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The aim of this review article is to assess the descriptive capabilities of the Hubbard-rooted LDA+U method and to clarify the conditions under which it can be expected to be most predictive. The paper illustrates the theoretical foundation of LDA+U and prototypical applications to the study of correlated materials, discusses the most relevant approximations used in its formulation, and makes a comparison with other approaches also developed for similar purposes. Open issues of the method are also discussed, including the calculation of the electronic couplings (the Hubbard U), the precise expression of the corrective functional and the possibility to use LDA+U for other classes of materials. The second part of the article presents recent extensions to the method and illustrates the significant improvements they have obtained in the description of several classes of different systems. The conclusive section finally discusses possible future developments of LDA+U to further enlarge its predictive power and its range of applicability.
The electronic structure and properties of PuO$_{2}$ and Pu$_{2}$O$_{3}$ have been studied from first principles by the all-electron projector-augmented-wave (PAW) method. The local density approximation (LDA)+$U$ and the generalized gradient approxi
The existence of band gaps in Mott insulators such as perovskite oxides with partially filled 3d shells has been traditionally explained in terms of strong, dynamic inter-electronic repulsion codified by the on-site repulsion energy U in the Hubbard
A novel approach to electronic correlations in magnetic crystals which takes into account a dynamical many-body effects is present. In order to to find a frequency dependence of the electron self energy, an effective quantum-impurity many-particle pr
We present a derivation of the exact expression for Pulay forces in density-functional theory calculations augmented with extended Hubbard functionals, and arising from the use of orthogonalized atomic orbitals as projectors for the Hubbard manifold.
Density-functional theory is widely used to predict the physical properties of materials. However, it usually fails for strongly correlated materials. A popular solution is to use the Hubbard corrections to treat strongly correlated electronic states