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.