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