The sum over histories representation for chemical kinetics: a quantitative theory based on chemical pathways

• Published in: International Reviews in Physical Chemistry Vol. 35; no. 4; pp. 539 - 567
• Main Authors: Bai, Shirong, Skodje, Rex T.
• Format: Journal Article Book Review
• Language: English
• Published: Abingdon Taylor & Francis 01-10-2016; Taylor & Francis Ltd
• Subjects: Catalysis; Chemical kinetics; combustion; Kinetics; path integrals; Physical chemistry; reaction pathway; Stochastic models; surface catalysis
• ISSN: 0144-235X; 1366-591X
• DOI: 10.1080/0144235X.2016.1220774

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.