Descending symmetry, method

Use the subgroup C2v in the method of descending symmetry to verify the correlation of Figure 9.3. 

Select an appropriate subgroup of Td and verify Figure 9.4 by the method of descending symmetry. 

To determine the states in a strong field we shall make use of Bethe s method of descending symmetry. This is based on (i) the fact that an electrostatic field does not affect the spin and (ii) that if ip(l, 2) = i (1) if (2), where if (1) forms a basis for Fz and ipJ(2) forms a basis for I /, then the product if (1) ivJ (2) forms a basis for the DP representation T / ITo implement Bethe s method we need to use two rules ... 

The solution using Bethe s method of descending symmetry is summarized in Table 7.8. In the strong-field limit the possible electron configurations derived from d2 in the free ion... 

Table 7.8. Application of the method of descending symmetry to the configuration d2 in Oh symmetry. 

In the case of the Eu(lll) ion, where ground and excited state manifolds are well-separated, this direct dependence of the number of My levels on the crystal field symmetry is often utilised to determine the point group symmetry of the metal ion in a complex or solid state material from the emission spectra. This method of descending symmetry is performed with the help of a diagram such as the one shown in Fig. 1.5 [41]. A similar analysis can also be performed on the basis of absorption spectra. 

Figure 1.5 Method of descending symmetry applied to the ) levels of the Eu(lll) ion to determine the point group symmetry of the metal ion [41]...

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