Multiplets description

Despite this controversial part concerning the final state multiplet description the importance of this pioneering work on highly radioactive actinide oxides must be emphasized XPS valence band spectra recorded afterwards for Np02 and Pu02 confirm these early results. 

As was mentioned in Section 6.2.3, phenomenological CF models have been extensively used in the past to rationalize the electronic structure of lanthanide complexes [4, 40-50], and they are still in use nowadays [38, 39, 78, 79]. The ab initio approach described above is, in principle, able to provide accurate energies and wave functions of multiplets in lanthanide complexes. Nevertheless, even if ab initio calculations appear to be successful, CF description is still of great... 

The purpose of the C(o i)-half-filter is to start the TOCSY experiment only with the magnetization of protons bound to C. No further C pulses are applied after the start of the evolution time t. For the description of the multiplet fine-structure of the resulting cross-peaks, it is instructive to consider a 3-spin system with the operators H, and C denoting the spins of two protons and one carbon. Starting from antiphase magnetiza-... 

On the basis of the known electronic properties of actinides (which have been discussed elsewhere in this book), theoreticians had distinguished the 5f itinerant behaviour of light actinide metals from the 5 f localized behaviour of heavy actinide metals from Am on. The crossover, presented often as a Mott transition, had been predicted to occur between Pu and Am metal, due to the localized character of the 5f state in the latter. Photoemission spectroscopy demonstrates this phenomenon directly with the observation of a 5 f multiplet away from the Fermi level. The detailed description of this peak is certainly complicated, as often happens for response of localized states in photoemission on the other hand (Fig. 17) the contrast to the emission of Pu metal is convincing. 

In sect. 4.1 the one-electron crystal-field model for the f configurations was introduced. Though this model is very successful in providing a description of the crystal-field splittings, certain anomalous multiplets are poorly fitted. Prominent examples are the Di multiplet of Pr3+, the 2H(2)n/2 multiplet of Nd3+, and the 3Ks multiplet of Ho3+. Almost independent of the host crystal, the calculated crystal-field levels of these multiplets show a much larger deviation from the experimental ones than all the other levels. 

On the other hand, a more practical approach is to analyze the various parameters with respect to their influence on the anomalous multiplets. According to this procedure Li and Reid (1990) could show that taking into account only the parameters G410Aq, a pronounced improvement for the description of the 2H(2)n/2 multiplet of Nd3+ could be achieved. To study the dependence of correlation effects on the interatomic distances, Jayasankar et al. (1993) analyzed spectroscopic data for LaCbiNd3"1" at pressures up to 10 GPa. Using the superposition model, they could derive the distance dependences of the intrinsic parameters B4 —4... 

Recently, the 5-function model has also been employed to analyze high-pressure results on LaCl3 Pr3+ and LaCl3 Nd3+ (Burdick and Troster, 2003). This model assumes the dominant contributions to the correlation crystal field interactions arising from paired electrons within the same orbital. It has been shown that this model is capable to greatly improve the description of anomalous multiplets like the lT>2 multiplet of Pr3+ at ambient pressure (Burdick and Richardson, 1997). 

NMR pulse sequence without getting tied up in the details of pulse phases and a mountain of sine and cosine terms only the essential elements of the sample net magnetization will be described at each point. Finally, the formal Hamiltonian description of solution-state NMR will be described and applied to explain two related phenomena strong coupling ( leaning of multiplets) and TOCSY mixing (the isotropic mixing sequence). 

If the separation between two resonances is A Hz and their coupling is J Hz, then the rales above hold if A J. The multiplet is said to be first-order. When AfJ <5, distortions and extra lines appear, and the multiplet is then second-order. See Abraham et a/3 for a good description of how to analyse such spectra. A first-order analysis is adequate for solving all the problems in this workbook, although many of the multiplets are distinctly second-order. 

DFT formalism describe the electronic ground state in a single determinant scheme. While this method was well established for the ground state and the lowest states within a symmetry class from its early days, its extension to excited-state description is still in development. The first option proposed in 1977 by Ziegler and Baerends, within the framework of the time-independent formalism, and generalized in 1994 by Daul (so-called A-SCF method) is based on symmetry-dictated combinations of determinants able to evaluate in a nonambiguous way the space and spin multiplets. It has been applied with success to a variety of highly symmetric molecules. However, several limitations make this approach only accessible to experts in the subject. 

A tremendous number of various fragments are used in structure-property studies atoms, bonds, topological torsions , chains, cycles, atom- and bond-centered fragments, maximum common substructures, line notation (WLN and SMILES) fragments, atom pairs and topological multiplets, substituents and molecular frameworks, basic subgraphs, etc. Their detailed description is given below. 

Lastly, in the two methods, the spectra provide a description of the final state. When an outer incomplete localized sub-shell is present, as is the case in the rare earths, the kinetic energy of photoelectrons reflect the final state configuration with (n — 1) electrons and possesses a multiplet structure 47). Then, in the rare earth 4/ photoelectron spectra, the final state is 4/" the observed demultiplication is well interpreted by this configuration 48). We have seen that in the process of the M y y emission and absorption, the final state has either the 4/ or 4/ " configuration. Indeed, the differences observed between the various spectroscopic results are compatible with this interpretation. 

We generated the input data for the absolute values of amplifudes based on fhe mean metabolite concentrations and also the description of mulfiplets and the total shape spectra for normal prosfafe tissues (glandular and stromal) and for the prostate cancer from Ref. [54]. We split the total metabolite concentrations into multiplets with the aim of attaining correspondence to the spectra of Ref. [54]. 

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