Correction to Slater exchange potential to yield exact Kohn-Sham potential generating the Hartree-Fock density

Kleinman has recently pointed out that the Slater, or average Fock approximation, to the exchange potential can be written as the partial functional derivative of an exchange energy functional. Here we demonstrate for an arbitrary N-electron system the explicit corrections to the Slater potential, which yield the Kohn-Sham-like exchange potential generating the exact Hartree-Fock density. The example of the four-electron spin-compensated system is worked out in detail.