Chapter 19 - Learning dipole moments and polarizabilities

Abstract

Machine learning (ML) of scalar molecular properties such as potential energy has enabled widespread applications. However, there are relatively few ML models targeting directional properties, including permanent and transition dipole (multipole) moments and polarizability. These properties are essential to determine intermolecular forces and molecular spectra. In this chapter, we review ML models for these tensorial properties, with a special focus on how to encode the rotational equivariance into these models by taking a similar form as the physical definition of these properties. We will then learn how to use an embedded atom neural network model to train dipole moments and polarizabilities of a representative molecule. The methodology discussed in this chapter can be extended to learn similar or higher-rank tensorial properties, such as magnetic dipole moments, non-adiabatic coupling vectors, and hyperpolarizabilities.