A Theoretical Study on the Electronic Structures of TiO2:  Effect of Hartree−Fock Exchange

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.