Electronic and optical properties of the fully and partially inverse CoFe2O4 spinel from first principles calculations including many-body effects

Using density functional theory calculations and many-body perturbation theory, we investigate the electronic and optical properties of the inverse spinel CoFe₂O₄, a common anode material for photocatalytic water splitting. Starting with different exchange-correlation functionals, at the independent particle (IP) level we obtain a direct band gap of 1.38 eV (PBE+U, U=4 eV) and 1.69 eV (SCAN+ U, U=3 eV), whereas HSE06 renders an indirect band gap of 2.02 eV. Including quasiparticle effects within G₀W₀, a larger and indirect band gap is obtained for all functionals: 1.78 eV (PBE+U, U=4 eV), 1.95 eV (SCAN+ U, U=3 eV), and 2.17 eV (HSE06). Excitonic effects, taken into account by solving the Bethe-Salpeter equation (BSE), lead to a redshift of the optical band gap to 1.50 (SCAN+ U, U=3 eV) and 1.61 eV (HSE06), in good agreement with the reported experimental values $1.50--2.0$ eV. We also explored the effect of the degree of inversion: while the band gap decreases at the IP level, including excitonic effects leads to an increase from 1.50 ($x=1$) to 1.57 ($x=0.5$), and 1.64 eV ($x=0)$. The lowest optical transitions in the visible range, identified based on the oscillator strength, are at 2.0, 3.5, and 5.0 eV for the inverse spinel, consistent with the experimental values at 2.0, 3.4, and 4.9 eV. Both $x=0.0$ and $x=0.5$ exhibit transitions below 1 eV with extremely small oscillator strengths that are absent in the inverse spinel. This corroborates previous suggestions that these transitions are related to the presence of Co²⁺ cations at the tetrahedral sites.