Spin-density functional theories and their $+U$ and $+J$ extensions: a comparative study of transition metals and transition metal oxides

TL;DR

This study compares spin-density functional theories and their +U and +J extensions for transition metals and oxides, highlighting the importance of charge density-based functionals and the effective Hund's interaction.

Contribution

It demonstrates that +U and +J extensions should be based on charge density functionals, emphasizing the role of spin-dependent exchange in transition metal systems.

Findings

Spin-dependent functionals act as an effective Hund's interaction.

Effective Hund's exchange exceeds 1 eV in studied functionals.

+U and +J extensions are best based on charge density only.

Abstract

Previous work on the physical content of exchange correlation functionals that depend on both charge and spin densities is extended to elemental transition metals and a wider range of perovskite transition metal oxides. A comparison of spectra and magnetic moments calculated using exchange correlation functionals depending on charge density only or on both charge and spin densities, as well as the $+U$ and $+J$ extensions of these methods confirms previous conclusions that the spin-dependent part of the exchange correlation functional provides an effective Hund's interaction acting on the transition metal $d$ orbitals. For the local spin density approximation and spin-dependent Perdew-Burke-Ernzerhof generalized gradient approximation, the effective Hund's exchange is found to be larger than 1 eV. The results indicate that at least as far as applications to transition metals and their oxides are concerned, $+U$, $+J$ and +dynamical mean field theory extensions of density functional theory should be based on exchange-correlation functionals of charge density only.