**4. Photocatalytic water splitting modeling**

Theoretical modeling studies of water splitting concern a number of aspects such as electron–hole transport/recombination, photocatalytic reaction, semiconductor band edge alignment, and photo redox chemistry [27–34]. DFT has been used extensively for the theoretical modeling of water splitting to predict the electronic structure of materials due to the modest cost and high accuracy reproducibility [35, 36, 42, 43]. However, the inaccurate predictions of band gaps are the major drawback of DFT. Hybrid materials have better performance for the prediction of band gap and the exited state position [44]. The band gap drawback and problems is tackled by perturbation theory which has a long-standing record of success [45, 46]. Computational methods are very helpful, especially in the prediction of impurities in photocatalysts induced by dopants in tuning with band gap for example TiO2. Theoretical and computational tools are given an understanding and idea about various aspects of material and its state. For example, BiVO4 in the band structures and density of states, migration energy profile of surface reactions, band structure, and density state, electron/hole pair generation comprehensive study. Also, electron–hole pairs driven to different crystal facets [47, 48]. All of these findings can obtain from comprehensive computational studies that are related to or compared with facet (011), (010) have lower absorption at 420 nm, better transport of electron–hole pair, and lower potential energy surfaces [49]. Theoretical studies are related to the improvement of band structure and morphology of the photocatalytic material.
