Learning Dipole Moments and Polarizabilities

TL;DR

This paper reviews machine learning models for tensorial molecular properties like dipole moments and polarizabilities, emphasizing rotational equivariance and demonstrating an embedded atom neural network approach.

Contribution

It introduces a methodology for encoding rotational equivariance in ML models for tensorial properties and demonstrates training dipole moments and polarizabilities with neural networks.

Findings

Effective encoding of rotational symmetry in ML models.

Successful training of dipole moments and polarizabilities.

Framework extendable to higher-rank tensor properties.

Abstract

Machine learning of scalar molecular properties such as potential energy has enabled widespread applications. However, there are relatively few machine learning models targeting directional properties, including permanent and transition dipole (multipole) moments, as well as polarizability. These properties are essential to determine intermolecular forces and molecular spectra. In this chapter, we review machine learning models for these tensorial properties, with special focus on how to encode the rotational equivariance into these models by taking a similar form as the physical definition of these properties. You 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.