Many-body perturbation theory in the GW approximation has been regarded as the most accurate and robust first-principles approach to electronic band structure of insulating materials. In this talk I will address the challenges of numerically accurate GW calculation based on our recent systematic investigation of the effects of including high-energy local orbitals (HLOs) in the linearized augmented plane waves (LAPW)-based all-electron GW calculations for both weakly and strongly correlated materials [1-5]. We found that both the accuracy of unoccupied states and the completeness in the summation of states are crucial for numerically accurate GW calculations, which can provide important clues to the construction of more accurate pseudopotentials and the development of new approaches that eliminate or reduce the efforts necessary for the summation of unoccupied states.

[1] H. Jiang et al. Computer Phys. Commun.,2013, 184:348.

[2] H. Jiang and P. Blaha, Phys. Rev. B, 2016, 93:115203.

[3] M.-Y. Zhang and H. Jiang, Phys. Rev. B. 2019, 100: 205123.

[4] H. Jiang, Phys. Rev. B, 2018, 97:245132.

[5] M.-Y. Zhang and H. Jiang, Frontiers of Chemistry, 2021, 9, 747972.