Precision benchmarks for solids: G₀W₀ calculations with different basis sets

The GW approximation within many-body perturbation theory is the state of the art for computing quasiparticle energies in solids. Typically, Kohn–Sham (KS) eigenvalues and eigenfunctions, obtained from a Density Functional Theory (DFT) calculation are used as a starting point to build the Green's function G and the screened Coulomb interaction W, yielding the one-shot G₀W₀ self-energy if no further update of these quantities are made. Multiple implementations exist for both the DFT and the subsequent G₀W₀ calculation, leading to possible differences in quasiparticle energies. In the present work, the G₀W₀ quasiparticle energies for states close to the band gap are calculated for six crystalline solids, using four different codes: Abinit, exciting, FHI-aims, and GPAW. This comparison helps to assess the impact of basis-set types (planewaves versus localized orbitals) and the treatment of core and valence electrons (all-electron full potentials versus pseudopotentials). The impact of unoccupied states as well as the algorithms for solving the quasiparticle equation are also briefly discussed. For the KS-DFT band gaps, we observe good agreement between all codes, with differences not exceeding 0.1 eV, while the G₀W₀ results deviate on the order of 0.1-0.3 eV. Between all-electron codes (FHI-aims and exciting), the agreement is better than 15 meV for KS-DFT and, with one exception, about 0.1 eV for G₀W₀ band gaps.