Uniform electron gases

We show that the traditional concept of the uniform electron gas (UEG)—a homogeneous system of finite density, consisting of an infinite number of electrons in an infinite volume—is inadequate to model the UEGs that arise in finite systems. We argue that, in general, a UEG is characterized by at least two parameters, viz. the usual one-electron density parameter ρ and a new two-electron parameter η. We outline a systematic strategy to determine a new density functional E (ρ, η) across the spectrum of possible ρ and η values.