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The optimized effective potential (OEP) method presents an unambiguous way toconstruct the Kohn-Sham potential corresponding to a given diagrammaticapproximation for the exchange-correlation functional. The OEP from therandom-phase approximation (RPA) has played an important role ever since theconception of the OEP formalism. However, the solution of the OEP equation iscomputationally fairly expensive and has to be done in a self-consistent way.So far, large scale solid state applications have therefore been performed onlyusing the quasiparticle approximation (QPA), neglecting certain dynamicalscreening effects. We obtain the exact RPA-OEP for 15 semiconductors andinsulators by direct solution of the linearized Sham-Schl\"uter equation. Weinvestigate the accuracy of the QPA on Kohn-Sham band gaps and dielectricconstants, and comment on the issue of self-consistency.

Optimized effective potentials from the random-phase approximation: Accuracy of the quasiparticle approximation