Ensemble density functional theory of ground and excited energy levels

TL;DR

This paper develops a density functional theory framework for calculating both ground and excited energy levels of many-electron systems using ensemble densities, providing a potentially exact approach with practical implementation options.

Contribution

It introduces a novel ensemble density functional approach that uses the ensemble density as the sole basic variable, differing from previous methods that relied on potential functionals.

Findings

Derivation of a Kohn-Sham energy expression for ensemble states.

Provision of equations to evaluate individual-state densities from response functions.

Recovery of standard orbital-optimized DFT for excited states at the ensemble Hartree-exchange-only level.

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.