Crystal Field or Stark Effects

L are die ligands responsible for the crystal field at a distance R, Z their charge and e the elementary charge. Often, instead of B, the equivalent structural parameters Af are utilised as shown below. 

The integer k mns in the range 0-7 and the parameters containing even values of k are responsible for the crystal field splitting, while those with odd values influence the intensity of the induced electronic dipole transitions (see Section 1.3.10 for more details) [8,9]. q is also an integer and its values depend on the symmetry of the crystal field and the magnitude of k, since k. The possible combinations of k and q for the crystal field parameters are given in Table 1.6 and the symmetry elements contained in the crystal field parameters are summarised in Table 1.7. 

The Bq coefficient is notably absent from these tables since it is spherically symmetric, it acts equally on all/ configurations. In energy level calculations it can therefore be incorporated into aU spherically symmetric interactions and does not need to be considered individually. 

The expression for 7/ /varies depending on the symmetry of the crystal field, as shown by the information in Tables 1.3 and 1.4. For example, if the metal ion is in a site of C2v symmetry, which includes two mirror planes and one C2 axis, the expression for 7/ /becomes  

Complete expressions for the summations for symmetry point groups of interest in coordination chemistry can be found for example in Refercnee [30]. 

---

In addition to the Coulomb interactions of electron-electron repulsion and electron-nucleus attraction, further perturbations influence the energy levels of the lanthanide ions, such as the coupling of the spin and angular momenta, commonly designated spin-orbit coupling, the crystal field or Stark effect, and the interaction with a magnetic field or Zeeman effect, which will be described in the following sections. 

---