Density functional theory on phase space

TL;DR

This paper explores a phase space formulation of density functional theory, examining its theoretical foundations, representability issues, and developing new functionals and proofs to advance electronic structure modeling.

Contribution

It introduces a phase space approach to density functional theory, including new results on Wigner functions, natural orbitals, and correlation functionals, linking to the Thomas-Fermi model.

Findings

Validated Hohenberg-Kohn-Levy theorems in phase space

Analyzed representability of reduced Wigner functions

Proved overbinding property of Mueller functional

Abstract

Forty-five years after the point de d\'epart [1] of density functional theory, its applications in chemistry and the study of electronic structures keep steadily growing. However, the precise form of the energy functional in terms of the electron density still eludes us -- and possibly will do so forever [2]. In what follows we examine a formulation in the same spirit with phase space variables. The validity of Hohenberg-Kohn-Levy-type theorems on phase space is recalled. We study the representability problem for reduced Wigner functions, and proceed to analyze properties of the new functional. Along the way, new results on states in the phase-space formalism of quantum mechanics are established. Natural Wigner orbital theory is developed in depth, with the final aim of constructing accurate correlation-exchange functionals on phase space. A new proof of the overbinding property of the Mueller functional is given. This exact theory supplies its home at long last to that illustrious ancestor, the Thomas-Fermi model.