Status of free-energy representations for the homogeneous electron gas
Renewed interest in the homogeneous electron gas (HEG) has been stimulated by recent accurate simulations of it over a wide range of densities and temperatures. Those data, combined with known theoretical limits, have led to analytical representations of the free energy. Such a representation is, at least in principle, the complete HEG equation of state. The initial objective here is to establish that the two best representations of the simulation data and constraints are effectively the same in both functional form and accuracy of representation. The second objective is to disclose and delineate a significant difficulty. Despite their expected accuracy for the free energy, the underlying functional form is not adequate for derived thermodynamic properties. As an example, the specific heats obtained from the representations exhibit anomalies suggesting the need first for additional simulation data in critical regimes, then for refined fitting functions. Here, the existing representations are, however, almost certainly adequate for applications based on the free energy alone (e.g., density functional theory for warm dense matter). The third objective is to show that, despite their inability to provide a complete thermodynamic description of the HEG, the best analytical representations do provide a fully adequate exchange-correlation local density approximation for free energy density functional calculations.