Angular momentum lanthanides

A complete decomposition of the ab initio computed CF matrix in irreducible tensor operators (ITOs) and in extended Stevens operators. The parameters of the multiplet-specific CF acting on the ground atomic multiplet of lanthanides, and the decomposition of the CASSCF/RASSI wave functions into functions with definite projections of the total angular momentum on the quantization axis are provided. 

Contributions from orbital angular momentum cause deviations from these values. For complexes containing heavier metal ions, the interaction of spin and orbital angular momenta is greater. For the lanthanides, the magnetic moment depends on... 

The value of J depends on the total orbital angular momentum quantum number, L, and the total spin angulur momentum quantum number, S (Appendix C). Some calculated and experimental magnetic moments for lanthanide complexes are shown in Table 11.25... 

J total angular momentum quantum number 2 blllk bulk paramagnetic shift induced by a lanthanide... 

In general, most of the properties of lanthanides and their variation allow one to classify them into subgroups, namely, f°-f3, f4- 7, f7-f10 and f10-f14. The properties of lanthanide ions and their complexes vary linearly with the total orbital angular momentum (L) values and give rise to a four segmented inclined W shape. Also the lanthanides have been classified into four groups when Ln3+ is involved. 

In the lanthanide series, we have 14 elements that result from the addition of electrons into the f orbitals. For the lanthanide series, the electron configurations are 4f (1—14). In the lanthanide series, the majority of the compounds are formed by trivalent M3+ ions. From a spectroscopic point of view, all the rare earth ions have a large spin-orbit coupling constants, resulting in electronic states being defined by the angular momentum... 

It should be emphasized that magnetic behavior depending on / values is qualitatively different from that depending on 5 values—that is, the spin-only behavior—which gives a fair approximation for many of the d-block transition elements. Only for the /°, f1, and /14 cases, where there is no orbital angular momentum (J = 5), do the two treatments give the same answer. For the lanthanides the external fields do not either appreciably split the free-ion terms nor quench the orbital angular momentum. 

Although we have treated the hyperfine interaction as an interaction between the nuclear spin I and the intrinsic spin s of the electron, it is in reality the interaction of I with the total angular momentum of the electron. Most lanthanide and actinide ions and some transition metal ions in high symmetry do not have their orbital momentum quenched by the crystal fields. In these cases a complete treatment of the hyperfine interaction must include the following term... 

Thus it seems that more than a passing reference is appropriate as to the relation of L-quantum number and the tetrad effect, and indeed Sin ha (58) has recently shown that the L-values exhibit the same periodicity as the tetrad effect in the lanthanide (actinide) series (Fig. 6), as well as that the properties of the/-transition metal ions vary linearly within each tetrad (58). It is a great pity that Klemm did not divide the lanthanide series based on the repeatation of the total angular momentum (L-values) values (see the above table), rather he showed and supported the classification of Endres (48). 

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