First principles calculations multiplet structures

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

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... 

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 1. The cluster model adopted for the first-principles calculation of the multiplet structure of ruby. The small black sphere at the center of the cluster represents the impurity chromium ion. Small gray spheres and lEtrge gray spheres represent aluminum ions emd oxygen ions, respectively. 

First-principles calculation for multiplet structure of emerald... 

KEYWORDS first-principles calculation, multiplet structure Corresponding author, e-mail tack dvxa4.mtl.kyoto-u.ac.jp... 

As we know, a few first-principles calculations for multiplet structure have been tried by several researchers. Ohnishi and Sugano calculated the energy positions of the (R line) and Ti (U band) states in ruby, under one-electron approximation (12). Xia et al. carried out similar calculations using more realistic model cluster (13). They could, however, only consider the energies of lower-lying two states in multiplet structure. Watanabe and Kamimura combined one-electron calculations with ligand field theory, and carried out first-principles calculation for the "full" multiplet structure of several transition metal impurities... 

First-Principles Calculation for Multiplet Structure of Emerald... 

First-Principles Calculation for Multiplet Structure of Emerald at DV sample points (22), such as,... 

Chromium doped alumina, or ruby, is needless to say, a beautiful gemstone and known as the first solid-state laser in history. It is also a material of central importance to high pressure science since the ruby pressure gauge using its fluorescence lines is particularly popular in the diamond anvil cell (DAC) experiments. The electronic structure of ruby has been studied extensively based on the ligand-field theory with some additional parameters such as the trigonal-field parameter or the spin-orbit interaction parameter . However, the reports on the first-principles calculation of the multiplet structure of ruby are rather limited . The electronic structure of a-A]2 03 V + has also been studied in details based on a similar semiem-pirical approach . ... 

Recently, a first-principles calculation of the entire multiplet structure of ruby has been carried out by Duan et al and the pressure dependence of the multiplet structure of ruby has been well reproduced. They predicted an anomalous local relaxation which could explain the observed frequency shifts. However, their calculation was based on the analytic multiplet approach using the atomic Racah parameters and the matrix elements were calculated in the octahedral approximation. Although the effect of the covalency was taken into account by multiplying the orbital deformation parameters on the electron-electron repulsion integrals, these parameters were adjusted to the optical spectra of ruby under zero pressure for the quantitative analysis of the pressure dependence of the multiplet structure. Moreover, it would be difficult for their approach to predict the intensity of the optical spectra, since the optical spectra of ruby are dominated by the electric-dipole transitions arising... 

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... 

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... 

The extension of the work described here to the Anderson lattice is an interesting but difficult problem. It would also be interesting to include more terms in the Anderson impurity model, describing for instance multiplet effects. Auger decay and the direct f-d Coulomb interaction. The determination of the parameters in the model from first principles is an important problem. Much progress has been made by Herbst et al. (1978) and by Herbst and Wilkins (1979) for 17, Ui and % and there are promising attempts to estimate from band structure calculations. 

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