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

John P. Perdew and Yue Wang
Phys. Rev. B 45, 13244 – Published 15 June 1992; Erratum Phys. Rev. B 98, 079904 (2018)
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Abstract

We propose a simple analytic representation of the correlation energy ɛc for a uniform electron gas, as a function of density parameter rs and relative spin polarization ζ. Within the random-phase approximation (RPA), this representation allows for the rs3/4 behavior as rs→∞. Close agreement with numerical RPA values for ɛc(rs,0), ɛc(rs,1), and the spin stiffness αc(rs)=2ɛc(rs, ζ=0)/δζ2, and recovery of the correct rslnrs term for rs→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 ζ-dependent coefficients in the high- and low-density expansions, and the rs-dependent spin susceptibility. We also present a conjecture for the exact low-density limit. The correlation potential μcσ(rs,ζ) is evaluated for use in self-consistent density-functional calculations.

  • Received 31 January 1992

DOI:https://doi.org/10.1103/PhysRevB.45.13244

©1992 American Physical Society

Erratum

Authors & Affiliations

John P. Perdew and Yue Wang

  • Department of Physics
  • Quantum Theory Group, Tulane University, New Orleans, Louisiana 70118

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Issue

Vol. 45, Iss. 23 — 15 June 1992

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