Connections between the correlation potential and the static correlation kernel for two-electron densities in high-density limit

New approximations with improved shapes of their corresponding potentials are especially needed for high-quality Kohn–Sham calculations. For two-electron densities, a new exact expression for the correlation potential vc([n]; r) in its high-density scaling limit is derived. Our formula links vc([n]; r) to an integral of the static correlation kernel fc([n]; r, r′), fc([n]; r, r′)=δvc([n]; r)/δn (r′), in the high-density limit. Numerical results, both exact and approximate, for ∫∫fc([n]; r, r′)n(r)n(r′ ) dr dr′ in the high-density limit for two model two-electron densities, are presented. It is shown that several popular functionals give the wrong sign for the latter.