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

摘要

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') = #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-electron densities, are presented. It is shown that several popular functionals give the wrong sign for the latter.