We propose a systematic approach to obtain various forms of insulating titanium oxynitrides Ti_nN_2O_2n-3 and we conduct a detailed study on its n=2 case, Ti_2N_2O. We study the energetics and the electronic structures of Ti_2N_2O and compare these results with those of pristine and nitrogen-doped TiO_2 within the framework of the density-functional theory (DFT) and the GW approximation. We find that Ti_2N_2O is semiconducting with the calculated band-gap of 1.81 eV, which is significantly

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... er than those of pristine TiO_2 rutile (3.14 eV) or anatase (3.55 eV). Furthermore, the reduction of the band-gap of Ti_2N_2O is realized not by lowering of the conduction-band minimum but by rising the valence-band maximum. Therefore the proposed Ti_2N_2O has suitable band-edge alignment for water-splitting photocatalysis. Finally, total energy calculations indicate that Ti_2N_2O is potentially easier to synthesize than nitrogen-doped TiO_2. Based on these results, we propose Ti_2N_2O as a promising visible-light photocatalytic material.