Spin Resolution of the Electron-Gas Correlation Energy: Positive same-spin contribution

TL;DR

This paper investigates the spin-resolved correlation energy of a uniform electron gas, revealing unexpected positive same-spin contributions at low density and providing interpolations aligned with Quantum Monte Carlo data.

Contribution

It introduces new interpolations for spin-resolved correlation energies that match Quantum Monte Carlo data and explains the positive same-spin correlation at low density.

Findings

Same-spin correlation energy is positive at low density for zero spin polarization.

Interpolations agree with available Quantum Monte Carlo data.

Provides estimates for up and down contributions to kinetic energy of correlation.

Abstract

The negative correlation energy per particle of a uniform electron gas of density parameter $r_s$ and spin polarization $\zeta$ is well known, but its spin resolution into up-down, up-up, and down-down contributions is not. Widely-used estimates are incorrect, and hamper the development of reliable density functionals and pair distribution functions. For the spin resolution, we present interpolations between high- and low-density limits that agree with available Quantum Monte Carlo data. In the low-density limit for $\zeta = 0$, we find that the same-spin correlation energy is unexpectedly positive, and we explain why. We also estimate the up and down contributions to the kinetic energy of correlation.