Does Hessian Data Improve the Performance of Machine Learning Potentials?

Integrating machine learning into reactive chemistry, materials discovery, and drug design is revolutionizing the development of novel molecules and materials. Machine Learning Interatomic Potentials (MLIPs) accurately predict energies and forces at quantum chemistry levels, surpassing traditional methods. Incorporating force fitting into MLIP training significantly improves the representation of potential-energy surfaces (PES), enhancing model transferability and reliability. This study introduces and evaluates incorporating Hessian matrix training into MLIPs, capturing second-order curvature information of PES. Our analysis specifically examines MLIPs trained solely on stable molecular geometries, assessing their extrapolation capabilities to non-equilibrium configurations. We show that integrating Hessian information substantially improves MLIP performance in predicting energies, forces, and Hessians for non-equilibrium structures. Hessian-trained MLIPs notably enhance reaction pathway modeling, transition state identification, and vibrational spectra accuracy, benefiting molecular dynamics simulations and Nudged Elastic Band (NEB) calculations. By comparing models trained with various combinations of energy, force, and Hessian data on a small-molecule reactive dataset, we demonstrate Hessian inclusion leads to improved accuracy in reaction modeling and vibrational analyses while simultaneously reducing the total data needed for effective training. The primary trade-off is increased computational expense, as Hessian training demands more resources than conventional methods. Our results offer comprehensive insights into the strengths and limitations of Hessian integration in MLIP training, enabling practitioners in computational chemistry to make informed decisions aligned with their research goals and available computational resources.