Understanding Combustion and Surface Kinetics Using the Sum Over Histories Representation

科罗拉多大学博尔德分校的雷克斯斯科杰获得了化学理论、模型和计算方法项目的一个奖项的支持，以开发一种新的化学动力学方法。自然界和技术中的许多重要系统都是由相互关联的化学反应组成的大型网络来描述的。 例如，发动机中的碳氢化合物燃烧可能涉及数千个单独的化学反应，因为燃料分子在到达其最终目的地的过程中分解并氧化为二氧化碳和水。 类似地，大型化学网络出现在大气化学、生命系统的生物化学、催化反应器的性能以及许多其他地方。 本项目使用一种新的方法来研究这些复杂的系统，该方法被称为历史上的总和表示（或SOHR）。 在SOHR方法中，复杂体系的化学是使用单个分子遵循的反应途径来定量描述的，而不是使用已经使用了世纪的传统速率方程方法。 这项工作有几个目标。 首先，数学方法是完善和高效的，以方便实施到非常大的化学系统。 其次，SOHR方法用于分析丙烷和庚烷等重要燃料的燃烧化学。 第三，SOHR方法用于模拟重要有机分子在工业相关材料（如镍和铂）表面上的催化反应。从基础科学的角度以及在实际应用中，拟议的研究计划的成功结果都是重要的。 SOHR方法旨在通过识别机制中的主要化学途径，将复杂的化学系统简化为最简单最透明的形式。 这将指导实际反应堆的设计和优化，并为自然发生的网络提供新的见解。SOHR方法取代了传统的动力学建模，后者涉及使用“局部”微分速率方程理论，该理论是从机制中每个物种的形成和破坏速率形成的。 SOHR方法使用“全局”化学途径。 化学路径遵循化学部分，例如“标记原子”，因为它在模拟过程中由于反应而从一个物种跳到另一个物种。 据发现，如果这些化学途径的足够数量的枚举，完整的化学模型可以定量描述。 SOHR方法的名称来源于费曼提出的量子力学的路径积分表示。 与量子力学的连续动力学路径不同，化学路径存在于离散的物种空间中。 然而，像量子模拟一样，SOHR方法可以通过对足够多的路径求和来产生收敛的定量解。 拟议的研究有两个主要目标。 首先，SOHR方法的方法是 进一步发展成为一个普遍适用的仿真工具。 这涉及到一个迭代的解决方案的方法来获得路径概率的介绍。 此外，正在开发图形搜索算法，以定位产品的最重要的化学路线。 第二个目标是解释化学机理发现燃烧化学和表面催化使用SOHR。 SOHR算法发现的化学途径作为产物形成的全局机制具有直接的物理意义。 因此，可以在现实模型中探索产物选择性、痕量物质形成和催化循环的出现等问题。 该方法将被应用于大型机制，如丙烷燃烧和甲醇-水蒸气重整反应的铜纳米颗粒催化剂。

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.