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

Abstract

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 v c([ n]; r ) in its high-density scaling limit is derived. Our formula links v c([ n]; r ) to an integral of the static correlation kernel f c([ n]; r , r ′), f c([ n]; r , r ′)=δ v c([ n]; r )/δ n ( r ′), in the high-density limit. Numerical results, both exact and approximate, for ∫∫ f c([ n]; r , r ′) n( r ) n( r ′ ) d r d r ′ 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.