# Reproducibility in $G_0W_0$ Calculations for Solids

## TL;DR

This paper investigates the reproducibility of $G_0W_0$ calculations for solids, analyzing convergence, implementation differences, and demonstrating consistent quasiparticle energies across multiple computational codes.

## Contribution

It provides the first comprehensive comparison of $G_0W_0$ implementations across different codes, addressing key approximations and convergence issues.

## Key findings

- Consistent quasiparticle energies obtained across BerkeleyGW, Abinit, and Yambo.
- Analysis of frequency-integration schemes and Coulomb divergence treatment.
- Identification of factors affecting $G_0W_0$ calculation variability.

## Abstract

Ab initio many-body perturbation theory within the $GW$ approximation is a Green's function formalism widely used in the calculation of quasiparticle excitation energies of solids. In what has become an increasingly standard approach, Kohn-Sham eigenenergies, generated from a DFT calculation with a strategically-chosen exchange correlation functional ``starting point'', are used to construct $G$ and $W$, and then perturbatively corrected by the resultant $GW$ self-energy. In practice, there are several ways to construct the $GW$ self-energy, and these can lead to variations in predicted quasiparticle energies. For example, for ZnO and TiO$_2$, reported $GW$ fundamental gaps can vary by more than 1 eV. In this work, we address the convergence and key approximations in contemporary $G_0W_0$ calculations, including frequency-integration schemes and the treatment of the Coulomb divergence in the exact-exchange term. We study several systems,and compare three different $GW$ codes: BerkeleyGW, Abinit and Yambo. We demonstrate, for the first time, that the same quasiparticle energies for systems in the condensed phase can be obtained with different codes, and we provide a comprehensive assessment of implementations of the $GW$ approximation.