Crystal-field independent methods

Lanthanide complexes with axial symmetry (i.e., possessing at least a threefold axis, see sect. 2.4.2) are exclusively considered because the principal magnetic z axis coincides with the molecular symmetry axis (Forsberg et al., 1995) and the c 2 spherical tensor operators do not contribute to the crystal-field potentials (Gorller-Walrand and Binne-mans, 1996). The rhombic term of Bleaney s approach V6B Hi (eqs. (42), (46)) thus vanishes and the crystal-field independent methods (eqs. (51), (53)) can be used without complications. 

The derivation of a general crystal-field independent method for polymetallic lanthanide complexes related to eq. (51) is precluded by the consideration of variable numbers of different crystal-field parameters (maximum n) depending on the exact symmetry of the axial complex (see sect. 4.1.1, Rigault et al. (2000a)). 

Oali et have developed new multi-center methods for analysing LIS data that are appropriate when the paramagnetic complex contains more the one lanthanide ion. Their specific chemical focus involves the solution structures of triple-stranded homotrimetallic lanthanide helicates, [Ln3(lig)3], (Ln = Ce-Yb, except Pm, Gd). The multi-center approach incorporates different crystal field parameters for the center and terminal lanthanide ions. In the same study, the authors developed and applied a novel 3-nucleus crystal field-independent method of analysis, which they used to demonstrate that all members of the... 

Crystal-field independent methods. The invariance of eiystal-field parameters is more problematic since the experimental parameters of lanthanide eomplexes in the sohd... 

The application of the two-nuclei crystal-field independent technique and the three-nuclei method provide convincing evidence for the proposed structural subdivision of the [R(L8-3H)(H20),] complexes (Geraldes et al., 2003). All the plots of 8 A/(S-), vs 8pkfa/ Sz)j... 

The phase transition rate in the crystallization of polymeric materials is of the same order as the rates of the heat exchange processes accompanying crystallization. Consequently, the boundary between phases becomes spatially dispersed. This excludes the possibility of using methods based on the front transition model proposed for metals to calculate residual stresses in plastics.148 It is possible to split the general problem and to find the temperature-conversion field independently. Then, assuming that the evolution of temperature T(x,t) and degree of crystallinity a(x,t) in time t and in space (x is the radius vector of an arbitrary point in a body) is known, we can analyze the mechanical problem.143... 

The angular overlap model is a relatively crude method which appears to yield results at least as good as those afforded by the crystal field model. As with all simple empirical models, the AOM depends on many approximations and assumptions which cannot be expected to be even approximately correct. Thus, for example, the parameter a is assumed to depend only on the identity of the metal and the ligand, and on the internuclear distance it is independent of the stoichiometry or stereochemistry. The theoretical basis for assuming the proportionality of the AOM matrix elements to overlap integrals is closely related to the Wolfs-berg-Helmholz approximation for the off-diagonal matrix elements of the one-electron operator ... 

Judd [8] and independently Ofelt [9] presented treatises about the calculation method for Laporte forbidden f-f transition intensities of Ln systems with using coupling scheme for angular momenta. The basic idea is that f-f transitions can be allowed because of the mixing of opposite parity configurations, such as 4f 5d or 4f - g states to 4f states due to the presence of odd parity crystal field generated by the ligands. In this theory [8, 9], the... 

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