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Approaching coupled-cluster accuracy for molecular electronic structures with multi-task learning

Nature Computational Science volume 5, pages 144–154 (2025)Cite this article

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An Author Correction to this article was published on 22 January 2025

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A preprint version of the article is available at arXiv.

Abstract

Machine learning plays an important role in quantum chemistry, providing fast-to-evaluate predictive models for various properties of molecules; however, most existing machine learning models for molecular electronic properties use density functional theory (DFT) databases as ground truth in training, and their prediction accuracy cannot surpass that of DFT. In this work we developed a unified machine learning method for electronic structures of organic molecules using the gold-standard CCSD(T) calculations as training data. Tested on hydrocarbon molecules, our model outperforms DFT with several widely used hybrid and double-hybrid functionals in terms of both computational cost and prediction accuracy of various quantum chemical properties. We apply the model to aromatic compounds and semiconducting polymers, evaluating both ground- and excited-state properties. The results demonstrate the model’s accuracy and generalization capability to complex systems that cannot be calculated using CCSD(T)-level methods due to scaling.

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Fig. 1: Schematic of the MEHnet electronic structure workflow.
Fig. 2: Benchmark of the model performance on the testing dataset.
Fig. 3: Validation of the MEHnet’s predictions on gas phase aromatic hydrocarbon molecules, as compared with experimental results.
Fig. 4: MEHnet predictions for the electronic properties of semiconducting polymers.

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Data availability

Raw computational data files and the training and testing datasets are available with this manuscript through FigShare at https://doi.org/10.6084/m9.figshare.25762212 (ref. 52). Source Data are provided with this paper.

Code availability

The source code to generate the training dataset, train the MEHnet model, and apply the trained MEHnet model to hydrocarbon molecules has been deposited into a publicly available GitHub repository at https://github.com/htang113/Multi-task-electronic (ref. 53), and is also available in the Supplementary Software. The repository contains two branches: the branch v.1.6 is for all results of hydrocarbon molecules in this paper, and the branch v.2.0 is for the benchmark on the QM9 dataset.

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Acknowledgements

This work was supported by Honda Research Institute (HRI-USA). H.T. acknowledges support from the Mathworks Engineering Fellowship. The calculations in this work were performed in part on the Matlantis high-speed universal atomistic simulator, the Texas Advanced Computing Center (TACC), the MIT SuperCloud, and the National Energy Research Scientific Computing (NERSC).

Author information

Authors and Affiliations

  1. Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

    Hao Tang & Ju Li

  2. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Brian Xiao

  3. The Center for Computational Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

    Wenhao He

  4. Honda Research Institute USA, San Jose, CA, USA

    Pero Subasic & Avetik R. Harutyunyan

  5. Department of Chemistry, Emory University, Atlanta, GA, USA

    Yao Wang & Fang Liu

  6. Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

    Haowei Xu & Ju Li

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Contributions

All authors contributed to the discussions of theory and results and to writing the manuscript. J.L. designed and guided the project and formulated the research goals. H.T., H.X., B.X. and W.H. designed and developed the computational method and code package, generated the quantum chemistry dataset, implemented the machine learningtraining and applications, and did data analysis and visualization. A.H. initiated the theme and formulated the research goals. Y.W., F.L. and P.S. provided important comments for the paper.

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Correspondence to Haowei Xu or Ju Li.

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Nature Computational Science thanks Debashree Ghosh and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Kaitlin McCardle, in collaboration with the Nature Computational Science team. Peer reviewer reports are available.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–6, Tables 1 and 2, and Supplementary Sections 1–5.

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Supplementary Data

Relaxed structure models and example input files.

Supplementary Code

Python code package of MEHnet.

Source data

Source Data Fig. 1

Plain data files of Fig. 1c (Statistical source data for Fig. 1c).

Source Data Fig. 2

Plain data files of Fig. 2a–c (Statistical source data for Fig. 2a–c).

Source Data Fig. 3

Plain data files of Fig. 3a,b (Statistical source data for Fig. 3a,b).

Source Data Fig. 4

Plain data files for Fig. 4b,c (Statistical source data for Fig. 4b,c).

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Tang, H., Xiao, B., He, W. et al. Approaching coupled-cluster accuracy for molecular electronic structures with multi-task learning. Nat Comput Sci 5, 144–154 (2025). https://doi.org/10.1038/s43588-024-00747-9

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