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We study the quasiparticle band gap of the hybrid organic-inorganic leadhalide perovskite CH$_3$NH$_3$PbI$_3$, using many-body perturbation theorybased on the $GW$ approximation. We perform a systematic analysis of the bandgap sensitivity to relativistic spin-orbit effects, to the description ofsemicore Pb-5$d$ and I-4$d$ electrons, and to the starting Kohn-Shameigenvalues. We find that the inclusion of semicore states increases thecalculated band gap by 0.2 eV, and self-consistency on the quasiparticleeigenvalues using a scissor correction increases the band gap by 0.4 eV withrespect to the $G_0W_0$ result. These findings allow us to resolve aninconsistency between previously reported $GW$ calculations forCH$_3$NH$_3$PbI$_3$. Our most accurate band gap is 1.65 eV, and is in goodagreement with the measured optical gap after considering a small excitonicshift as determined in experiments.

physical review. b, condensed matter and materials physics

GW quasiparticle band gap of the hybrid organic-inorganic perovskite  CH$_3$NH$_3$PbI$_3$: Effect of spin-orbit interaction, semicore electrons,  and self-consistency