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

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.

new version, to appear in PRB Rapid Communication

References in corpus (5)

• Zero Temperature Phases of the Electron Gas
• Analytic structure factors and pair-correlation functions for the unpolarized homogeneous electron gas
• Pair distribution function of the spin-polarized electron gas: A first-principles analytic model for all uniform densities
• Momentum distribution of the uniform electron gas: improved parametrization and exact limits of the cumulant expansion
• Spin dynamics from time-dependent spin density-functional theory

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• Correlation energy of the spin-polarized uniform electron gas at high density
• Spin and temperature dependent study of exchange and correlation in thick two-dimensional electron layers
• Parameter-free density functional for the correlation energy in two dimensions
• First-principles wavevector- and frequency-dependent exchange-correlation kernel for jellium at all densities
• Spin-resolved second-order correlation energy of the two-dimensional uniform electron gas
• A spin-polarized scheme for obtaining quasi-particle energies within the density functional theory
• The on-top pair-correlation density in the homogeneous electron liquid
• Ground-state energy and Wigner crystallization in thick 2D-electron systems