Lieb variation principle in density-functional theory

2022/04/26 by Helgaker, Trygve, Teale, Andrew M. · 2 citations
#Chemical Physics (physics.chem-ph) #FOS: Physical sciences

paper · doi:10.48550/arxiv.2204.12216

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.

Cited by

• Neural network approximation of regularized density functionals
• Perspective on Moreau-Yosida Regularization in Density-Functional Theory

Related

• Variational derivation of density functional theory
• Density functional theory: An introduction
• Ground-state densities from the Rayleigh--Ritz variation principle and\n from density-functional theory
• A bird's-eye view of density-functional theory
• A Verbose Note on Density Functional Theory