpy.array((dm*.5, dm*.5))

init_guess_by_chkfile = uhf.init_guess_by_chkfile

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

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


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 hasattr(mo_energy, 'mo_ea'):
        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
    ncore = nelec[1]
    nocc  = nelec[0]
    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

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 hasattr(fock, 'focka'):
        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.T.conj(), focka, mo_coeff))
    fockb = reduce(numpy.dot, (mo_coeff.T.conj(), 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]

def make_rdm1(mo_coeff, mo_occ, **kwargs):
    '''One-particle densit matrix.  mo_occ is a 1D array, with occupancy 1 or 2.
    '''
    mo_a = mo_coeff[:,mo_occ>0]
    mo_b = mo_coeff[:,mo_occ==2]
    dm_a = numpy.dot(mo_a, mo_a.T)
    dm_b = numpy.dot(mo_b, mo_b.T)
    return numpy.array((dm_a, dm_b))

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

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:
        log.note('**** MO energy ****')
        if hasattr(mo_energy, 'mo_ea'):
            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.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

def canonicalize(mf, mo_coeff, mo_occ, fock=None):
    '''Canonicalization diagonalizes the Fock matrix within occupied, open,
    virtual subspaces separatedly (without change occupancy).
    '''
    if not hasattr(fock, 'focka'):
        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)
    if hasattr(fock, 'focka'):
        mo_ea = numpy.einsum('pi,pi->i', mo_coeff, fock.focka.dot(mo_coeff))
        mo_eb = numpy.einsum('pi,pi->i', mo_coeff, fock.fockb.dot(mo_coeff))
        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

[docs]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 self._nelec 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 def dump_flags(self): hf.SCF.dump_flags(self) nelec = self.nelec logger.info(self, 'num. doubly occ = %d num. singly occ = %d', nelec[1], nelec[0]-nelec[1]) def init_guess_by_minao(self, mol=None): if mol is None: mol = self.mol return init_guess_by_minao(mol) 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) 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) 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 @lib.with_doc(hf.eig.__doc__)
[docs] def eig(self, fock, s): e, c = self._eigh(fock, s) if hasattr(fock, 'focka'): mo_ea = numpy.einsum('pi,pi->i', c, fock.focka.dot(c)) mo_eb = numpy.einsum('pi,pi->i', c, fock.fockb.dot(c)) e = lib.tag_array(e, mo_ea=mo_ea, mo_eb=mo_eb) return e, c
@lib.with_doc(get_grad.__doc__)
[docs] 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)
@lib.with_doc(make_rdm1.__doc__)
[docs] 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 return make_rdm1(mo_coeff, mo_occ, **kwargs)
energy_elec = energy_elec @lib.with_doc(uhf.get_veff.__doc__)
[docs] 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 or mol.incore_anyway or self._is_mem_enough()): if hasattr(dm, 'mo_coeff'): mo_coeff = dm.mo_coeff mo_occ_a = (dm.mo_occ > 0).astype(numpy.double) mo_occ_b = (dm.mo_occ ==2).astype(numpy.double) dm = lib.tag_array(dm, mo_coeff=(mo_coeff,mo_coeff), mo_occ=(mo_occ_a,mo_occ_b)) 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
@lib.with_doc(analyze.__doc__)
[docs] 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''' if getattr(self, 'nelec', None) is None: neleca, nelecb = self.mol.nelec else: 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): ''' 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. Returns: The return value includes two set of orbitals which are more close to the required stable condition. ''' from pyscf.scf.stability import rohf_stability return rohf_stability(self, internal, external, verbose)
def nuc_grad_method(self): from pyscf.grad import rohf return rohf.Gradients(self)
class HF1e(ROHF): def scf(self, *args): logger.info(self, '\n') logger.info(self, '******** 1 electron system ********') self.converged = True h1e = self.get_hcore(self.mol) s1e = self.get_ovlp(self.mol) self.mo_energy, self.mo_coeff = self.eig(h1e, s1e) self.mo_occ = self.get_occ(self.mo_energy, self.mo_coeff) self.e_tot = self.mo_energy[self.mo_occ>0][0] + self.mol.energy_nuc() self._finalize() return self.e_tot del(WITH_META_LOWDIN)