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THE CALCULATION OF MULTIPLET
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6-j symbol angular momentum operators anti-bonding approximate Atomic Multiplet atomic orbitals basis functions calculating matrix Chapter character table charge density combination of determinants commute complicated Consider coordinates corresponding coupling coefficients defined degeneracy determinantal functions diagram double group effect eigenfunctions eigenvalues evaluated example F)op Figure fractional parentage free ion full rotation group gives H)op Hamiltonian operator Hartree-Fock Hartree-Fock equations integrals irreducible representations ligand linear combinations method molecular orbitals molecule multiplet energies multiplet structure Nielson and Koster notation number of electrons obtained one-electron atom one-electron operators orbital angular momentum orthogonal parameters permutations Phys point group problem product functions projection operators quantum numbers Racah radial reduced matrix reduced matrix elements represented singlet Slater solution spherical harmonics spin spin-orbit coupling spin-orbit interaction splitting symmetry group symmetry operations tabulated technique tensor operator transform triplet two-electron variation principle wave function