Machine learning the molecular dipole moment with atomic partial charges and atomic dipoles*

The gas-phase molecular dipole moment is a central quantity in chemistry. It is essential in predicting molecular infrared and sum-frequency-generation spectra, as well as in describing long-range interactions. Here we fit a machine learning model on an accurate quantum chemical reference dipole set. We represent the dipole with a physically-inspired machine learning model that captures the two distinct physical effects contributing to molecular polarization: Local atomic polarization is captured within the symmetry-adapted Gaussian process regression (SA-GPR) framework, while long-range movement of charge is captured by assigning a scalar charge to each atom. Not only does the model achieve state-of-the-art interpolation and extrapolation performance on the standard QM9 reference set, it also gives useful insights into the physics of polarization and charge transfer for a variety of challenging test examples. The results show how transparency and physical interpretability can aid not only the understanding of a machine learning model, but allow it to achieve higher accuracy as well. Extensions to the condensed phase, within the context of the modern theory of polarization, are discussed.