47
SECTION 5.2. QUANTUM-MECHANICAL TREATMENT
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.