Understanding Combustion and Surface Kinetics Using the Sum Over Histories Representation

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Rex Skodje, of the University of Colorado, Boulder is supported by an award from the Chemical Theory, Models and Computational Methods program to develop a novel approach to chemical kinetics. Many important systems in nature and technology are described by large networks of interconnected chemical reactions. For example, hydrocarbon combustion in engines can involve thousands of individual chemical reactions as the fuel molecules break up and oxidize in route to their final destination as carbon dioxide and water. Similarly, large chemical networks arise in the study of the chemistry of the atmosphere, the biochemistry of living systems, the performance of catalytic reactors, and many other places. The present project studies these complex systems using a new methodology termed the Sum Over Histories Representation (or SOHR). In the SOHR method, the chemistry of complex systems is quantitatively described using the reaction pathways followed by individual molecules rather than by the conventional rate equation approach that has been employed for over a century. There are several objectives of this work. First, the mathematical methodology is refined and made efficient to facilitate the implementation to extremely large chemical systems. Second, the SOHR method is used to analyze the chemistry of combustion for important fuels such as propane and heptane. Third, the SOHR method is used to model catalytic reactions of important organic molecules on the surfaces industrially relevant materials such as nickel and platinum. The successful outcome of the proposed research program is important both from a fundamental scientific standpoint as well as in practical application. The SOHR method is designed to allow complicated chemical systems to be reduced to their simplest most transparent forms by identifying the dominant chemical pathways in the mechanism. This will guide the design and optimization of practical reactors and provide new insight into naturally occurring networks. The innovative approach is being implemented in user-friendly software that is made available to the larger research community.The SOHR method replaces conventional kinetic modeling that involves use of a "local" differential rate equations theory formed from the rates of formation and destruction of each species in a mechanism. The SOHR method instead uses "global" chemical pathways. A chemical pathway follows a chemical moiety, such as a "tagged atom", as it hops from species to species due to reaction during the course of the simulation. It is found that if a sufficient number of these chemical pathways are enumerated, the full chemistry of the model can be quantitatively described. The SOHR method derives in name from the path integral representation of quantum mechanics proposed by Feynman. Unlike the continuous dynamical pathways of quantum mechanics, the chemical pathways exist in a discrete species space. However, like the quantum analog, the SOHR method can yield a convergent quantitative solution by summing enough paths. The proposed research has two main objectives. First, the methodology of the SOHR method is further developed into a generally applicable simulation tool. This involve the introduction of an iterative solution method to obtain the pathway probabilities. Also, graph searching algorithms is being developed to locate the most important chemical routes to a product. The second objective is to interpret chemical mechanism found in combustion chemistry and surface catalysis using SOHR. The chemical pathways found by the SOHR algorithm have direct physical meaning as the global mechanism for product formation. Therefore, issues such as product selectivity, trace species formation, and emergence of catalytic cycles can be explored in realistic models. The methodology will be applied to large mechanisms such as propane combustion and methanol-steam reforming reactions on Cu-nanoparticle catalysts.