  The theory of the macroscopic field appearing in the Kohn-Sham
exchange-correlation potential for dielectric materials, as introduced by
Gonze, Ghosez and Godby, is reexamined. It is shown that this Kohn-Sham field
cannot be determined from a knowledge of the local state of the material (local
crystal potential, electric field, and polarization) alone. Instead, it has an
intrinsically nonlocal dependence on the global electrostatic configuration.
For example, it vanishes in simple transverse configurations of a polarized
dielectric, but not in longitudinal ones.
