SECTION 5.2. QUANTUM-MECHANICAL TREATMENT 47
In several uniaxial crystal structures, symmetry causes the term to be absent. It may
be easily checked in Table 5.2.1 that the perturbation matrix is then already diagonal in m.
The three doublets are and
All results described above follow from symmetry considerations. In order to obtain
the relative energy positions of the three doublet levels, one has to know the sign and
magnitude of The energy level scheme for is shown in Fig. 5.2.2. If the ligand
charges are known accurately, the values of can be calculated by means of
the point-charge model. It is possible, however, to consider as a parameter that can be
determined experimentally. For instance, an experimental value for can be obtained if
the magnetic susceptibility is calculated by determining the thermal average
of over the crystal-field-split states for each temperature on the basis of Eq. (3.1.4),
with and the concomitant level splitting as adjustable parameters. The calculated
curve is then fitted with the experimental curve. Another relatively simple method to
obtain an experimental value for consists in measuring the temperature dependence of
the specific heat.