Correlated metals and theLDA+Umethod

While the $\mathrm{LDA}+U$ method is well established for strongly correlated materials with well localized orbitals, its application to weakly correlated metals is questionable. By extending the LDA Stoner approach onto $\mathrm{LDA}+U,$ we show that $\mathrm{LDA}+U$ enhances the Stoner factor, while reducing the density of states. Arguably the most important correlation effects in metals, fluctuation-induced mass renormalization, and suppression of the Stoner factor, are missing from $\mathrm{LDA}+U.$ On the other hand, for moderately correlated metals $\mathrm{LDA}+U$ may be useful. With this in mind, we derive a version of $\mathrm{LDA}+U$ that is consistent with the Hohenberg-Kohn theorem and can be formulated as a constrained density functional theory. We illustrate all of the above on concrete examples, including the controversial case of magnetism in FeAl.