  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 (MC) 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 the present 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.
