Crystal field approximation

The breadth of the band near 10,100 cm-1 in the a and y spectra of grunerite and the shoulder at 8,500 cm-1 are attributed to absorption by Fe2+ ions in the Ml, M2 and M3 positions. Assuming a lower-level splitting of 500 cm-1 for the t2g orbitals of Fe2+ ions located in these relatively undistorted octahedral sites, an energy level diagram similar to that for the orthopyroxene Ml site (fig. 5.16) may be constructed leading to the approximate crystal field parameters... 

As was the case with lanthanide crystal spectra (25), we found that a systematic analysis could be developed by examining differences, AP, between experimentally-established actinide parameter values and those computed using Hartree-Fock methods with the inclusion of relativistic corrections (24), as illustrated in Table IV for An3+. Crystal-field effects were approximated based on selected published results. By forming tabulations similar to Table IV for 2+, 4+, 5+ and 6+ spectra, to the extent that any experimental data were available to test the predictions, we found that the AP-values for Pu3+ provided a good starting point for approximating the structure of plutonium spectra in other valence states. However,... 

The electrostatic and spin-orbit parameters for Pu + which we have deduced are similar to those proposed by Conway some years ago (32). However, inclusion of the crystal-field interaction in the computation of the energy level structure, which was not done earlier, significantly modifies previous predictions. As an approximation, we have chosen to use the crystal-field parameters derived for CS2UCI6 (33), Table VII, which together with the free-ion parameters lead to the prediction of a distinct group of levels near 1100 cm-. Of course a weaker field would lead to crystal-field levels intermediate between 0 and 1000 cm-1. Similar model calculations have been indicated in Fig. 8 for Nplt+, Pu1 "1 and Amlt+ compared to the solution spectra of the ions. For Am t+ the reference is Am4" in 15 M NHhF solution (34). 

Again, however, this is strictly applicable only for free ions. Even though spin-orbit coupling is much less important for the first row of the d block, this formula provides a far less good approximation for d -block complexes than Eq. (5.6) does for lanthanide complexes. The reason is that the ground, and other, terms in these d complexes differ grossly from those of the corresponding free ion. These differences are one result of the crystal field. 

When the Zeeman energy is large compared to the crystal field interaction, the electronic wave functions are approximately the 5z) states with energy... 

A quantitative consideration on the origin of the EFG should be based on reliable results from molecular orbital or DPT calculations, as pointed out in detail in Chap. 5. For a qualitative discussion, however, it will suffice to use the easy-to-handle one-electron approximation of the crystal field model. In this framework, it is easy to realize that in nickel(II) complexes of Oh and symmetry and in tetragonally distorted octahedral nickel(II) complexes, no valence electron contribution to the EFG should be expected (cf. Fig. 7.7 and Table 4.2). A temperature-dependent valence electron contribution is to be expected in distorted tetrahedral nickel(n) complexes for tetragonal distortion, e.g., Fzz = (4/7)e(r )3 for com-... 

Foyt et al. [137] interpreted the quadrupole-splitting parameters of low-spin ruthenium(II) complexes in terms of a crystal field model in the strong-field approximation with the configuration treated as an equivalent one-electron problem. They have shown that, starting from pure octahedral symmetry with zero quadrupole splitting, A q increases as the ratio of the axial distortion to the spin-orbit coupling increases. 

While the enthalpy of formation is the property of interest in chemical thermodynamics of materials, many books focus on the lattice enthalpy when considering trends in stability. The static non-vibrational part of the lattice enthalpy can be deconvoluted into contributions of electrostatic nature, due to electron-electron repulsion, dispersion or van der Waals attraction, polarization and crystal field effects. The lattice enthalpy is in the 0 K approximation given as a sum of the potential energies of the different contributions ... 

The 4f-> 5d transitions of nearly all Ln + ions have been observed in CaF2 (9). Luminescence from these transitions has been studied in detail for Eu2+ 10), Sm + (77) and Yh + (12). In good approximation these spectra can be ascribed as transitions between the 4/ ground state and the d crystal-field components of the state. The influence of the surroundings on these transi-... 

---