Calculations were performed using pseudopotential plane wave density functional theory (DFT) as implemented in the Vienna Ab initio Simulation Package (VASP) code. Initial structures of CaTiO 3 , SrTiO 3 and BaTiO 3 in the Pnma, I4/mcm and R3m structures, respectively, were taken from the Materials Project (MP) database (mp-4019, mp-4651, mp-5020) and optimised to tight tolerances of 10 -8 eV on the total energy and 10 -3 eV Å -1 on the forces.