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for centrosymmetric octahedral systems 97 11 3 Secondorder spinorbit
ments 9 2 4 Symmetry of the coupling coefficients 9 2 5 V coefficients
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a a a a"ShM abaft abcy antisymmetrized atomic orbitals axis ba'fta calculated Chapter coefficient of fractional columns configurations coupling coefficients coupling scheme define derived dihedral group direct product discussed double tensor operator ef(a eigenstates electron example Fano and Racah follows from Eq formula fractional parentage give Griffith 26 Hence independent invariant irreducible product irreducible representations kets and bras left-hand side molecular symmetry multiplied n-electron systems non-zero notation obtain occur octahedral group odd permutation one-electron operator orbitals orthogonal orthogonal matrix orthonormal pair phase properties quantity recoupling reduced matrix elements relation representation of degree respectively right-hand side rotation group Section set of coupling set of functions sets of kets simple span spin functions spin-independent operator spin-orbit coupling energy spinor group symmetry groups tabulated Tanabe theory tions transforming trigonal two-electron systems values vector write zero unless