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The accuracy of physical property predictions using classical moleculardynamics simulations is determined by the quality of the empirical interatomicpotentials (EIPs). We introduce a training approach for EIPs, based on directcomparisons of the second- and third-order interatomic force constants (IFCs)between EIP and density functional theory (DFT) calculations. This work'sunique aspect is the utilization of irreducible derivatives (IDs) of the totalenergy, which leverage on the symmetry of the crystalline structure and providea minimal representation of the IFCs. Our approach is tailored toward accuratepredictions of thermal conductivity, thus requiring knowledge of both harmonicand anharmonic IFCs by matching second- and third-order displacementderivatives, whereas second-order strain derivatives are needed for determiningthe elastic constants. We demonstrate this approach as an efficient and robustmanner in which to train EIPs for predicting phonons and related properties, byoptimizing parameters of an embedded-atom method potential for ThO$_2$, whichis used as a model system for fluorite oxides. Our ID-trained EIP providesthermophysical properties in great agreement with DFT, and outperformspreviously widely utilized EIP for ThO$_2$ in phonon dispersion and thermalconductivity calculations. It also provides reasonable estimates of thermalexpansion and the formation energies of simple defects.

Improving empirical interatomic potentials for predicting thermophysical  properties by using an irreducible derivatives approach: The case of thorium  dioxide