Unification of Perdew-Zunger Self-Interaction Correction, DFT+U, and Rung 3.5 Density Functionals

TL;DR

This paper presents a unified formalism that integrates PZSIC, DFT+U, and Rung 3.5 density functionals by modifying the Kohn-Sham system, enabling new insights and applications across different levels of density functional theory.

Contribution

It introduces a unified framework that connects PZSIC, DFT+U, and Rung 3.5 functionals through the Adiabatic Projection formalism, allowing for systematic comparisons and new functional variants.

Findings

Typical Hubbard U parameters approximate scaled-down PZSIC.

A Rung 3.5 variant of DFT+U can open a band gap in the homogeneous electron gas.

The formalism recovers PZSIC, DFT+U, and Rung 3.5 by choosing different localized states.

Abstract

We unify the Perdew-Zunger self-interaction correction (PZSIC) to approximate density functional theory (DFT), the Hubbard correction DFT+U, and Rung 3.5 functionals within the Adiabatic Projection formalism. We modify the Kohn-Sham reference system, introducing electron self-interaction in selected states. Choosing those states as localized orbitals, localized atomic states, or states at each point in space recovers PZSIC, DFT+U, and Rung 3.5. Typical Hubbard U parameters approximate scaled-down PZSIC. A Rung 3.5 variant of DFT+U opens a band gap in the homogeneous electron gas.