Converged <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>G</mml:mi><mml:mi>W</mml:mi></mml:mrow></mml:math> quasiparticle energies for transition metal oxide perovskites

The ab initio calculation of quasiparticle (QP) energies is a technically and computationally challenging problem. In condensed matter physics, the most widely used approach to determine QP energies is the $GW$ approximation. Although the $GW$ method has been widely applied to many typical semiconductors and insulators, its application to more complex compounds such as transition metal oxide perovskites has been comparatively rare, and its proper use is not well established from a technical point of view. In this work, we have applied the single-shot ${G}_{0}{W}_{0}$ method to a representative set of transition metal oxide perovskites including $3d$ (${\mathrm{SrTiO}}_{3}, {\mathrm{LaScO}}_{3}, {\mathrm{SrMnO}}_{3}, {\mathrm{LaTiO}}_{3}, {\mathrm{LaVO}}_{3}, {\mathrm{LaCrO}}_{3}, {\mathrm{LaMnO}}_{3}$, and ${\mathrm{LaFeO}}_{3}$), $4d$ (${\mathrm{SrZrO}}_{3}, {\mathrm{SrTcO}}_{3}$, and ${\mathrm{Ca}}_{2}{\mathrm{RuO}}_{4}$), and $5d$ (${\mathrm{SrHfO}}_{3}, {\mathrm{KTaO}}_{3}$, and ${\mathrm{NaOsO}}_{3}$) compounds with different electronic configurations, magnetic orderings, structural characteristics, and band gaps ranging from 0.1 to 6.1 eV. We discuss the proper procedure to obtain well-converged QP energies and accurate band gaps within single-shot ${G}_{0}{W}_{0}$ by comparing the conventional approach based on an incremental variation of a specific set of parameters (number of bands, energy cutoff for the plane-wave expansion and number of k points) and the basis-set extrapolation scheme [J. Klime\ifmmode \check{s}\else \v{s}\fi{} et al., Phys. Rev. B 90, 075125 (2014)]. Although the conventional scheme is not supported by a formal proof of convergence, for most cases it delivers QP energies in reasonably good agreement with those obtained by the basis-set correction procedure and it is by construction more useful for calculating band structures. In addition, we have inspected the difference between the adoption of norm-conserving and ultrasoft potentials in $GW$ calculations and found that the norm violation for the $d$ shell can lead to less accurate results in particular for charge-transfer systems and late transition metals. A minimal statistical analysis indicates that the correlation of the $GW$ data with the density functional theory gap is more robust than the correlation with the experimental gaps; moreover, we identify the static dielectric constant as alternative useful parameter for the approximation of $GW$ gap in high-throughput automatic procedures. Finally, we compute the QP band structure and spectra within the random phase approximation and compare the results with available experimental data.