Uniform electron-gas exchange energy
= Uniform electron-gas exchange energy
In a three-dimensional unpolarized gas, exchange <energy> per particle is $-3e^2k_F/(16\pi^2\varepsilon)$, with Coulomb convention $e^2/(4\pi\varepsilon r)$. It scales as minus the inverse dimensionless spacing radius, while kinetic <energy> scales as its inverse square. Exchange acts only between equal-spin occupied orbitals.