Shell Model of BaTiO$_3$ derived from {\it{ab-initio}} DFT Calculations

A shell model for ferroelectric perovskites fitted to properties of first-principles density functional theory (DFT) is strongly affected by approximations made in the exchange-correlation functional within DFT and in general not as accurate as a shell model derived from experimental data. We have developed an isotropic shell model for BaTiO$_3$ based on the PBEsol exchange-correlation functional, which was specifically designed for solids and gives overall good agreement for the lattice parameters of all BaTiO$_3$ phases. Our shell model reproduces the sequence of phases of BaTiO$_3$ (rhombohedral, orthorhombic, tetragonal, cubic) and shows good agreement with experimental lattice constants at all temperatures, however the phase transition temperatures are too low. The energy scale can be improved by a simple scaling of the {\it{ab-initio}} potential energy surface. The polarization in the shell model is qualitatively correct but too small by approximately 30\% compared to the experimental value.