Towards predictive band gaps for halide perovskites: Lessons from one-shot and eigenvalue self-consistent GW

Halide perovskites constitute a chemically-diverse class of crystals with great promise as photovoltaic absorber materials, featuring band gaps between about 1 and 3.5 eV depending on composition. Their diversity calls for a general computational approach to predicting their band gaps. However, such an approach is still lacking. Here, we use density functional theory (DFT) and many-body perturbation theory within the GW approximation to compute the quasiparticle or fundamental band gap of a set of ten representative halide perovskites: CH$_3$NH$_3$PbI$_3$ (MAPbI$_3$), MAPbBr$_3$, CsSnBr$_3$, (MA)$_2$BiTlBr$_6$, Cs$_2$TlAgBr$_6$, Cs$_2$TlAgCl$_6$, Cs$_2$BiAgBr$_6$, Cs$_2$InAgCl$_6$, Cs$_2$SnBr$_6$, and Cs$_2$Au$_2$I$_6$. Comparing with recent measurements, we find that a standard generalized gradient exchange-correlation functional can significantly underestimate the experimental band gaps of these perovskites, particularly in cases with strong spin-orbit coupling (SOC) and highly dispersive band edges, to a degree that varies with composition. We show that these nonsystematic errors are inherited by one-shot G$_0$W$_0$ and eigenvalue self-consistent GW$_0$ calculations, demonstrating that semilocal DFT starting points are insufficient for MAPbI$_3$, MAPbBr$_3$, CsSnBr$_3$, (MA)$_2$BiTlBr$_6$, Cs$_2$TlAgBr$_6$, and Cs$_2$TlAgCl$_6$. On the other hand, we find that DFT with hybrid functionals leads to an improved starting point and GW$_0$ results in better agreement with experiment for these perovskites. Our results suggest that GW$_0$ with hybrid functional-based starting points are promising for predicting band gaps of systems with large SOC and dispersive bands in this technologically important class of semiconducting crystals.