Molecular electrostatic potentials from machine learning models for dipole and quadrupole predictions

The molecular electrostatic potential (MEP) is a key quantity for describing and predicting intermolecular and ion–molecule interactions. Here, we assess the ability of machine-learning (ML) models to infer the MEP, based on the equivariant graph-convolutional neural network architecture PiNet2 and trained on dipole and quadrupole moments. For the established QM9 dataset, we find that including the quadrupole contribution in the ML models substantially improves their ability to recover the MEP compared to dipole-only models. This trend is confirmed on the SPICE dataset, which spans a much broader region of organic chemical space. Together, this study underscores the central role of the quadrupole moment as a fitting target for ML models aiming at rapid access to the MEP.