# Hessian QM9: A quantum chemistry database of molecular Hessians in implicit solvents

arXiv: https://arxiv.org/abs/2408.08006 · HTML: https://mlsanity.com/paper/2408.08006/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 20 references that are in the map.
- First posted on arXiv 15 Aug 2024.

## Builds on (most cited first, 4 of 4)

- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [Transition1x -- a Dataset for Building Generalizable Reactive Machine Learning Potentials](https://mlsanity.com/paper/2207.12858/) (2022)
- [Algorithmic Differentiation for Automated Modeling of Machine Learned Force Fields](https://mlsanity.com/paper/2208.12104/) (2022)

## Built on by (most cited first, 7 of 7)

- [Learning Smooth and Expressive Interatomic Potentials for Physical Property Prediction](https://mlsanity.com/paper/2502.12147/) (2025)
- [HIP: Hessian Interatomic Potentials without derivatives](https://mlsanity.com/paper/2509.21624/) (2025)
- [OrbitAll: A Unified Quantum Mechanical Representation Deep Learning Framework for All Molecular Systems](https://mlsanity.com/paper/2507.03853/) (2025)
- [Projected Hessian Learning: Fast Curvature Supervision for Accurate Machine-Learning Interatomic Potentials](https://mlsanity.com/paper/2603.04523/) (2026)
- [Data-driven construction of machine-learning-based interatomic potentials for gas-surface scattering dynamics: the case of NO on graphite](https://mlsanity.com/paper/2603.18864/) (2026)
- [Hessian-informed machine learning interatomic potential towards bridging theory and experiments](https://mlsanity.com/paper/2603.25373/) (2026)
- [Hessian-Informed Conformation Augmentation for Potential Energy Surface Curvature in Machine Learning Interatomic Potentials](https://mlsanity.com/paper/2609.05233/) (2026)

## Abstract (arXiv)

A significant challenge in computational chemistry is developing approximations that accelerate ab initio methods while preserving accuracy. Machine learning interatomic potentials (MLIPs) have emerged as a promising solution for constructing atomistic potentials that can be transferred across different molecular and crystalline systems. Most MLIPs are trained only on energies and forces in vacuum, while an improved description of the potential energy surface could be achieved by including the curvature of the potential energy surface. We present Hessian QM9, the first database of equilibrium configurations and numerical Hessian matrices, consisting of 41,645 molecules from the QM9 dataset at the ωB97x/6-31G* level. Molecular Hessians were calculated in vacuum, as well as water, tetrahydrofuran, and toluene using an implicit solvation model. To demonstrate the utility of this dataset, we show that incorporating second derivatives of the potential energy surface into the loss function of a MLIP significantly improves the prediction of vibrational frequencies in all solvent environments, thus making this dataset extremely useful for studying organic molecules in realistic solvent environments for experimental characterization.