  Gross--Oliveira--Kohn (GOK) ensemble density-functional theory (GOK-DFT) is a
time-\textit{independent} extension of density-functional theory (DFT) which
allows to compute excited-state energies via the derivatives of the ensemble
energy with respect to the ensemble weights. Contrary to the time-dependent
version of DFT (TD-DFT), double excitations can be easily computed within
GOK-DFT. However, to take full advantage of this formalism, one must have
access to a \textit{weight-dependent} exchange-correlation functional in order
to model the infamous ensemble derivative contribution to the excitation
energies. In the present article, we discuss the construction of first-rung
(i.e., local) weight-dependent exchange-correlation density-functional
approximations 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-step
system-dependent procedure is proposed to obtain accurate energies associated
with double excitations.
