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Many-electron systems at substantial finite temperatures and densitiespresent a major challenge to density functional theory. Very little is knownabout the free-energy behavior over the temperature range of interest, forexample, in the study of warm dense matter. As a result, it is difficult toassess the validity of proposed approximate free-energy density functionals.Here we address, at least in part, this need for detailed results onwell-characterized systems for purposes of testing and calibration of proposedapproximate functionals. We present results on a comparatively simple,well-defined, but computationally feasible model, namely thermally occupiedHartree-Fock states for eight one-electron atoms at arbitrary positions in ahard-walled box. We discuss the main technical tasks (defining a suitable basisand evaluation of the required matrix elements) and discuss the physics whichemerges from the calculations.

Temperature-Dependent Behavior of Confined Many-electron Systems in the Hartree-Fock Approximation