Interatomic potentials approximate the potential energy of atoms as a function of their coordinates. Their main application is the effective simulation of many-atom systems. Here, we review empirical interatomic potentials designed to reproduce elastic properties, defect energies, bond breaking, bond formation, and even redox reactions. We discuss popular two-body potentials, embedded-atom models for metals, bond-order potentials for covalently bonded systems, polarizable potentials including charge-transfer approaches for ionic systems and quantum-Drude oscillator models mimicking higher-order and many-body dispersion. Particular emphasis is laid on the question what constraints ensue from the functional form of a potential, e.g., in what way Cauchy relations for elastic tensor elements can be violated and what this entails for the ratio of defect and cohesive energies, or why the ratio of boiling to melting temperature tends to be large for potentials describing metals but small for short-ranged pair potentials. The review is meant to be pedagogical rather than encyclopedic. This is why we highlight potentials with functional forms sufficiently simple to remain amenable to analytical treatments. Our main objective is to provide a stimulus for how existing approaches can be advanced or meaningfully combined to extent the scope of simulations based on empirical potentials.
A general-purpose atomic cluster expansion interatomic potential for niobium
Center for Advanced Systems Understanding (CASUS)（先进系统理解中心）；Helmholtz-Zentrum Dresden-Rossendorf (HZDR)（德累斯顿-罗斯多夫亥姆霍兹中心）；ICAMS, Ruhr-Universität Bochum（波鸿鲁尔大学综合分析与建模中心）
Equivariant Many-body Message Passing Interatomic Potentials for Magnetic Materials
University of British Columbia（不列颠哥伦比亚大学）；Symmetric Group（对称集团）；MatNex；University of Cambridge（剑桥大学）；Max Planck Institute for Polymer Research（马克斯·普朗克高分子研究所）
Predicting Interface Structure using the Minima Hopping Method with a Machine Learning Interatomic Potential
Northwestern University（西北大学）；Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University（哈佛大学约翰·A·保尔森工程与应用科学学院）；Max Planck Institute for Solid State Research（马克斯·普朗克固相研究所）；The Grainger College of Engineering, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校格兰格工程学院）；Materials Research Laboratory, The Grainger College of Engineering, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校格兰格工程学院材料研究实验室）；Robert Bosch Research and Technology Center（罗伯特·博世研究与技术中心）
Bayesian Neural Networks versus deep ensembles for uncertainty quantification in machine learning interatomic potentials
Leitat Technological Center（Leitat技术中心）；Universitat de Barcelona（巴塞罗那大学）；Utrecht University（乌得勒支大学）；ICREA (Institucio Catalana de Recerca i Estudis Avançats)（加泰罗尼亚研究与高等研究院）
An Active Learning Interatomic Potential For Defect-Engineered CoCrFeMnNi High-Entropy Alloy
University of Tokyo（东京大学）；Indian Institute of Technology Gandhinagar（甘地纳加尔印度理工学院）；Herbert Gleiter International Institute, Liaoning Academy of Materials（赫伯特·盖勒国际研究所，辽宁材料研究院）；Regional Institute of Education（地区教育学院）
Elucidation of the atomic-scale mechanism of the anisotropic oxidation rate of 4H-SiC between the ($0001$) Si-face and ($000\overline{1}$) C-face by using a new Si-O-C interatomic potential
Phonon-Mediated Thermal Transport in Nanocrystalline Silicon Using Machine-Learning Interatomic Potentials
International Iberian Nanotechnology Laboratory (INL)（伊比利亚纳米技术国际实验室）；Universitat de Barcelona (UB)（巴塞罗那大学）；Institute of Nanoscience and Nanotechnology (IN2UB)（纳米科学与技术研究所）；Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST（加泰罗尼亚纳米科学技术研究所（ICN2）, 西班牙国家研究委员会和巴塞罗那智能科技学院）；Nanomaterials and Nanotechnology Research Center (CINN-CSIC), Universidad de Oviedo (UO)（纳米材料与纳米技术研究中心（CINN-CSIC）, 奥维耶多大学）
Machine-learning octet $AB$-type binary compounds across chemical space with domain knowledge of the interatomic bond
Ruhr-Universität Bochum（波鸿鲁尔大学）；Federal Institute for Materials Research and Testing（联邦材料研究与测试研究所）；Friedrich-Schiller-Universität Jena（耶拿弗里德里希·席勒大学）；Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）
Global Universal Scaling and Ultra-Small Parameterization in Machine Learning Interatomic Potentials with Super-Linearity
Southern University of Science and Technology（南方科技大学）；Shanghai University（上海大学）；Materials Genome Institute（材料基因组研究院）；Institute of Innovative Materials（创新材料研究院）
Revealing Hydroxide Ion Transport Mechanisms in Commercial Anion-Exchange Membranes at Nano-Scale from Machine-learned Interatomic Potential Simulations
Technische Universität Ilmenau（伊尔梅瑙工业大学）；Fraunhofer-Institut für Keramische Technologien und Systeme IKTS（弗劳恩霍夫陶瓷技术与系统研究所）
dpti: An Automated Thermodynamic Integration Workflow for Phase Diagram Calculations with Machine Learning Interatomic Potentials
University of Alabama at Birmingham（阿拉巴马大学伯明翰分校）；Princeton University（普林斯顿大学）；University of Science and Technology of China（中国科学技术大学）；Suzhou Institute for Advanced Research, University of Science and Technology of China（中国科学技术大学苏州高等研究院）；Suzhou Big Data & AI Research and Engineering Center（苏州大数据与人工智能研究与工程中心）；AI for Science Institute（科学智能研究所）；DP Technology（深势科技）；Institute of Applied Physics and Computational Mathematics（应用物理与计算数学研究所）；College of Engineering, Peking University（北京大学工学院）
Mixture of Experts Framework in Machine Learning Interatomic Potentials for Atomistic Simulations
Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA（材料科学与工程系，麻省理工学院，剑桥，马萨诸塞州，美国）；John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA（约翰·A·波尔森工程与应用科学学院，哈佛大学，剑桥，马萨诸塞州，美国）；Robert Bosch LLC Research and Technology Center, Watertown, MA, USA（罗伯特·博世 LLC 研究与技术中心，沃特敦，马萨诸塞州，美国）
Evaluating approaches for on-the-fly machine learning interatomic potential for activated mechanisms sampling with the activation-relaxation technique nouveau
Revisiting quantum effects on dislocation glide in bcc metals from DFT calculations and machine-learning potentials
ASNR/PSN-RES/SEMIA/LSMA Centre d’études de Cadarache（法国原子能和替代能源委员会卡达拉舍研究中心）；Université Paris-Saclay, CEA, Service de recherche en Corrosion et Comportement des Matériaux, SRMP（巴黎萨克雷大学，法国原子能和替代能源委员会材料腐蚀与行为研究服务处）；Univ. Lyon, UCBL, Institut Lumière Matière, UMR CNRS 5306（里昂大学，里昂第一大学，光物质研究所）
Long-range electrostatics for machine learning interatomic potentials is easier than we thought
Department of Chemistry, UC Berkeley, California 94720, United States（加州大学伯克利分校化学系）；Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California, 94720, United States（伯克利国家实验室化学科学部）；Bakar Institute of Digital Materials for the Planet, UC Berkeley, California 94720, United States（为地球数字化材料研究所）；The Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria（奥地利科学与技术研究所）
Universal Machine Learning Interatomic Potentials are Ready for Solid Ion Conductors
School of Materials Science and Engineering, Shanghai Jiao Tong University（上海交通大学材料科学与工程学院）；Zhangjiang Institute for Advanced Study, Shanghai Jiao Tong University（上海交通大学张江高等研究院）；Materials Genome Initiative Center, Shanghai Jiao Tong University（上海交通大学材料基因组计划中心）
