Condensation energy of the homogeneous electron gas from the density functional theory for superconductors
The condensation energy of the homogeneous electron gas is calculated within the density functional theory for superconductors. Purely electronic considerations include the exchange energy exactly and the correlation energy on a level of the random phase approximation. The singlet superconductivity is assumed, and the Coulomb interaction is studied with a model pairing potential at the angular momentum up to $l$=9 and at densities 1$\leq$$r_s$$\leq$10. The homogeneous gas remains nonsuperconducting up to $r_s$$\simeq$9. Very weak negative value of the condensation energy has been found for f-waves and higher-$l$ pairing at $r_s$=10.