{"title":"The sum over histories representation for chemical kinetics: a quantitative theory based on chemical pathways","authors":"Shirong Bai, R. T. Skodje","doi":"10.1080/0144235X.2016.1220774","DOIUrl":null,"url":null,"abstract":"A new representation for chemical kinetics based on a sum over histories formulation is discussed. The description of the time-dependent chemistry of a reaction network is provided by chemical pathways defined at a molecular level. Using this methodology, the quantitative time evolution of the kinetics is described by enumerating the most important pathways followed by a chemical moiety such as a tagged atom. An explicit formula for the pathway probabilities is derived which takes the form of an integral over a time-ordered product. This expression has a simple and computationally efficient Monte Carlo representation which permits the method to be applied to a wide range of problems. For small reaction networks, the chemical pathways can be enumerated using graph theoretic methods. More complicated networks can be explored using random walks computed from a stochastic algorithm. The workings of the method are illustrated using a simple network of 20 chemical species which react via first-order kinetics. The application of the sum over histories representation to problems in surface catalysis and hydrogen combustion provide more realistic applications.","PeriodicalId":54932,"journal":{"name":"International Reviews in Physical Chemistry","volume":"77 1","pages":"539 - 567"},"PeriodicalIF":2.5000,"publicationDate":"2016-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Reviews in Physical Chemistry","FirstCategoryId":"92","ListUrlMain":"https://doi.org/10.1080/0144235X.2016.1220774","RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"CHEMISTRY, PHYSICAL","Score":null,"Total":0}
引用次数: 11
Abstract
A new representation for chemical kinetics based on a sum over histories formulation is discussed. The description of the time-dependent chemistry of a reaction network is provided by chemical pathways defined at a molecular level. Using this methodology, the quantitative time evolution of the kinetics is described by enumerating the most important pathways followed by a chemical moiety such as a tagged atom. An explicit formula for the pathway probabilities is derived which takes the form of an integral over a time-ordered product. This expression has a simple and computationally efficient Monte Carlo representation which permits the method to be applied to a wide range of problems. For small reaction networks, the chemical pathways can be enumerated using graph theoretic methods. More complicated networks can be explored using random walks computed from a stochastic algorithm. The workings of the method are illustrated using a simple network of 20 chemical species which react via first-order kinetics. The application of the sum over histories representation to problems in surface catalysis and hydrogen combustion provide more realistic applications.
期刊介绍:
International Reviews in Physical Chemistry publishes review articles describing frontier research areas in physical chemistry. Internationally renowned scientists describe their own research in the wider context of the field. The articles are of interest not only to specialists but also to those wishing to read general and authoritative accounts of recent developments in physical chemistry, chemical physics and theoretical chemistry. The journal appeals to research workers, lecturers and research students alike.