def kernel(self, mo1=None): if len(self.nuc_pair) == 0: return cput0 = (logger.process_clock(), logger.perf_counter()) self.check_sanity() self.dump_flags() mol = self.mol dm0 = self._scf.make_rdm1() mo_coeff = self._scf.mo_coeff mo_occ = self._scf.mo_occ ssc_dia = self.make_dso(mol, dm0) if mo1 is None: mo1 = self.mo10 = self.solve_mo1()[0] ssc_pso = self.make_pso(mol, mo1, mo_coeff, mo_occ) e11 = ssc_dia + ssc_pso if self.with_fcsd: ssc_fcsd = self.make_fcsd(self.nuc_pair) e11 += ssc_fcsd elif self.with_fc: ssc_fc = self.make_fc(self.nuc_pair) e11 += ssc_fc logger.timer(self, 'spin-spin coupling', *cput0) if self.verbose > logger.QUIET: nuc_mag = .5 * (nist.E_MASS / nist.PROTON_MASS) # e*hbar/2m au2Hz = nist.HARTREE2J / nist.PLANCK #logger.debug('Unit AU -> Hz %s', au2Hz*nuc_mag**2) iso_ssc = au2Hz * nuc_mag**2 * numpy.einsum('kii->k', e11) / 3 natm = mol.natm ktensor = numpy.zeros((natm, natm)) for k, (i, j) in enumerate(self.nuc_pair): ktensor[i, j] = ktensor[j, i] = iso_ssc[k] if self.verbose >= logger.DEBUG: _write( self.stdout, e11[k], '\nSSC E11 between %d %s and %d %s' % (i, self.mol.atom_symbol(i), j, self.mol.atom_symbol(j))) # _write(self.stdout, ssc_dia [k], 'dia-magnetism') # _write(self.stdout, ssc_para[k], 'para-magnetism') gyro = rhf_ssc._atom_gyro_list(mol) jtensor = numpy.einsum('ij,i,j->ij', ktensor, gyro, gyro) label = [ '%2d %-2s' % (ia, mol.atom_symbol(ia)) for ia in range(natm) ] logger.note(self, 'Reduced spin-spin coupling constant K (Hz)') tools.dump_mat.dump_tri(self.stdout, ktensor, label) logger.info(self, '\nNuclear g factor %s', gyro) logger.note(self, 'Spin-spin coupling constant J (Hz)') tools.dump_mat.dump_tri(self.stdout, jtensor, label) return e11
def kernel(self, mo1=None): if len(self.nuc_pair) == 0: return cput0 = (time.clock(), time.time()) self.check_sanity() self.dump_flags() mol = self.mol dm0 = self._scf.make_rdm1() mo_coeff = self._scf.mo_coeff mo_occ = self._scf.mo_occ ssc_dia = self.make_dso(mol, dm0) if mo1 is None: mo1 = self.mo10 = self.solve_mo1()[0] ssc_pso = self.make_pso(mol, mo1, mo_coeff, mo_occ) e11 = ssc_dia + ssc_pso if self.with_fcsd: ssc_fcsd = self.make_fcsd(self.nuc_pair) e11 += ssc_fcsd elif self.with_fc: ssc_fc = self.make_fc(self.nuc_pair) e11 += ssc_fc logger.timer(self, 'spin-spin coupling', *cput0) if self.verbose > logger.QUIET: nuc_mag = .5 * (nist.E_MASS/nist.PROTON_MASS) # e*hbar/2m au2Hz = nist.HARTREE2J / nist.PLANCK #logger.debug('Unit AU -> Hz %s', au2Hz*nuc_mag**2) iso_ssc = au2Hz * nuc_mag ** 2 * numpy.einsum('kii->k', e11) / 3 natm = mol.natm ktensor = numpy.zeros((natm,natm)) for k, (i, j) in enumerate(self.nuc_pair): ktensor[i,j] = ktensor[j,i] = iso_ssc[k] if self.verbose >= logger.DEBUG: _write(self.stdout, ssc_dia[k]+ssc_para[k], '\nSSC E11 between %d %s and %d %s' \ % (i, self.mol.atom_symbol(i), j, self.mol.atom_symbol(j))) # _write(self.stdout, ssc_dia [k], 'dia-magnetism') # _write(self.stdout, ssc_para[k], 'para-magnetism') gyro = rhf_ssc._atom_gyro_list(mol) jtensor = numpy.einsum('ij,i,j->ij', ktensor, gyro, gyro) label = ['%2d %-2s'%(ia, mol.atom_symbol(ia)) for ia in range(natm)] logger.note(self, 'Reduced spin-spin coupling constant K (Hz)') tools.dump_mat.dump_tri(self.stdout, ktensor, label) logger.info(self, '\nNuclear g factor %s', gyro) logger.note(self, 'Spin-spin coupling constant J (Hz)') tools.dump_mat.dump_tri(self.stdout, jtensor, label) return e11
def para(nsrobj, mo10=None, mo_coeff=None, mo_occ=None, shielding_nuc=None): '''Paramagnetic part of NSR shielding tensors. ''' if shielding_nuc is None: shielding_nuc = nsrobj.shielding_nuc # The first order Hamiltonian for rotation part is the same to the # first order Hamiltonian for magnetic field except a factor of 2. nsr_para = rhf_nmr.para(nsrobj, mo10, mo_coeff, mo_occ, shielding_nuc)[0] * 2 mol = nsrobj.mol im, mass_center = inertia_tensor(mol) nsr_para = _safe_solve(im, nsr_para) unit = _atom_gyro_list(mol)[shielding_nuc] * nist.ALPHA**2 return numpy.einsum('ixy,i->ixy', nsr_para, unit)
def nuc(mol, shielding_nuc): '''Nuclear contributions''' im, mass_center = inertia_tensor(mol) charges = mol.atom_charges() coords = mol.atom_coords() nsr_nuc = [] for n, atm_id in enumerate(shielding_nuc): rkl = coords - coords[atm_id] d = numpy.linalg.norm(rkl, axis=1) d[atm_id] = 1e100 e11 = numpy.einsum('z,zx,zy->xy', charges / d**3, rkl, rkl) e11 = numpy.eye(3) * e11.trace() - e11 nsr_nuc.append(e11) nsr_nuc = _safe_solve(im, numpy.asarray(nsr_nuc)) unit = _atom_gyro_list(mol)[shielding_nuc] * nist.ALPHA**2 return numpy.einsum('ixy,i->ixy', nsr_nuc, unit)
def dia(nsrobj, gauge_orig=None, shielding_nuc=None, dm0=None): '''Diamagnetic part of NSR tensors. ''' if shielding_nuc is None: shielding_nuc = nsrobj.shielding_nuc if dm0 is None: dm0 = nsrobj._scf.make_rdm1() mol = nsrobj.mol im, mass_center = inertia_tensor(mol) if gauge_orig is None: ao_coords = rhf_mag._get_ao_coords(mol) # Eq. (34) of JCP, 105, 2804 nsr_dia = rhf_nmr.dia(nsrobj, gauge_orig, shielding_nuc, dm0) for n, atm_id in enumerate(shielding_nuc): coord = mol.atom_coord(atm_id) with mol.with_common_origin(coord): with mol.with_rinv_origin(coord): # a11part = (B dot) -1/2 frac{\vec{r}_N}{r_N^3} r_N (dot mu) h11 = mol.intor('int1e_cg_a11part', comp=9) e11 = numpy.einsum('xpq,qp->x', h11, dm0).reshape(3, 3) nsr_dia[n] -= e11 - numpy.eye(3) * e11.trace() nsr_dia[n] *= 2 else: nsr_dia = [] for n, atm_id in enumerate(shielding_nuc): coord = mol.atom_coord(atm_id) with mol.with_rinv_origin(coord): with mol.with_common_origin(gauge_orig): # a11part = (B dot) -1/2 frac{\vec{r}_N}{r_N^3} (r-R_c) (dot mu) h11 = mol.intor('int1e_cg_a11part', comp=9) e11 = numpy.einsum('xpq,qp->x', h11, dm0).reshape(3, 3) with mol.with_common_origin(coord): # a11part = (B dot) -1/2 frac{\vec{r}_N}{r_N^3} r_N (dot mu) h11 = mol.intor('int1e_cg_a11part', comp=9) # e11 ~ (B dot) -1/2 frac{\vec{r}_N}{r_N^3} (R_N-R_c) (dot mu) e11 -= numpy.einsum('xpq,qp->x', h11, dm0).reshape(3, 3) e11 = e11 - numpy.eye(3) * e11.trace() nsr_dia.append(e11) nsr_dia = _safe_solve(im, numpy.asarray(nsr_dia)) unit = _atom_gyro_list(mol)[shielding_nuc] * nist.ALPHA**2 return numpy.einsum('ixy,i->ixy', nsr_dia, unit)