# Review of ground-state density-functional theory

# Review of ground-state density-functional theory

This chapter presents a self-contained review of ground-state density-functional theory. The first section discusses the formal framework of static density-functional theory, including the Hohenberg-Kohn theorem, the constrained-search formulation, and the Kohn-Sham equations. Many of the exact properties of the ground-state exchange-correlation energy and potential are reviewed, such as asymptotic behaviour, self-interaction, derivative discontinuities, or the uniform limit. The last section gives an overview of the most important approximate exchange-correlation functionals. These include the local-density approximation, generalized gradient approximations, hybrid functionals, and orbital-dependent and self-interaction corrected functionals.

*Keywords:*
density-functional theory, Hohenberg-Kohn theorem, constrained-search formulation, Kohn-Sham equations, exchange-correlation energy, exchange-correlation potential, local-density approximation, generalized gradient approximation, corrected functionals

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