When Coulomb interactions between f3 and other electronic configurations are taken to third and higher orders of perturbation theory, it becomes necessary to augment the standard set of thirteen electrostatic parameters with eight more. The operators associated with these eight parameters are orthogonalized to the standard set of operators, and a complete set of the matrix elements of all 21 orthogonalized operators is given for f3. The group-theoretical properties of these operators are examined. Each operator corresponds to a unique pair of irreducible representations of R7 (the rotation group in the seven-dimensional orbital space of an f electron) and of G2 (Cartan’s first exceptional group), but the associated quasispin ranks and irreducible representations of Sp14 (the symplectic group in the 14-dimensional spin–orbital space of an f electron) are sometimes mixed. The combinations of quasispin ranks are odd for the three-electron operators t and even for the two-electron operators e.
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