Comparison between PBE and HSE06 functionals for the calculation of electronic band-structure of TiO2

Electronic structure of various structures of TiO2 were calculated using PBE and HSE06 functionals. Calculated band gap in HSE06 level for rutile and anatase phases was 3.4 and 3.58 eV respectively which are in agreement with experimental values of 3 and 3.2 eV. Calculated bulk moduli for the mentioned phases were to be 226 and 205 Gpa. The difference of these values with reported experimental values are %7 and %14 respectively. Comparison between the two mentioned functionals shows that the overall form of band structures is independent of the functional. Especially the top of valence band and the bottom of conduction band are the same in PBE and HSE06. So both functionals give the same result for the type (direct or indirect) of band-gap. Distance between conduction and valence bands, and so the band-gap, is the main difference in calculating the band-structure using these two functionals. Band-gap difference calculated by these functionals is almost 1.6 eV for all structures studied in here. So one can calculate the band-gap of TiO2 with PBE and sum the result by 1.6 eV instead of calculating the band gap in expensive HSE06 level which is close to experimental value.