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

TL;DR

This paper extends the ionization potential theorem in density functional theory to localized electron removal, providing a rigorous theoretical foundation for a recently successful Wannier-localization based tuning method.

Contribution

It establishes a new ionization potential condition for localized electrons in DFT, generalizing existing theorems and supporting the Wannier-based tuning approach with theoretical justification.

Findings

Theoretical extension of the ionization potential condition for localized electrons.

Numerical evidence supporting the new theoretical framework.

Enhanced understanding of electron removal in periodic systems.

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.