Localization and delocalization errors in density functional theory and implications for band-gap prediction

TL;DR

This paper analyzes the origins of localization and delocalization errors in density functional theory (DFT) and discusses their impact on band-gap predictions, offering insights to improve the accuracy of DFT calculations.

Contribution

It provides a detailed explanation of how fractional charge energy deviations cause errors in DFT, revealing the link between functional convexity/concavity and localization/delocalization errors.

Findings

Convex functionals like LDA cause delocalization errors in bulk systems.

Concave functionals induce localization errors, affecting symmetry and energy calculations.

Understanding these errors opens pathways to more accurate band-gap predictions in DFT.

Abstract

The band-gap problem and other systematic failures of approximate functionals are explained from an analysis of total energy for fractional charges. The deviation from the correct intrinsic linear behavior in finite systems leads to delocalization and localization errors in large or bulk systems. Functionals whose energy is convex for fractional charges such as LDA display an incorrect apparent linearity in the bulk limit, due to the delocalization error. Concave functionals also have an incorrect apparent linearity in the bulk calculation, due to the localization error and imposed symmetry. This resolves an important paradox and opens the possibility to obtain accurate band-gaps from DFT.