Fig. 4 Density of states (DOS) and corresponding accumulated oscillator strength of defective anatase TiO 2 . a – c DOS of TiO 2 surface with 1O v , 2O v , and 4O v per slab, respectively. d – f Oscillator strength of TiO 2 surface with 1O v , 2O v , and 4O v per slab, respectively. The oscillator strength was calculated for transitions from gap states to conduction band (CB). The orange, blue, and light green area in the DOS stand for projected DOS of Ti 4 + ions, Ti 3 + ions, and O 2 − ions, respectively. The gap state, valence band maximum (VBM), and conduction band minimum (CBM) are indicated in the DOS. Accumulated oscillator strength is calculated by summing the component data of y and z direction in Supplementary Fig.