# A Large Scale Molecular Hessian Database for Optimizing Reactive Machine Learning Interatomic Potentials

## TL;DR

This paper introduces HORM, a large quantum-chemistry Hessian dataset that improves the accuracy and efficiency of machine-learning interatomic potentials for modeling chemical reactions.

## Contribution

The paper presents HORM, the largest Hessian dataset for reactive systems, and a novel training method that leverages second-order information for MLIPs.

## Key findings

- HORM contains 1.84 million Hessian matrices at the ωB97x/6-31G(d) level.
- HORM reduces Hessian mean absolute error by up to 63% and improves TS-search efficiency by up to 200×.
- The proposed method enables scalable and accurate reaction network exploration.

## Abstract

Transition-state (TS) characterization underpins reaction modeling but conventional DFT is costly. Machine-learning interatomic potentials (MLIPs) promise quantum-level accuracy at lower cost, yet, lacking large-scale Hessian data, most are pretrained only on energies and forces, limiting TS optimization. We present HORM, the largest quantum-chemistry Hessian dataset for reactive systems: 1.84 million matrices at the ωB97x/6-31G(d) level. To exploit second-order information efficiently, we propose Hessian-informed training with stochastic row sampling, which controls the computational overhead of incorporating Hessians. Across diverse MLIP architectures and force-learning schemes, HORM yields up to 63% lower Hessian mean absolute error and up to 200× improvement in TS-search efficiency versus counterparts trained without Hessians. HORM thus fills critical data and methodological gaps, enabling more accurate, robust reactive MLIPs and scalable exploration of reaction networks.