GW with linearized augmented plane waves extended by high-energy local orbitals

Many-body perturbation theory in the GW approximation is currently the most accurate and robust first-principles approach to determine the electronic band structure of weakly correlated insulating materials without any empirical input. Recent GW results for ZnO with more careful investigation of the convergence with respect to the number of unoccupied states have led to heated debates regarding the numerical accuracy of previously reported GW results using either pseudopotential plane waves or all-electron linearized augmented plane waves (LAPWs). The latter has been arguably regarded as the most accurate scheme for electronic-structure theory for solids. This work aims to solve the ZnO puzzle via a systematic investigation of the effects of including high-energy local orbitals (HLOs) in the LAPW-based GW calculations of semiconductors. Using ZnO as the prototypical example, it is shown that the inclusion of HLOs has two main effects: it improves the description of high-lying unoccupied states by reducing the linearization errors of the standard LAPW basis, and in addition it provides an efficient way to achieve the completeness in the summation of states in GW calculations. By investigating the convergence of GW band gaps with respect to the number of HLOs for several other typical examples, it was found that the effects of HLOs are highly system-dependent, and in most cases the inclusion of HLOs changes the band gap by less than 0.2 eV. Compared to its effects on the band gap, the consideration of HLOs has even stronger effects on the GW correction to the valence-band maximum, which is of great significance for the GW prediction of the ionization potentials of semiconductors. By considering an extended set of semiconductors with relatively well established experimental band gaps, it was found that in general using a HLO-enhanced LAPW basis significantly improves the agreement with experiment for both the band gap and the ionization potential, and overall the partially self-consistent GW(0) approach based on the generalized gradient approximation gives an optimal performance.