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Unified deep learning framework for many-body quantum chemistry via Green’s functions

Nature Computational Science volume 5, pages 502–513 (2025)Cite this article

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A preprint version of the article is available at arXiv.

Abstract

Quantum many-body methods provide a systematic route to computing electronic properties of molecules and materials, but high computational costs restrict their use in large-scale applications. Owing to the complexity in many-electron wavefunctions, machine learning models capable of capturing fundamental many-body physics remain limited. Here we present a deep learning framework targeting the many-body Green’s function, which unifies predictions of electronic properties in ground and excited states, while offering physical insights into many-electron correlation effects. By learning the many-body perturbation theory or coupled-cluster self-energy from mean-field features, our graph neural network achieves competitive performance in predicting one- and two-particle excitations and quantities derivable from a one-particle density matrix. We demonstrate its high data efficiency and good transferability across chemical species, system sizes, molecular conformations and correlation strengths in bond breaking, through multiple molecular and nanomaterial benchmarks. This work opens up opportunities for utilizing machine learning to solve many-electron problems.

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Fig. 1: Overview of the MBGF-Net workflow and architecture.
Fig. 2: MBGF-Net predictions of electronic properties of QM7 and QM9 molecules at the G0W0@PBE0 level.
Fig. 3: MBGF-Net predictions of excited-state properties of silicon nanoclusters at the G0W0@PBE0 level.
Fig. 4: MBGF-Net predictions of band gaps of azobenzene derivatives at the G0W0@PBE0 level.
Fig. 5: MBGF-Net predictions of orbital-specific many-body properties and downstream simulations in C–O single-bond breaking.

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Data availability

Source data are provided with this paper. The datasets used in this work are available via Zenodo at https://doi.org/10.5281/zenodo.15131927 (ref. 72).

Code availability

The code used in this work is available via Zenodo at https://doi.org/10.5281/zenodo.15175905 (ref. 73) and via GitHub at https://github.com/ZhuGroup-Yale/mlgf. Its implementation uses the fcDMFT code available at https://github.com/ZhuGroup-Yale/fcdmft and PySCF at https://github.com/pyscf/pyscf.

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Acknowledgements

The development of the MBGF-Net model was supported by the National Science Foundation under award number CHE-2337991 (C.V. and T.Z.) and the National Science Foundation Engines Development Award: Advancing Quantum Technologies (CT) under award number 2302908 (C.H.). The development of the Green’s function property analysis and the BSE code was supported by the Air Force Office of Scientific Research under award number FA9550-24-1-0096 (J. Li). C.V. acknowledges partial support from the Department of Defense through the National Defense Science and Engineering Graduate (NDSEG) Fellowship Program. J. Li acknowledges partial support from the Tony Massini Postdoctoral Fellowship in Data Science from Yale University. We thank the Yale Center for Research Computing for guidance and use of the research computing infrastructure.

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Authors and Affiliations

  1. Department of Chemistry, Yale University, New Haven, CT, USA

    Christian Venturella, Jiachen Li, Christopher Hillenbrand, Ximena Leyva Peralta, Jessica Liu & Tianyu Zhu

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  1. Christian Venturella
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  2. Jiachen Li
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  3. Christopher Hillenbrand
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Contributions

C.V. and T.Z. designed the project and wrote the manuscript. C.V. developed the GNN model and code. C.V., J. Li and T.Z. developed the Green’s function postprocessing workflow. J. Li and C.H. developed the BSE code. C.V., C.H., X.L.P. and J. Liu performed Green’s function calculations and data analyses. T.Z. supervised the project. All authors contributed to the discussion of the results as well as the writing and editing of the manuscript.

Corresponding author

Correspondence to Tianyu Zhu.

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Nature Computational Science thanks Yong Xu and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Jie Pan, in collaboration with the Nature Computational Science team.

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Supplementary information

Supplementary Information

Supplementary Sections 1–11, Figs. 1–14, Tables 1–4, Algorithm 1 and references.

Source data

Source Data Fig. 2

QM9 benchmark results.

Source Data Fig. 3

Nanocluster benchmark results.

Source Data Fig. 4

Azobenzene benchmark results.

Source Data Fig. 5

Bond-stretching benchmark results.

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Venturella, C., Li, J., Hillenbrand, C. et al. Unified deep learning framework for many-body quantum chemistry via Green’s functions. Nat Comput Sci 5, 502–513 (2025). https://doi.org/10.1038/s43588-025-00810-z

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