Crystal-field calculations

Rotating single-crystal measurements also permitted the extraction of the orientation of the magnetic tensor in the molecular reference frame and the experimental easy axis was found to coincide with the idealized tetragonal axis of the coordination dodecahedron of Dy. Crystal field calculations assuming idealized tetragonal symmetry permitted the reproduction of magnetic susceptibility data for gz = 19.9 and gxy 0 [121]. More elaborated calculations such as ab initio post Hartree-Fock CASSCF confirmed this simple analysis [119]. 

The A00(r) term in Eq. (27) is by far the largest, but it does not remove the degeneracy of the ground state and only contributes a constant term which drops out when energy differences are computed. For this reason, it is customarily dropped from Vc in crystal field calculations. An alternative expression to that given in Eq. (27), using Cartesian coordinates in place of polar coordinates is... 

M[N(SiMe3)2 ] 3, M = Sc, Ti, Cr, and Fe, are stable, relatively volatile compounds that proved suitable for UPS measurements (200). With the exception of Sc[N(SiMe3)2 ] 3, which possesses a pyramidal (C3) structure (143), these compounds are expected to adopt Z)3 MN3 skeletal geometries. The dihedral angle 0 between the NSi2 and MN3 planes is not generally known for all the compounds however, 0 is 49° for Fe[N(SiMe3)2 ] 3 (41). Crystal field calculations... 

When the matrix elements are calculated for states built from /-electron configurations it is always found that the constants A% (these quantities are related to the strength of crystal field) always occur with (the sharp brackets denote integration with respect to 4/ radial function). A parameters play an important role in crystal field calculations and can be used as parameters in describing the crystal field. For the lowest L S J state they can easily be determined by using the operator equivalent technique of Elliott and Stevens [545—547] and with the help of existing tables of matrix elements. Wybotjbne [548], however, feels that a better approach is to expand Vc in terms of the tensor operators,, as... 

Crystal-Field Calculations for 3+ Actinides in High Symmetry Host Crystals, W.T. Car-nail, H.M. Crosswhite, H. Crosswhite, J.P. Hessler, C. Aderhold, J.A. Caird, A. Paszek, and F.W. Wagner Jr. In Proceedings of the 2nd International Conference on the Electronic Structure of the Actinides, Wroclaw, Poland, September 13-16, 1976. J. Mulak, W. Suski, and R. Troc (Eds.), Ossolineum, Wroclaw, 1977, pp. 105-110. 

The crystal field parameters given in Tables 8.6 and 8.7 show an uneven variation with atomic number. The crystal field calculations are not of the same degree of reliability. In some cases, crystal field interactions between ion levels have been ignored. In other cases, the calculations included only levels derived from the ground multiplets while in some cases intermediate coupling effects have not been included. The validity of the data depends on whether all the available information has been used and the discrepancies are not due to incomplete treatment of the problem. 

Crystal field calculations for the absorption spectrum of EuCb in LaCl3 lattice [167] using the parameters... 

The calculation reveals that the octahedral crystal field removes the fivefold orbital degeneracy of the free ion state, yielding a threefold degenerate state at —4Dq and a twofold degenerate state at +6Dq. The results of the crystal-field calculation are collected in Table 4. The representations spanned by the crystal-field states are determined by an examination of the transformation properties of, ..., in the point group O, since it is known that d wave functions are even under inversion and Oh is O y<. i. In Oh, these become and Eg, respectively. In this manner, it has been determined that the octahedral crystal field removes the orbital degeneracy of the free ion state, resulting in the formation... 

Many of the results obtained for the octahedral crystal-field calculation can be used for the description of the magnetic properties of ions in tetrahedral environments. If an 5 4 axis of the tetrahedron is taken as the axis of quantization (being collinear with the C4 axis of quantization of the octahedron), and the C3 axes of the tetrahedron are collinear with the C3 axes of the octahedron, then the crystal-field potential energy... 

Data from reference 10, which also includes magnetic susceptibilities, electron paramagnetic resonance data, and crystal field calculations. 

---