The structural, electronic, optical, and magneto-optical properties of the three Bi 12 MO 20 sillenites (BMO; M ¼ Ti, Ge, and Si) have been investigated on the basis of the first-principles calculations performed by the full potential augmented plane wave method. The BMO's linear optical responses are found to be very similar, but their optical rotatory powers and Faraday ellipticities exhibit notable differences in both visible and ultraviolet parts of the spectra. These differences originate from the subtle differences within the BMO's electronic structures, such as different band-gaps and different offsets of the valence band tops. The latter are found to be caused not by the influence of the M ion electronic states, but by particular behavior of the M-O and the Bi-O chemical bonds. V

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Ab-initio calculations based on density functional theory have been employed to study the structural, electronic, and optical properties of yttrium (Y), scandium (Sc), zirconium (Zr), and niobium (Nb) doped a-Al 2 O 3 with corundum structure. Exchange and correlation effects between electrons have been treated by generalized gradient approximation within the Perdew-Burk-Ezrenhof parameterization and by recently developed Tran-Blaha modified Becke-Johnson approach. Most attention in the work has been paid to the impurity d states, whose energy splitting has been analyzed in terms of the crystal field theory and whose influence on the gap size and the offset of the bands around it has been carefully evaluated. The influence of these states on modification of the optical absorption edge and the static dielectric constant of the doped systems has been also studied. It is concluded that only the Y doped a-Al 2 O 3 (1) preserves the size of the band gap of the pure alumina, (2) does not change significantly the band offset around it, and (3) elevates the value of the static dielectric constant of the compound. These three conditions, necessary for usability of the doped material as a high-e dielectric gate, are not satisfied by the Sc-, Zr-, and Nb-doped alumina compounds. Therefore, only the Y-doped a-Al 2 O 3 exhibits potential to be further explored for employment in the semiconductor industry. V C 2012 American Institute of Physics. [http://dx.

Ab initio calculations based on density-functional theory have been employed to study structural and electronic properties of Bi 4 Ge 3 O 12 ͑BGO͒ and Bi 4 Si 3 O 12 ͑BSO͒, as well as their optical characteristics in ultraviolet region, up to 40 eV. The electronic structure around the band gap is found to be similar in both compounds, dominated by the O p-and the Bi s-states ͑valence band top͒ and the Bi p-states ͑conduction band bottom͒. The gap is found to be indirect in both BGO and BSO. The optical spectra are analyzed, compared, and interpreted in terms of calculated band structures. It is shown that the absorption process involves significant energy flow from the O ions to the Bi ions. This fact stresses importance of the first neighborhood of the Bi ͑six O's forming an octahedron͒, which is more distorted in the BSO than in the BGO. The latter difference is mainly responsible for the different absorption characteristics of the BGO and BSO.

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