The effects of the Fock exchange on the geometries and electronic structures of TiO2 have been investigated by introducing a portion of Hartree-Fock (HF) exchange into the traditional density functional. Our results indicate that the functional with 13% HF exchange can correctly predict the band gap and the electronic structures of rutile TiO2, and such an approach is also suitable to describe the structural and electronic properties of anatase and brookite phases. For the TiO2 (110) surfaces, although the surface relaxations are insensitive to the variation of HF exchange, there are larger effects on the positions of the occupied surface-induced states. When 13% HF exchange is employed, the predicted band gap of the perfect surface and position of defect state of the reduced surface are consistent with the experimental values. Moreover, the electronic structures of TiO2 (110) surface are carefully reexamined by using this hybrid density functional method.
The Ti-doped SnO2(110) surface has been investigated by using first-principles method with a slab model. The geometrical optimizations and band-structure calculations have been performed for four possible doping models. Our results indicate that the substitution of Ti for sixfold-coordinated Sn atom at the top layer is most energetically favorable. Compared to the undoped surface, those Sn and O atoms located above Ti atom tend to move toward the bulk side. Besides the surface relaxations, the doping of Ti has significant influences on the electronic structures of SnO2(110) surface, including the value and position of minimum band gap, the components of valence and conduction bands, the distributions of the charge densities, and the work function of the surface. Furthermore, the effects introduced by the substitution of Ti atom observed in the experiments can be well explained when the sixfold-coordinated Sn atom at the first layer is replaced by Ti atom.
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