Local Density Approximation for Excited States

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 excited states by considering a particular class of nonthermal 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 and time-dependent LDA fail. Published by the American Physical Society 2024