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

TL;DR

This paper computes the exact RPA-optimized effective potential for 15 semiconductors and insulators, evaluating the quasiparticle approximation's accuracy for band gaps and dielectric constants, and discusses self-consistency issues.

Contribution

It provides the first direct solution of the RPA-OEP for multiple materials, assessing the quasiparticle approximation's validity in this context.

Findings

QPA underestimates band gaps compared to exact RPA-OEP

Dielectric constants are affected by the approximation used

Self-consistency considerations influence the results

Abstract

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.