Correlation energy of the spin-polarized uniform electron gas at high density

Abstract

The correlation energy per electron in the high-density uniform electron gas can be written as $\Ec(r_s,ζ) = \lam_0(ζ) \ln r_s + \eps_0(ζ) + \lam_1(ζ) \,r_s \ln r_s + O(r_s)$, where $r_s$ is the Seitz radius and $\zeta$ is the relative spin polarization. We derive an expression for $\lam_1(ζ)$ which is exact for any $\zeta$, including the paramagnetic and ferromagnetic limits, $\lam_1(0)$ and $\lam_1(1)$, and discover that the previously published $\lam_1(1)$ value is incorrect. We trace this error to an integration and limit that do not commute. The spin-resolution of $\lam_1(ζ)$ into contributions of electron pairs is also derived.

arXiv comment4+ pages, 2 figures, 2 tables, submitted to Phys. Rev. B

References in corpus (5)

• Zero Temperature Phases of the Electron Gas
• Effects of Backflow Correlation in the Three-Dimensional Electron Gas: Quantum Monte Carlo Study
• Spin Polarization of the Low Density 3D Electron Gas
• The Hartree-Fock ground state of the three-dimensional electron gas
• Spin Resolution of the Electron-Gas Correlation Energy: Positive same-spin contribution

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• Generalized local-density approximation and one-dimensional finite uniform electron gases
• Comment on "Communication: Simple and accurate uniform electron gas correlation energy for the full range of densities" [J. Chem. Phys. 145, 021101 (2016)]
• Nodal surfaces and interdimensional degeneracies
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• Symmetry-broken local-density approximation for one-dimensional systems
• Accurate Correlation Energy Functional for Uniform Electron Gas from an Interpolation Ansatz without Fitting Parameters
• Excited States of the Uniform Electron Gas
• Homogeneous electron gas in arbitrary dimensions
• Correlation energy of the spin-polarized electron liquid by quantum Monte Carlo
• Effective Summation and Interpolation of Series by Self-Similar Root Approximants