Lieb variation principle in density-functional theory

Trygve Helgaker; Andrew M. Teale

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arXiv · 2204.12216

Lieb variation principle in density-functional theory

Trygve Helgaker·Andrew M. Teale

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Abstract

Lieb's convex formulation of density-functional theory is presented in a pedagogical manner, emphasizing its connection to Hohenberg-Kohn theory and to Levy's constrained-search theory. The Hohenberg-Kohn and Lieb variation principles are discussed, highlighting the dual relationship between the ground-state energy and the universal density functional. Applications of the Lieb variation principle are reviewed, demonstrating how it may be utilized to calculate the Kohn-Sham potential of atoms and molecules, to study the exchange-correlation functional and the adiabatic connection by high-precision many-body methods, and to calculate the exchange-correlation hole and energy densities of atoms and molecules.

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Trygve Helgaker, Andrew M. Teale. 2022-04-26. Lieb variation principle in density-functional theory. https://arxiv.org/abs/2204.12216

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