Explicit Particle-number Dependence in Density Functional Theory

With rare exceptions, explicit particle number dependence (Ne-dependence) in approximate density functionals is viewed as a serious deficiency because of apparent size-consistency issues. In contrast, there are multiple manifestations of explicit Ne-dependence in density functional bounds (including the Gazquez-Robles kinetic energy bound), constraints, and approximations. We argue that these constitute inescapable motivation for exploring Ne-dependent approxi- mate functionals. Doing so would be consistent with a mostly-ignored result of Lieb about properties of the universal functional.