On the exactness of simple natural spin-orbital functionals for a high-density homogeneous electron gas

Detailed analysis of the Euler equation pertaining to the natural spin-orbital functional of the form V-ee =1/2 Sigmap not equalq[n(p)n(q)J(pq) - Omega (n(p),n(q))K-pq], where V-ee is the electron-electron repulsion energy, {n(p)}are the occupancy numbers, and {J(pq)} and {K-pq} are the respective Coulomb and exchange integrals, reveals that the large- and small-k asymptotics of the momentum distribution n(k) of a high-density homogeneous electron gas rigorously determine the behavior of the function Omega (x,y) for each of its arguments approaching either 0 or 1. However, since the resulting Omega (x,y) does not give rise to n(k) with a proper discontinuity at the Fermi level, such functionals cannot be exact for this system.