A nonempirical scaling correction approach for density functional methods involving substantial amount of...

A nonempirical scaling correction (SC) approach has been developed for improving bandgap prediction in density functional theory [X. Zheng, A. J. Cohen, P. Mori-Sánchez, X. Hu, and W. Yang, Phys. Rev. Lett. 107, 026403 (2011)]. For finite systems such as atoms and molecules, the SC approach restores the Perdew-Parr-Levy-Balduz condition [Phys. Rev. Lett. 49, 1691 (1982)] that the total electronic energy should scale linearly with number of electrons between integers. Although the original SC approach is applicable to a variety of mainstream density functional approximations, it gives zero correction to the Hartree-Fock method. This is because the relaxation of orbitals with the change in electron number is completely neglected. In this work, with an iterative scheme for the evaluation of Fukui function, the orbital relaxation effects are accounted for explicitly via a perturbative treatment. In doing so, the SC approach is extended to density functionals involving substantial amount of Hartree-Fock exchange. Our new SC approach is demonstrated to improve systematically the predicted Kohn-Sham frontier orbital energies, and alleviate significantly the mismatch between fundamental and derivative gaps.