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.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2022
- DOI:
- 10.48550/arXiv.2204.12216
- arXiv:
- arXiv:2204.12216
- Bibcode:
- 2022arXiv220412216H
- Keywords:
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- Physics - Chemical Physics
- E-Print:
- 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