  Linearized augmented plane wave (LAPW) calculations are performed for
periodic (001) and (111) slabs of BaTiO$_3$ to understand the effects of
surfaces on ferroelectric BaTiO$_3$. The (111) slab is found to be much less
stable than the (001) slab. The average surface energies are respectively 3700
erg/cm$^2$ and 1600 erg/cm$^2$. The depolarization field is sufficiently large
in the ideal unrelaxated slab to completely inhibit the ferroelectric
instability. No mid-gap surface states are evident, but there are surface
states in the upper gap in the unrelaxed slab and at the top of the valence
band. The dangling surface Ti bonds self-heal making the Ti-O surface very
reactive and an excellent epitaxial substrate. The charge density on atoms only
one unit cell away from the surface are almost identical to the bulk.
  Keywords: ferroelectric, surface, slab, electronic structure, depolarization,
BaTiO$_3$, thin film
