Kohn-Sham potential with discontinuity for band gap materials

We model a Kohn-Sham potential with the discontinuity at integer particle numbers starting from the approximation by (GLLB) Gritsenko et al. [Phys. Rev. A 51, 1944 (1995)]. 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 generalized gradient approximation (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.

Figure 1

(Color online) Fundamental, i.e., minimum, band gap (in eV) of five semiconductors as a function of the lattice constant. The KS gap (dashed curve) and the quasiparticle gaps (solid curve) from our GLLB-SC are shown. The LDA (square), PBE (plus), and PBEsol (circle) data are shown for their minimum energy lattice constants, respectively. Similarly, the experimental data is denoted by the star. For references, see Table .

Figure 2

(Color online) Kohn-Sham band gap (three leftmost, green) and the discontinuity (on top) contribution to the quasiparticle (total) gap from our LDA, GLLB exchange only, and GLLB-SC calculations. The True DFT KS gaps (rightmost, yellow) with the discontinuity from GW (top, red) are shown for comparison.

Figure 3

(Color online) Calculated Kohn-Sham band structures (without discontinuity) of compounds Si, GaAs, and AlAs using LDA, GLLB, and GLLB-SC approaches.

Figure 4

(Color online) Calculated Kohn-Sham band structures (without discontinuity) of C, LiF, and Ar using LDA, GLLB, and GLLB-SC approaches.