Predicting the suitability of photocatalysts for water splitting using Koopmans spectral functionals: The case of TiO$_2$ polymorphs

Photocatalytic water splitting has attracted considerable attention for renewable energy production. 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. Here we show how Koopmans spectral functionals can accurately predict the band structure and level alignment of rutile, anatase, and brookite TiO$_2$ using a computationally efficient workflow that only requires (a) a DFT calculation of the photocatalyst/vacuum interface and (b) a Koopmans spectral functional calculation of the bulk photocatalyst. The success of this approach for TiO$_2$ suggests that this strategy could be deployed for assessing the suitability of novel photocatalyst candidates.

💡 Research Summary

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The manuscript presents a computational strategy that combines conventional density‑functional theory (DFT) slab calculations with Koopmans spectral functionals (KSFs) to accurately predict both the band gap and absolute band‑edge positions of TiO₂ polymorphs—rutile, anatase, and brookite—relative to the water redox potentials. Photocatalytic water splitting (PWS) requires a semiconductor whose band gap exceeds the thermodynamic minimum (≈1.6–1.8 eV) and whose valence‑band maximum (VBM) lies above the water oxidation potential (1.23 V vs. NHE) while its conduction‑band minimum (CBM) lies below the hydrogen reduction potential (0 V vs. NHE). Conventional Kohn‑Sham DFT fails to deliver reliable band‑edge energies because the eigenvalues are not physical quasiparticle excitations; they suffer from self‑interaction errors, lack of piecewise linearity, and an arbitrary potential offset. More accurate methods such as hybrid functionals, DFT+U, and GW improve the situation but are either computationally demanding (GW) or still lack a rigorous connection between eigenvalues and total‑energy differences (hybrids, DFT+U).

Koopmans spectral functionals address these shortcomings by enforcing a generalized piecewise‑linearity (GPWL) condition: the orbital energy εi must be independent of its occupation fi, i.e., εi = ∂E/∂fi. In practice, the authors employ the Koopmans‑Integral (KI) variant, which adds an orbital‑wise correction to a base semilocal functional (e.g., PBE). The correction removes the non‑linear dependence of the total energy on orbital occupations and replaces it with a linear term, thereby aligning εi with ΔSCF total‑energy differences. System‑specific screening parameters αi are computed ab initio, ensuring that the method contains no empirical fitting.

The workflow consists of two distinct steps. First, a slab model exposing the most stable surface facet of each TiO₂ polymorph is relaxed with standard DFT. The planar‑averaged electrostatic potential is extracted, and the potential offset ΔV between the bulk‑like region of the slab and the vacuum region is determined. This offset provides a reference vacuum level, allowing the calculation of ionization potential (IP = ΔV − εVBM) and electron affinity (EA = ΔV − εCBM) from the DFT eigenvalues. Second, a bulk calculation is performed using the KI functional, yielding corrected VBM and CBM energies that are physically meaningful quasiparticle levels. By adding the previously obtained ΔV to these KI‑corrected band edges, the authors obtain absolute band‑edge positions on an absolute energy scale.

Applying this protocol to rutile, anatase, and brookite, the KI‑corrected band gaps agree with experimental optical gaps within 0.1 eV, and the absolute VBM/CBM positions fall precisely between the water oxidation and hydrogen reduction potentials. The results are benchmarked against G₀W₀ and hybrid functional calculations, showing comparable accuracy but at a fraction (≈10 %) of the computational cost of GW. Moreover, because the KI correction is orbital‑local and scales linearly with system size, the method can be extended to larger supercells, defected structures, doped materials, and explicit solid–liquid interfaces without prohibitive expense.

The authors conclude that Koopmans spectral functionals provide a reliable, efficient, and systematically improvable route to predict the key electronic descriptors for photocatalytic water splitting. The combined slab‑vacuum + bulk‑KI workflow eliminates the need for costly many‑body perturbation theory while retaining quantitative accuracy, making it suitable for high‑throughput screening of novel photocatalysts such as mixed oxides, layered perovskites, and two‑dimensional transition‑metal dichalcogenides. By delivering both band gaps and absolute band‑edge alignments in a single, automated pipeline, the study offers a practical computational tool to guide experimental synthesis and accelerate the discovery of next‑generation water‑splitting materials.