“…Origin of the deep defect states is very disputable. Various experimental techniques, including photoelectron spectroscopy, scanning tunneling microscopy, transmission Fourier-transform infrared spectroscopy, resonant photoelectron diffraction, electron paramagnetic resonance measurement, have been employed to explore the nature of deep defect states. − Massive first-principles calculations at the level of density functional theory (DFT), especially DFT + U and hybrid DFT using B3LYP and HSE functionals to describe the exchange–correlation interactions, provide very valuable information to help us understand the electronic properties of defects. ,,− With the development of theoretical approaches and computer power, GW method within the many-body Green’s function theory, which is considered to be superior to DFT in electronic structure calculations, is being applied to study defective TiO 2 recently. − According to the results from DFT + U and hybrid DFT, presently it is commonly thought that the deep defect states in rutile and anatase arise from small polarons induced by the excess electrons from oxygen vacancies (Ov) or hydroxyl groups. However, according to their experiments, Wendt et al ascribed the deep defect state in rutile to Ti interstitials (Ti-ints); Brandão et al proposed that Ov in rutile can only lead to shallow defect states near the CBM .…”