Understanding The Degree of Cluster Expansions

The cluster expansion (CE) method developed to model disorder in alloys has seen active use in computational materials science since it was proposed 30 years ago. Notable extensions to include multi-lattice systems, and the use of new regression techniques have established the CE as a standard method in the computational study of multicomponent crystals. Recent interest in high entropy alloys (HEA) and cation-disordered rocksalt (DRX) cathode materials has opened a prime setting for continued development of the CE. Studying large multi-component systems involves exploration of high-dimensional spaces. Although the current formulation of the CE is applicable in these high-dimensional spaces, issues surrounding specific sampling and regression techniques necessary to obtain manageable and accurate models for treatment of HEA and DRX material systems remain largely unsettled. We re-examine the CE formalism, and explore the relationship of structural relaxations and composition in setting the maximal degree of the CE. Limiting the degree while preserving predictive accuracy is crucial in controlling model complexity and ensuring interpretability needed for successful use of the CE when studying large multi-component systems.