For multipole moments, we partitioned the dataset into a training set and a test set using a random 9:1 split and trained this data with E3NN. Figure illustrates the correlations of charge, atomic dipole moment and traceless quadrupole moments between the NN-predicted values and the QM counterparts for the test sets. The QM data presented in Figure (a), (c), and (e) were obtained using the BS-ISA approach. In contrast, the data in Figure (b), (d), and (f) were generated using the Hirshfeld method. Notably, the Hirshfeld charges are generally lower than the BS-ISA-derived charges, which is a known feature of the Hirshfeld method, as discussed in the literature. On the other hand, this is compensated for by larger higher-ranking moments, therefore, atomic dipole moments derived from the Hirshfeld Figure : Schematic data construction workflow for asymptotic parameters. method tend to be higher than those obtained via the BS-ISA approach. In terms of E3NN accuracy, for either BS-ISA or Hirshfeld multipole moments, the E3NN prediction exhibit an excellent R 2 value of approximately 0.999. Moreover, the mean absolute error (MAE) for the predicted monopole moment (charges) is in the order of 10 -3 e. For dipole moments, the MAE is in the order of 10 -4 e • Å, and for quadrupole moments, the MAE is about 1.5 10 -3 e • Å2 . The E3NN models achieve a slightly superior performance in predicting the Hirshfeld multipoles compared to those obtained via BS-ISA. This is probably due to the fact that the BS-ISA multipoles display more geometric fluctuations compare to the Hirshfeld results, thus are more difficult to fit (see below for more details). Nevertheless, the accuracies of both fittings are adequate to give excellent descriptions to the long-range electrostatic interactions, as we will show below.