LONG-WAVELENGTH BEHAVIOR OF THE EXCHANGE-CORRELATION KERNEL IN THE KOHN-SHAM THEORY OF PERIODIC-SYSTEMS

The polarization dependence of the exchange-correlation (re) energy fu nctional of periodic insulators within Kohn-Sham (KS) density-function al theory requires a O(1/q(2)) divergence in the re kernel for small v ectors q. This behavior, exemplified for a one-dimensional model semic onductor, is also observed when an insulator happens to be described a sa KS metal, or vice versa. Although it can occur in the exchange-only kernel, it is not found in the usual local, semilocal, or even nonloc al 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-m entioned approximations.