The performance of atomistic calculations using interionic potentials has been examined in detail with respect to the structures and energetic stabilities of ten configurational isomers (i.e., distinct Ce3+/Ce4+ cationic orderings) of a low energy octahedral ceria nanoparticle Ce19O32. The outcome of these calculations is compared with the results of corresponding density-functional (DF) calculations employing local and gradient corrected functionals with an additional corrective onsite Coulombic interaction applied to the f-electrons (i.e., LDA+U and GGA+U, respectively). Strikingly similar relative energy ordering of the isomers and atomic scale structural trends (e.g., cation-cation distances) are obtained in both the DF and interionic-potential calculations. The surprisingly good agreement between the DF electronic structure calculations and the relatively simple classical potentials is not found to be due to a single dominant interaction type but is due to a sensitive balance between long range electrostatics and local bonding contributions to the energy. Considering the relatively high computational cost and technical difficulty involved in obtaining charge-localized electronic solutions for reduced ceria using DF calculations, the use of interionic potentials for rapid and reliable preselection of the most stable Ce3+/Ce4+ cationic orderings is of considerable benefit.