. 2017 Mar 6;114(11):2801–2806. doi: 10.1073/pnas.1621352114

Table 3.

KS(PBE) and OEP/KS and GKS(PBE0) band gap g and fundamental energy gaps G of solid Ar, calculated according to Eq. 1 with orbitals of the neutral N-electron system G_non-SCF, or with orbitals of separate self-consistent calculations of N-, (N − 1), and (N + 1)-electron systems G_SCF, in electron volts, as discussed in the text

	PBE			PBE0
Grid size	g	G_non-SCF	G_SCF	g_OEP	g	G_non-SCF	G_SCF
1 × 1 × 1	7.621	9.130	8.482	7.901	12.079	11.944	11.311
2 × 2 × 2	8.640	8.793	8.658	8.831	10.947	11.065	10.948
3 × 3 × 3	8.688	8.735	8.694	8.923	11.091	11.108	11.073
4 × 4 × 4	8.691	8.711	8.699	8.938	11.120	11.123	11.108
5 × 5 × 5	8.692	8.702	8.693	8.942	11.121	11.126	11.119
6 × 6 × 6	8.692	8.697	8.693	8.944	11.122	11.126	11.122
7 × 7 × 7	8.692	8.695	8.692	8.945	11.123	11.126	11.123
8 × 8 × 8	8.692	8.694	8.692	8.945	11.123	11.125	11.124

The experimental band gap (53) of Ar is 14.20 eV. For a recent comparison of GKS band gaps for many solids from GGA hybrid functionals, including PBE0 and HSE, see ref. 54.