where α is a cluster, m α is the multiplicity of the cluster, Γ α ′ (σ) are the cluster functions constructed as a product basis fulfilling certain symmetry conditions, ⟨• • • ⟩ denotes the average over symmetry equivalent clusters, and J α are the effective cluster interactions (ECI), which are the parameters to be determined from fitting to DFT data. In practice, the fitting of effective cluster interactions requires a range of structural relaxations with DFT of different (random or enumerated) configurations of the species forming the solid solution. From the determined ECIs one can then predict the energy of any configuration, including those in much larger supercells than what can be simulated with DFT.