Abstract: GW is presently the best available first-principles methodology for the prediction of electronic structure, including band gaps. However, dealing with GW calculations is always challenging, not simply due to unfavorable scaling with system size, or possible lack of symmetry, but also due to the large number of parameters of such calculations. As a consequence, systematic GW benchmarks for large sets of materials are much more limited than for density-functional theory.
In the present work, we pave the way beyond the study of Van Setten and coworkers , who examined 70 materials, however aiming to a limited target accuracy. Indeed we consider a convergence criterion of 0.02 eV in the GW band gap, more stringent than the 0.05 eV target of this previous study. Moreover, the latter relied on a plasmon-pole model, while the present analysis also focus on contour-deformation and analytic continuation methodologies which are computationally more expensive and theoretically better justified. Like Van Setten et al, we use ABINIT  and stay at the non-self-consistent G0W0 level. Besides, the parallel speedup and efficiency of the implementation have been investigated.
We focus on three systems that are representative of pure, doped, and two-dimensional materials respectively. The first system, ZrO2, contains 3 atoms per primitive cell, the second system, Zr2Y2O7, is a ZrO2 crystal doped with 50% yttrium oxide and contains 11 atoms, and the third system, MoS2-WS2, is a van der Waals bilayer, containing 6 atoms. First, wavefunctions and eigenfunctions are computed at the density functional theory (DFT) level with pseudodojo pseudopotentials . Convergence studies with respect to both number of plane waves used in the wavefunction basis set and the Brillouin Zone sampling showed that the Kohn-Sham eigenenergies were converged well below the 0.02 eV level. For GW calculations, an additional double convergence study must be performed over the number of unoccupied bands and the energy cut-off for the dielectric matrix noted EcX. Reaching convergence within our criterion for Zr2Y2O7 benefits from techniques introduced in  and . In the latter, the gap is extrapolated as a function of EcX, as ∆E(EcX) = ∆Eg(∞) + B3 × EcX(−3/2) + B5 × EcX(−5/2). With these techniques, the convergence criteria can be met. Using contour deformation technique and the optimized parameters, the GW band gaps are 5.35 eV, 4.05 eV, and 2.03 eV for ZrO2, Zr2Y2O7, and MoS2-WS2 respectively. The influence of parameters and of different treatment is analyzed. The time scaling analysis confirms that the most time-consuming part of the calculation is the calculations of the screening matrix.
 M. J. van Setten, M. Giantomassi, X. Gonze, G.-M. Rignanese and G. Hautier, Phys. Rev. B 96, 155207 (2017)
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