Ensemble density functional theory of ground and excited energy levels

Abstract

A Kohn-Sham density-functional energy expression is derived for any (ground or excited) state within a given many-electron ensemble along with the stationarity condition it fulfills with respect to the ensemble density, thus giving access to both physical energy levels and individual-state densities, in principle exactly. We also provide working equations for the evaluation of the latter from the true static ensemble density-density linear response function. Unlike in Gould's recent ensemble potential functional approach to excited states [arXiv:2404.12593], we use the ensemble density as sole basic variable. While a state-specific KS potential naturally emerges from the present formalism, at the exact ensemble Hartree-exchange-only (Hx) level of approximation, the standard implementation of orbital-optimized DFT for excited states is recovered when recycling the regular ground-state Hx-correlation functional in this context.

14 pages, special issue in honour of Trygve Helgaker

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• Building Kohn-Sham potentials for ground and excited states
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• Neutral electronic excitations and derivative discontinuities: An extended $N$-centered ensemble density functional theory perspective
• Extended $N$-centered ensemble density functional theory of double electronic excitations

Cited by in corpus (8)

• Stationary conditions for excited states: the surprising impact of density-driven correlations
• Freeze-and-release direct optimization method for variational calculations of excited electronic states
• Excited-State-Specific Kohn-Sham Formalism for the Asymmetric Hubbard Dimer
• State-specific density functionals for excited states from ensembles
• Excited States of the Uniform Electron Gas
• Exact static linear response of excited states from ensemble density functional theory
• Ensemble density functional theory of excited states: Exact N-centered formalism and practical opportunities
• Refining ensemble $N$-representability of one-body density matrices from partial information