Multiplet structures results

All nuclear multiplet structures due to coupling of nonequivalent nuclei are, as noted earlier, subject to effects on line shapes by chemical or positional exchange. For those multiplet structures arising from coupling of nuclei, one of which has a nonzero nuclear quadrupole moment, effects of quadrupole relaxation must be considered. For example, if a proton or fluorine atom is bonded to a nitrogen nucleus (I = 1), a triplet resonance will be expected in the proton or fluorine spectrum. For observation of this fine structure it is necessary that the lifetimes of the nuclear spin states of nitrogen (m = 1, 0, —1) be greater than the inverse frequency separation between multiplet components, i.e., t > l/ANx (106). The lifetimes of N14 spin states can become comparable to or less than 1 /A as a result of quadrupole relaxation. When the N14 spin-state lifetimes are comparable... 

In addition to the aromatic multiplet, the H spectrum of 2//-chromene (4) exhibits a quartet at 8 4.53 (2-CH2) and peaks at 5.38 (3-H) and 6.20 (4-H) (Figure 1). The last peaks are particularly significant, appearing in a variety of multiplet structures, the nature of which depends on the substitution pattern. However, the benzylic proton always appears downfield of H-3. Alkyl-substitution at C-2 causes an upheld shift of both alkenic protons, but disubstitution results in shifts to lower field. In the widely occurring 2,2-dimethylchrom-... 

The reason why the previous treatment (Section 6.1, Fig. 25) gave reasonable results for the 4 p level shift can now be easily understood The effective level (case (e)) lies with the correct weight approximately at the centre-of-gravity of the multiplet structure (Fig. 28 g) and simulates the correct spectral repulsion. 

The 3d levels in lanthanides are far removed from 4f levels and the overlap of these two levels if any is very small. As a result, multiplet structure in the 3d region is not expected. Although this is the case, XPS of some lanthanide compounds, particularly elements from lanthanum to neodymium, exhibit splitting in the bands apart from the doublet due to spin-orbit interaction. This type of structure is shown in Figs. 9.10, 9.11 and 9.12. These splittings are known as satellites and originate from multielectronic excitations. In general,... 

In our previous report, however, the calculated multiplet energies tend to be overestimated especially for the doublets. This is due to the underestimation of the effect of electron correlations. Recently, we have developed a simple method to take into account the remaining effect of electron correlations. In this method, the electron-electron repulsion integrals are multiplied by a certain reduction factor (correlation correction factor), c, and the value of c is determined by the consistency between the spin-unrestricted one-electron calculations and the multiplet calculations. The details of this method will be described in another paper (5). In the present paper, the effect of electron correlations on the multiplet structure of ruby is investigated by the comparison between the results with and without the correlation corrections. 

Although the ligand field theory is based on the several critical approximations, a first-principles calculation based on the ligand field theory can also provide a useful information when the results are compared to those of the DV-ME calculations. For example, a comparison between the calculations based on the LFT using the pme atomic orbitals (AOs) and the DV-ME calculations using the molecular orbitals (MOs) provide a clear separation of the effect of covalency. Therefore, in the present work, we also carried out the calculation of the multiplet structure of ruby based on the LFT. In this approach, the parameters representing the electron-electron repulsion are calculated using the pure 3d atomic orbitals of the... 

Fig 3. The multiplet structures of ruby calculated by the DV-LFT method using the point charge model and the cluster model, together with the peak positions in the absorption spectra of ruby reported by Fedrbank et al. (13). In each result, the doublets are shown at left and quartets eire at right. 

The multiplet structures of ruby calculated by the DV-ME method with and without the correlation correction are shown in Fig. 4. The experimental values are also shown together. In this case, the multiplet structures are calculated directly using the molecular orbitals of the impurity states obtained by the cluster calculation. In the calculated results, each level is broadened by the presence of the trigonal crystal field. Although the split of each peak seems to be somewhat overestimated due to the computational errors, it can be improved by increasing the number of sampling points (2). 

From the Table I, moreover, we can see that the contributions of Cv-3d orbital are significantly different between the MOs with ng and eg symmetry. This result indicates that the difference of interaction between the impurity and the ligand orbitals according to the direction of spatial extension of the orbitals is very important for the calculation of multiplet structure. Why the empirical method has been seemed to be successfully explained the multiplet structure, nevertheless it approximates the radial parts of wave functions to be the same one, is supposed that it "hides" and "rounds off the errors by adjusting the parameters arbitrarily to the experimental data. 

---