Spin resolution of the electron-gas correlation energy: Positive same spin contributions

Abstract

The negative correlation energy ${\ensuremath{\epsilon}}_{c}{(r}_{s},\ensuremath{\zeta})$ per particle of a uniform electron gas of density parameter ${r}_{s}$ and spin polarization $\ensuremath{\zeta}$ is well known, but its spin resolution into $\ensuremath{\uparrow}\ensuremath{\downarrow},$ $\ensuremath{\uparrow}\ensuremath{\uparrow},$ and $\ensuremath{\downarrow}\ensuremath{\downarrow}$ 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 $\ensuremath{\zeta}=0,$ we find that the same-spin correlation energy is unexpectedly positive, and we explain why. We also estimate the $\ensuremath{\uparrow}$ and $\ensuremath{\downarrow}$ contributions to the kinetic energy of correlation.