  Ensemble Density Functional Theory (EDFT) is a generalization of ground-state
Density Functional Theory (GS DFT), which is based on an exact formal theory of
finite collections of a system's ground and excited states. EDFT in various
forms has been shown to improve the accuracy of calculated energy level
differences in isolated model systems, atoms, and molecules, but it is not yet
clear how EDFT could be used to calculate band gaps for periodic systems. We
extend the application of EDFT toward periodic systems by estimating the
thermodynamic limit with increasingly large finite one-dimensional ``particle
in a box'' systems, which approach the uniform electron gas (UEG). Using
ensemble-generalized Hartree and Local Spin Density Approximation (LSDA)
exchange-correlation functionals, we find that corrections go to zero in the
infinite limit, as expected for a metallic system. However, there is a
correction to the effective mass, with results comparable to other calculations
on 1D, 2D, and 3D UEGs, which indicates promise for non-trivial results from
EDFT on periodic systems.
