  The polarization-dependence of the exchange-correlation (XC) energy
functional of periodic insulators within Kohn-Sham (KS) density-functional
theory requires a ${\cal O} (1/q^2)$ divergence in the XC kernel for small
vectors q. This behaviour, exemplified for a one-dimensional model
semiconductor, is also observed when an insulator happens to be described as a
KS metal, or vice-versa. Although it can occur in the exchange-only kernel, it
is not found in the usual local, semi-local or even non-local approximations to
KS theory. We also show that the test-charge and electronic definitions of the
macroscopic dielectric constant differ from one another in exact KS theory, but
are equivalent in the above-mentioned approximations.
