Accurate and simple analytic representation of the electron-gas correlation energy

We propose a simple analytic representation of the correlation energy ₂ for a uniform electron gas, as a function of density parameter rₒ and relative spin polarization. Within the random-phase approximation (RPA), this representation allows for the rₒ^-3/4 behavior as rₒ. Close agreement with numerical RPA values for ₂ (rₒ, 0), ₂ (rₒ, 1), and the spin stiffness ₂ (rₒ) =^2₂ (rₒ, =0) /^2, and recovery of the correct rₒlnrₒ term for rₒ0, indicate the appropriateness of the chosen analytic form. Beyond RPA, different parameters for the same analytic form are found by fitting to the Green's-function Monte Carlo data of Ceperley and Alder Phys. Rev. Lett. 45, 566 (1980), taking into account data uncertainties that have been ignored in earlier fits by Vosko, Wilk, and Nusair (VWN) Can. J. Phys. 58, 1200 (1980) or by Perdew and Zunger (PZ) Phys. Rev. B 23, 5048 (1981). While we confirm the practical accuracy of the VWN and PZ representations, we eliminate some minor problems with these forms. We study the -dependent coefficients in the high- and low-density expansions, and the rₒ-dependent spin susceptibility. We also present a conjecture for the exact low-density limit. The correlation potential ₂^ (rₒ, ) is evaluated for use in self-consistent density-functional calculations.