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. However, a general computational approach to predicting their band gaps is still lacking. Here, we use density functional theory (DFT) and ab initio 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 significantly underestimates the experimental band gaps of these perovskites, particularly in cases with strong spin-orbit coupling (SOC) and highly dispersive band edges. Moreover, we find that the magnitude of the underestimate can vary dramatically with composition. Importantly, 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 materials.