5d crystal field parameters

Crystal-field parameters Crystal-field parameters for the 5d electron are typically 10-20 times the magnitude of the parameters for the 4f electrons. This is due to the fact that the 5d orbital has a much greater overlap with the ligands than does the more localized 4f orbitals, as shown in fig. 1. The 5d crystal field parameters may be determined from the Ce3+ spectra and extrapolated to ions across the lanthanide series, as additional electrons in the 4f -1 core are not expected to have a great influence upon the 5d orbital distribution. 

A major difference between the 5d and 4f orbitals is that the 5d crystal-field strength remains relatively constant across the lanthanide series. This means that it is usually possible to get a good estimate of the 5d crystal-field parameters from the Ce3+ spectrum, though fine-tuning will be necessary. Sometimes it is possible to determine 5d crystal field parameters directly from the 4f 15d spectra, as was done by Laroche et al. (2000) for LiYF Pr3"1". However, values of the 5d crystal field parameters may most easily be determined from examination of the Ce3+ spectra, values which can then be applied to ions across the lanthanide series. 

Independently, Reid et al. (2000) published their first parametrized analysis of the 4F -> 4f -15d absorption spectra of Ce3+, Pr3+ and Nd3+ ions doped inLiYF4. The main difference between the early approaches of Laroche et al. and Reid et al. were that Reid employed the Ce3+ 5d configuration energy levels to determine the 5d crystal-field parameters to be used... 

The Wyboume crystal field parameters B (f, f), B (d, d), and Bjj(f, d), which describe the interaction due to the presence of the ligands onto the electrons of the lanthanide center. They are deduced from the ligand field energies and wave functions obtained from Kohn—Sham orbitals of restricted DFT calculations within the average of configuration (AOC) reference by placing evenly n — 1 electrons in the 4f orbitals and one electron in the 5d.33... 

Crystal field parameters involving the 5d electron are determined from the Ce3+ spectrum. 

Crystal-field parameters would be expected to change across the series roughly in proportion to the radial integrals r2 and r4 (and r6 for 4f electrons). These integrals decrease dramatically across the lanthanide series for the 4f electrons (because their orbitals contract dramatically) but only by a few percent for the 5d electron. Thus, crystal-field parameters determined for Ce3+ may be used across the lanthanide series, with only a small scaling factor for the heavy ions. 

For the 4f configuration it is possible to perform detailed parameter fittings. This is not generally the case for the 4f 15d configuration because the broad vibronic bands makes identification of individual transitions difficult. As discussed in the previous section the parameters for the 4f 1 core are expected to be closely related to the parameters for 4f" configuration for the same ion/host combination, which are usually known. So we need to determine the crystal-field parameters and the free-ion parameters that involve the 5d electron. 

Fig. 5. Splitting of the five 4f 5d crystal-field states of Tb + in LiYp4 (taken from van Pieterson et al., 2002b). The parameter A represents the f-d interactions as explained in the text. On the left (A = 0) the parameters for these interactions are set to zero and on the right (A = 1) they have the values from Hartree-Fock calculations for the free...

---