Accurate predictions of excited states properties are critical for computational screening and design of materials for energy and electronics applications. While density functional theory (DFT) within the local density approximation (LDA) or the generalized gradient approximation (GGA) has been very successful in describing materials ground-state properties, the Kohn-Sham (KS) eigenstates in principle cannot be compared directly with quasiparticle (QP) excitations. The GW approximation, systematically derived from the perturbative expansion of electron self-energy, is widely recognized as one of the most accurate methods for predicting excited states properties of materials.
Unfortunately, despite the tremendous success, accurate and efficient predictions of excited-states properties of complex solid systems remain a major challenge due to complication of the convergence issue and the unfavorable scaling of the computational cost (both in terms of the computational time and the storage and memory requirements) with respect to the system size. is is particularly true for systems containing substantially localized electronic states and/or with large unit cells (e.g., nanostructures, complex multinary compounds, surfaces and interfaces, and defects in solids). For example, it has been shown that for simple materials such as ZnO one has to include as many as 3,000 empty states in conventional GW calculations to acheive properly converged results. Although ZnO has probably received the most research attention, the convergence problem of GW calculations is not just limited to this single material. In fact, GW calculations for many systems, including MgO, CuCl, AgBr, and CdO (to name a few), suffer similar convergence problems. Recently, it was shown that about 6,000 bands are need to to converge the GW band gap for monolayer MoS2 to within 50 meV, and that for MoSe2 is as large as 10,000.
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