Band gaps in pseudopotential self-consistent GW calculations
  For materials which are incorrectly predicted by density functional theory to be metallic, an iterative procedure must be adopted in order to perform GW calculations. In this paper we test two iterative schemes based on the quasi-particle and pseudopotential approximations for a number of inorganic semiconductors whose electronic structures are well known from experiment. Iterating just the quasi-particle energies yields a systematic, but modest overestimate of the band gaps, confirming conclusions drawn earlier for CaB_6 and YH_3. Iterating the quasi-particle wave functions as well gives rise to an imbalance between the Hartree and Fock potentials and results in bandgaps in far poorer agreement with experiment. 
V.A. Popa, G. Brocks, and P.J. Kelly