Marcos E. González Laffitte, Klaus Weinbauer, Tieu-Long Phan, Nora Beier, Nico Domschke, Christoph Flamm, Thomas Gatter, Daniel Merkle, Peter F. Stadler
{"title":"部分虚过渡态(ITS)图:研究和分析不平衡化学反应原子到原子映射及其补全的形式框架","authors":"Marcos E. González Laffitte, Klaus Weinbauer, Tieu-Long Phan, Nora Beier, Nico Domschke, Christoph Flamm, Thomas Gatter, Daniel Merkle, Peter F. Stadler","doi":"10.3390/sym16091217","DOIUrl":null,"url":null,"abstract":"Atom-to-atom maps (AAMs) are bijections that establish the correspondence of reactant and product atoms across chemical reactions. They capture crucial features of the reaction mechanism and thus play a central role in modeling chemistry at the level of graph transformations. AAMs are equivalent to so-called “imaginary transition state” (ITS) graphs, making it possible to reduce tasks such as the computational comparison of AAMs to testing graph isomorphisms. In many application scenarios, nonetheless, only partial information is available, i.e., only partial maps or, equivalently, only subgraphs of the ITS graphs, are known. Here, we investigate whether and how, and to what extent, such partial chemical data can be completed and compared. The focus of this contribution is entirely on the development of a solid mathematical foundation for the analysis of partial AAMs and their associated partial ITS graphs.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"593 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Partial Imaginary Transition State (ITS) Graphs: A Formal Framework for Research and Analysis of Atom-to-Atom Maps of Unbalanced Chemical Reactions and Their Completions\",\"authors\":\"Marcos E. González Laffitte, Klaus Weinbauer, Tieu-Long Phan, Nora Beier, Nico Domschke, Christoph Flamm, Thomas Gatter, Daniel Merkle, Peter F. Stadler\",\"doi\":\"10.3390/sym16091217\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Atom-to-atom maps (AAMs) are bijections that establish the correspondence of reactant and product atoms across chemical reactions. They capture crucial features of the reaction mechanism and thus play a central role in modeling chemistry at the level of graph transformations. AAMs are equivalent to so-called “imaginary transition state” (ITS) graphs, making it possible to reduce tasks such as the computational comparison of AAMs to testing graph isomorphisms. In many application scenarios, nonetheless, only partial information is available, i.e., only partial maps or, equivalently, only subgraphs of the ITS graphs, are known. Here, we investigate whether and how, and to what extent, such partial chemical data can be completed and compared. The focus of this contribution is entirely on the development of a solid mathematical foundation for the analysis of partial AAMs and their associated partial ITS graphs.\",\"PeriodicalId\":501198,\"journal\":{\"name\":\"Symmetry\",\"volume\":\"593 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Symmetry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3390/sym16091217\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Symmetry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3390/sym16091217","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
原子到原子图谱(AAM)是建立化学反应中反应物和生成物原子对应关系的双射。它们捕捉了反应机理的关键特征,因此在图变换层面的化学建模中发挥着核心作用。AAM 等同于所谓的 "假想过渡态"(ITS)图,因此可以将 AAM 的计算比较等任务简化为测试图的同构性。然而,在许多应用场景中,只有部分信息可用,即只知道部分映射,或者等同于只知道 ITS 图的子图。在此,我们将研究是否可以、如何以及在多大程度上完成并比较这些部分化学数据。本文的重点完全在于为分析部分 AAM 及其相关的部分 ITS 图奠定坚实的数学基础。
Partial Imaginary Transition State (ITS) Graphs: A Formal Framework for Research and Analysis of Atom-to-Atom Maps of Unbalanced Chemical Reactions and Their Completions
Atom-to-atom maps (AAMs) are bijections that establish the correspondence of reactant and product atoms across chemical reactions. They capture crucial features of the reaction mechanism and thus play a central role in modeling chemistry at the level of graph transformations. AAMs are equivalent to so-called “imaginary transition state” (ITS) graphs, making it possible to reduce tasks such as the computational comparison of AAMs to testing graph isomorphisms. In many application scenarios, nonetheless, only partial information is available, i.e., only partial maps or, equivalently, only subgraphs of the ITS graphs, are known. Here, we investigate whether and how, and to what extent, such partial chemical data can be completed and compared. The focus of this contribution is entirely on the development of a solid mathematical foundation for the analysis of partial AAMs and their associated partial ITS graphs.