[{"fulldoi":"https://doi.org/10.1038/s41467-026-77117-8","date_published":"2026-09-01T00:00:00Z","oa":1,"publication_identifier":{"eissn":["2041-1723"]},"scopus_import":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"corr_author":"1","publication":"Nature Communications","researchdata_availability":"yes","article_number":"10382","title":"Hydrogen-helium immiscibility boundary in gas-giant planetary interiors from machine-learning molecular dynamics","day":"01","language":[{"iso":"eng"}],"acknowledged_ssus":[{"_id":"ScienComp"}],"pmid":1,"dataavailabilitystatement":"The training data, fitted MLPs, MLP molecular dynamics results, and source data underlying all figures and tables in the main text and Supplementary Information have been deposited in the Zenodo repository: https://doi.org/10.5281/zenodo.21632034. The data-analysis and plotting scripts used to generate the figures and tables in the main text and Supplementary Information are available in the GitHub repository: https://github.com/ChengUCB/HighPressure_HHe.","acknowledgement":"The authors are thankful to Armin Bergermann and Ronald Redmer for generously sharing AIMD trajectories and data, and for valuable discussions and feedback on the manuscript. The authors also acknowledge the research computing facilities provided by the high-performance computing (HPC) cluster at the Institute of Science and Technology Austria (ISTA), Berkeley Research Computing (BRC) at the University of California, Berkeley (UCB), and Lawrence Livermore National Laboratory (LLNL). B.C. was supported by the Laboratory Directed Research and Development (LDRD) Program at Lawrence Berkeley National Laboratory (LBNL) under project ID 110990-001. Part of this work was performed under the auspices of the U.S. Department of Energy by LLNL under Contract DE-AC52-07NA27344. S.H. was supported by the LDRD Program at LLNL under project tracking code 23-SI-006.","DOAJ_listed":"1","volume":17,"type":"journal_article","file":[{"success":1,"date_created":"2026-10-12T10:57:42Z","file_name":"2026_NatureComm_Wang.pdf","relation":"main_file","file_id":"23107","date_updated":"2026-10-12T10:57:42Z","content_type":"application/pdf","checksum":"f39b50a550623a65aea2405b527e068c","access_level":"open_access","creator":"dernst","file_size":1559219}],"article_type":"original","oa_version":"Published Version","_id":"23089","year":"2026","date_updated":"2026-10-12T11:00:16Z","publication_status":"published","month":"09","supplementarymaterial":"yes","external_id":{"pmid":["42816492"]},"quality_controlled":"1","status":"public","OA_place":"publisher","date_created":"2026-10-11T22:02:04Z","das_tickbox":"1","OA_type":"gold","citation":{"ista":"Wang X, Hamel S, Cheng B. 2026. Hydrogen-helium immiscibility boundary in gas-giant planetary interiors from machine-learning molecular dynamics. Nature Communications. 17, 10382.","short":"X. Wang, S. Hamel, B. Cheng, Nature Communications 17 (2026).","apa":"Wang, X., Hamel, S., &#38; Cheng, B. (2026). Hydrogen-helium immiscibility boundary in gas-giant planetary interiors from machine-learning molecular dynamics. <i>Nature Communications</i>. Springer Nature. <a href=\"https://doi.org/10.1038/s41467-026-77117-8\">https://doi.org/10.1038/s41467-026-77117-8</a>","ieee":"X. Wang, S. Hamel, and B. Cheng, “Hydrogen-helium immiscibility boundary in gas-giant planetary interiors from machine-learning molecular dynamics,” <i>Nature Communications</i>, vol. 17. Springer Nature, 2026.","ama":"Wang X, Hamel S, Cheng B. Hydrogen-helium immiscibility boundary in gas-giant planetary interiors from machine-learning molecular dynamics. <i>Nature Communications</i>. 2026;17. doi:<a href=\"https://doi.org/10.1038/s41467-026-77117-8\">10.1038/s41467-026-77117-8</a>","chicago":"Wang, Xiaoyu, Sebastien Hamel, and Bingqing Cheng. “Hydrogen-Helium Immiscibility Boundary in Gas-Giant Planetary Interiors from Machine-Learning Molecular Dynamics.” <i>Nature Communications</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1038/s41467-026-77117-8\">https://doi.org/10.1038/s41467-026-77117-8</a>.","mla":"Wang, Xiaoyu, et al. “Hydrogen-Helium Immiscibility Boundary in Gas-Giant Planetary Interiors from Machine-Learning Molecular Dynamics.” <i>Nature Communications</i>, vol. 17, 10382, Springer Nature, 2026, doi:<a href=\"https://doi.org/10.1038/s41467-026-77117-8\">10.1038/s41467-026-77117-8</a>."},"ddc":["540"],"intvolume":"        17","doi":"10.1038/s41467-026-77117-8","author":[{"first_name":"Xiaoyu","full_name":"Wang, Xiaoyu","last_name":"Wang","id":"8dff9c62-32b0-11ee-9fa8-fc73025e10f3"},{"last_name":"Hamel","full_name":"Hamel, Sebastien","first_name":"Sebastien"},{"last_name":"Cheng","id":"cbe3cda4-d82c-11eb-8dc7-8ff94289fcc9","orcid":"0000-0002-3584-9632","full_name":"Cheng, Bingqing","first_name":"Bingqing"}],"publisher":"Springer Nature","has_accepted_license":"1","department":[{"_id":"GradSch"},{"_id":"BiCh"}],"file_date_updated":"2026-10-12T10:57:42Z","article_processing_charge":"Yes","abstract":[{"lang":"eng","text":"The location of the hydrogen-helium (H/He) immiscibility boundary controls whether and where helium rain occurs in giant planets, yet it remains uncertain because high-pressure experiments are challenging and ab initio simulations are limited in system size and simulation time. We map this boundary by computing composition-dependent chemical potentials from large-scale molecular dynamics driven by machine learning potentials trained on three density functional approximations (PBE, vdW-DF, and the hybrid HSE). Across the pressure range of 100-1000 GPa, the demixing temperatures are typically  ~ 2000 K lower than previous ab initio simulations using small system sizes, and this discrepancy is larger than the estimated error from the chosen density functionals, machine learning potentials, neglect of nuclear quantum effects, and statistical uncertainties. Fitting the H/He mixing free energy to a Redlich-Kister regular solution model rationalizes the thermodynamic driving force for phase separation, and provides a predictive representation of the boundary. Comparing with current planetary interior profiles indicates that helium rain is plausible in Saturn but unlikely in the warmer interior of Jupiter. Our results narrow the uncertainty in the H/He immiscibility boundary and provide inputs for planetary models that couple demixing, heat transport, and composition gradients in gas giants."}]},{"publication_identifier":{"eissn":["1549-9626"],"issn":["1549-9618"]},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","scopus_import":"1","page":"12709-12724","corr_author":"1","fulldoi":"https://doi.org/10.1021/acs.jctc.5c01400","date_published":"2025-12-10T00:00:00Z","oa":1,"title":"A universal augmentation framework for long-range electrostatics in machine learning interatomic potentials","day":"10","researchdata_availability":"no","publication":"Journal of Chemical Theory and Computation","volume":21,"type":"journal_article","language":[{"iso":"eng"}],"pmid":1,"acknowledgement":"Research reported in this publication was supported by the National Institute Of General Medical Sciences of the National Institutes of Health under Award Number R35GM159986. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. D.K. and B.C. acknowledge funding from Toyota Research Institute Synthesis Advanced Research Challenge. T.J.I., D.S.K. and P.Z. acknowledge funding from BIDMaP Postdoctoral Fellowship. T.J.I. used resources of the National Energy Research Scientific Computing Center (NERSC), a Department of Energy Office of Science User Facility using NERSC award DOEERCAP0031751 ′GenAI@NERSC’. The authors thank Bowen Deng for valuable discussions on MatGL implementation, and thank Gabor Csanyi for stimulating discussions.","dataavailabilitystatement":"The training sets, training scripts, and trained potentials are available at https://github.com/ChengUCB/les_fit. The LES library is publicly available at https://github.com/ChengUCB/les. The CACE package with the LES implementation is available at https://github.com/BingqingCheng/cace. The MACE package with the LES implementation is available at https://github.com/ACEsuit/mace. The NequIP and Allegro LES extension package is available at https://github.com/ChengUCB/NequIP-LES. The MatGL package with the LES implementation is available at https://github.com/ChengUCB/matgl. The UMA package with the LES implementation is available at https://github.com/santi921/fairchem/tree/les_branch.","_id":"20926","oa_version":"Preprint","year":"2025","arxiv":1,"article_type":"original","month":"12","issue":"24","date_updated":"2026-08-07T09:35:25Z","publication_status":"published","status":"public","OA_place":"repository","date_created":"2026-01-04T23:01:33Z","das_tickbox":"1","OA_type":"green","supplementarymaterial":"no","external_id":{"arxiv":["2507.14302"],"pmid":["41368735 "]},"quality_controlled":"1","intvolume":"        21","doi":"10.1021/acs.jctc.5c01400","author":[{"last_name":"Kim","first_name":"Dongjin","full_name":"Kim, Dongjin"},{"full_name":"Wang, Xiaoyu","first_name":"Xiaoyu","id":"8dff9c62-32b0-11ee-9fa8-fc73025e10f3","last_name":"Wang"},{"last_name":"Vargas","first_name":"Santiago","full_name":"Vargas, Santiago"},{"first_name":"Peichen","full_name":"Zhong, Peichen","last_name":"Zhong"},{"full_name":"King, Daniel S.","first_name":"Daniel S.","last_name":"King"},{"full_name":"Inizan, Theo Jaffrelot","first_name":"Theo Jaffrelot","last_name":"Inizan"},{"id":"cbe3cda4-d82c-11eb-8dc7-8ff94289fcc9","orcid":"0000-0002-3584-9632","last_name":"Cheng","full_name":"Cheng, Bingqing","first_name":"Bingqing"}],"citation":{"apa":"Kim, D., Wang, X., Vargas, S., Zhong, P., King, D. S., Inizan, T. J., &#38; Cheng, B. (2025). A universal augmentation framework for long-range electrostatics in machine learning interatomic potentials. <i>Journal of Chemical Theory and Computation</i>. American Chemical Society. <a href=\"https://doi.org/10.1021/acs.jctc.5c01400\">https://doi.org/10.1021/acs.jctc.5c01400</a>","ama":"Kim D, Wang X, Vargas S, et al. A universal augmentation framework for long-range electrostatics in machine learning interatomic potentials. <i>Journal of Chemical Theory and Computation</i>. 2025;21(24):12709-12724. doi:<a href=\"https://doi.org/10.1021/acs.jctc.5c01400\">10.1021/acs.jctc.5c01400</a>","ieee":"D. Kim <i>et al.</i>, “A universal augmentation framework for long-range electrostatics in machine learning interatomic potentials,” <i>Journal of Chemical Theory and Computation</i>, vol. 21, no. 24. American Chemical Society, pp. 12709–12724, 2025.","chicago":"Kim, Dongjin, Xiaoyu Wang, Santiago Vargas, Peichen Zhong, Daniel S. King, Theo Jaffrelot Inizan, and Bingqing Cheng. “A Universal Augmentation Framework for Long-Range Electrostatics in Machine Learning Interatomic Potentials.” <i>Journal of Chemical Theory and Computation</i>. American Chemical Society, 2025. <a href=\"https://doi.org/10.1021/acs.jctc.5c01400\">https://doi.org/10.1021/acs.jctc.5c01400</a>.","mla":"Kim, Dongjin, et al. “A Universal Augmentation Framework for Long-Range Electrostatics in Machine Learning Interatomic Potentials.” <i>Journal of Chemical Theory and Computation</i>, vol. 21, no. 24, American Chemical Society, 2025, pp. 12709–24, doi:<a href=\"https://doi.org/10.1021/acs.jctc.5c01400\">10.1021/acs.jctc.5c01400</a>.","short":"D. Kim, X. Wang, S. Vargas, P. Zhong, D.S. King, T.J. Inizan, B. Cheng, Journal of Chemical Theory and Computation 21 (2025) 12709–12724.","ista":"Kim D, Wang X, Vargas S, Zhong P, King DS, Inizan TJ, Cheng B. 2025. A universal augmentation framework for long-range electrostatics in machine learning interatomic potentials. Journal of Chemical Theory and Computation. 21(24), 12709–12724."},"department":[{"_id":"GradSch"},{"_id":"BiCh"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2507.14302"}],"article_processing_charge":"No","abstract":[{"text":"Most current machine learning interatomic potentials (MLIPs) rely on short-range approximations, without explicit treatment of long-range electrostatics. To address this, we recently developed the Latent Ewald Summation (LES) method, which infers electrostatic interactions, polarization, and Born effective charges (BECs), just by learning from energy and force training data. Here, we present LES as a standalone library, compatible with any short-range MLIP, and demonstrate its integration with methods such as MACE, NequIP, Allegro, CACE, CHGNet, and UMA. We benchmark LES-enhanced models on distinct systems, including bulk water, polar dipeptides, and gold dimer adsorption on defective substrates, and show that LES not only captures correct electrostatics but also improves accuracy. Additionally, we scale LES to large and chemically diverse data by training MACELES-OFF on the SPICE set containing molecules and clusters, making a universal MLIP with electrostatics for organic systems, including biomolecules. MACELES-OFF is more accurate than its short-range counterpart (MACE-OFF) trained on the same data set, predicts dipoles and BECs reliably, and has better descriptions of bulk liquids. By enabling efficient long-range electrostatics without directly training on electrical properties, LES paves the way for electrostatic foundation MLIPs.","lang":"eng"}],"publisher":"American Chemical Society"},{"day":"14","article_number":"034111","title":"Integrating molecular dynamics simulations and experimental data for azeotrope predictions in binary mixtures","publication":"Journal of Chemical Physics","researchdata_availability":"no","corr_author":"1","related_material":{"link":[{"url":"https://github.com/Xiaoyu-Wang-Stone/Azeotrope_S0","relation":"software"}]},"publication_identifier":{"eissn":["1089-7690"],"issn":["0021-9606"]},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","scopus_import":"1","isi":1,"oa":1,"date_published":"2024-07-14T00:00:00Z","fulldoi":"https://doi.org/10.1063/5.0217232","arxiv":1,"year":"2024","oa_version":"Preprint","_id":"17278","article_type":"original","type":"journal_article","volume":161,"acknowledgement":"B.C. thanks Alessandro Laio, who introduced the phenomenon of azeotrope and suggested using the S0 method to compute it. B.C. and X.W. thank Felix Wodaczek for the insightful comments and suggestions on the manuscript. B.C. and X.W. acknowledge the resources provided by the Cambridge Tier-2 system operated by the University of Cambridge Research Computing Service, funded by EPSRC Tier-2 capital (Grant No. EP/P020259/1).","dataavailabilitystatement":"All simulation setups, analysis scripts, and raw data in the study are available in the SI repository https://github.com/Xiaoyu-Wang-Stone/Azeotrope_S0.","pmid":1,"language":[{"iso":"eng"}],"date_created":"2024-07-21T22:01:00Z","das_tickbox":"1","status":"public","quality_controlled":"1","supplementarymaterial":"no","external_id":{"arxiv":["2405.02216"],"isi":["001281819100016"],"pmid":["39007379"]},"month":"07","publication_status":"published","date_updated":"2026-08-07T10:38:59Z","issue":"3","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2405.02216","open_access":"1"}],"article_processing_charge":"No","abstract":[{"lang":"eng","text":"An azeotrope is a constant boiling point mixture, and its behavior is important for fluid separation processes. Predicting azeotropes from atomistic simulations is difficult due to the complexities and convergence problems of Monte Carlo and free-energy perturbation techniques. Here, we present a methodology for predicting the azeotropes of binary mixtures, which computes the compositional dependence of chemical potentials from molecular dynamics simulations using the S0 method and employs experimental boiling point and vaporization enthalpy data. Using this methodology, we reproduce the azeotropes, or lack thereof, in five case studies, including ethanol/water, ethanol/isooctane, methanol/water, hydrazine/water, and acetone/chloroform mixtures. We find that it is crucial to use the experimental boiling point and vaporization enthalpy for reliable azeotrope predictions, as empirical force fields are not accurate enough for these quantities. Finally, we use regular solution models to rationalize the azeotropes and reveal that they tend to form when the mixture components have similar boiling points and strong interactions."}],"department":[{"_id":"BiCh"},{"_id":"GradSch"}],"publisher":"AIP Publishing","author":[{"last_name":"Wang","id":"8dff9c62-32b0-11ee-9fa8-fc73025e10f3","full_name":"Wang, Xiaoyu","first_name":"Xiaoyu"},{"orcid":"0000-0002-3584-9632","id":"cbe3cda4-d82c-11eb-8dc7-8ff94289fcc9","last_name":"Cheng","first_name":"Bingqing","full_name":"Cheng, Bingqing"}],"doi":"10.1063/5.0217232","intvolume":"       161","citation":{"ieee":"X. Wang and B. Cheng, “Integrating molecular dynamics simulations and experimental data for azeotrope predictions in binary mixtures,” <i>Journal of Chemical Physics</i>, vol. 161, no. 3. AIP Publishing, 2024.","apa":"Wang, X., &#38; Cheng, B. (2024). Integrating molecular dynamics simulations and experimental data for azeotrope predictions in binary mixtures. <i>Journal of Chemical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0217232\">https://doi.org/10.1063/5.0217232</a>","ama":"Wang X, Cheng B. Integrating molecular dynamics simulations and experimental data for azeotrope predictions in binary mixtures. <i>Journal of Chemical Physics</i>. 2024;161(3). doi:<a href=\"https://doi.org/10.1063/5.0217232\">10.1063/5.0217232</a>","chicago":"Wang, Xiaoyu, and Bingqing Cheng. “Integrating Molecular Dynamics Simulations and Experimental Data for Azeotrope Predictions in Binary Mixtures.” <i>Journal of Chemical Physics</i>. AIP Publishing, 2024. <a href=\"https://doi.org/10.1063/5.0217232\">https://doi.org/10.1063/5.0217232</a>.","mla":"Wang, Xiaoyu, and Bingqing Cheng. “Integrating Molecular Dynamics Simulations and Experimental Data for Azeotrope Predictions in Binary Mixtures.” <i>Journal of Chemical Physics</i>, vol. 161, no. 3, 034111, AIP Publishing, 2024, doi:<a href=\"https://doi.org/10.1063/5.0217232\">10.1063/5.0217232</a>.","short":"X. Wang, B. Cheng, Journal of Chemical Physics 161 (2024).","ista":"Wang X, Cheng B. 2024. Integrating molecular dynamics simulations and experimental data for azeotrope predictions in binary mixtures. Journal of Chemical Physics. 161(3), 034111."}}]