F vib is given as in Eq. ( ), but with thermally renormalized phonon frequencies, and U 0 is a temperature dependent renormalized baseline energy. Phonon free energies, including the SCPH and TDEP expressions, can be augmented by perturbative corrections . These include the so-called bubble correction based on third-order force constants as well as higher order corrections. These free energy methods have seen their merits in predicting thermal expansion beyond the QHA, including the negative thermal expansion of ScF 3 . For applications to phase stability, TDEP has been used to obtain a phase diagram of SnSe, for which the high temperature Cmcm phase is dynamically unstable, and for CrN, for which the vibrational entropy contributes significantly to the magnetic and structural phase transition. Two recent examples for phase stability using the SCPH methodology are the pressure induced wurtzite to rocksalt transition in GaN, and the relative free energy between four phases of CsPbI 3 . Finally, rather than relying on calculating the free energy based on the phonon dispersion to a given anharmonic order, it is also possible to minimize the free energy during structure optimisation. This is the approach used in the stochastic self-consistent harmonic approximation (SSCHA) method, where the free energy surface is sampled stochastically. It has been successfully employed to predict the ground-state structure of superconducting LaH 10 including zero-point anharmonic effects, and to study the phase transitions in several materials, including SnSe. So far, the main use of this method has been in terms of phase stability for materials with second-order phase transitions but, as it gives access to the free energy directly, predictions of stability between phases that are not related through soft-mode transitions should be straightforward.