First-principles calculations were

First-principles calculations were implemented in the Vienna ab initio simulation package (29,30) based on density functional theory (DFT). The ion–electron interactions were described by the projector-augmented wave method. (31) We set 500 eV as the plane-wave basis cutoff energy and employed 10 × 10 × 1 and 20 × 20 × 1 k-point meshes for structural relaxations and quasiparticle (QP) band structures, respectively. The atomic positions were fully relaxed until the Hellmann–Feynman forces acting on each atom were less than 10–2 eV Å–1. The Perdew–Burke–Ernzerhof functional (32) combined with the one-shot G0W0 (33) correction was employed, and the excitonic effects were considered using Bethe–Salpeter equation (BSE) (34,35) method. To obtain the QP band structures, the wave function was expanded using maximally localized Wannier (36) functions basis. For G0W0–BSE calculations, the cutoff energy for the response functions parameter (ENCUTGW) was set to 200 eV. The vacuum layers of 25 Å were used for QP band structures and BSE calculations. The semiempirical DFT-D3 (37) correction was included to evaluate the van der Waals interactions.