  The optimized effective potential (OEP) method presents an unambiguous way to
construct the Kohn-Sham potential corresponding to a given diagrammatic
approximation for the exchange-correlation functional. The OEP from the
random-phase approximation (RPA) has played an important role ever since the
conception of the OEP formalism. However, the solution of the OEP equation is
computationally fairly expensive and has to be done in a self-consistent way.
So far, large scale solid state applications have therefore been performed only
using the quasiparticle approximation (QPA), neglecting certain dynamical
screening effects. We obtain the exact RPA-OEP for 15 semiconductors and
insulators by direct solution of the linearized Sham-Schl\"uter equation. We
investigate the accuracy of the QPA on Kohn-Sham band gaps and dielectric
constants, and comment on the issue of self-consistency.
