Band convergence and linearization error correction of all-electron GW calculations: The extreme case of zinc oxide

Recently, Shih et al. [Phys. Rev. Lett. 105, 146401 (2010)] published a theoretical band gap for wurtzite ZnO, calculated with the non-self-consistent GW approximation, that agreed surprisingly well with experiment while deviating strongly from previous studies. They showed that a very large number of empty bands is necessary to converge the gap. We reexamine the GW calculation with the full-potential linearized augmented-plane-wave method and find that even with 3000 bands the band gap is not completely converged. A hyperbolical fit is used to extrapolate to infinite bands. Furthermore, we eliminate the linearization error for high-lying states with local orbitals. In fact, our calculated band gap is considerably larger than in previous studies, but somewhat smaller than that of Shih et al..