Tensor Operator Algebra for Point Groups

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Abstract

Originally, the method of irreducible tensor operators was developed by Racah12–15 for the symmetry of the three-dimensional rotation group SO(3), which is of importance in the theory of free atoms and ions. This formalism may be easily generalized to a finite or compact group of arbitrary symmetry. In the following, we will consider some basic relations of the Racah algebra that are of relevance in the theory of transition metal ions in crystals or coordination compounds.