How Important are Exact Conditions in Ensemble Density Functional Theory?

Ensemble density functional theory (EDFT) is resurfacing as a potential alternative to time-dependent density functional theory (TD-DFT) for computationally efficient and accurate excitation energies. As the field is developing, it is important to determine careful guidelines for reasonable approximations for novel and existing EDFT energy functionals. In this work, we prove various uniform scaling inequalities and test available EDFT functionals to determine if they meet these exact conditions. Our work highlights the importance of considering exact conditions when creating new functional for EDFT and is a precursor to future functional development based on a solid theoretical footing.