The Ions in a Ligand Field

The above developments are valid for free ions. When a Ln ion is inserted into a chemical environment, the spherical symmetry of its electronic structure is destroyed and the remaining (2/ +1) degeneracy of its spectroscopic levels is partly lifted, depending on the exact symmetry of the metal-ion site. In view of the 

With the parameterization introduced by B. G. Wyboume in 1965, the final Hamiltonian becomes  

The maximum numbers of hgand-field (or Stark) sublevels depend on the point group of symmetry they are given in Table 3 versus values of J. This can be exploited for the determination of the symmetry point group from f-f absorption or emission spectra, at least when J is integer. 

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