Assuming that the configurational and vibrational origins of entropy can be separated due to their different time scales, the vibrational entropy can be calculated for each configuration and introduced into the cluster expansion, by replacing the total (internal) energy, ∆E mix , in eq. 1 with the free energy, ∆F vib = ∆E mix + ∆E vib -T ∆S vib . The straightforward procedure would be to perform lattice dynamics calculations for each structure in the training set to determine the vibrational free energy within the harmonic phonon approximation. However, DFT based lattice dynamics calculations require the calculation of large supercells, and are thus usually not feasible for the hundreds of (low symmetry) training structures often used for fitting cluster expansions. Thus, in practice simple surrogate models based on, e.g., bond length vs. bond strength relations or empirical potentials are often used to determine force constants for lattice dynamics calculations-even today despite the increases in computational power .