Abstract
Nanomaterials with high-index facets have desirable properties but are often challenging to synthesize. One way to realize such structures is by incorporating guest metal or metalloid atoms that can stabilize high-index facets by influencing surface energies. However, the effect of different guest atoms can vary substantially, and the vast parameter set (possible combinations of host nanoparticles and guest species) makes a trial-and-error experimental approach to explore every combination impractical. Here we report a data-driven approach incorporating high-throughput density functional theory calculations to assess surface energies of low- and high-index facets of nanoparticles (9 transition metals) with surfaces modified by 13 guest atoms. Machine-learning techniques are then used to understand the critical features leading to energetically favoured high-index facet formation in the context of tetrahexahedron. The predictions are validated by chemical synthesis, demonstrating the efficacy of this approach in accelerating the synthesis of tetrahexahedron materials with exposed {210} facets.

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Data availability
The data supporting the findings of the study are available in the paper and its Supplementary Information. Source data are provided with this paper. All DFT calculation data are published in the OQMD (https://oqmd.org).
Code availability
The code used in this work is deposited in Github (https://github.com/dohunkang/HTDFT_THH).
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Acknowledgements
We thank T. Sengupta (Northwestern University) for professional editorial advice. Research was sponsored by the Army Research Office under grants W911NF-23-1-0141 and W911NF-23-1-0285, the Toyota Research Institute, Inc., and the Sherman Fairchild Foundation, Inc. D.K. acknowledges funding from the International Institute for Nanotechnology. Z.Y. and D.K. acknowledge partial support from the Predictive Science and Engineering Design (PSED) programme at Northwestern University. J.S. acknowledges support from the MRSEC programme (DMR-1720139) at the Materials Research Center of Northwestern University. This work made use of the EPIC and BioCryo facilities of Northwestern University’s NUANCE Center, which has received support from the SHyNE Resource (NSF ECCS-2025633), the International Institute for Nanotechnology and Northwestern’s MRSEC programme (NSF DMR-1720139). We acknowledge the computational resources provided by the Quest high-performance computing facility at Northwestern University.
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C.A.M. and C.M.W. supervised the research. Z.Y. and B.S. performed materials synthesis, characterization and analysis. D.K. performed HF-DFT calculation and machine learning. J.S., J.H., Z.W. and L.H. participated in discussions and provided suggestions. All authors contributed to the writing.
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Nature Synthesis thanks Rao Huang, Tung-Han Yang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Alison Stoddart, in collaboration with the Nature Synthesis team.
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Ye, Z., Shen, B., Kang, D. et al. A data-driven approach for the guided regulation of exposed facets in nanoparticles. Nat. Synth 3, 922–929 (2024). https://doi.org/10.1038/s44160-024-00561-1
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DOI: https://doi.org/10.1038/s44160-024-00561-1
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