DescriptionThis thesis consists of the development and application of computational methods, models, and tools for investigating and designing functional materials. We begin with an overview of density functional theory, ferroelectricity, the modern theory of polarization, and the present state of the field of first principles materials design. After this review a new first principles method is introduced for computing changes in polarization, referred to as Berry flux diagonalization. This method eliminates the requirement of previous approaches to construct a switching path between oppositely polarized states, enabling for more robust automation, and significantly lower computational cost. Calculations on common ferroelectrics are presented along with comparison to previous approaches. Subsequently, a model for predicting superlattice properties from data computed only for the bulk constituents is presented and expanded to predict dielectric and piezoelectric responses. Several example systems are investigated both with the model and with full superlattice first principles calculations.
One such system, PbTiO$_{3}$/BaTiO$_{3}$, exhibits an enhanced dielectric response at certain layer ratios. The model can be used to efficiently discover superlattice combinations which give rise to such enhancements, as well to understand the physics which leads to those enhancement. Finally, a new set of tools for integrating group theoretical methods with first principles calculations and materials databases is introduced. An example application is given where all perovskite structures in the materials project database are identified and classified by the symmetry adapted distortion modes that relate them to the ideal cubic structure. This grouping of structures can be used to identify competing low energy structures of a given material which may be stabilized under certain conditions.