A machine learning interatomic potential to directly predict the Hessian. Trained on the HORM Hessian dataset, which consists of off-equilibrium geometries of small, neutral organic molecules, contained H, C, N, O, based on the T1x and RGD1 datasets, at the $\omega$B97X/6-31G(d) level of theory.

Compared to autograd Hessians:

• 10-70x faster for a single molecule of 5-30 atoms
• 70x faster for a typical T1x batch in batched prediction
• 3x memory reduction
• Better accuracy (Hessian, Hessian eigenvalues and eigenvectors)
• Better downstream accuracy (relaxation, transition state search, frequency analysis)

Install uv (if not already installed)

curl -LsSf https://astral.sh/uv/install.sh | sh
export PATH="$HOME/.local/bin:$PATH"

git clone git@github.com:BurgerAndreas/hip.git
cd hip

# Create virtual environment and install base dependencies
uv venv .venv --python 3.11
source .venv/bin/activate
uv sync

# Install PyTorch with CUDA support
uv pip install torch==2.7.0 --index-url https://download.pytorch.org/whl/cu126

# Install PyTorch Geometric packages with CUDA support
uv pip install torch-scatter -f https://data.pyg.org/whl/torch-2.7.0+cu126.html
uv pip install torch-cluster -f https://data.pyg.org/whl/torch-2.7.0+cu126.html
uv pip install torch-geometric

# Install the package in development mode
uv pip install -e .

Download the checkpoint from HuggingFace

wget https://huggingface.co/andreasburger/heigen/resolve/main/ckpt/hip_v2.ckpt -O ckpt/hip_v2.ckpt

uv run example.py

Kaggle automatically downloads to the ~/.cache folder. I highly recommend to set up a symbolic link to a local folder to avoid running out of space on your home directory:

PROJECT = <folder where you want to store the dataset>
mkdir -p ${PROJECT}/.cache
ln -s ${PROJECT}/.cache ${HOME}/.cache

Get the HORM dataset:

uv run scripts/download_horm_data_kaggle.py

If you found this code useful, please consider citing:

@misc{burger2025hiphessian,
      title={Shoot from the HIP: Hessian Interatomic Potentials without derivatives}, 
      author={Andreas Burger and Luca Thiede and Nikolaj Rønne and Varinia Bernales and Nandita Vijaykumar and Tejs Vegge and Arghya Bhowmik and Alan Aspuru-Guzik},
      year={2025},
      eprint={2509.21624},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2509.21624}, 
}

The training code and the dataset are based on the HORM paper, dataset, and code We thank the authors of from DeepPrinciple for making their code and data openly available.