Local exchange-correlation potentials by density inversion in solids

Following Hollins [], we invert the electronic ground-state densities for various semiconducting and insulating solids calculated using several density functional approximations within the generalized Kohn-Sham (GKS) scheme, which includes Hartree-Fock (HF) theory, hybrid schemes, and the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>LDA</a:mi><a:mo>+</a:mo><a:mi>U</a:mi></a:mrow></a:math> method. To appraise the role of locality versus nonlocality in the effective KS/GKS potential, the band structures from the resulting (LXC) Kohn-Sham potential are then compared with the band structures of the original GKS method. We find the LXC potential obtained from the HF density systematically predicts band gaps in good agreement with experiment, including for strongly correlated transition metal monoxides. Furthermore, we find that the HSE06 and PBE0 hybrid functionals yield similar densities and LXC potentials to each other. In weakly correlated systems, these potentials are also similar to PBE. For <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>LDA</b:mi><b:mo>+</b:mo><b:mi>U</b:mi></b:mrow></b:math> densities, the LXC potential partly reverses the excessive flattening of bands caused by too-large Hubbard <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>U</c:mi></c:math> values. For meta-GGAs, we find only small differences between the GKS and LXC results, demonstrating that the nonlocality of meta-GGAs is weak.