Hubbard-corrected DFT energy functionals: the LDA+U description of correlated systems

TL;DR

This review evaluates the LDA+U method's effectiveness for modeling correlated materials, discussing its theoretical basis, applications, limitations, recent improvements, and future prospects to enhance its predictive capabilities.

Contribution

It provides a comprehensive assessment of LDA+U, clarifying its theoretical foundation, comparing it with other methods, and presenting recent extensions that improve its accuracy.

Findings

LDA+U effectively describes correlated systems with specific conditions.

Recent extensions significantly improve the method's predictive power.

Open issues include calculating Hubbard U and extending to new material classes.

Abstract

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.