Exchange-correlation energy for the 3D homogeneous electron gas at arbitrary temperature

TL;DR

This paper develops a fitting formula for the exchange-correlation energy of the 3D homogeneous electron gas at finite temperatures, covering warm-dense regimes and connecting to known theoretical limits.

Contribution

It introduces a Padé approximant that accurately models the exchange-correlation energy across temperature and density regimes, bridging finite-temperature and zero-temperature theories.

Findings

The approximant matches quantum Monte Carlo results at zero temperature.

It reproduces Debye-Hückel theory in the high-temperature, low-density limit.

Provides a unified model for exchange-correlation energy in warm-dense matter.

Abstract

We fit finite-temperature path integral Monte Carlo calculations of the exchange-correlation energy of the 3D finite-temperature homogeneous electron gas in the warm-dense regime (r_{s} = (3/4\pi n)^{1/3} a_{B}^{-1} < 40 and \Theta = T/T_{F} > 0.0625). In doing so, we construct a Pad\'{e} approximant which collapses to Debye-H\"{u}ckel theory in the high-temperature, low-density limit. Likewise, the zero-temperature limit matches the numerical results of ground-state quantum Monte Carlo, as well as analytical results in the high-density limit.