Correction of band-gap energy and dielectric function of BiOX bulk with GW and BSE

•We study the electronic structures of bismuth oxyhalides BiOXs.•The bismuth oxyhalide show some promise in the photocatalytic.•The GW results indicate that the bandgaps are agreement with the experimental values.•The bandgap can be reduced under an external electric field. Using the DFT method and beyond with GW approximation, we investigate the electronic structures of bismuth oxyhalides BiOXs (where X = F, Cl, Br, and I). The optical properties such as dielectric function and absorption coefficient of BiOXs except BiOI are fully computed with different methods, i.e., DFT, ACFDT in RPA, and with BSE. Our results show that the band-gap nature of BiOF is direct, whereas the band-gaps of BiOCl, BiOBr, and BiOI are indirect. Also, our GW results indicate that the band-gaps of BiOX are very well agreement with the experimental values. Besides, we show that under an external electric field a semiconductor can be changed to a metal with a strong field of more than 0.5 V/Å. Further, we found that the BSE method is the best way to describe the optical properties of BiOXs.