Photocatalytic water splitting has drawn considerable attention as an alternative way to produce renewable energy rather than relying on fossil fuels. Although extensively studied from both engineering and scientific perspectives, this process still has some issues that need to be addressed. Since the first reported photocatalytic water splitting by titanium dioxide, this material remains one of the most promising photocatalysts, due to its suitable band gap and band-edge positions. However, predicting both of these properties is a challenging task for existing computational methods. Density functional theory --- a workhorse of materials science more generally --- lacks the ability to obtain the right electronic gap as well as excitation energies. It is not just the band gap that we need to get right: we need to capture band alignment and even more complicated physics such as charge carriers and polaronic states. All of these properties can pose a challenge to a semi-local DFT. Higher levels of theory such as GW or hybrid functional provide better results, but at increased computational cost and/or scaling. Therefore, here I present novel computational strategies based on Koopmans spectral functionals with the idea to break new ground when it comes to light-driven reactions. These orbital-density dependent functionals are proven to be reliable when it comes to calculating the spectral properties of materials, such as the ionization potentials and electron affinities of molecules, as well as the band gaps of solids. Furthermore, they predict reliable trends when it comes to studying band alignments with and without accounting for solvation.

In this thesis, I present the main advantage of this method over standard DFT in addressing the spectral properties and give some ideas regarding the potential use of this method in studying the role of polarons in photocatalytic processes. The research is focused on the prototypical photocatalyst TiO2. Overall, this work demonstrates the capabilities of Koopmans functionals in terms of modeling photocatalytic materials, bridging the accuracy and computational cost. While this method seems promising for spectral properties, challenges remain in modeling polaron localization. Addressing these limitations --- in particular, the role of screening parameters in systems energetics and alternative electronic minimization strategies --- will be a key focus of future work.
More broadly, this thesis opens new avenues for modeling photocatalytic materials with implications for solar fuels and energy conversion.