Multiplet structures calculations

Fig. 9.20. XPE spectra of SmB in the 4f region compared with the combined multiplet structures calculated for...

It has been empirically known that the energies of the lowest excited state of tetrahedrally coordinated metals decrease in the order Cr + < Mn + < Fe ". As in the case of 3cf elements, this tendency has been considered to originate from the difference in covalency, which reduced two-electron repulsion between the electrons occupying 3d orbitals. Recently this question was treated using first-principles electronic-structure calculation (Ishii et al. 2002). The same tendencies were found as for the 3d ions. Distance dependent multiplet-energy diagrams for these elements have been obtained (Fig. 5.34), which enable us to envisage the typical shapes of the possible emissions. As in... 

Due to the localization of the 5 f electrons in the oxides a final state multiplet structure is expected. Therefore, these spectra have been compared with final state intensities calculated in an intermediate coupling scheme which accoimts for the strong spin-orbit... 

First-principles calculations of multiplet structures of metal ions in solids... 

Historically the first non-empirical calculation of entire multiplet structures of transition metal (TM) ions in crystals was performed by Watanabe and Kamimura based on the combination of a local density approximation (LDA) calculation and the ligand field theory (Watanabe and... 

In order to analyze the 4f2—4f5d transitions, multiplet structures for the 4f2 and 4f5d configurations were calculated by the relativistic DVME method. The MOs mainly consisting of Pr 4f or Pr 5d states were used in the Slater determinants. 

Poster 9. Kazuhiro Fujikawa, Hisashi Yoshida and Kazuyoshi Ogasawara (Kwansei Gakuin University, NEC Lighting. Co. Ltd.) First Principles Calculation of Multiplet Structures and Absorption Spectra of ns2-type Ions... 

Medium fields with ALs < Ac/ Aei It is the relative energies that are important the multiplet splitting may vary from 10 l to 104 cm-1 (see Sommerfeld s (594) fine structure formula). In this case Fei is the first perturbation effect, and the cubic part of Vcf is treated as a perturbation before spin-orbit effects are calculated. For distortions from cubic symmetry, it is necessary to consider carefully the relative magnitudes of Vt (that part of VCf due to departures from cubic symmetry) and Vis S. Weak fields with ACf ls - In this case the ligand fields merely perturb the multiplet structure of the free atom. 

The NMR spectrum of quinazoline in [ Hj,]DMSO shows two sharp signals at 97.8 (Nl) and 86.5 (N3) ppm with respect to external neat nitromethane. This assignment is in accordance with INDO/S-SOS shielding calculations. The more-shielded signal in the proton-coupled spectrum has a doublet splitting of 13.8 Hz, whereas the less-shielded signal has a multiplet structure. 

For further accurate calculation, the many-electron effects like the multiplet structure should be taken into account. Although this type of calculation is feasible with the first-principles DV multi-electron method any details will not be described here. 

Separation of the effects of charge transfer, covalency and electron correlations on the multiplet structure of ruby based on first-principles cluster calculations... 

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... 

However, as we have already pointed out, the value of Sgg — t2g is quite insensitive to the electronic configuration (2). Therefore, in the present paper, we approximated all of these effective crystal-field splittings by the value of eg — t2g Calculated in the ground state. On the other hand, the Racah parameters represent the electron-electron repulsion interaction and can be calculated by the radial part of the pure 3d atomic orbitals of the impurity chromium ion (1). After evaluating the value of these parameters, the multiplet structure of ruby can be obtained by diagonalizing the Tanabe-Sugemo matrices. 

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