Local density approximation for excited states

TL;DR

This paper introduces a local density approximation for excited states within ensemble density functional theory, enabling better predictions of low-lying excitations in atoms and molecules compared to previous methods.

Contribution

The paper develops the ensemble-LDA for excited states, extending the traditional LDA to non-thermal ensemble states and improving excitation predictions.

Findings

Successfully predicts low-lying excitations in atoms and molecules.

Outperforms LSDA and time-dependent-LDA in challenging cases.

Provides a foundation for excited state density functional approximations.

Abstract

The ground state of an homogeneous electron gas is a paradigmatic state that has been used to model and predict the electronic structure of matter at equilibrium for nearly a century. For half a century, it has been successfully used to predict ground states of quantum systems via the local density approximation (LDA) of density functional theory (DFT); and systematic improvements in the form of generalized gradient approximations and evolution thereon. Here, we introduce the LDA for \emph{excited} states by considering a particular class of non-thermal ensemble states of the homogeneous electron gas. These states find sound foundation and application in ensemble-DFT -- a generalization of DFT that can deal with ground and excited states on equal footing. The ensemble-LDA is shown to successfully predict difficult low-lying excitations in atoms and molecules for which approximations based on local spin density approximation (LSDA) and time-dependent-LDA fail.