To the best of our knowledge, the present article reports, for the first
time, a local \textit{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 case of ensembles.
We show that the present weight-dependent correlation functional delivers accurate excitation energies for both single and double excitations in one-dimensional non-homogeneous many-electron systems.
Comparison with TD-DFT shows that the present methodology is not only robust in the weakly-correlated regime, but also in presence of strong correlation where TD-DFT fails.
Although the present weight-dependent functional has been specifically
designed for one-dimensional systems, the methodology proposed here is
general, {\it i.e.}, directly applicable to the construction of weight-dependent functionals for realistic three-dimensional systems, such as molecules and solids.
Because of the large impact of our work in the DFT community and beyond, we expect it to be of interest to a wide audience within the chemistry and physics communities.
