The overall development of the machine learning force field (MLFF) has advanced rapidly, with a wide range of models emerging in recent years. However, some fundamental questions remain underexplored, such as why certain systems are intrinsically more difficult to train than others. Understanding this question can help us to propose different models and prepare appropriate datasets for different situations. We constructed Metal-43, a high-quality dataset comprising elemental structures of 43 metallic elements. Through systematic analysis, we reveal regular trends of fitting accuracies of these elemental metals in the periodic table. Unlike previous approaches that generally attribute fitting challenges to a vague notion of a “complex potential energy surface (PES)”, which is almost a synonym of the fitting difficulty, we provide a physical picture which connects the Fermi surface complexity to this complexity of PES. Furthermore, we demonstrate that current MLFF models still face clear limitations in capturing the complex PES even for elemental materials. These findings can provide a theoretical foundation and directional guidance for the development of more general and accurate MLFF models in the future.
{"title":"Origin of the machine learning forces field errors across metal elements","authors":"Xingze Geng, Wentao Zhang, Lin-Wang Wang, Xiangying Meng","doi":"10.1038/s41524-026-01977-3","DOIUrl":"https://doi.org/10.1038/s41524-026-01977-3","url":null,"abstract":"The overall development of the machine learning force field (MLFF) has advanced rapidly, with a wide range of models emerging in recent years. However, some fundamental questions remain underexplored, such as why certain systems are intrinsically more difficult to train than others. Understanding this question can help us to propose different models and prepare appropriate datasets for different situations. We constructed Metal-43, a high-quality dataset comprising elemental structures of 43 metallic elements. Through systematic analysis, we reveal regular trends of fitting accuracies of these elemental metals in the periodic table. Unlike previous approaches that generally attribute fitting challenges to a vague notion of a “complex potential energy surface (PES)”, which is almost a synonym of the fitting difficulty, we provide a physical picture which connects the Fermi surface complexity to this complexity of PES. Furthermore, we demonstrate that current MLFF models still face clear limitations in capturing the complex PES even for elemental materials. These findings can provide a theoretical foundation and directional guidance for the development of more general and accurate MLFF models in the future.","PeriodicalId":19342,"journal":{"name":"npj Computational Materials","volume":"1 1","pages":""},"PeriodicalIF":9.7,"publicationDate":"2026-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146057181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Colossal magnetoresistance (CMR) is typically observed in manganites and magnetic semiconductors, marked by a resistivity peak near the magnetic transition temperature that is significantly suppressed by an applied magnetic field, commonly referred to as peak-type CMR. This type of CMR has attracted extensive research efforts over the past decades. However, in some materials such as Mn3Si2Te6, both peak-type and upturn-type CMR coexist—the latter characterized by a sharp resistivity upturn at low temperatures that is also strongly suppressed by an external field. Research on the coexistence of these two types of CMR remains relatively unexplored. In our work, we propose a theoretical framework to unravel the mechanisms underlying the above mentioned CMR phenomenon in magnetic semiconductors, and apply it to the ferrimagnetic semiconductor Mn3Si2Te6. The experimentally observed ρ(B, T) behaviors are accurately reproduced, including the upturn-type CMR, peak-type CMR, and movement of Tc (or resistivity peak) with fields. Additionally, the suppression of Tc and resistivity with increasing direct currents, possibly associated with current control of the chiral orbital current (COC) state in the previous work, can also be reproduced within our framework by properly accounting for the Joule heating effects. Our work provides a new perspective for quantitatively calculating and analyzing the unusual resistivity responses to temperature, field, and current in magnetic semiconductors.
{"title":"Colossal magnetoresistance and unusual resistivity behaviors in magnetic semiconductors: Mn3Si2Te6 as a case study","authors":"Zhihao Liu, Zhong Fang, Hongming Weng, Quansheng Wu","doi":"10.1038/s41524-026-01963-9","DOIUrl":"https://doi.org/10.1038/s41524-026-01963-9","url":null,"abstract":"Colossal magnetoresistance (CMR) is typically observed in manganites and magnetic semiconductors, marked by a resistivity peak near the magnetic transition temperature that is significantly suppressed by an applied magnetic field, commonly referred to as peak-type CMR. This type of CMR has attracted extensive research efforts over the past decades. However, in some materials such as Mn3Si2Te6, both peak-type and upturn-type CMR coexist—the latter characterized by a sharp resistivity upturn at low temperatures that is also strongly suppressed by an external field. Research on the coexistence of these two types of CMR remains relatively unexplored. In our work, we propose a theoretical framework to unravel the mechanisms underlying the above mentioned CMR phenomenon in magnetic semiconductors, and apply it to the ferrimagnetic semiconductor Mn3Si2Te6. The experimentally observed ρ(B, T) behaviors are accurately reproduced, including the upturn-type CMR, peak-type CMR, and movement of Tc (or resistivity peak) with fields. Additionally, the suppression of Tc and resistivity with increasing direct currents, possibly associated with current control of the chiral orbital current (COC) state in the previous work, can also be reproduced within our framework by properly accounting for the Joule heating effects. Our work provides a new perspective for quantitatively calculating and analyzing the unusual resistivity responses to temperature, field, and current in magnetic semiconductors.","PeriodicalId":19342,"journal":{"name":"npj Computational Materials","volume":"86 1","pages":""},"PeriodicalIF":9.7,"publicationDate":"2026-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146057183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-26DOI: 10.1038/s41524-026-01971-9
Jiaxiang Li, Junwei Feng, Jie Luo, Bowen Jiang, Xiangyu Zheng, Qigang Song, Jian Lv, Keith Butler, Hanyu Liu, Congwei Xie, Yu Xie, Yanming Ma
Machine learning interatomic potentials have revolutionized complex materials design by enabling rapid exploration of material configurational spaces via crystal structure prediction with ab initio accuracy. However, critical challenges persist in ensuring robust generalization to unknown structures and minimizing the requirement for substantial expert knowledge and time-consuming manual interventions. Here, we propose an automated crystal structure prediction framework built upon the attention-coupled neural network potential to address these limitations. The generalizability of the potential is achieved by sampling regions across the local minima of the potential energy surface, where the self-evolving pipeline autonomously refines the potential iteratively while minimizing human intervention. The workflow is validated on Mg-Ca-H ternary and Be-P-N-O quaternary systems by exploring nearly 10 million configurations, demonstrating substantial speedup compared to first-principles calculations. These results underscore the effectiveness of our approach in accelerating the exploration and discovery of complex multi-component functional materials.
{"title":"Self-optimizing machine learning potential assisted automated workflow for highly efficient complex systems material design","authors":"Jiaxiang Li, Junwei Feng, Jie Luo, Bowen Jiang, Xiangyu Zheng, Qigang Song, Jian Lv, Keith Butler, Hanyu Liu, Congwei Xie, Yu Xie, Yanming Ma","doi":"10.1038/s41524-026-01971-9","DOIUrl":"https://doi.org/10.1038/s41524-026-01971-9","url":null,"abstract":"Machine learning interatomic potentials have revolutionized complex materials design by enabling rapid exploration of material configurational spaces via crystal structure prediction with ab initio accuracy. However, critical challenges persist in ensuring robust generalization to unknown structures and minimizing the requirement for substantial expert knowledge and time-consuming manual interventions. Here, we propose an automated crystal structure prediction framework built upon the attention-coupled neural network potential to address these limitations. The generalizability of the potential is achieved by sampling regions across the local minima of the potential energy surface, where the self-evolving pipeline autonomously refines the potential iteratively while minimizing human intervention. The workflow is validated on Mg-Ca-H ternary and Be-P-N-O quaternary systems by exploring nearly 10 million configurations, demonstrating substantial speedup compared to first-principles calculations. These results underscore the effectiveness of our approach in accelerating the exploration and discovery of complex multi-component functional materials.","PeriodicalId":19342,"journal":{"name":"npj Computational Materials","volume":"67 1","pages":""},"PeriodicalIF":9.7,"publicationDate":"2026-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146048274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-24DOI: 10.1038/s41524-026-01973-7
Francesco Belli, Eva Zurek, Ion Errea
Quantum nuclear effects (QNEs) can significantly alter a material’s crystal structure and phonon spectra, impacting properties such as thermal conductivity and superconductivity. However, predicting a priori whether these effects will enhance or suppress superconductivity, or destabilize a structure, remains a grand challenge. Herein, we address this unresolved problem by introducing two possible descriptors, based upon the integrated crystal orbital bonding index (iCOBI) or the bond valence function, to predict the influence of QNEs on a crystal lattice’s dynamic stability, phonon spectra and superconducting properties. We find that structures with atoms in symmetric chemical bonding environments exhibit greater resilience to structural perturbations induced by QNEs, while those with atoms in asymmetric bonding environments are more susceptible to structural alterations, resulting in enhanced superconducting critical temperatures.
{"title":"A chemical bonding based descriptor for predicting the role of anharmonicity induced by quantum nuclear effects in hydride superconductors","authors":"Francesco Belli, Eva Zurek, Ion Errea","doi":"10.1038/s41524-026-01973-7","DOIUrl":"https://doi.org/10.1038/s41524-026-01973-7","url":null,"abstract":"Quantum nuclear effects (QNEs) can significantly alter a material’s crystal structure and phonon spectra, impacting properties such as thermal conductivity and superconductivity. However, predicting a priori whether these effects will enhance or suppress superconductivity, or destabilize a structure, remains a grand challenge. Herein, we address this unresolved problem by introducing two possible descriptors, based upon the integrated crystal orbital bonding index (iCOBI) or the bond valence function, to predict the influence of QNEs on a crystal lattice’s dynamic stability, phonon spectra and superconducting properties. We find that structures with atoms in symmetric chemical bonding environments exhibit greater resilience to structural perturbations induced by QNEs, while those with atoms in asymmetric bonding environments are more susceptible to structural alterations, resulting in enhanced superconducting critical temperatures.","PeriodicalId":19342,"journal":{"name":"npj Computational Materials","volume":"31 1","pages":""},"PeriodicalIF":9.7,"publicationDate":"2026-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146043183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-23DOI: 10.1038/s41524-025-01940-8
Pierre-Paul De Breuck, Hashim A. Piracha, Gian-Marco Rignanese, Miguel A. L. Marques
Materials play a critical role in various technological applications. Identifying and enumerating stable compounds—those near the convex hull—is therefore essential. Despite recent progress, generative models either have a relatively low rate of stable compounds, are computationally expensive, or lack symmetry. In this work we present Matra-Genoa, an autoregressive transformer model built on invertible tokenized representations of symmetrized crystals, including free coordinates. This approach enables sampling from a hybrid action space. The model is trained across the periodic table and space groups and can be conditioned on specific properties. We demonstrate its ability to generate stable, novel, and unique crystal structures by conditioning on the distance to the convex hull. Resulting structures are 8 times more likely to be stable than baselines using PyXtal with charge compensation, while maintaining high computational efficiency. We also release a dataset of 3 million unique crystals generated by our method, including 4000 compounds verified by density-functional theory to be within 0.001 eV/atom of the convex hull.
{"title":"A generative material transformer using Wyckoff representation","authors":"Pierre-Paul De Breuck, Hashim A. Piracha, Gian-Marco Rignanese, Miguel A. L. Marques","doi":"10.1038/s41524-025-01940-8","DOIUrl":"https://doi.org/10.1038/s41524-025-01940-8","url":null,"abstract":"Materials play a critical role in various technological applications. Identifying and enumerating stable compounds—those near the convex hull—is therefore essential. Despite recent progress, generative models either have a relatively low rate of stable compounds, are computationally expensive, or lack symmetry. In this work we present Matra-Genoa, an autoregressive transformer model built on invertible tokenized representations of symmetrized crystals, including free coordinates. This approach enables sampling from a hybrid action space. The model is trained across the periodic table and space groups and can be conditioned on specific properties. We demonstrate its ability to generate stable, novel, and unique crystal structures by conditioning on the distance to the convex hull. Resulting structures are 8 times more likely to be stable than baselines using PyXtal with charge compensation, while maintaining high computational efficiency. We also release a dataset of 3 million unique crystals generated by our method, including 4000 compounds verified by density-functional theory to be within 0.001 eV/atom of the convex hull.","PeriodicalId":19342,"journal":{"name":"npj Computational Materials","volume":"1 1","pages":""},"PeriodicalIF":9.7,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033776","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"aLLoyM: a large language model for alloy phase diagram prediction","authors":"Yuna Oikawa, Guillaume Deffrennes, Rintaro Shimayoshi, Taichi Abe, Ryo Tamura, Koji Tsuda","doi":"10.1038/s41524-026-01966-6","DOIUrl":"https://doi.org/10.1038/s41524-026-01966-6","url":null,"abstract":"","PeriodicalId":19342,"journal":{"name":"npj Computational Materials","volume":"50 1","pages":""},"PeriodicalIF":9.7,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033777","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-22DOI: 10.1038/s41524-026-01961-x
Maksim Sokolov, Kai S. Exner
Oxygen evolution reaction (OER)—2H 2 O → O 2 + 4H + + 4e − —remains the primary bottleneck in electrochemical water splitting for green hydrogen production. Pentlandite, a bimetallic chalcogenide mineral, has recently shown promise under alkaline conditions, although the elementary processes at the atomic level remain largely unclear. Using density functional theory calculations, we report three generations of pentlandite surface models with varying complexity to decipher the contributions of Fe and Ni sites to OER activity. The first-generation model is based on the pristine pentlandite surface and purports that no OER catalytic activity is observed. The second-generation model takes surface coverage by adsorbed oxygen or hydroxyl into account and suggests that Fe corresponds to the active site in the OER. In contrast, the third-generation model considers not only the surface coverage but also the surface oxidation of pentlandite by exchanging lattice sulfur atoms with oxygen, as observed experimentally. Only this extension shows that both Fe and Ni sites are active centers for OER and that Fe and Ni exhibit distinct limiting steps depending on applied bias, as determined by a degree of span control analysis. Our results demonstrate that when assessing pentlandite with regard to OER, surface oxidation and coverage effects must be explicitly considered in addition to the mechanistic breadth. The reported modeling approach provides the basis for the rational design of next-generation catalysts by highlighting the importance of considering surface oxidation in the theoretical description of energy conversion processes.
{"title":"Unraveling the role of Fe and Ni in oxygen evolution reaction on pentlandite using three generations of computational surface models","authors":"Maksim Sokolov, Kai S. Exner","doi":"10.1038/s41524-026-01961-x","DOIUrl":"https://doi.org/10.1038/s41524-026-01961-x","url":null,"abstract":"Oxygen evolution reaction (OER)—2H <jats:sub>2</jats:sub> O → O <jats:sub>2</jats:sub> + 4H <jats:sup>+</jats:sup> + 4e <jats:sup>−</jats:sup> —remains the primary bottleneck in electrochemical water splitting for green hydrogen production. Pentlandite, a bimetallic chalcogenide mineral, has recently shown promise under alkaline conditions, although the elementary processes at the atomic level remain largely unclear. Using density functional theory calculations, we report three generations of pentlandite surface models with varying complexity to decipher the contributions of Fe and Ni sites to OER activity. The first-generation model is based on the pristine pentlandite surface and purports that no OER catalytic activity is observed. The second-generation model takes surface coverage by adsorbed oxygen or hydroxyl into account and suggests that Fe corresponds to the active site in the OER. In contrast, the third-generation model considers not only the surface coverage but also the surface oxidation of pentlandite by exchanging lattice sulfur atoms with oxygen, as observed experimentally. Only this extension shows that both Fe and Ni sites are active centers for OER and that Fe and Ni exhibit distinct limiting steps depending on applied bias, as determined by a degree of span control analysis. Our results demonstrate that when assessing pentlandite with regard to OER, surface oxidation and coverage effects must be explicitly considered in addition to the mechanistic breadth. The reported modeling approach provides the basis for the rational design of next-generation catalysts by highlighting the importance of considering surface oxidation in the theoretical description of energy conversion processes.","PeriodicalId":19342,"journal":{"name":"npj Computational Materials","volume":"273 1","pages":""},"PeriodicalIF":9.7,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-21DOI: 10.1038/s41524-025-01513-9
Cono Di Paola, Evgeny Plekhanov, Michal Krompiec, Chandan Kumar, Emanuele Marsili, Fengmin Du, Daniel Weber, Jasper Simon Krauser, Elvira Shishenina, David Muñoz Ramo
{"title":"Publisher Correction: Platinum-based catalysts for oxygen reduction reaction simulated with a quantum computer","authors":"Cono Di Paola, Evgeny Plekhanov, Michal Krompiec, Chandan Kumar, Emanuele Marsili, Fengmin Du, Daniel Weber, Jasper Simon Krauser, Elvira Shishenina, David Muñoz Ramo","doi":"10.1038/s41524-025-01513-9","DOIUrl":"https://doi.org/10.1038/s41524-025-01513-9","url":null,"abstract":"","PeriodicalId":19342,"journal":{"name":"npj Computational Materials","volume":"102 1","pages":""},"PeriodicalIF":9.7,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033790","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-21DOI: 10.1038/s41524-025-01755-7
Elena Gazzarrini, Rose K. Cersonsky, Marnik Bercx, Carl S. Adorf, Nicola Marzari
The Rule of Four captures the observation that in experimentally known inorganic stoichiometric compounds the number of atoms in the primitive cell shows an unusual abundance of cases where that number is a multiple of four. The previous comment provides some insightful and appealing explanations of this abundance, some of which we had already considered, and in response we provide further data and analysis. We do not find confirmations of these explanations in our data, despite structural and compositional modulations, and suggest that the origins of the Rule of Four remain elusive, and open for further investigation.
{"title":"Reply to: An explanation for the Rule of Four in Inorganic Materials","authors":"Elena Gazzarrini, Rose K. Cersonsky, Marnik Bercx, Carl S. Adorf, Nicola Marzari","doi":"10.1038/s41524-025-01755-7","DOIUrl":"https://doi.org/10.1038/s41524-025-01755-7","url":null,"abstract":"The Rule of Four captures the observation that in experimentally known inorganic stoichiometric compounds the number of atoms in the primitive cell shows an unusual abundance of cases where that number is a multiple of four. The previous comment provides some insightful and appealing explanations of this abundance, some of which we had already considered, and in response we provide further data and analysis. We do not find confirmations of these explanations in our data, despite structural and compositional modulations, and suggest that the origins of the Rule of Four remain elusive, and open for further investigation.","PeriodicalId":19342,"journal":{"name":"npj Computational Materials","volume":"63 1","pages":""},"PeriodicalIF":9.7,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146006142","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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