Paths for Evaluating Energy Levels

In atoms, atomic ions, and transition-metal complexes we need to consider the following crucial interactions. 

The involvement of the CF operator provides a passage from the free-atom group R3 to a finite point group G. The interaction matrix Hy = 

The symmetry-adaptation coefficients = (LMi LFya) introduced through the orbital-part transformation 

As depicted in Fig. 3, one can follow several paths for obtaining the CFMs. An alternative to the above process was developed by Konig and Krem-mer [61,62], They followed the path (a) - (c) - (b) starting with the basis set of atomic multiplets their weak-field theory required that the symmetry-adapted coefficients = (JM JFya) enter the transformation 

---