Density-driven correlations in many-electron ensembles: theory and application for excited states

TL;DR

This paper develops a theoretical framework for understanding and approximating density-driven correlations in many-electron ensembles, enhancing excited state density functional theory with practical decomposition and approximation methods.

Contribution

It introduces a novel decomposition of the correlation energy functional into state- and density-driven parts, facilitating better approximations for excited states.

Findings

Density-driven correlations are significant in ensemble DFT.

A new approximation for density-driven correlations improves excited state calculations.

The decomposition enables practical handling of low-lying excited states.

Abstract

Density functional theory can be extended to excited states by means of a unified variational approach for passive state ensembles. This extension overcomes the restriction of the typical density functional approach to ground states, and offers useful formal and demonstrated practical benefits. The correlation energy functional in the generalized case acquires higher complexity than its ground state counterpart, however. Little is known about its internal structure nor how to effectively approximate it in general. Here we show that such a functional can be broken down into natural components, including what we call "state-" and "density-driven" correlations, with the former amenable to conventional approximations, and the latter being a unique feature of ensembles. Such a decomposition, summarised in eq. (6), provides us with a pathway to general approximations that are able to routinely handle low-lying excited states. The importance of density-driven correlations is demonstrated, an approximation for them is introduced and shown to be useful.