First-principles study of the optical transitions ofFcenters in the bulk and on the (0001) surface ofα−Al2O3

Abstract

The electronic structure and spectroscopic features of the optical spectra of oxygen vacancies in the bulk and on the ͑0001͒ surface of ␣-Al 2 O 3 have been studied by first-principles methods. The effect of oxygen vacancies on the crystalline structure has been determined by the appropriate atomic structure optimization carried out using a periodic model and density functional theory ͑DFT͒ calculations. Both, neutral ͑F center͒ and charged ͑F + center͒ oxygen vacancies have been considered. Optical transitions arising from the excitations of the electron͑s͒ trapped in the F + and F centers, both on the surface and in the bulk of the material, have been studied using a suitable embedded cluster model approach. The cluster geometry, including the relaxation around the vacancy, has been taken from the periodic calculations. The transition energies and intensities have been obtained by applying the explicitly correlated multiconfigurational second-order perturbation theory method and also time-dependent DFT approaches. The present results are in good agreement with available experimental data for the bulk and provide a guide to interpret forthcoming experiments involving the spectroscopy of oxygen vacancies present in irradiated or defective ␣-Al 2 O 3 ͑0001͒ surfaces.

Periodic models in quantum chemical simulations of F centers in crystalline metal oxides

“…(This difference shows noticeable dependence of results on hidden DFT parameters, while using the same periodic model.) The periodic DFT‐B3LYP calculations give 8.5 eV 110, whereas both the TD‐DFT embedded cluster calculations 104 and semi‐empirical INDO cluster calculations 105 overestimate this value: 9.9 and 10.1 eV, respectively.…”

“…Unlike alkali halides and alkali earth oxides, creation of the F center in corundum crystal results in a substantial lowering of a local symmetry ( D →C 2 ). Probably, the noticeably smaller number of theoretical simulations on oxygen vacancies in α‐Al 2 O 3 3, 7, 9, 10, 100–106 may be explained by this low‐symmetrical structure and, thus, complexity of calculations required significant computational time and resources as well as interpretation of their results 102. The following methods and models were used for the F center studies in corundum: (i) periodic DFT calculations 9, 10, 100–104; (ii) time‐dependent (TD) DFT calculations on embedded clusters 7, 104 using the GAUSSIAN code 107; (iii) semi‐empirical embedded 3, 105 and cyclic 9, 106 cluster calculations by the INDO and MSINDO methods, respectively.…”

First-principles calculations of the atomic and electronic structure ofFcenters in the bulk and on the (001) surface ofSrTiO3

“…In ionic oxides, the ground state of the F center involves two electrons well localized in the vacancy giving rise to energy levels in the band gap region with typical optical absorption around 5 -6 eV. 7,[20][21][22][23] For perovskite oxides such as SrTiO 3 , the electronic structure of the F-type defects is a subject of a long debate. 24 Several theoretical studies have suggested major and identical contributions from the 3d orbitals of the two Ti ions on both sides of O vacancy to the electron density of the F center, 13,19,26 although others indicate a partial or total localization of the electrons in the vacancy.…”

Ab initio study of the optical transitions on low-coordinated sites of an intermediate F center: The Fs+(OH)− center on MgO(100) surface

“…For the terrace site we also carried out Time Dependent DFT calculations to obtain the transition energies to the lowest electronic states. This method has proven to be able to describe excitations of bulk and surface color centers of both MgO [33] and Al 2 O 3 [45]. However, in the TD-DFT calculations it is not possible to directly compute the excitations of interest and to reach them it is often necessary to include an exceedingly large number of states with nearly vanishing oscillator strength and, hence, very low transition probabilities.…”