  The structure, polarization, and zone-center phonons of bulk tetragonal
BaTiO$_3$ under compressive epitaxial stress are calculated using density
functional theory within the local density approximation. The polarization,
computed using the Berry-phase formalism, increases with increasing
tetragonality and is found to be enhanced by nearly 70% for the largest
compressive misfit strain considered (-2.28%). The results are expected to be
useful for the analysis of coherent epitaxial BaTiO$_3$ thin films and
heterostructures grown on perovskite substrates having a smaller lattice
constant, such as SrTiO$_3$.
