  Organic-inorganic metal halide perovskites (HaPs) are intensively studied for
their light-harvesting properties. Owing to the interplay between strong
electron-electron interaction and spin-orbit coupling (SOC), their quantitative
theoretical description is still a challenge as evidenced by the wide variety
of results available in literature. Here, various methodologies for computing
their electronic structure are evaluated, also accounting for SOC. More
specific, the GW approach as well as variants of the hybrid functionals PBE0
and HSE are at the center of our investigations. For both functionals, we
explore methods to determine the mixing parameter $\alpha$, and for HSE, we
investigate the impact of the screening-parameter $\omega$. An extensive
investigation of PbI2, a precursor of many HaPs, leads to the conclusion that
hybrid functionals with $\alpha$ tuned by the density-based mixing method are
most suitable for obtaining band gaps comparable to $G_0W_0$ results. Moreover,
this methodology is transferable to CsPbI3, and the same behaviour is expected
for the entire family of lead-iodine perovskites.
