Source code for pyscf.scf.dhf

#!/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.
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# Author: Qiming Sun <osirpt.sun@gmail.com>
#

'''
Dirac Hartree-Fock
'''

import time
from functools import reduce
import numpy
import scipy.linalg
from pyscf import lib
from pyscf import gto
from pyscf.lib import logger
from pyscf.scf import hf
from pyscf.scf import _vhf
from pyscf.scf import chkfile
from pyscf.data import nist
from pyscf import __config__


[docs]def kernel(mf, conv_tol=1e-9, conv_tol_grad=None, dump_chk=True, dm0=None, callback=None, conv_check=True): '''the modified SCF kernel for Dirac-Hartree-Fock. In this kernel, the SCF is carried out in three steps. First the 2-electron part is approximated by large component integrals (LL|LL); Next, (SS|LL) the interaction between large and small components are added; Finally, converge the SCF with the small component contributions (SS|SS) ''' if conv_tol_grad is None: conv_tol_grad = numpy.sqrt(conv_tol) logger.info(mf, 'Set gradient conv threshold to %g', conv_tol_grad) if dm0 is None: dm = mf.get_init_guess() else: dm = dm0 mf._coulomb_now = 'LLLL' if dm0 is None and mf._coulomb_now.upper() == 'LLLL': scf_conv, e_tot, mo_energy, mo_coeff, mo_occ \ = hf.kernel(mf, 1e-2, 1e-1, dump_chk, dm0=dm, callback=callback, conv_check=False) dm = mf.make_rdm1(mo_coeff, mo_occ) mf._coulomb_now = 'SSLL' if dm0 is None and (mf._coulomb_now.upper() == 'SSLL' or mf._coulomb_now.upper() == 'LLSS'): scf_conv, e_tot, mo_energy, mo_coeff, mo_occ \ = hf.kernel(mf, 1e-3, 1e-1, dump_chk, dm0=dm, callback=callback, conv_check=False) dm = mf.make_rdm1(mo_coeff, mo_occ) mf._coulomb_now = 'SSSS' if mf.with_ssss: mf._coulomb_now = 'SSSS' else: mf._coulomb_now = 'SSLL' return hf.kernel(mf, conv_tol, conv_tol_grad, dump_chk, dm0=dm, callback=callback, conv_check=conv_check)
def get_jk_coulomb(mol, dm, hermi=1, coulomb_allow='SSSS', opt_llll=None, opt_ssll=None, opt_ssss=None, verbose=None): log = logger.new_logger(mol, verbose) if coulomb_allow.upper() == 'LLLL': log.debug('Coulomb integral: (LL|LL)') j1, k1 = _call_veff_llll(mol, dm, hermi, opt_llll) n2c = j1.shape[1] vj = numpy.zeros_like(dm) vk = numpy.zeros_like(dm) vj[...,:n2c,:n2c] = j1 vk[...,:n2c,:n2c] = k1 elif coulomb_allow.upper() == 'SSLL' \ or coulomb_allow.upper() == 'LLSS': log.debug('Coulomb integral: (LL|LL) + (SS|LL)') vj, vk = _call_veff_ssll(mol, dm, hermi, opt_ssll) j1, k1 = _call_veff_llll(mol, dm, hermi, opt_llll) n2c = j1.shape[1] vj[...,:n2c,:n2c] += j1 vk[...,:n2c,:n2c] += k1 else: # coulomb_allow == 'SSSS' log.debug('Coulomb integral: (LL|LL) + (SS|LL) + (SS|SS)') vj, vk = _call_veff_ssll(mol, dm, hermi, opt_ssll) j1, k1 = _call_veff_llll(mol, dm, hermi, opt_llll) n2c = j1.shape[1] vj[...,:n2c,:n2c] += j1 vk[...,:n2c,:n2c] += k1 j1, k1 = _call_veff_ssss(mol, dm, hermi, opt_ssss) vj[...,n2c:,n2c:] += j1 vk[...,n2c:,n2c:] += k1 return vj, vk get_jk = get_jk_coulomb def get_hcore(mol): n2c = mol.nao_2c() n4c = n2c * 2 c = lib.param.LIGHT_SPEED t = mol.intor_symmetric('int1e_spsp_spinor') * .5 vn = mol.intor_symmetric('int1e_nuc_spinor') wn = mol.intor_symmetric('int1e_spnucsp_spinor') h1e = numpy.empty((n4c, n4c), numpy.complex) h1e[:n2c,:n2c] = vn h1e[n2c:,:n2c] = t h1e[:n2c,n2c:] = t h1e[n2c:,n2c:] = wn * (.25/c**2) - t return h1e def get_ovlp(mol): n2c = mol.nao_2c() n4c = n2c * 2 c = lib.param.LIGHT_SPEED s = mol.intor_symmetric('int1e_ovlp_spinor') t = mol.intor_symmetric('int1e_spsp_spinor') s1e = numpy.zeros((n4c, n4c), numpy.complex) s1e[:n2c,:n2c] = s s1e[n2c:,n2c:] = t * (.5/c)**2 return s1e make_rdm1 = hf.make_rdm1
[docs]def init_guess_by_minao(mol): '''Initial guess in terms of the overlap to minimal basis.''' dm = hf.init_guess_by_minao(mol) return _proj_dmll(mol, dm, mol)
[docs]def init_guess_by_1e(mol): '''Initial guess from one electron system.''' return UHF(mol).init_guess_by_1e(mol)
[docs]def init_guess_by_atom(mol): '''Initial guess from atom calculation.''' dm = hf.init_guess_by_atom(mol) return _proj_dmll(mol, dm, mol)
[docs]def init_guess_by_chkfile(mol, chkfile_name, project=None): '''Read SCF chkfile and make the density matrix for 4C-DHF initial guess. Kwargs: project : None or bool Whether to project chkfile's orbitals to the new basis. Note when the geometry of the chkfile and the given molecule are very different, this projection can produce very poor initial guess. In PES scanning, it is recommended to swith off project. If project is set to None, the projection is only applied when the basis sets of the chkfile's molecule are different to the basis sets of the given molecule (regardless whether the geometry of the two molecules are different). Note the basis sets are considered to be different if the two molecules are derived from the same molecule with different ordering of atoms. ''' from pyscf.scf import addons chk_mol, scf_rec = chkfile.load_scf(chkfile_name) if project is None: project = not gto.same_basis_set(chk_mol, mol) # Check whether the two molecules are similar def inertia_momentum(mol): im = gto.inertia_momentum(mol._atom, mol.atom_charges(), mol.atom_coords()) return scipy.linalg.eigh(im)[0] if abs(inertia_momentum(mol) - inertia_momentum(chk_mol)).sum() > 0.5: logger.warn(mol, "Large deviations found between the input " "molecule and the molecule from chkfile\n" "Initial guess density matrix may have large error.") if project: s = get_ovlp(mol) def fproj(mo): #TODO: check if mo is GHF orbital if project: mo = addons.project_mo_r2r(chk_mol, mo, mol) norm = numpy.einsum('pi,pi->i', mo.conj(), s.dot(mo)) mo /= numpy.sqrt(norm) return mo mo = scf_rec['mo_coeff'] mo_occ = scf_rec['mo_occ'] if numpy.iscomplexobj(mo[0]): # DHF dm = make_rdm1(fproj(mo), mo_occ) else: if mo[0].ndim == 1: # nr-RHF dm = reduce(numpy.dot, (mo*mo_occ, mo.T)) else: # nr-UHF dm = reduce(numpy.dot, (mo[0]*mo_occ[0], mo[0].T)) \ + reduce(numpy.dot, (mo[1]*mo_occ[1], mo[1].T)) dm = _proj_dmll(chk_mol, dm, mol) return dm
[docs]def get_init_guess(mol, key='minao'): '''Generate density matrix for initial guess Kwargs: key : str One of 'minao', 'atom', 'hcore', '1e', 'chkfile'. ''' return UHF(mol).get_init_guess(mol, key)
[docs]def time_reversal_matrix(mol, mat): ''' T(A_ij) = A[T(i),T(j)]^* ''' n2c = mol.nao_2c() tao = numpy.asarray(mol.time_reversal_map()) # tao(i) = -j means T(f_i) = -f_j # tao(i) = j means T(f_i) = f_j idx = abs(tao)-1 # -1 for C indexing convention #:signL = [(1 if x>0 else -1) for x in tao] #:sign = numpy.hstack((signL, signL)) #:tmat = numpy.empty_like(mat) #:for j in range(mat.__len__()): #: for i in range(mat.__len__()): #: tmat[idx[i],idx[j]] = mat[i,j] * sign[i]*sign[j] #:return tmat.conjugate() sign_mask = tao<0 if mat.shape[0] == n2c*2: idx = numpy.hstack((idx, idx+n2c)) sign_mask = numpy.hstack((sign_mask, sign_mask)) tmat = mat.take(idx,axis=0).take(idx,axis=1) tmat[sign_mask,:] *= -1 tmat[:,sign_mask] *= -1 return tmat.T
def analyze(mf, verbose=logger.DEBUG, **kwargs): from pyscf.tools import dump_mat log = logger.new_logger(mf, verbose) mo_energy = mf.mo_energy mo_occ = mf.mo_occ mo_coeff = mf.mo_coeff log.info('**** MO energy ****') for i in range(len(mo_energy)): if mo_occ[i] > 0: log.info('occupied MO #%d energy= %.15g occ= %g', \ i+1, mo_energy[i], mo_occ[i]) else: log.info('virtual MO #%d energy= %.15g occ= %g', \ i+1, mo_energy[i], mo_occ[i]) mol = mf.mol if mf.verbose >= logger.DEBUG1: log.debug(' ** MO coefficients of large component of postive state (real part) **') label = mol.spinor_labels() n2c = mo_coeff.shape[0] // 2 dump_mat.dump_rec(mf.stdout, mo_coeff[n2c:,:n2c].real, label, start=1) dm = mf.make_rdm1(mo_coeff, mo_occ) pop_chg = mf.mulliken_pop(mol, dm, mf.get_ovlp(), log) dip = mf.dip_moment(mol, dm, verbose=log) return pop_chg, dip
[docs]def mulliken_pop(mol, dm, s=None, verbose=logger.DEBUG): r'''Mulliken population analysis .. math:: M_{ij} = D_{ij} S_{ji} Mulliken charges .. math:: \delta_i = \sum_j M_{ij} ''' if s is None: s = get_ovlp(mol) log = logger.new_logger(mol, verbose) pop = numpy.einsum('ij,ji->i', dm, s).real log.info(' ** Mulliken pop **') for i, s in enumerate(mol.spinor_labels()): log.info('pop of %s %10.5f', s, pop[i]) log.note(' ** Mulliken atomic charges **') chg = numpy.zeros(mol.natm) for i, s in enumerate(mol.spinor_labels(fmt=None)): chg[s[0]] += pop[i] chg = mol.atom_charges() - chg for ia in range(mol.natm): symb = mol.atom_symbol(ia) log.note('charge of %d%s = %10.5f', ia, symb, chg[ia]) return pop, chg
[docs]def dip_moment(mol, dm, unit='Debye', verbose=logger.NOTE, **kwargs): r''' Dipole moment calculation .. math:: \mu_x = -\sum_{\mu}\sum_{\nu} P_{\mu\nu}(\nu|x|\mu) + \sum_A Q_A X_A\\ \mu_y = -\sum_{\mu}\sum_{\nu} P_{\mu\nu}(\nu|y|\mu) + \sum_A Q_A Y_A\\ \mu_z = -\sum_{\mu}\sum_{\nu} P_{\mu\nu}(\nu|z|\mu) + \sum_A Q_A Z_A where :math:`\mu_x, \mu_y, \mu_z` are the x, y and z components of dipole moment Args: mol: an instance of :class:`Mole` dm : a 2D ndarrays density matrices Return: A list: the dipole moment on x, y and z component ''' log = logger.new_logger(mol, verbose) charges = mol.atom_charges() coords = mol.atom_coords() charge_center = numpy.einsum('i,ix->x', charges, coords) with mol.with_common_orig(charge_center): ll_dip = mol.intor_symmetric('int1e_r_spinor', comp=3) ss_dip = mol.intor_symmetric('int1e_sprsp_spinor', comp=3) n2c = mol.nao_2c() c = lib.param.LIGHT_SPEED dip = numpy.einsum('xij,ji->x', ll_dip, dm[:n2c,:n2c]).real dip+= numpy.einsum('xij,ji->x', ss_dip, dm[n2c:,n2c:]).real * (.5/c**2) if unit.upper() == 'DEBYE': dip *= nist.AU2DEBYE log.note('Dipole moment(X, Y, Z, Debye): %8.5f, %8.5f, %8.5f', *dip) else: log.note('Dipole moment(X, Y, Z, A.U.): %8.5f, %8.5f, %8.5f', *dip) return dip
[docs]def get_grad(mo_coeff, mo_occ, fock_ao): '''DHF Gradients''' occidx = mo_occ > 0 viridx = ~occidx g = reduce(numpy.dot, (mo_coeff[:,viridx].T.conj(), fock_ao, mo_coeff[:,occidx])) return g.ravel()
[docs]class UHF(hf.SCF): __doc__ = hf.SCF.__doc__ + ''' Attributes for Dirac-Hartree-Fock with_ssss : bool, for Dirac-Hartree-Fock only If False, ignore small component integrals (SS|SS). Default is True. with_gaunt : bool, for Dirac-Hartree-Fock only Default is False. with_breit : bool, for Dirac-Hartree-Fock only Gaunt + gauge term. Default is False. Examples: >>> mol = gto.M(atom='H 0 0 0; H 0 0 1', basis='ccpvdz', verbose=0) >>> mf = scf.RHF(mol) >>> e0 = mf.scf() >>> mf = scf.DHF(mol) >>> e1 = mf.scf() >>> print('Relativistic effects = %.12f' % (e1-e0)) Relativistic effects = -0.000008854205 ''' conv_tol = getattr(__config__, 'scf_dhf_SCF_conv_tol', 1e-8) with_ssss = getattr(__config__, 'scf_dhf_SCF_with_ssss', True) with_gaunt = getattr(__config__, 'scf_dhf_SCF_with_gaunt', False) with_breit = getattr(__config__, 'scf_dhf_SCF_with_breit', False) def __init__(self, mol): hf.SCF.__init__(self, mol) self._coulomb_now = 'SSSS' # 'SSSS' ~ LLLL+LLSS+SSSS self.opt = (None, None, None, None) # (opt_llll, opt_ssll, opt_ssss, opt_gaunt) self._keys.update(('conv_tol', 'with_ssss', 'with_gaunt', 'with_breit', 'opt')) def dump_flags(self): hf.SCF.dump_flags(self) logger.info(self, 'with_ssss %s, with_gaunt %s, with_breit %s', self.with_ssss, self.with_gaunt, self.with_breit) logger.info(self, 'light speed = %s', lib.param.LIGHT_SPEED) return self @lib.with_doc(get_hcore.__doc__) def get_hcore(self, mol=None): if mol is None: mol = self.mol return get_hcore(mol) @lib.with_doc(get_ovlp.__doc__) def get_ovlp(self, mol=None): if mol is None: mol = self.mol return get_ovlp(mol) 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)
[docs] def init_guess_by_minao(self, mol=None): '''Initial guess in terms of the overlap to minimal basis.''' 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 return init_guess_by_atom(mol) 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) def build(self, mol=None): if self.verbose >= logger.WARN: self.check_sanity() if self.direct_scf: self.opt = self.init_direct_scf(self.mol) def get_occ(self, mo_energy=None, mo_coeff=None): if mo_energy is None: mo_energy = self.mo_energy mol = self.mol c = lib.param.LIGHT_SPEED n4c = len(mo_energy) n2c = n4c // 2 mo_occ = numpy.zeros(n2c * 2) if mo_energy[n2c] > -1.999 * c**2: mo_occ[n2c:n2c+mol.nelectron] = 1 else: lumo = mo_energy[mo_energy > -1.999 * c**2][mol.nelectron] mo_occ[mo_energy > -1.999 * c**2] = 1 mo_occ[mo_energy >= lumo] = 0 if self.verbose >= logger.INFO: logger.info(self, 'HOMO %d = %.12g LUMO %d = %.12g', n2c+mol.nelectron, mo_energy[n2c+mol.nelectron-1], n2c+mol.nelectron+1, mo_energy[n2c+mol.nelectron]) logger.debug1(self, 'NES mo_energy = %s', mo_energy[:n2c]) logger.debug(self, 'PES mo_energy = %s', mo_energy[n2c:]) return mo_occ # full density matrix for UHF 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) def init_direct_scf(self, mol=None): if mol is None: mol = self.mol def set_vkscreen(opt, name): opt._this.contents.r_vkscreen = _vhf._fpointer(name) opt_llll = _vhf.VHFOpt(mol, 'int2e_spinor', 'CVHFrkbllll_prescreen', 'CVHFrkbllll_direct_scf', 'CVHFrkbllll_direct_scf_dm') opt_llll.direct_scf_tol = self.direct_scf_tol set_vkscreen(opt_llll, 'CVHFrkbllll_vkscreen') opt_ssss = _vhf.VHFOpt(mol, 'int2e_spsp1spsp2_spinor', 'CVHFrkbllll_prescreen', 'CVHFrkbssss_direct_scf', 'CVHFrkbssss_direct_scf_dm') opt_ssss.direct_scf_tol = self.direct_scf_tol set_vkscreen(opt_ssss, 'CVHFrkbllll_vkscreen') opt_ssll = _vhf.VHFOpt(mol, 'int2e_spsp1_spinor', 'CVHFrkbssll_prescreen', 'CVHFrkbssll_direct_scf', 'CVHFrkbssll_direct_scf_dm') opt_ssll.direct_scf_tol = self.direct_scf_tol set_vkscreen(opt_ssll, 'CVHFrkbssll_vkscreen') #TODO: prescreen for gaunt opt_gaunt = None return opt_llll, opt_ssll, opt_ssss, opt_gaunt def get_jk(self, mol=None, dm=None, hermi=1): if mol is None: mol = self.mol if dm is None: dm = self.make_rdm1() t0 = (time.clock(), time.time()) log = logger.new_logger(self) if self.direct_scf and self.opt[0] is None: self.opt = self.init_direct_scf(mol) opt_llll, opt_ssll, opt_ssss, opt_gaunt = self.opt vj, vk = get_jk_coulomb(mol, dm, hermi, self._coulomb_now, opt_llll, opt_ssll, opt_ssss, log) if self.with_breit: if 'SSSS' in self._coulomb_now.upper(): vj1, vk1 = _call_veff_gaunt_breit(mol, dm, hermi, opt_gaunt, True) log.debug('Add Breit term') vj += vj1 vk += vk1 elif self.with_gaunt and 'SS' in self._coulomb_now.upper(): log.debug('Add Gaunt term') vj1, vk1 = _call_veff_gaunt_breit(mol, dm, hermi, opt_gaunt, False) vj += vj1 vk += vk1 log.timer('vj and vk', *t0) return vj, vk
[docs] def get_veff(self, mol=None, dm=None, dm_last=0, vhf_last=0, hermi=1): '''Dirac-Coulomb''' if mol is None: mol = self.mol if dm is None: dm = self.make_rdm1() if self.direct_scf: ddm = numpy.array(dm, copy=False) - numpy.array(dm_last, copy=False) vj, vk = self.get_jk(mol, ddm, hermi=hermi) return numpy.array(vhf_last, copy=False) + vj - vk else: vj, vk = self.get_jk(mol, dm, hermi=hermi) return vj - vk
def scf(self, dm0=None): cput0 = (time.clock(), time.time()) self.build() self.dump_flags() self.converged, self.e_tot, \ self.mo_energy, self.mo_coeff, self.mo_occ \ = kernel(self, self.conv_tol, self.conv_tol_grad, dm0=dm0, callback=self.callback, conv_check=self.conv_check) logger.timer(self, 'SCF', *cput0) self._finalize() return self.e_tot def analyze(self, verbose=None): if verbose is None: verbose = self.verbose return analyze(self, verbose) @lib.with_doc(mulliken_pop.__doc__)
[docs] def mulliken_pop(self, mol=None, dm=None, s=None, verbose=logger.DEBUG): if mol is None: mol = self.mol if dm is None: dm = self.make_rdm1() if s is None: s = self.get_ovlp(mol) return mulliken_pop(mol, dm, s=s, verbose=verbose)
@lib.with_doc(dip_moment.__doc__)
[docs] def dip_moment(self, mol=None, dm=None, unit='Debye', verbose=logger.NOTE, **kwargs): if mol is None: mol = self.mol if dm is None: dm =self.make_rdm1() return dip_moment(mol, dm, unit, verbose=verbose, **kwargs)
def sfx2c1e(self): raise NotImplementedError def x2c1e(self): from pyscf.x2c import x2c x2chf = x2c.UHF(self.mol) x2c_keys = x2chf._keys x2chf.__dict__.update(self.__dict__) x2chf._keys = self._keys.union(x2c_keys) return x2chf x2c = x2c1e def nuc_grad_method(self): from pyscf.grad import dhf return dhf.Gradients(self)
DHF = UHF class HF1e(UHF): 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
[docs]class RHF(UHF): '''Dirac-RHF''' def __init__(self, mol): if mol.nelectron.__mod__(2) != 0: raise ValueError('Invalid electron number %i.' % mol.nelectron) UHF.__init__(self, mol) # full density matrix for RHF
[docs] def make_rdm1(self, mo_coeff=None, mo_occ=None, **kwargs): r'''D/2 = \psi_i^\dag\psi_i = \psi_{Ti}^\dag\psi_{Ti} D(UHF) = \psi_i^\dag\psi_i + \psi_{Ti}^\dag\psi_{Ti} RHF average the density of spin up and spin down: D(RHF) = (D(UHF) + T[D(UHF)])/2 ''' if mo_coeff is None: mo_coeff = self.mo_coeff if mo_occ is None: mo_occ = self.mo_occ dm = make_rdm1(mo_coeff, mo_occ, **kwargs) return (dm + time_reversal_matrix(self.mol, dm)) * .5
def _jk_triu_(vj, vk, hermi): if hermi == 0: if vj.ndim == 2: vj = lib.hermi_triu(vj, 1) else: for i in range(vj.shape[0]): vj[i] = lib.hermi_triu(vj[i], 1) else: if vj.ndim == 2: vj = lib.hermi_triu(vj, hermi) vk = lib.hermi_triu(vk, hermi) else: for i in range(vj.shape[0]): vj[i] = lib.hermi_triu(vj[i], hermi) vk[i] = lib.hermi_triu(vk[i], hermi) return vj, vk def _call_veff_llll(mol, dm, hermi=1, mf_opt=None): if isinstance(dm, numpy.ndarray) and dm.ndim == 2: n2c = dm.shape[0] // 2 dms = dm[:n2c,:n2c].copy() else: n2c = dm[0].shape[0] // 2 dms = [] for dmi in dm: dms.append(dmi[:n2c,:n2c].copy()) vj, vk = _vhf.rdirect_mapdm('int2e_spinor', 's8', ('ji->s2kl', 'jk->s1il'), dms, 1, mol._atm, mol._bas, mol._env, mf_opt) return _jk_triu_(vj, vk, hermi) def _call_veff_ssll(mol, dm, hermi=1, mf_opt=None): if isinstance(dm, numpy.ndarray) and dm.ndim == 2: n_dm = 1 n2c = dm.shape[0] // 2 dmll = dm[:n2c,:n2c].copy() dmsl = dm[n2c:,:n2c].copy() dmss = dm[n2c:,n2c:].copy() dms = (dmll, dmss, dmsl) else: n_dm = len(dm) n2c = dm[0].shape[0] // 2 dms = [dmi[:n2c,:n2c].copy() for dmi in dm] \ + [dmi[n2c:,n2c:].copy() for dmi in dm] \ + [dmi[n2c:,:n2c].copy() for dmi in dm] jks = ('lk->s2ij',) * n_dm \ + ('ji->s2kl',) * n_dm \ + ('jk->s1il',) * n_dm c1 = .5 / lib.param.LIGHT_SPEED vx = _vhf.rdirect_bindm('int2e_spsp1_spinor', 's4', jks, dms, 1, mol._atm, mol._bas, mol._env, mf_opt) * c1**2 vj = numpy.zeros((n_dm,n2c*2,n2c*2), dtype=numpy.complex) vk = numpy.zeros((n_dm,n2c*2,n2c*2), dtype=numpy.complex) vj[:,n2c:,n2c:] = vx[ :n_dm ,:,:] vj[:,:n2c,:n2c] = vx[n_dm :n_dm*2,:,:] vk[:,n2c:,:n2c] = vx[n_dm*2: ,:,:] if n_dm == 1: vj = vj.reshape(vj.shape[1:]) vk = vk.reshape(vk.shape[1:]) return _jk_triu_(vj, vk, hermi) def _call_veff_ssss(mol, dm, hermi=1, mf_opt=None): c1 = .5 / lib.param.LIGHT_SPEED if isinstance(dm, numpy.ndarray) and dm.ndim == 2: n2c = dm.shape[0] // 2 dms = dm[n2c:,n2c:].copy() else: n2c = dm[0].shape[0] // 2 dms = [] for dmi in dm: dms.append(dmi[n2c:,n2c:].copy()) vj, vk = _vhf.rdirect_mapdm('int2e_spsp1spsp2_spinor', 's8', ('ji->s2kl', 'jk->s1il'), dms, 1, mol._atm, mol._bas, mol._env, mf_opt) * c1**4 return _jk_triu_(vj, vk, hermi) def _call_veff_gaunt_breit(mol, dm, hermi=1, mf_opt=None, with_breit=False): if with_breit: intor_prefix = 'int2e_breit_' else: intor_prefix = 'int2e_' if isinstance(dm, numpy.ndarray) and dm.ndim == 2: n_dm = 1 n2c = dm.shape[0] // 2 dmls = dm[:n2c,n2c:].copy() dmsl = dm[n2c:,:n2c].copy() dmll = dm[:n2c,:n2c].copy() dmss = dm[n2c:,n2c:].copy() dms = [dmsl, dmsl, dmls, dmll, dmss] else: n_dm = len(dm) n2c = dm[0].shape[0] // 2 dmll = [dmi[:n2c,:n2c].copy() for dmi in dm] dmls = [dmi[:n2c,n2c:].copy() for dmi in dm] dmsl = [dmi[n2c:,:n2c].copy() for dmi in dm] dmss = [dmi[n2c:,n2c:].copy() for dmi in dm] dms = dmsl + dmsl + dmls + dmll + dmss vj = numpy.zeros((n_dm,n2c*2,n2c*2), dtype=numpy.complex) vk = numpy.zeros((n_dm,n2c*2,n2c*2), dtype=numpy.complex) jks = ('lk->s1ij',) * n_dm \ + ('jk->s1il',) * n_dm vx = _vhf.rdirect_bindm(intor_prefix+'ssp1ssp2_spinor', 's1', jks, dms[:n_dm*2], 1, mol._atm, mol._bas, mol._env, mf_opt) vj[:,:n2c,n2c:] = vx[:n_dm,:,:] vk[:,:n2c,n2c:] = vx[n_dm:,:,:] jks = ('lk->s1ij',) * n_dm \ + ('li->s1kj',) * n_dm \ + ('jk->s1il',) * n_dm vx = _vhf.rdirect_bindm(intor_prefix+'ssp1sps2_spinor', 's1', jks, dms[n_dm*2:], 1, mol._atm, mol._bas, mol._env, mf_opt) vj[:,:n2c,n2c:]+= vx[ :n_dm ,:,:] vk[:,n2c:,n2c:] = vx[n_dm :n_dm*2,:,:] vk[:,:n2c,:n2c] = vx[n_dm*2: ,:,:] if hermi == 1: vj[:,n2c:,:n2c] = vj[:,:n2c,n2c:].transpose(0,2,1).conj() vk[:,n2c:,:n2c] = vk[:,:n2c,n2c:].transpose(0,2,1).conj() elif hermi == 2: vj[:,n2c:,:n2c] = -vj[:,:n2c,n2c:].transpose(0,2,1).conj() vk[:,n2c:,:n2c] = -vk[:,:n2c,n2c:].transpose(0,2,1).conj() else: raise NotImplementedError if n_dm == 1: vj = vj.reshape(n2c*2,n2c*2) vk = vk.reshape(n2c*2,n2c*2) c1 = .5 / lib.param.LIGHT_SPEED if with_breit: return vj*c1**2, vk*c1**2 else: return -vj*c1**2, -vk*c1**2 def _proj_dmll(mol_nr, dm_nr, mol): '''Project non-relativistic atomic density matrix to large component spinor representation ''' from pyscf.scf import addons proj = addons.project_mo_nr2r(mol_nr, numpy.eye(mol_nr.nao_nr()), mol) n2c = proj.shape[0] n4c = n2c * 2 dm = numpy.zeros((n4c,n4c), dtype=complex) # *.5 because alpha and beta are summed in project_mo_nr2r dm_ll = reduce(numpy.dot, (proj, dm_nr*.5, proj.T.conj())) dm[:n2c,:n2c] = (dm_ll + time_reversal_matrix(mol, dm_ll)) * .5 return dm if __name__ == '__main__': import pyscf.gto mol = pyscf.gto.Mole() mol.verbose = 5 mol.output = 'out_dhf' mol.atom.extend([['He', (0.,0.,0.)], ]) mol.basis = { 'He': [(0, 0, (1, 1)), (0, 0, (3, 1)), (1, 0, (1, 1)), ]} mol.build() ############## # SCF result method = UHF(mol) energy = method.scf() #-2.38146942868 print(energy) method.with_gaunt = True print(method.scf()) # -2.38138339005 method.with_breit = True print(method.scf()) # -2.38138339005