Moment Tensor Machine-Learning Potential: Development and Applications
Received date: 2025-09-28
Revised date: 2025-11-18
Online published: 2026-01-12
Supported by
National Natural Science Foundation of China(52422112);National Natural Science Foundation of China(52188101);Advanced Materials-National Science and Technology Major Project(2025ZD0618901);Strategic Priority Research Program of Chinese Academy of Sciences(XDA041040402);Science and Technology Major Project of Liaoning Province(2024JH1/11700032)
In recent years, artificial intelligence-based computational materials modeling has advanced rapidly, with machine learning potentials (MLPs) emerging as a central research direction. By fitting ab initio reference data into continuous and differentiable functional forms, MLPs retain near-quantum-mechanical accuracy while substantially reducing computational cost. This capability alleviates the limitations of ab initio methods in simulations of large-scale systems and long timescales. Consequently, MLPs serve as a critical link between atomistic simulations and macroscopic material property predictions, enabling new possibilities in computational materials science. This review focuses on the moment tensor potential (MTP), which offers an excellent balance between accuracy and computational efficiency. This paper provides a systematic overview from three perspectives: theoretical framework, algorithmic optimization, and practical applications. First, the mathematical foundations and design principles of MTP are analyzed. Next, strategies for improving accuracy and accelerating computation are discussed. Finally, representative case studies on typical material systems are presented to demonstrate the performance of MTP, and future development directions are outlined.
CHEN Xing-Qiu , WANG Jiantao , LIU Peitao . Moment Tensor Machine-Learning Potential: Development and Applications[J]. Acta Metall Sin, 2026 , 62(5) : 785 -802 . DOI: 10.11900/0412.1961.2025.00289
| [1] | Agrawal A, Choudhary A. Perspective: Materials informatics and big data: Realization of the “fourth paradigm” of science in materials science [J]. APL Mater., 2016, 4: 053208 |
| [2] | Meyer M, Pontikis V. Computer Simulation in Materials Science [M]. Dordrecht: Springer, 1991, 205: 3 |
| [3] | Hafner J. Atomic-scale computational materials science [J]. Acta Mater., 2000, 48: 71 |
| [4] | Steinhauser M O, Hiermaier S. A review of computational methods in materials science: Examples from shock-wave and polymer physics [J]. Int. J. Mol. Sci., 2009, 10: 5135 |
| [5] | Daw M S, Baskes M I. Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals [J]. Phys. Rev., 1984, 29B: 6443 |
| [6] | Finnis M W, Sinclair J E. A simple empirical N-body potential for transition metals [J]. Philos. Mag., 1984, 50A: 45 |
| [7] | Baskes M I. Modified embedded-atom potentials for cubic materials and impurities [J]. Phys. Rev., 1992, 46B: 2727 |
| [8] | Tersoff J. New empirical approach for the structure and energy of covalent systems [J]. Phys. Rev., 1988, 37B: 6991 |
| [9] | Blank T B, Brown S D, Calhoun A W, et al. Neural network models of potential energy surfaces [J]. J. Chem. Phys., 1995, 103: 4129 |
| [10] | Brown D F R, Gibbs M N, Clary D C. Combining ab initio computations, neural networks, and diffusion Monte Carlo: An efficient method to treat weakly bound molecules [J]. J. Chem. Phys., 1996, 105: 7597 |
| [11] | Gassner H, Probst M, Lauenstein A, et al. Representation of intermolecular potential functions by neural networks [J]. J. Phys. Chem., 1998, 102A: 4596 |
| [12] | Prudente F V, Acioli P H, Neto J J S. The fitting of potential energy surfaces using neural networks: Application to the study of vibrational levels of H 3 + [J]. J. Chem. Phys., 1998, 109: 8801 |
| [13] | Huang X C, Braams B J, Bowman J M. Ab initio potential energy and dipole moment surfaces for H 5 O 2 + [J]. J. Chem. Phys., 2005, 122: 044308 |
| [14] | Manzhos S, Carrington T. Using neural networks to represent potential surfaces as sums of products [J]. J. Chem. Phys., 2006, 125: 194105 |
| [15] | Behler J, Parrinello M. Generalized neural-network representation of high-dimensional potential-energy surfaces [J]. Phys. Rev. Lett., 2007, 98: 146401 |
| [16] | Bartók A P, Payne M C, Kondor R, et al. Gaussian approximation potentials: The accuracy of quantum mechanics, without the electrons [J]. Phys. Rev. Lett., 2010, 104: 136403 |
| [17] | Bart?k A P. The gaussian approximation potential: An interatomic potential derived from first principles quantum mechanics [D]. Berlin, Heidelberg: Springer, 2010 |
| [18] | Bartók A P, Kondor R, Csányi G. On representing chemical environments [J]. Phys. Rev., 2013, 87B: 184115 |
| [19] | Jinnouchi R, Karsai F, Kresse G. On-the-fly machine learning force field generation: Application to melting points [J]. Phys. Rev., 2019, 100B: 014105 |
| [20] | Jinnouchi R, Lahnsteiner J, Karsai F, et al. Phase transitions of hybrid perovskites simulated by machine-learning force fields trained on the fly with Bayesian inference [J]. Phys. Rev. Lett., 2019, 122: 225701 |
| [21] | Shapeev A V. Moment tensor potentials: A class of systematically improvable interatomic potentials [J]. Multiscale Model. Simul., 2016, 14: 1153 |
| [22] | Thompson A P, Swiler L P, Trott C R, et al. Spectral neighbor analysis method for automated generation of quantum-accurate interatomic potentials [J]. J. Comput. Phys., 2015, 285: 316 |
| [23] | Wood M A, Thompson A P. Extending the accuracy of the SNAP interatomic potential form [J]. J. Chem. Phys., 2018, 148: 241721 |
| [24] | Drautz R. Atomic cluster expansion for accurate and transferable interatomic potentials [J]. Phys. Rev., 2019, 99B: 014104 |
| [25] | Huang S D, Shang C, Kang P L, et al. LASP: Fast global potential energy surface exploration [J]. WIREs Comput. Mol. Sci., 2019, 9: e1415 |
| [26] | Kang P L, Shang C, Liu Z P. Recent implementations in LASP 3.0: Global neural network potential with multiple elements and better long-range description [J]. Chin. J. Chem. Phys., 2021, 34: 583 |
| [27] | Kang P L, Shang C, Liu Z P. Glucose to 5-hydroxymethylfurfural: Origin of site-selectivity resolved by machine learning based reaction sampling [J]. J. Am. Chem. Soc., 2019, 141: 20525 |
| [28] | Ma S C, Huang S D, Liu Z P. Dynamic coordination of cations and catalytic selectivity on zinc-chromium oxide alloys during syngas conversion [J]. Nat. Catal., 2019, 2: 671 |
| [29] | Huang S D, Shang C, Kang P L, et al. Atomic structure of boron resolved using machine learning and global sampling [J]. Chem. Sci., 2018, 9: 8644 |
| [30] | Huang S D, Shang C, Zhang X J, et al. Material discovery by combining stochastic surface walking global optimization with a neural network [J]. Chem. Sci., 2017, 8: 6327 |
| [31] | Eckhoff M, Behler J. High-dimensional neural network potentials for magnetic systems using spin-dependent atom-centered symmetry functions [J]. npj Comput. Mater., 2021, 7: 170 |
| [32] | Behler J. Four generations of high-dimensional neural network potentials [J]. Chem. Rev., 2021, 121: 10037 |
| [33] | Ko T W, Finkler J A, Goedecker S, et al. A fourth-generation high-dimensional neural network potential with accurate electrostatics including non-local charge transfer [J]. Nat. Commun., 2021, 12: 398 |
| [34] | Han J Q, Zhang L F, Car R, et al. Deep potential: A general representation of a many-body potential energy surface [J]. Commun. Comput. Phys., 2018, 23: 629 |
| [35] | Wang H, Zhang L F, Han J Q, et al. DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics [J]. Comput. Phys. Commun., 2018, 228: 178 |
| [36] | Chen M Y, Hu J W, Yu Y C, et al. Advances in machine learning molecular dynamics to assist materials nucleation and solidification research [J]. Acta Metall. Sin., 2024, 60: 1329 |
| 陈名毅, 胡俊伟, 余耀辰 等. 机器学习分子动力学辅助材料凝固形核研究进展 [J]. 金属学报, 2024, 60: 1329 | |
| [37] | Liu S, Huang J W, Wu J. Application of machine learning force fields for modeling ferroelectric materials [J]. Acta Metall. Sin., 2024, 60: 1312 |
| 刘 仕, 黄佳玮, 武 静. 机器学习势在铁电材料研究中的应用 [J]. 金属学报, 2024, 60: 1312 | |
| [38] | Wen T Q, Zhang L F, Wang H, et al. Deep potentials for materials science [J]. Mater. Futures, 2022, 1: 022601 |
| [39] | Gilmer J, Schoenholz S S, Riley P F, et al. Neural message passing for quantum chemistry [A]. Proceedings of the 34th International Conference on Machine Learning [C]. Sydney: PMLR, 2017 |
| [40] | Schütt K T, Sauceda H E, Kindermans P J, et al. SchNet—A deep learning architecture for molecules and materials [J]. J. Chem. Phys., 2018, 148: 241722 |
| [41] | Unke O T, Meuwly M. PhysNet: A neural network for predicting energies, forces, dipole moments, and partial charges [J]. J. Chem. Theory Comput., 2019, 15: 3678 |
| [42] | Klicpera J, Gro? J, Günnemann S. Directional message passing for molecular graphs [A]. Proceedings of the 8th International Conference on Learning Representations [C]. Addis Ababa: OpenReview.net, 2020 |
| [43] | Schütt K T, Unke O T, Gastegger M. Equivariant message passing for the prediction of tensorial properties and molecular spectra [J]. arXiv: 2102. 03150, 2021 |
| [44] | Batzner S, Musaelian A, Sun L X, et al. E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials [J]. Nat. Commun., 2022, 13: 2453 |
| [45] | Musaelian A, Batzner S, Johansson A, et al. Learning local equivariant representations for large-scale atomistic dynamics [J]. Nat. Commun., 2023, 14: 579 |
| [46] | Batatia I, Kovács D P, Simm G N C, et al. MACE: Higher order equivariant message passing neural networks for fast and accurate force fields [J]. arXiv: 2206. 07697, 2023 |
| [47] | Wu Y B, Xia J F, Zhang Y L, et al. A simple and efficient equivariant message-passing neural network model for non-local potential energy surface [J]. J. Phys. Chem., 2024, 128A: 11061 |
| [48] | Batatia I, Batzner S, Kovács D P, et al. The design space of E(3)-equivariant atom-centered interatomic potentials [J]. arXiv: 2205. 06643, 2022 |
| [49] | Cheng B Q. Latent Ewald summation for machine learning of long-range interactions [J]. npj Comput. Mater., 2025, 11: 80 |
| [50] | Jain A, Ong S P, Hautier G, et al. Commentary: The materials project: A materials genome approach to accelerating materials innovation [J]. APL Mater., 2013, 1: 011002 |
| [51] | Chen C, Ye W K, Zuo Y X, et al. Graph networks as a universal machine learning framework for molecules and crystals [J]. Chem. Mater., 2019, 31: 3564 |
| [52] | Chen C, Ong S P. A universal graph deep learning interatomic potential for the periodic table [J]. Nat. Comput. Sci., 2022, 2: 718 |
| [53] | Deng B W, Zhong P C, Jun K, et al. CHGNet as a pretrained universal neural network potential for charge-informed atomistic modelling [J]. Nat. Mach. Intell., 2023, 5: 1031 |
| [54] | Merchant A, Batzner S, Schoenholz S S, et al. Scaling deep learning for materials discovery [J]. Nature, 2023, 624: 80 |
| [55] | Zhang D, Bi H R, Dai F Z, et al. Pretraining of attention-based deep learning potential model for molecular simulation [J]. npj Comput. Mater., 2024, 10: 94 |
| [56] | Zhang D, Liu X Z J, Zhang X Y, et al. DPA-2: A large atomic model as a multi-task learner [J]. npj Comput. Mater., 2024, 10: 293 |
| [57] | Batatia I, Benner P, Chiang Y, et al. A foundation model for atomistic materials chemistry [J]. J. Chem. Phys., 2025, 163: 184110 |
| [58] | Xie F K, Lu T L, Meng S, et al. GPTFF: A high-accuracy out-of-the-box universal AI force field for arbitrary inorganic materials [J]. Sci. Bull., 2024, 69: 3525 |
| [59] | Han T, Li J, Liu L P, et al. Accuracy evaluation of different machine learning force field features [J]. New J. Phys., 2023, 25: 093007 |
| [60] | Zuo Y X, Chen C, Li X G, et al. A performance and cost assessment of machine learning interatomic potentials [J]. J. Phys. Chem., 2020, 124A: 731 |
| [61] | Dusson G, Bachmayr M, Csányi G, et al. Atomic cluster expansion: Completeness, efficiency and stability [J]. J. Comput. Phys., 2022, 454: 110946 |
| [62] | Hodapp M, Shapeev A. Equivariant tensor network potentials [J]. Mach. Learn.: Sci. Technol., 2024, 5: 035075 |
| [63] | Podryabinkin E V, Shapeev A V. Active learning of linearly parametrized interatomic potentials [J]. Comput. Mater. Sci., 2017, 140: 171 |
| [64] | Gubaev K, Podryabinkin E V, Shapeev A V. Machine learning of molecular properties: Locality and active learning [J]. J. Chem. Phys., 2018, 148: 241727 |
| [65] | Novikov I S, Gubaev K, Podryabinkin E V, et al. The MLIP package: Moment tensor potentials with MPI and active learning [J]. Mach. Learn.: Sci. Technol., 2021, 2: 025002 |
| [66] | Wang J T, Liu P T, Zhu H T, et al. Efficient moment tensor machine-learning interatomic potential for accurate description of defects in Ni-Al Alloys [J]. Phys. Rev. Mater., 2025, 9: 053805 |
| [67] | Cohn D A, Ghahramani Z, Jordan M I. Active learning with statistical models [J]. J. Artif. Intell. Res., 1996, 4: 129 |
| [68] | Jinnouchi R, Miwa K, Karsai F, et al. On-the-fly active learning of interatomic potentials for large-scale atomistic simulations [J]. J. Phys. Chem. Lett., 2020, 11: 6946 |
| [69] | Friederich P, H?se F, Proppe J, et al. Machine-learned potentials for next-generation matter simulations [J]. Nat. Mater., 2021, 20: 750 |
| [70] | Laio A, Parrinello M. Escaping free-energy minima [J]. Proc. Natl. Acad. Sci. USA, 2002, 99: 12562 |
| [71] | Allen R J, Frenkel D, ten Wolde P R. Simulating rare events in equilibrium or nonequilibrium stochastic systems [J]. J. Chem. Phys., 2006, 124: 024102 |
| [72] | Barducci A, Bussi G, Parrinello M. Well-tempered metadynamics: A smoothly converging and tunable free-energy method [J]. Phys. Rev. Lett., 2008, 100: 020603 |
| [73] | Han X, Lei Y K, Li M D, et al. A brief review of integrated tempering sampling molecular simulation [J]. Chem. Phys. Rev., 2024, 5: 011308 |
| [74] | Castellano A, Béjaud R, Richard P, et al. Machine learning assisted canonical sampling (MLACS) [J]. Comput. Phys. Commun., 2025, 316: 109730 |
| [75] | Ramakrishnan R, Dral P O, Rupp M, et al. Quantum chemistry structures and properties of 134 kilo molecules [J]. Sci. Data, 2014, 1: 140022 |
| [76] | Glass C W, Oganov A R, Hansen N. USPEX—Evolutionary crystal structure prediction [J]. Comput. Phys. Commun., 2006, 175: 713 |
| [77] | Wang J J, Gao H, Han Y, et al. MAGUS: Machine learning and graph theory assisted universal structure searcher [J]. Natl. Sci. Rev., 2023, 10: nwad128 |
| [78] | Podryabinkin E V, Tikhonov E V, Shapeev A V, et al. Accelerating crystal structure prediction by machine-learning interatomic potentials with active learning [J]. Phys. Rev., 2019, 99B: 064114 |
| [79] | Gubaev K, Podryabinkin E V, Hart G L W, et al. Accelerating high-throughput searches for new alloys with active learning of interatomic potentials [J]. Comput. Mater. Sci., 2019, 156: 148 |
| [80] | Novoselov I I, Yanilkin A V, Shapeev A V, et al. Moment tensor potentials as a promising tool to study diffusion processes [J]. Comput. Mater. Sci., 2019, 164: 46 |
| [81] | Shapeev A V, Podryabinkin E V, Gubaev K, et al. Elinvar effect in β-Ti simulated by on-the-fly trained moment tensor potential [J]. New J. Phys., 2020, 22: 113005 |
| [82] | Mukhamedov B, Tasnádi F, Abrikosov I A. Machine learning interatomic potential for the low-modulus Ti-Nb-Zr alloys in the vicinity of dynamical instability [J]. Mater. Des., 2025, 253: 113865 |
| [83] | Mei H J, Cheng L Y, Chen L, et al. Development of machine learning interatomic potential for zinc [J]. Comput. Mater. Sci., 2024, 233: 112723 |
| [84] | Forslund A, Ruban A. Ab initio surface free energies of tungsten with full account of thermal excitations [J]. Phys. Rev., 2022, 105B: 045403 |
| [85] | Forslund A, Jung J H, Srinivasan P, et al. Thermodynamic properties on the homologous temperature scale from direct upsampling: Understanding electron-vibration coupling and thermal vacancies in bcc refractory metals [J]. Phys. Rev., 2023, 107B: 174309 |
| [86] | Srinivasan P, Shapeev A, Neugebauer J, et al. Anharmonicity in bcc refractory elements: A detailed ab initio analysis [J]. Phys. Rev., 2023, 107B: 014301 |
| [87] | Zhu L F, Srinivasan P, Gong Y L, et al. Melting properties of the refractory metals V and W and the binary VW alloy fully from first principles [J]. Phys. Rev., 2024, 109B: 094110 |
| [88] | Jung J H, Srinivasan P, Forslund A, et al. High-accuracy thermodynamic properties to the melting point from ab initio calculations aided by machine-learning potentials [J]. npj Comput. Mater., 2023, 9: 3 |
| [89] | Zhang X, Divinski S V, Grabowski B. Ab initio machine-learning unveils strong anharmonicity in non-Arrhenius self-diffusion of tungsten [J]. Nat. Commun., 2025, 16: 394 |
| [90] | Duff A I, Davey T, Korbmacher D, et al. Improved method of calculating ab initio high-temperature thermodynamic properties with application to ZrC [J]. Phys. Rev., 2015, 91B: 214311 |
| [91] | Grabowski B, Ikeda Y, Srinivasan P, et al. Ab initio vibrational free energies including anharmonicity for multicomponent alloys [J]. npj Comput. Mater., 2019, 5: 80 |
| [92] | Zotov N, Gubaev K, W?rner J, et al. Moment tensor potential for static and dynamic investigations of screw dislocations in bcc Nb [J]. Modell. Simul. Mater. Sci. Eng., 2024, 32: 035032 |
| [93] | Wang Y, Liu J B, Li J H, et al. Machine-learning interatomic potential for radiation damage effects in bcc-iron [J]. Comput. Mater. Sci., 2022, 202: 110960 |
| [94] | Kwon H, Shiga M, Kimizuka H, et al. Accurate description of hydrogen diffusivity in bcc metals using machine-learning moment tensor potentials and path-integral methods [J]. Acta Mater., 2023, 247: 118739 |
| [95] | Kumar P, K?rmann F, Grabowski B, et al. Machine learning potentials for hydrogen absorption in TiCr2 Laves phases [J]. Acta Mater., 2025, 297: 121319 |
| [96] | Xu X, Zhang X, Ruban A, et al. Accurate complex-stacking-fault Gibbs energy in Ni3Al at high temperatures [J]. Scr. Mater., 2024, 242: 115934 |
| [97] | Xu X, Zhang X, Bitzek E, et al. Origin of the yield stress anomaly in L12 intermetallics unveiled with physically informed machine-learning potentials [J]. Acta Mater., 2024, 281: 120423 |
| [98] | Novikov B, Grabowski B, K?rmann F, et al. Magnetic Moment Tensor Potentials for collinear spin-polarized materials reproduce different magnetic states of bcc Fe [J]. npj Comput. Mater., 2022, 8: 13 |
| [99] | Kotykhov A S, Gubaev K, Hodapp M, et al. Constrained DFT-based magnetic machine-learning potentials for magnetic alloys: a case study of Fe-Al [J]. Sci. Rep., 2023, 13: 19728 |
| [100] | Kotykhov A S, Gubaev K, Sotskov V, et al. Fitting to magnetic forces improves the reliability of magnetic moment tensor potentials [J]. Comput. Mater. Sci., 2024, 245: 113331 |
| [101] | Taylor A, Jones R M. Constitution and magnetic properties of iron-rich iron-aluminum alloys [J]. J. Phys. Chem. Solids, 1958, 6: 16 |
| [102] | Srinivasan P, Demuriya D, Grabowski B, et al. Electronic moment tensor potentials include both electronic and vibrational degrees of freedom [J]. npj Comput. Mater., 2024, 10: 41 |
| [103] | Gubaev K, Zaverkin V, Srinivasan P, et al. Performance of two complementary machine-learned potentials in modelling chemically complex systems [J]. npj Comput. Mater., 2023, 9: 129 |
| [104] | Shuang F, Ji Y C, Laurenti L, et al. Size-dependent strength superiority in multi-principal element alloys versus constituent metals: Insights from machine-learning atomistic simulations [J]. Int. J. Plast., 2025, 188: 104308 |
| [105] | Yin S, Zuo Y X, Abu-Odeh A, et al. Atomistic simulations of dislocation mobility in refractory high-entropy alloys and the effect of chemical short-range order [J]. Nat. Commun., 2021, 12: 4873 |
| [106] | Jafary-Zadeh M, Khoo K H, Laskowski R, et al. Applying a machine learning interatomic potential to unravel the effects of local lattice distortion on the elastic properties of multi-principal element alloys [J]. J. Alloys Compd., 2019, 803: 1054 |
| [107] | Gubaev K, Ikeda Y, Tasnádi F, et al. Finite-temperature interplay of structural stability, chemical complexity, and elastic properties of bcc multicomponent alloys from ab initio trained machine-learning potentials [J]. Phys. Rev. Mater., 2021, 5: 073801 |
| [108] | Hodapp M, Shapeev A. Machine-learning potentials enable predictive and tractable high-throughput screening of random alloys [J]. Phys. Rev. Mater., 2021, 5: 113802 |
| [109] | Zhu L F, K?rmann F, Chen Q, et al. Accelerating ab initio melting property calculations with machine learning: Application to the high entropy alloy TaVCrW [J]. npj Comput. Mater., 2024, 10: 274 |
| [110] | Song Y M, Xian J W, Xu Y J, et al. Machine learning accelerated study on temperature dependent elastic properties of Ti-based refractory high entropy alloys [J]. Mater. Today Commun., 2025, 42: 111559 |
| [111] | Liu M F, Wang J T, Hu J W, et al. Layer-by-layer phase transformation in Ti3O5 revealed by machine-learning molecular dynamics simulations [J]. Nat. Commun., 2024, 15: 3079 |
| [112] | Liu M F, Wang J T, Liu P T, et al. Diverse polymorphs and phase transitions in van der Waals In2Se3 [J]. 2025, arXiv: 2506. 21248v1, 2025 |
| [113] | Wang J T, Zhang Y C, Liu Y, et al. Atomistic mechanisms of phase transitions in all-temperature barocaloric material KPF6 [J]. J. Mater. Sci. Technol., 2026, 263: 211 |
| [114] | Jung J H, Forslund A, Srinivasan P, et al. Dynamically stabilized phases with full ab initio accuracy: Thermodynamics of Ti, Zr, Hf with a focus on the hcp-bcc transition [J]. Phys. Rev., 2023, 108B: 184107 |
| [115] | Zhao X T, Zhang Z, Hattori T, et al. All-temperature barocaloric effects at pressure-induced phase transitions [J]. Nat. Commun., 2025, 16: 7713 |
| [116] | Chen B W J, Zhang X L, Zhang J. Accelerating explicit solvent models of heterogeneous catalysts with machine learning interatomic potentials [J]. Chem. Sci., 2023, 14: 8338 |
| [117] | Klimanova O, Rybin N, Shapeev A. Accelerating the global search of adsorbate molecule positions using machine-learning interatomic potentials with active learning [J]. Phys. Chem. Chem. Phys., 2025, 27: 9201 |
| [118] | Feibelman P J, Hammer B, N?rskov J K, et al. The CO/Pt(111) puzzle [J]. J. Phys. Chem., 2001, 105B: 4018 |
| [119] | Grinberg I, Yourdshahyan Y, Rappe A M. CO on Pt(111) puzzle: A possible solution [J]. J. Chem. Phys., 2002, 117: 2264 |
| [120] | Ren X G, Rinke P, Joas C, et al. Random-phase approximation and its applications in computational chemistry and materials science [J]. J. Mater. Sci., 2012, 47: 7447 |
| [121] | Liu P T, Wang J T, Avargues N, et al. Combining machine learning and many-body calculations: Coverage-dependent adsorption of CO on Rh(111) [J]. Phys. Rev. Lett., 2023, 130: 078001 |
| [122] | Cao Y, Wang J T, Liu M F, et al. Quantum delocalization enables water dissociation on Ru(0001) [J]. Phys. Rev. Lett., 2025, 134: 178001 |
| [123] | Ou Y L, Ikeda Y, Scholz L, et al. Atomistic modeling of bulk and grain boundary diffusion in solid electrolyte Li6PS5Cl using machine-learning interatomic potentials [J]. Phys. Rev. Mater., 2024, 8: 115407 |
| [124] | Kim J H, Jun B, Jang Y J, et al. Highly reliable and large-scale simulations of promising argyrodite solid-state electrolytes using a machine-learned moment tensor potential [J]. Nano Energy, 2024, 124: 109436 |
| [125] | Holekevi Chandrappa M L, Qi J, Chen C, et al. Thermodynamics and kinetics of the cathode-electrolyte interface in all-solid-state Li-S batteries [J]. J. Am. Chem. Soc., 2022, 144: 18009 |
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