We have evaluated the self-energy of solids within different self-consistent approximations, from bare and screened exchange to screened exchange plus Coulomb hole (COHSEX) and $GW$ approximations. Our calculations for silicon, aluminum, and argon assess the quality of the local-density approximation (LDA) valence wave functions and density with respect to their $GW$ counterparts. The LDA conduction wave functions are shown to be of significantly poorer quality, in particular for not highly symmetric points of the Brillouin zone. Comparing the different approaches we show that screened exchange alone is not reliable and we propose to combine a self-consistent COHSEX with a subsequent perturbative $GW$ calculation that gives a reasonable estimate of the self-consistent $GW$ results, at a much lower computational cost. The calculations are based on the pseudopotential method; they confirm its reliability.

• Received 27 January 2006

DOI:https://doi.org/10.1103/PhysRevB.74.045102