Correlation Energy of the Uniform Electron Gas Revisited

Analytic parametrizations of the correlation energy per particle of a uniform electron gas are the common ingredient of nearly all density functional approximations. Standard parametrizations such as Vosko-Wilk-Nusair (VWN81), Perdew-Zunger (PZ81), and Perdew-Wang (PW92) are fitted to the Quantum Monte Carlo (QMC) results of Ceperley and Alder (1980), with additional information from the exact high- and low-density limits. They agree well with one another in the spin-unpolarized and fully polarized limits, but for density parameter r_s=0.5 they are more negative by about 0.1 eV (5 to 10%) than the QMC results of Spink, Needs, and Drummond (2013). Another approach, based almost entirely on satisfaction of all known exact constraints on the high- and low-density limits, was proposed by Sun et al. PRB 81, 085123 (2010) in their Density Parameter Interpolation (DPI). Here we correct a high-density-expansion coefficient for full spin polarization used in the original DPI. Our new coefficient agrees with that of Ref. [1]. We find that DPI still agrees more closely with VWN, PZ, and PW than with the QMC of Spink et al. The dependence upon relative spin polarization has also been studied.
[1] P.-F. M. C. Loos et al. Phys. Rev. B 84, 033103(2011)