Phonon predictions with E(3)-equivariant graph neural networks

TL;DR

This paper introduces an E(3)-equivariant neural network that predicts vibrational and phonon modes of molecules and crystals by evaluating Hessian matrices, enabling efficient phonon property predictions and improved energy models.

Contribution

It presents a novel equivariant neural network architecture that directly predicts vibrational properties and enhances energy models using second derivatives, bridging computational predictions with experimental vibrational data.

Findings

Accurately predicts phonon dispersion and density of states for inorganic crystals.

Derives symmetry constraints for IR/Raman active modes in molecules.

Improves energy models by incorporating Hessian-based higher-order training data.

Abstract

We present an equivariant neural network for predicting vibrational and phonon modes of molecules and periodic crystals, respectively. These predictions are made by evaluating the second derivative Hessian matrices of the learned energy model that is trained with the energy and force data. Using this method, we are able to efficiently predict phonon dispersion and the density of states for inorganic crystal materials. For molecules, we also derive the symmetry constraints for IR/Raman active modes by analyzing the phonon mode irreducible representations. Additionally, we demonstrate that using Hessian as a new type of higher-order training data improves energy models beyond models that only use lower-order energy and force data. With this second derivative approach, one can directly relate the energy models to the experimental observations for the vibrational properties. This approach further connects to a broader class of physical observables with a generalized energy model that includes external fields.