SECTION 5.4. THE POINT-CHARGE APPROXIMATION AND ITS LIMITATIONS 53The only benefit one may derive from the point-charge approximation is that it can be used
to predict trends when crystal-field effects are compared within a series of compounds with
similar structure.
A special complication exists in intermetallic compounds of rare-earth elements. This
complication is due to the 5d and 6p valence electrons of the rare-earth elements. When
placed in the crystal lattice of an intermetallic compound, the charge cloud associated with
these valence electrons will no longer be spherically symmetric but may become strongly
aspherical. This may be illustrated by means of Fig. 5.4.1, showing the orientations of
d-electron-charge clouds with shapes appropriate for a uniaxial environment.
Depending on the nature of the ligand atoms, the energy levels corresponding to the
different shapes in Fig. 5.4.1 will no longer be equally populated and produce an over
all aspherical 5d-charge cloud surrounding the 4f-charge cloud. Similar arguments were
already presented for p electrons in Fig. 5.1.1. Since the 5d and 6p valence electrons are
located on the same atom as the 4f electrons, this on-site valence-electron asphericity pro
duces an electrostatic field that may be much larger than that due to the charges of the
considerably more remote ligand atoms. It is clear that results obtained by means of the
point-charge approximation are not expected to be correct in these cases. Band-structure cal
culations made for several types of intermetallic compounds have confirmed the important
role of the on-site valence-electron asphericities in determining the crystal field experienced
by the 4f electrons (Coehoorn, 1992).