Asymptotics of the metal-surface Kohn-Sham exact exchange potential revisited

The asymptotics of the Kohn-Sham (KS) exact exchange potential $V_x(z)$ a jelliumlike semi-infinite metal is investigated, in framework optimized-effective-potential formalism density-functional theory. Our numerical calculations clearly show that deep into vacuum side surface $V_x(z) \propto e^2 \ln(az) / z$, with $a$ being system-dependent constant, thus confirming analytical reported Phys. Rev. B {\bf 81}, 121106(R) (2010). A criticism this work published 85}, 115124 (2012) shown to be incorrect. rigorous exchange-only results provide strong constraints both for building approximate functionals and determination still unknown KS correlation potential.