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