Theoretical unification of hybrid-DFT and DFT+U methods for the treatment of localized orbitals

TL;DR

This paper unifies hybrid-DFT and DFT+U methods by formulating an on-site occupation dependent exchange correlation energy, providing a theoretical basis for hybrid-DFT+U-like corrections to better treat localized orbitals.

Contribution

It introduces a theoretical framework connecting hybrid-DFT and DFT+U, leading to the hybrid-DFT+Vw scheme for improved localized state treatment.

Findings

Hybrid-DFT+Vw scheme effectively corrects overscreening issues.

Test cases show improved accuracy for impurity states in materials.

Theoretical justification enhances understanding of localized orbital treatments.

Abstract

We formulate the on-site occupation dependent exchange correlation energy and effective potential of hybrid functionals for localized states and connect them to the on-site correction term of the DFT+U method. Our derivation provides a theoretical justification for adding a DFT+U-like onsite potential in hybrid DFT calculations to resolve issues caused by overscreening of localized states. The resulting scheme, hybrid- DFT+Vw, is tested for chromium impurity in wurtzite AlN and vanadium impurity in 4H-SiC, which are paradigm examples of systems with different degree of localization between host and impurity orbitals.