How accurate are the parametrized correlation energies of the uniform electron gas?

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Abstract
Density functional approximations to the exchange-correlation energy are designed to be exact for an electron gas of uniform density parameter r(s) and relative spin polarization zeta, requiring a parametrization of the correlation energy per electron is an element of(c)(r(s),zeta). We consider three widely used parametnzations [J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981) or PZ81, S. H. Vosko, L. Wilk, and M. Nusair, Can. J. Phys. 58, 1200 (1980) or VWN80, and J. P. Perdew and Y. Wang, Phys. Rev. B 45, 13244 (1992) or PW92] that interpolate the quantum Monte Carlo (QMC) correlation energies of Ceperley-Alder [Phys. Rev. Lett. 45, 566 (1980)], while extrapolating them to known high-(r(s) -> 0) and low- (r(s) -> infinity) density limits. For the physically important range 0.5 <= r(s) <= 20, they agree closely with one another, with differences of 0.01 eV (0.5%) or less between the latter two. The density parameter interpolation (DPI), designed to predict these energies by interpolation between the known high- and low-density limits, with almost no other input (and none for zeta = 0), is also reasonably close, both in its original version and with corrections for zeta not equal 0. Moreover, the DPI and PW92 at r(s) = 0.5 are very close to the high-density expansion. The larger discrepancies with the QMC of Spink et al. [Phys. Rev. B 88, 085121 (2013)], of order 0.1 eV (5%) at r(s) = 0.5, are thus surprising, suggesting that the constraint-based PW92 and VWN80 parametrizations are more accurate than the QMC for r(s) < 2. For r(s) > 2, however, the QMC of Spink et al. confirms the dependence upon relative spin polarization predicted by the parametrizations.
Funding Information
  • National Science Foundation (DMR-1607868)