Long-Range Interactions in High-Dimensional Neural Network Potentials: A Benchmark Study for Small Organic Molecules

Many machine learning potentials (MLPs) rely on representations of the total energy in terms of the positions of the atoms in their local environment, using either a cutoff radius or a limited number of message-passing layers. This restricts their ability to model long-range intermolecular interactions accurately. This limitation can be addressed by explicitly incorporating long-range electrostatic and dispersion interactions into the MLP framework. In this paper, we investigate the impact of augmenting high-dimensional neural network potentials (HDNNPs) with both electrostatic and dispersion corrections on the prediction of gas-phase intermolecular interactions between small organic molecules. We employ a machine learning-based charge equilibration (QEq) scheme to model electrostatics and the Machine-Learning eXchange-hole Dipole Moment (MLXDM) model to account for dispersion. The resulting model, CombineNet, integrates these long-range terms with short-range atomic energies trained on density functional theory (DFT) data and achieves a low mean absolute error (MAE) of 0.59~kcal/mol (root mean square error (RMSE) of 3.38~meV/atom) against CCSD(T)/CBS benchmarks on the DES370K test set. Notably, electrostatic interactions derived from Hirshfeld charges tend to underestimate long-range effects, whereas the Minimal Basis Iterative Stockholder (MBIS) charges yield more accurate interaction trends. For reliable modeling of molecular dimers, the training set must capture both the dissociation limit and the transition region near the cutoff radius. For reliable modeling of molecular dimers, the training set must cover the full range of interest of intermolecular distances.