Temperature-dependent behavior of confined many-electron systems in the Hartree-Fock approximation

Many-electron systems confined at substantial finite temperatures and densities present a major challenge to density functional theory. In particular, there is comparatively little systematic knowledge about the behavior of free-energy density functionals for temperatures and pressures of interest, for example, in the study of warm dense matter (WDM). As with ground-state functionals, development of approximate free-energy functionals is faced with significant needs for reliable assessment and calibration data. Here we address, in part, this need for detailed results on well-characterized systems. We present results on a comparatively simple, well-defined, computationally feasible but previously unexplored model, the thermal Hartree-Fock approximation. We discuss the main technical tasks (defining a suitable basis and evaluation of the required matrix elements) and give an illustrative initial application that probes both the content of the model and the solution techniques: a system of eight one-electron atoms with nuclei at fixed, arbitrary positions in a hard-walled box. Even this simple system produces physical behavior different from that produced by simple ground-state density functionals used at finite temperature (a common approximation in the study of WDM).