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A weight-dependent local correlation density-functional approximation for ensembles

We report a local, weight-dependent correlation density-functional approximation that incorporates information about both ground and excited states in the context of density-functional theory for ensembles (eDFT). This density-functional approximation for ensembles is specially designed for the computation of single and double excitations within Gross--Oliveira--Kohn (GOK) DFT (i.e., eDFT for neutral excitations), and can be seen as a natural extension of the ubiquitous local-density approximation in the context of ensembles. The resulting density-functional approximation, based on both finite and infinite uniform electron gas models, automatically incorporates the infamous derivative discontinuity contributions to the excitation energies through its explicit ensemble weight dependence. Its accuracy is illustrated by computing single and double excitations in one-dimensional many-electron systems in the weak, intermediate and strong correlation regimes. Although the present weight-dependent functional has been specifically designed for one-dimensional systems, the methodology proposed here is general, i.e., directly applicable to the construction of weight-dependent functionals for realistic three-dimensional systems, such as molecules and solids.