Tensor Atomic Cluster Expansion#

Documentation Structure#

Contents

Changelog

Overview#

Currently, the officially supported properties include:

  • Energy

  • Forces (conservative | direct)

  • Hessian (conservative, predict only)

  • Stress (conservative | direct)

  • Virials (conservative | direct)

  • Charges (lagrangian or uniform_distribution)

  • Dipole moment (conservative | direct)

  • Polarization (conservative, multi-value for PBC systems)

  • Polarizability (conservative | direct)

  • Born effective charges (conservative, under electric field or LES) (LES predict only)

  • Atomic stresses (conservative, predict only)

  • Atomic virials (conservative, predict only)

  • absolute final collinear magmoms

  • Noncollinear magnetic forces (O(3))

For embedding property, we support:

  • fidelity_idx (different computational levels)

  • charges

  • total charge

  • electric field

  • initial (non)collinear magmoms

  • magnetic field (O(3))

Plugins#

TACE currently supports the following plugin:

  • LES (Latent Ewald Summation)

Interfaces#

  • ✅ Supports integration with ASE Calculator.

  • ✅ Supports integration with LAMMPS-ML-IAP.

  • ✅ Supports integration with TorchSim.

  • ✅ Supports integration with OpenMM-ML (OpenMM-ML -> ASE -> TACE).

  • ✅ Supports integration with USPEX (USPEX -> LAMMPS-ML-IAP -> TACE) (Python=3.9).

Citing#

If you use TACE, please cite our papers:

@misc{xu2026spectralspatialtensoratomiccluster,
      title={Spectral/Spatial Tensor Atomic Cluster Expansion with Universal Embeddings in Cartesian Space},
      author={Zemin Xu and Wenbo Xie and P. Hu},
      year={2026},
      eprint={2509.14961},
      archivePrefix={arXiv},
      primaryClass={stat.ML},
      url={https://arxiv.org/abs/2509.14961},
}

@misc{xu2026edgeclusterexpansionradial,
      title={Edge Cluster Expansion with Radial Rotary Attention for Interatomic Potentials},
      author={Zemin Xu and Wenbo Xie and P. Hu},
      year={2026},
      eprint={2607.10664},
      archivePrefix={arXiv},
      primaryClass={stat.ML},
      url={https://arxiv.org/abs/2607.10664},
}

If you use cartnn, Cartesian-3j, cMACE, cNequIP, cAllegro, please cite our papers:

@inproceedings{
   xu2026a,
   title={A Cartesian-3j Framework for Machine Learning Interatomic Potentials},
   author={Zemin Xu and Chenyu Wu and Wenbo Xie and Peijun Hu},
   booktitle={Forty-third International Conference on Machine Learning},
   year={2026},
   url={https://openreview.net/forum?id=9ZWK6gneWq}
}

Contact#

For bugs or feature requests, please use xvzemin/tace#issues.

License#

The TACE code is published and distributed under the MIT License.