Review of approximations for the exchange-correlation energy in density-functional theory

TL;DR

This review comprehensively covers the ground-state Kohn-Sham density-functional theory, detailing exact expressions, constraints, and various approximation methods for exchange-correlation energy used in electronic structure calculations.

Contribution

It provides a unified overview and detailed descriptions of key approximation families for exchange-correlation energy in density-functional theory.

Findings

Summarizes main families of exchange-correlation approximations.

Details exact expressions and constraints for functionals.

Provides a comprehensive overview suitable for diverse scientific audiences.

Abstract

In this chapter, we provide a review of ground-state Kohn-Sham density-functional theory of electronic systems and some of its extensions, we present exact expressions and constraints for the exchange and correlation density functionals, and we discuss the main families of approximations for the exchange-correlation energy: semilocal approximations, single-determinant hybrid approximations, multideterminant hybrid approximations, dispersion-corrected approximations, as well as orbital-dependent exchange-correlation density functionals. The chapter aims at providing both a consistent bird's-eye view of the field and a detailed description of some of the most used approximations. It is intended to be readable by chemists/physicists and applied mathematicians.