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Gross--Oliveira--Kohn (GOK) ensemble density-functional theory (GOK-DFT) is atime-\textit{independent} extension of density-functional theory (DFT) whichallows to compute excited-state energies via the derivatives of the ensembleenergy with respect to the ensemble weights. Contrary to the time-dependentversion of DFT (TD-DFT), double excitations can be easily computed withinGOK-DFT. However, to take full advantage of this formalism, one must haveaccess to a \textit{weight-dependent} exchange-correlation functional in orderto model the infamous ensemble derivative contribution to the excitationenergies. In the present article, we discuss the construction of first-rung(i.e., local) weight-dependent exchange-correlation density-functionalapproximations for two-electron atomic and molecular systems (He and H$_2$)specifically designed for the computation of double excitations within GOK-DFT.In the spirit of optimally-tuned range-separated hybrid functionals, a two-stepsystem-dependent procedure is proposed to obtain accurate energies associatedwith double excitations.

Weight Dependence of Local Exchange-Correlation Functionals in Ensemble Density-Functional Theory: Double Excitations in Two-Electron Systems