Ligand field theory ruby structure

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... 

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... 

In solid-state laser materials, such as ruby (chromium doped alumina, AljOjiCr " ) (1) and emerald (chromium doped beryl, Be,Al,(Si03)5 Cr ) (2), transitions between multiplets of impurity states are utilized. These states mainly consist of 3d orbitals of the impurity chromium ions. For the analysis of these multiplet structures, the semi-empirical ligand-field theory (LFT) has been frequently used (3). However, this theory can be applied only to the high symmetry systems such as O, (or T ). Therefore, the effect of low symmetry is always ignored in the analysis based on the LFT, although most of the practical solid-state laser materials actually possess more or less distorted local structures. For example, in ruby and emerald, the impurity chromium ions are substituted for the aluminum ions in the host crystals and the site symmetry of the aluminum ions are C, in alumina and D, in beryl. Therefore, it is important to clarify the effect of low symmetry on the multiplet structure, in order to understand the electronic structure of ruby and emerald. 

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 . ... 

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