ACCURATE AND SIMPLE ANALYTIC REPRESENTATION OF THE ELECTRON-GAS CORRELATION-ENERGY

We propose a simple analytic representation of the correlation energy epsilon(c) for a uniform electron gas, as a function of density parameter r(s) and relative spin polarization-zeta. Within the random-phase approximation (RPA), this representation allows for the r(s)-3/4 behavior as r(s)-->infinity. Close agreement with numerical RPA values for epsilon(c)(r(s),0), epsilon(c)(r(s), 1), and the spin stiffness alpha(c)(r(s))=partial derivative 2-epsilon(c) (r(s), zeta=0)/delta-zeta-2, and recovery of the correct r(s)lnr(s) term for r(s)-->0, 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 zeta-dependent coefficients in the high- and low-density expansions, and the r(s)-dependent spin susceptibility. We also present a conjecture for the exact low-density limit. The correlation potential mu(c)sigma(r(s),zeta) is evaluated for use in self-consistent density-functional calculations.