Uniform electron gas at finite temperatures

We calculate the free energy of the quantum uniform electron gas for temperatures from near 0 to 100 times the Fermi energy, approaching the classical limit. An extension of the Vashista-Singwi theory to finite temperatures and a self-consistent compressibility sum rule is presented. Comparisons are made to other local-field correction methods, as well as recent quantum Monte Carlo simulation and classical map-based results. Accurate fits to the exchange-correlation free energy from both theory and simulation are given for future practical applications.

Figure 1

Top: Compressibility ratio from the sum rule is plotted for various approximate dielectric functions, along with the ratio from the equation of state. Bottom: The self-consistent $a(r_s,t)$ which satisfies the CSR at $t=1$.

Figure 2

Interaction energy from RPIMC data and fits for RPIMC, VSa, and STLS as given in the Appendix. The bottom panel shows differences of RPIMC data and VSa and STLS fits compared with the RPIMC fit.

Figure 3

XC free energy for several calculations, with the classical limit plotted for comparison, relative to the known zero-temperature XC energy.

Figure 4

Pair correlation functions at given $t$ and $r_s$. The $y$ and $x$ axes represent $g\left(r\right)$ and $r$ (in units of $q_F^{-1}$), respectively.

Figure 5

Compressibility ratio ${\kappa }_0/\kappa$ ($y$ axis) as a function of $r_s$ ($x$ axis) for a given $t$.

Figure 6

Comparison of XC free energies for large $t$ at $r_s=1$. In the bottom plot the exchange free energy $f_x$ has been added to the classical results.