All-electron<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>GW</mml:mi></mml:math>calculation based on the LAPW method: Application to wurtzite ZnO

We present an all-electron implementation of the $\mathrm{GW}$ approximation and apply it to wurtzite ZnO. Eigenfunctions computed in the local-density approximation (LDA) by the full-potential linearized augmented-plane-wave or the linearized muffin-tin-orbital method supply the input for generating the Green function G and the screened Coulomb interaction W. A mixed basis is used for the expansion of W, consisting of plane waves in the interstitial region and augmented-wave-function products in the augmentation-sphere regions. The frequency dependence of the dielectric function is computed within the random-phase approximation (RPA), without a plasmon-pole approximation. The Zn $3d$ orbitals are treated as valence states within the LDA; both core and valence states are included in the self-energy calculation. The calculated band gap is smaller than experiment by $\ensuremath{\sim}1\mathrm{eV},$ in contrast to previously reported $\mathrm{GW}$ results. Self-energy corrections are orbital dependent and push down the deep O $2s$ and Zn $3d$ levels by $\ensuremath{\sim}1\mathrm{eV}$ relative to the LDA. The d level shifts closer to experiment but the size of shift is underestimated, suggesting that the RPA overscreens localized states.