  In the first-principles bulk-layer model the superlattice structure and
polarization are determined by first-principles computation of the bulk
responses of the constituents to the electrical and mechanical boundary
conditions in an insulating superlattice. In this work the model is extended to
predict functional properties, specifically dielectric permittivity and
piezoelectric response. A detailed comparison between the bulk-layer model and
full first-principles calculations for three sets of perovskite oxide
superlattices, PbTiO$_3$/BaTiO$_3$, BaTiO$_3$/SrTiO$_3$ and
PbTiO$_3$/SrTiO$_3$, is presented. The bulk-layer model is shown to give an
excellent first approximation to these important functional properties, and to
allow for the identification and investigation of additional physics, including
interface reconstruction and finite size effects. Technical issues in the
generation of the necessary data for constituent compounds are addressed. These
results form the foundation for a powerful data-driven method to facilitate
discovery and design of superlattice systems with enhanced and tunable
polarization, dielectric permittivity, and piezoelectric response.
