Ensemble Density Functional Theory of Neutral and Charged Excitations

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.

The present review article (81 pages, 5 figures) is part of the "Topics in Current Chemistry'' topical collection entitled "New Horizon in Computational Chemistry Software''

References in corpus (19)

• Localization and delocalization errors in density functional theory and implications for band-gap prediction
• Fractional charge perspective on the band-gap in density-functional theory
• Delta Self-Consistent Field as a method to obtain potential energy surfaces of excited molecules on surfaces
• Piecewise Linearity of Approximate Density Functionals Revisited: Implications for Frontier Orbital Energies
• Multi-configuration time-dependent density-functional theory based on range separation
• On the "Causality Paradox" of Time-Dependent Density Functional Theory
• 'Hartree-exchange' in ensemble density functional theory: Avoiding the non-uniqueness disaster
• Kohn-Sham potentials in exact density-functional theory at non-integer electron numbers
• Exact ensemble density functional theory for excited states in a model system: investigating the weight dependence of the correlation energy
• Efficient ab initio calculations of bound and continuum excitons
• Ensemble reduced density matrix functional theory for excited states and hierarchical generalization of Pauli's exclusion principle
• On the exact formulation of multi-configuration density-functional theory: electron density versus orbitals occupation
• Accurate electronic band gaps of two-dimensional materials from the local modified Becke-Johnson potential
• N-centered ensemble density-functional theory for open systems
• Weight Dependence of Local Exchange-Correlation Functionals in Ensemble Density-Functional Theory: Double Excitations in Two-Electron Systems
• On derivatives of the energy with respect to total electron number and orbital occupation numbers. A critique of Janak's theorem
• Variations of the Hartree-Fock fractional-spin error for one electron
• Fundamental gaps of quantum dots on the cheap
• Double and Charge-Transfer Excitations in Time-Dependent Density Functional Theory

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