DENSITY-FUNCTIONAL THEORY OF POLAR INSULATORS

We examine the density-functional theory of macroscopic insulators, ob tained in the large-cluster limit or under periodic boundary condition s. For polar crystals, we find that the two procedures are not equival ent. In a large-cluster case, the exact exchange-correlation potential acquires a homogeneous ''electric field'' which is absent from the us ual local approximations, and the Kohn-Sham electronic system becomes metallic. With periodic boundary conditions, such a field ist forbidde n, and the polarization deduced from Kohn-Sham wave functions is incor rect even if the exact functional is used.