Kohn-Sham potential with discontinuity for band gap materials

TL;DR

This paper introduces a modified Kohn-Sham potential with a discontinuity at integer particle numbers, enabling accurate calculation of band gaps in materials and comparison with experimental and many-body results.

Contribution

We develop a GGA-based Kohn-Sham potential with a discontinuity, improving band gap predictions while maintaining computational efficiency.

Findings

Good agreement with experimental band gaps

Comparable to many-body perturbation theory results

Efficient implementation in GPAW code

Abstract

We model a Kohn-Sham potential with a discontinuity at integer particle numbers derived from the GLLB approximation of Gritsenko et al. We evaluate the Kohn-Sham gap and the discontinuity to obtain the quasiparticle gap. This allows us to compare the Kohn-Sham gaps to those obtained by accurate many-body perturbation theory based optimized potential methods. In addition, the resulting quasiparticle band gap is compared to experimental gaps. In the GLLB model potential, the exchange-correlation hole is modeled using a GGA energy density and the response of the hole to density variations is evaluated by using the common-denominator approximation and homogeneous electron gas based assumptions. In our modification, we have chosen the PBEsol potential as the GGA to model the exchange hole, and add a consistent correlation potential. The method is implemented in the GPAW code, which allows efficient parallelization to study large systems. A fair agreement for Kohn-Sham and the quasiparticle band gaps with semiconductors and other band gap materials is obtained with a potential which is as fast as GGA to calculate.