Incorporating Coulomb interactions with fixed charges in moment tensor potentials and equivariant tensor network potentials

In this work, we incorporate long-range electrostatic interactions in the form of the Coulomb model with fixed charges into the functional form of short-range machine-learning interatomic potentials (MLIPs), particularly in the moment tensor potential and equivariant tensor network potential. We show that the explicit incorporation of the Coulomb interactions with fixed charges leads to a significant reduction of energy fitting errors, namely, more than four times, of short-range MLIPs trained on organic dimers of charged molecules. Furthermore, with our long-range models, we demonstrate a significant improvement in the prediction of the binding curves of the organic dimers of charged molecules. Finally, we show that the results calculated with MLIPs are in good correspondence with those obtained with density functional theory for organic dimers of charged molecules.