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Structural constraint integration in a generative model for the discovery of quantum materials

Nature Materials (2025)Cite this article

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Abstract

Billions of organic molecules have been computationally generated, yet functional inorganic materials remain scarce due to limited data and structural complexity. Here we introduce Structural Constraint Integration in a GENerative model (SCIGEN), a framework that enforces geometric constraints, such as honeycomb and kagome lattices, within diffusion-based generative models to discover stable quantum materials candidates. SCIGEN enables conditional sampling from the original distribution, preserving output validity while guiding structural motifs. This approach generates ten million inorganic compounds with Archimedean and Lieb lattices, over 10% of which pass multistage stability screening. High-throughput density functional theory calculations on 26,000 candidates shows over 95% convergence and 53% structural stability. A graph neural network classifier detects magnetic ordering in 41% of relaxed structures. Furthermore, we synthesize and characterize two predicted materials, TiPd0.22Bi0.88 and Ti0.5Pd1.5Sb, which display paramagnetic and diamagnetic behaviour, respectively. Our results indicate that SCIGEN provides a scalable path for generating quantum materials guided by lattice geometry.

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Fig. 1: Schematic overview of material generation with geometric patterns as constraints.
Fig. 2: Generated materials with three primary types of ALs.
Fig. 3: Generated materials with other AL structures.
Fig. 4: Generated materials of a Lieb-like lattice.

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Data availability

We have compiled a comprehensive database of AL materials generated by SCIGEN. The dataset provides the folders of all generated materials (10.06 million), the materials that survived after the four-stage prescreening process (1.01 million materials) and DFT-relaxed structures (24,743). The folder with DFT calculation contains materials structures before and after relaxation. The Supplementary Dataset is available from figshare via https://doi.org/10.6084/m9.figshare.c.7283062 (ref. 50.) Source data are provided with this paper.

Code availability

The source code is available from GitHub via https://github.com/RyotaroOKabe/SCIGEN.

Change history

  • 28 October 2025

    In the version of this article initially published, the Supplementary Data file was mislabeled, and is now amended in the HTML version of the article.

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Acknowledgements

R.O. and M.L. thank C. Batista, A. Christianson, F. Frenkel, A. May, R. Moore, B. Ortiz and F. Ronning for helpful discussions. R.O. acknowledges support from the US Department of Energy (DOE), Office of Science (SC), Basic Energy Sciences (BES), award number DE-SC0021940 and the Heiwa Nakajima Foundation. A.C. acknowledges support from National Science Foundation (NSF) Designing Materials to Revolutionize and Engineer Our Future (DMREF) Program with award number DMR-2118448. B.H. and Y.C. are partially supported by the Artificial Intelligence Initiative as part of the Laboratory Directed Research and Development (LDRD) program of Oak Ridge National Laboratory (ORNL), managed by UT-Battelle, LLC, for the US Department of Energy under contract DE-AC05-00OR22725. This research used resources of the National Energy Research Scientific Computing Center (NERSC), a Department of Energy Office of Science User Facility using NERSC award DDR-ERCAP0030758. Computing resources for a portion of the work were made available through the VirtuES project, funded by the LDRD Program and Compute and Data Environment for Science (CADES) at ORNL. Another portion of simulation results were obtained using the Frontera computing system at the Texas Advanced Computing Center. W.X. and R.C. were supported by the Department of Energy, grant DE-FG02-98ER45706. W.X. and R.C. thank G. J. Miller for offering clusters to perform LMTO calculations. M.L. acknowledges the support from NSF ITE-2345084, the Class of 1947 Career Development Chair and support from R. Wachnik.

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Authors and Affiliations

  1. Quantum Measurement Group, Massachusetts Institute of Technology, Cambridge, MA, USA

    Ryotaro Okabe, Mouyang Cheng, Abhijatmedhi Chotrattanapituk, Manasi Mandal, Kiran Mak, Denisse Córdova Carrizales, Nguyen Tuan Hung & Mingda Li

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

    Ryotaro Okabe

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

    Mouyang Cheng & Kiran Mak

  4. Center for Computational Science & Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

    Mouyang Cheng

  5. Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA

    Abhijatmedhi Chotrattanapituk, Xiang Fu & Tommi S. Jaakkola

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

    Manasi Mandal, Denisse Córdova Carrizales, Nguyen Tuan Hung & Mingda Li

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

    Kiran Mak

  8. Frontier Research Institute for Interdisciplinary Sciences, Tohoku University, Sendai, Japan

    Nguyen Tuan Hung

  9. Chemical Spectroscopy Group, Spectroscopy Section, Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA

    Bowen Han & Yongqiang Cheng

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

    Yao Wang

  11. Department of Chemistry, Michigan State University, East Lansing, MI, USA

    Weiwei Xie

  12. Department of Chemistry, Princeton University, Princeton, NJ, USA

    Robert J. Cava

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Contributions

R.O. led the project, developed the framework, implemented the code, trained the generative model and constructed the database. M.C. performed DFT calculations for electronic band structures and prepared related figures. A.C. developed the theoretical proof of our proposed method. N.T.H., B.H. and Y.C. performed DFT structural relaxations. M.M. carried out an analysis of experimental data. K.M. analysed the generated materials dataset. W.X. and R.J.C. performed experimental synthesis and characterization. Y.W. contributed to the establishment of evaluation metrics and proposal writing for computational resources. X.F. and T.S.J. contributed to method discussions. M.L. supervised the overall project. R.O., M.C., A.C., M.M., K.M., D.C.C., Y.C. and M.L. contributed to writing the manuscript.

Corresponding authors

Correspondence to Ryotaro Okabe, Weiwei Xie, Yongqiang Cheng or Mingda Li.

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Nature Materials thanks the anonymous reviewers for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Discussion, Figs. 1–28 and Tables 1–3.

Supplementary Data

Supplementary PDF file (532 pages) for generated materials after structure relaxation (24k).

Source data

Source Data Fig. 2

a–c, CIF files of the presented materials. d,e, Raw data for bar charts.

Source Data Fig. 3

a–g, CIF files of the presented materials.

Source Data Fig. 4

c,d, CIF files of the presented materials. c, Raw data for subplots.

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Okabe, R., Cheng, M., Chotrattanapituk, A. et al. Structural constraint integration in a generative model for the discovery of quantum materials. Nat. Mater. (2025). https://doi.org/10.1038/s41563-025-02355-y

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