Supporting Code for “Machine Learning-Accelerated Path Integral Molecular Dynamics and ¹³C NMR Simulations Unlock New Insights Into Quantum Effects in C₆₀ Fullerene”

Graphical Abstract

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📄 Authors: Ouail Zakary and Ossi Laurila

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👤 Corresponding Author: Ouail Zakary

• 📧 Email: Ouail.Zakary@oulu.fi
• 🔗 ORCID: 0000-0002-7793-3306
• 🌐 Website: Personal Webpage
• 📁 Portfolio: Academic Portfolio

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This is the supporting code for the manuscript “Machine Learning-Accelerated Path Integral Molecular Dynamics and ¹³C NMR Simulations Unlock New Insights Into Quantum Effects in C₆₀ Fullerene”. [DOI: https://doi.org/10.1021/acs.jpca.6c00238]

The repository comprises the following sections:

1. Dataset preparation for the three MLIP models:
   i. Configuration generation using semi-empirical MD simulations. (directory)
   ii. DFT calculations of the generated SE-MD configurations for training the three MLIP models. (directory)
   iii. Dataset format of the MLIP models. (directory)
2. Example of training, validation, and testing processes for the MLIP model using NEP3 architecture. (directory)
3. Machine learning-assisted path-integral MD simulations. (directory)
4. Dataset preparation for the NMR-ML model:
   i. Configuration generation using semi-empirical MD simulations. (directory)
   ii. DFT calculations for the NMR-ML model. (directory)
   iii. Dataset format for the NMR-ML model. (directory)
5. Training, validation, and testing processes for the NMR-ML model using SchNet architecture on NMR magnetic shielding parameters, including the skew, span, and σ_iso. (directory)
6. Prediction of NMR isotropic magnetic shielding values, σ_iso, from the pre-trained NMR-ML model. (directory)
7. Python scripts and raw numerical data for all figures related to the NMR-ML model included in the main manuscript and the Supporting Information. (directory)

Citations

If you use this data, please cite the following:

Paper

@article{laurila_2025_c60_ml,
  title={Machine Learning-Accelerated Path Integral Molecular Dynamics and $^{13}$C NMR Simulations Unlock New Insights Into Quantum Effects in C$_{60}$ Fullerene},
  author={Laurila, Ossi, and Jacklin, Tiia, and Zakary, Ouail and Lantto, Perttu},
  journal={J. Phys. Chem. A},
  year={2026},
  volume = {130},
  number = {10},
  pages = {2169--2181},
  doi={10.1021/acs.jpca.6c00238},
  url={https://doi.org/10.1021/acs.jpca.6c00238}
}

Dataset

@dataset{laurila_2025_data_c60_ml,
  author = {Laurila, Ossi, and Jacklin, Tiia, and Zakary, Ouail and Lantto, Perttu},
  title = {Supporting Data for "Machine Learning-Accelerated Path Integral Molecular Dynamics and $^{13}$C NMR Simulations Unlock New Insights Into Quantum Effects in C$_{60}$ Fullerene"},
  year = {2025},
  publisher = {Fairdata},
  doi = {10.23729/fd-c64c043e-473e-371d-9586-8fd3d04e2fb0},
  url = {https://doi.org/10.23729/fd-c64c043e-473e-371d-9586-8fd3d04e2fb0}
}

Code

@misc{laurila_2025_github_c60_ml,
  author = {Laurila, Ossi, and Jacklin, Tiia, and Zakary, Ouail and Lantto, Perttu},
  title = {Supporting Code for "Machine Learning-Accelerated Path Integral Molecular Dynamics and $^{13}$C NMR Simulations Unlock New Insights Into Quantum Effects in C$_{60}$ Fullerene"},
  year = {2025},
  publisher = {GitHub},
  journal = {GitHub repository},
  howpublished = {\url{https://github.com/ozakary/data-C60_ML}},
  url = {https://github.com/ozakary/data-C60_ML}
}

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For further details, please refer to the respective folders or contact the author via the provided email.