Lieb variation principle in density-functional theory
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.
Cite
@article{arxiv.2204.12216,
title = {Lieb variation principle in density-functional theory},
author = {Trygve Helgaker and Andrew M. Teale},
journal= {arXiv preprint arXiv:2204.12216},
year = {2022}
}
Comments
Submitted to the book in honour of Elliott Lieb's 90th birthday, edited by Rupert L. Frank, Ari Laptev, Mathieu Lewin and Robert Seiringer, published by EMS Press