Semi-Local Exchange-Correlation Approximations in Density Functional Theory

[2602.17333] Semi-Local Exchange-Correlation Approximations in Density Functional Theory Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Physics > Chemical Physics arXiv:2602.17333 (physics) [Submitted on 19 Feb 2026 ( v1 ), last revised 12 Jun 2026 (this version, v2)] Title: Semi-Local Exchange-Correlation Approximations in Density Functional Theory Authors: Fabien Tran , Susi Lehtola , Stefano Pittalis , Miguel A. L. Marques View a PDF of the paper titled Semi-Local Exchange-Correlation Approximations in Density Functional Theory, by Fabien Tran and Susi Lehtola and Stefano Pittalis and Miguel A. L. Marques View PDF HTML (experimental) Abstract: Density functional theory has become the workhorse of modern electronic structure calculations, with wide-ranging applications in chemistry, physics, materials science, biochemistry, etc. At its heart lies the exchange-correlation functional, a quantity which exactly encapsulates the many-body effects stemming from the quantum mechanical interactions between the electrons. Yet, the exact functional is unknown, and computationally tractable approximations are therefore necessary for practical applications. Over the past six decades, hundreds of density functional approximations have been proposed with varying accuracy and computational efficiency. This review surveys the theoretical foundations of semi-local functionals, including local density approximations, generalized gradient approximations, and meta-generalized gradient approximations. We provide a comprehensive, consistently organized discussion that consolidates both historical developments and recent advances in this field. Beginning with the essentials of Kohn-Sham density functional theory, we present the construction principles of semi-local exchange-correlation functionals. Special attention is given to the physical motivations underlying functional development, the mathematical properties that guide their construction, and the practical considerations that determine their applicability across different chemical and physical systems. This work is intended to serve as both an introduction for newcomers to the field and a comprehensive reference for practitioners. By consolidating the extensive literature on semi-local functionals and providing a unified framework for their construction and application, we aim to facilitate further developments in density functional approximations and their use in tackling the diverse challenges of modern computational chemistry and condensed matter physics. Comments: 202 pages, 2 figures Subjects: Chemical Physics (physics.chem-ph) ; Computational Physics (physics.comp-ph) Cite as: arXiv:2602.17333 [physics.chem-ph] (or arXiv:2602.17333v2 [physics.chem-ph] for this version) https://doi.org/10.48550/arXiv.2602.17333 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1021/acs.chemrev.6c00170 Focus to learn more DOI(s) linking to related resources Submission history From: Susi Lehtola [ view email ] [v1] Thu, 19 Feb 2026 12:59:51 UTC (756 KB) [v2] Fri, 12 Jun 2026 12:14:43 UTC (867 KB) Full-text links: Access Paper: View a PDF of the paper titled Semi-Local Exchange-Correlation Approximations in Density Functional Theory, by Fabien Tran and Susi Lehtola and Stefano Pittalis and Miguel A. L. 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