  The self-consistent GW band gaps are known to be significantly overestimated.
We show that this overestimation is, to a large extent, due to the neglect of
the contribution of the lattice polarization to the screening of the
electron-electron interaction. To solve this problem, we derive within the GW
formalism a generalized plasmon-pole model that accounts for lattice
polarization. The resulting GW self-energy is used to calculate the band
structures of a set of binary semiconductors and insulators. The lattice
contribution always decreases the band gap. The shrinkage increases with the
size of the longitudinal-transverse optical splitting and it can represent more
than 15% of the band gap in highly polar compounds, reducing the band-gap
percentage error by a factor of three.
