Local Density Approximation for the Short-Range Exchange Free Energy Functional

[Image: see text] Analytical expressions for the exchange free energy per particle of the uniform electron gas (UEG) associated with the short-range (SR) interelectronic interaction at the low- and high-temperature limits are examined, yielding an accurate analytical parametrization for the SR exchange free energy per particle of the UEG as a function of the uniform electron density, temperature, and range-separation parameter. This parametrization constitutes the local density approximation for the SR exchange free energy functional, which can be the first step toward finding generally accurate range-separated hybrid functionals in both finite-temperature density functional theory and thermally assisted-occupation density functional theory.