Density driven correlations in ensemble density functional theory: insights from simple excitations in atoms

TL;DR

This paper investigates how density-driven correlations in ensemble density functional theory vary with atomic excitations, revealing their dependence on orbital angular momentum and providing estimations through approximate methods.

Contribution

It introduces an approximation for density-driven correlations in ensemble DFT based on exact conditions and Kohn-Sham inversion, focusing on atomic excitations.

Findings

DD correlations vary significantly with orbital angular momentum.

The magnitude of DD correlations depends on the type of atomic transition.

Approximate estimations align with expected behaviors in weakly correlated systems.

Abstract

Ensemble density functional theory extends the usual Kohn-Sham machinery to quantum state ensembles involving ground- and excited states. Recent work by the authors [Phys. Rev. Lett. 119, 243001 (2017); 123, 016401 (2019)] has shown that both the Hartree-exchange and correlation energies can attain unusual features in ensembles. Density-driven(DD) correlations -- which account for the fact that pure-state densities in Kohn-Sham ensembles do not necessarily reproduce those of interacting pure states -- are one such feature. Here we study atoms (specifically $S$--$P$ and $S$--$S$ transitions) and show that the magnitude and behaviour of DD correlations can vary greatly with the variation of the orbital angular momentum of the involved states. Such estimations are obtained through an approximation for DD correlations built from relevant exact conditions Kohn-Sham inversion, and plausible assumptions for weakly correlated systems.