Correlated metals and the LDA+U method

While 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 LDA+U, we show that 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 LDA+U. On the other hand, for {\it moderately} correlated metals LDA+U may be useful. With this in mind, we derive a new version of 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.