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 Gnon-SCF, or with orbitals of separate self-consistent calculations of N-, (N − 1), and (N + 1)-electron systems GSCF, in electron volts, as discussed in the text

PBEPBE0
Grid sizegGnon-SCFGSCFgOEPgGnon-SCFGSCF
1 × 1 × 17.6219.1308.4827.90112.07911.94411.311
2 × 2 × 28.6408.7938.6588.83110.94711.06510.948
3 × 3 × 38.6888.7358.6948.92311.09111.10811.073
4 × 4 × 48.6918.7118.6998.93811.12011.12311.108
5 × 5 × 58.6928.7028.6938.94211.12111.12611.119
6 × 6 × 68.6928.6978.6938.94411.12211.12611.122
7 × 7 × 78.6928.6958.6928.94511.12311.12611.123
8 × 8 × 88.6928.6948.6928.94511.12311.12511.124
  • 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.