Vladimir V. Gusev, Duncan Adamson, Argyrios Deligkas, Dmytro Antypov, Christopher M. Collins, Piotr Krysta, Igor Potapov, George R. Darling, Matthew S. Dyer, Paul Spirakis, Matthew J. Rosseinsky
{"title":"Optimality guarantees for crystal structure prediction","authors":"Vladimir V. Gusev, Duncan Adamson, Argyrios Deligkas, Dmytro Antypov, Christopher M. Collins, Piotr Krysta, Igor Potapov, George R. Darling, Matthew S. Dyer, Paul Spirakis, Matthew J. Rosseinsky","doi":"10.1038/s41586-023-06071-y","DOIUrl":null,"url":null,"abstract":"Crystalline materials enable essential technologies, and their properties are determined by their structures. Crystal structure prediction can thus play a central part in the design of new functional materials1,2. Researchers have developed efficient heuristics to identify structural minima on the potential energy surface3–5. Although these methods can often access all configurations in principle, there is no guarantee that the lowest energy structure has been found. Here we show that the structure of a crystalline material can be predicted with energy guarantees by an algorithm that finds all the unknown atomic positions within a unit cell by combining combinatorial and continuous optimization. We encode the combinatorial task of finding the lowest energy periodic allocation of all atoms on a lattice as a mathematical optimization problem of integer programming6,7, enabling guaranteed identification of the global optimum using well-developed algorithms. A single subsequent local minimization of the resulting atom allocations then reaches the correct structures of key inorganic materials directly, proving their energetic optimality under clear assumptions. This formulation of crystal structure prediction establishes a connection to the theory of algorithms and provides the absolute energetic status of observed or predicted materials. It provides the ground truth for heuristic or data-driven structure prediction methods and is uniquely suitable for quantum annealers8–10, opening a path to overcome the combinatorial explosion of atomic configurations. An algorithm has been developed that can provably predict the lowest energy structure of crystalline materials using a combination of combinatorial optimization and integer programming.","PeriodicalId":18787,"journal":{"name":"Nature","volume":null,"pages":null},"PeriodicalIF":50.5000,"publicationDate":"2023-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nature","FirstCategoryId":"103","ListUrlMain":"https://www.nature.com/articles/s41586-023-06071-y","RegionNum":1,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
引用次数: 1
Abstract
Crystalline materials enable essential technologies, and their properties are determined by their structures. Crystal structure prediction can thus play a central part in the design of new functional materials1,2. Researchers have developed efficient heuristics to identify structural minima on the potential energy surface3–5. Although these methods can often access all configurations in principle, there is no guarantee that the lowest energy structure has been found. Here we show that the structure of a crystalline material can be predicted with energy guarantees by an algorithm that finds all the unknown atomic positions within a unit cell by combining combinatorial and continuous optimization. We encode the combinatorial task of finding the lowest energy periodic allocation of all atoms on a lattice as a mathematical optimization problem of integer programming6,7, enabling guaranteed identification of the global optimum using well-developed algorithms. A single subsequent local minimization of the resulting atom allocations then reaches the correct structures of key inorganic materials directly, proving their energetic optimality under clear assumptions. This formulation of crystal structure prediction establishes a connection to the theory of algorithms and provides the absolute energetic status of observed or predicted materials. It provides the ground truth for heuristic or data-driven structure prediction methods and is uniquely suitable for quantum annealers8–10, opening a path to overcome the combinatorial explosion of atomic configurations. An algorithm has been developed that can provably predict the lowest energy structure of crystalline materials using a combination of combinatorial optimization and integer programming.
期刊介绍:
Nature is a prestigious international journal that publishes peer-reviewed research in various scientific and technological fields. The selection of articles is based on criteria such as originality, importance, interdisciplinary relevance, timeliness, accessibility, elegance, and surprising conclusions. In addition to showcasing significant scientific advances, Nature delivers rapid, authoritative, insightful news, and interpretation of current and upcoming trends impacting science, scientists, and the broader public. The journal serves a dual purpose: firstly, to promptly share noteworthy scientific advances and foster discussions among scientists, and secondly, to ensure the swift dissemination of scientific results globally, emphasizing their significance for knowledge, culture, and daily life.