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 a re especially needed for high-quality Kohn-Sham calculations. For two-elect ron 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') = delta v(c)([n]; r)/delta n(r'), in the high-density limit . Numerical results, both exact and approximate, for integral integral f(c) ([n]; r, r')n(r)n(r') dr dr' in the high-density limit for two model two-el ectron densities, are presented. It is shown that several popular functiona ls give the wrong sign for the latter. (C) 1999 Elsevier Science B.V. All r ights reserved.