Foundations of the ionization potential condition for localized electron removal in density functional theory

Abstract

Optimal tuning of functional parameters in density functional theory approximations, based on enforcing the ionization potential theorem, has emerged as the method of choice for the non-empirical prediction of the electronic structure of finite systems. This method has recently been extended to the bulk limit, based on an ansatz that generalizes the ionization potential theorem to the removal of an electron from a localized Wannier orbital. This Wannier-localization based optimal tuning method has been shown to be highly successful for a wide range of periodic systems, accurately predicting electronic and optical properties. However, a rigorous theoretical justification for its foundational ansatz has been lacking. Here, we establish an ionization potential condition for the removal of a localized electron, by extending the piecewise linearity and Janak's theorems in density functional theory. We also provide numerical evidence supporting our theory.

Figures (1)

• Figure 1: Total energy as a function of the fraction of Wannier orbital removed, for Si, ZnO, and LiF. The DFAs considered are PBE, Hartree-Fock plus semilocal correlation (HFc), SRSH that overestimates the band gap (SRSH$\uparrow$), SRSH that underestimates the band gap (SRSH$\downarrow$), and WOT-SRSH.