Machine learning interatomic potentials (MLIPs) have been widely employed in simulations of materials. In many systems, particularly ionic systems, long-range interactions often dominate and significantly influence their dynamical behavior. However, long-range effects such as Coulomb and van der Waals interactions are not considered in most MLIPs. To address this issue, we propose a method that incorporates long-range effects into local MLIPs using a reciprocal-space neural network. The structure information in real space is firstly transformed into reciprocal space and then encoded into a reciprocal-space potential (RSP) or a reciprocal-space descriptor (RSD) that takes complete atomic interactions into account. The RSP and RSD keep full invariance of Euclidean symmetry and unit-cell choice. Benefiting from the reciprocal-space information, MLIPs are enabled to describe not only Coulomb but also other types of long-range interactions. We demonstrate the advantages of our method using a model NaCl system with Coulomb and van der Waals interactions, ${\mathrm{Ga}}_x{\mathrm{N}}_y$ system, and ${\mathrm{HfO}}_2$ system with defects. At the same time, our approach helps to improve the prediction accuracy of some global properties such as the band gap where atomic interactions beyond local atomic environments play a very important role.

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• Defects
• Interatomic & molecular potentials
• Long-range interactions
• Artificial intelligence
• Machine learning