How to simulate a structural phase transition by the first-principles method?

We outline the procedure and approximations used to study the structural phase transition. The standard ab initio programs provide the Hellmann-Feynman forces, which allow, by the direct method, to describe the dispersion curves including the soft mode. The values of the anharmonic terms of the order parameter and order parameter-strain coupling terms, found from symmetry analysis, can be calculated within the ab initio total energy approach, by earring on the calculations for a variety of atom configurations. The method is used to describe the cubic-tetragonal phase transition in SrTiO₃, for which a soft mode and anharmonic coefficients have been found.