Transient uniform electron gases

The uniform electron gas (UEG), a hypothetical system with finite homogenous electron density composed by an infinite number of electrons in a box of infinite volume, is the practical pillar of density-functional theory (DFT) and the foundation of the most acclaimed approximation of DFT, the local-density approximation (LDA). In the last thirty years, the knowledge of analytical parametrizations of the infinite UEG (IUEG) exchange-correlation energy has allowed researchers to perform a countless number of approximate electronic structure calculations for atoms, molecules, and solids. Recently, it has been shown that the traditional concept of the IUEG is not the unique example of UEGs, and systems, in their lowest-energy state, consisting of electrons that are confined to the surface of a sphere provide a new family of UEGs with more customisable properties. Here, we show that, some of the excited states associated with these systems can be classified as transient UEGs (TUEGs) as their electron density is only homogenous for very specific values of the radius of the sphere even though the electronic wave function is not rotationally invariant. Concrete examples are provided in the case of two-electron systems.