Ensemble Density Functional Theory of Neutral and Charged Excitations

TL;DR

This paper reviews recent advances in ensemble density-functional theory (DFT) for excited states, highlighting exact results, variational methods, and potential improvements for practical calculations.

Contribution

It provides a comprehensive overview of formal developments, exact results, and new approaches in ensemble DFT for excited states, aiming to enhance its reliability and applicability.

Findings

Equivalence between derivative discontinuity and weight dependence in exchange-correlation functional.

Discussion of variational evaluation of orbital-dependent ensemble Hartree-exchange energies.

Exploration of density-driven correlation to improve ensemble correlation functionals.

Abstract

Recent progress in the field of (time-independent) ensemble density-functional theory (DFT) for excited states are reviewed. Both Gross-Oliveira-Kohn (GOK) and $N$-centered ensemble formalisms, which are mathematically very similar and allow for an in-principle-exact description of neutral and charged electronic excitations, respectively, are discussed. Key exact results like, for example, the equivalence between the infamous derivative discontinuity problem and the description of weight dependencies in the ensemble exchange-correlation density functional, are highlighted. The variational evaluation of orbital-dependent ensemble Hartree-exchange (Hx) energies is discussed in detail. We show in passing that state-averaging individual exact Hx energies can lead to severe (solvable though) $v$-representability issues. Finally, we explore the possibility to use the concept of density-driven correlation, which has been recently introduced and does not exist in regular ground-state DFT, for improving state-of-the-art correlation density-functional approximations for ensembles. The present review reflects the efforts of a growing community to turn ensemble DFT into a rigorous and reliable low-cost computational method for excited states. We hope that, in the near future, this contribution will stimulate new formal and practical developments in the field.