Cluster expansion of multicomponent ionic systems with controlled accuracy: importance of long-range interactions in heterovalent ionic systems

We have been examining factors determining the accuracy of cluster expansion (CE), which is used in combination with many density functional theory (DFT) calculations. With the exception of multicomponent metallic or isovalent ionic systems, the contributions of long-range effective cluster interactions (ECIs) to configurational energetics are not negligible, which is ascribed to long-range electrostatic interactions. The truncation of ECIs in such systems leads to systematic errors. A typical problem with such errors can be seen in Monte Carlo simulations, since simulation supercells composed of a larger number of atoms than those of the input DFT structures are used. The prediction errors for long-period structures beyond the cell size of the input DFT structures in addition to those for short-period structures within the cell size of the input DFT structures need to be carefully examined to control the accuracy of CE. In this study, we quantitatively discuss the contribution of the truncation of long-range ECIs to the accuracy of CE. Two types of system, namely a point-charge spinel lattice and a real MgAl2O4 spinel crystal, are examined. The prediction error of the long-period structures can be improved both by increasing the number of pairs and by also considering the effective screened electrostatic energy.