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Cluster expansion (CE) is effective in modeling the stability of metallicalloys, but sometimes cluster expansions fail. Failures are often attributed toatomic relaxation in the DFT-calculated data, but there is no metric forquantifying the degree of relaxation. Additionally, numerical errors can alsobe responsible for slow CE convergence. We studied over one hundred differentHamiltonians and identified a heuristic, based on a normalized mean-squareddisplacement of atomic positions in a crystal, to determine if the effects ofrelaxation in CE data are too severe to build a reliable CE model. Using thisheuristic, CE practitioners can determine a priori whether or not an alloysystem can be reliably expanded in the cluster basis. We also examined theerror distributions of the fitting data. We find no clear relationship betweenthe type of error distribution and CE prediction ability, but there are clearcorrelations between CE formalism reliability, model complexity, and the numberof significant terms in the model. Our results show that the \emph{size} of theerrors is much more important than their distribution.

The Robustness of Cluster Expansion: Assessing the Roles of Relaxation and Numerical Error