Understanding Combustion and Surface Kinetics Using the Sum Over Histories Representation

来自科罗拉多大学博尔德分校的Rex Skodje获得了化学理论、模型和计算方法项目的奖励，他开发了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，碳氢化合物在发动机中的燃烧可能涉及数千个单独的化学反应，因为燃料分子在以二氧化碳和水的形式到达最终目的地的过程中分解和氧化。同样，大型化学网络也出现在大气化学、生命系统生物化学、催化反应器性能和许多其他领域的研究中。目前的项目研究这些复杂的系统使用一种新的方法称为历史总和表示（或SOHR）。在SOHR方法中，复杂系统的化学反应是用单个分子的反应路径来定量描述的，而不是用一个多世纪以来一直使用的传统的速率方程方法。这项工作有几个目标。首先，数学方法得到了改进，使其更有效，以方便对超大型化学系统的实施。其次，SOHR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）表面的催化反应。所提出的研究计划的成功结果无论从基础科学的角度还是在实际应用中都是重要的。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。这种创新的方法正在用户友好的软件中得到实施，并提供给更大的研究界。SOHR方法取代了传统的动力学模型，该模型涉及使用由机制中每个物种的形成和破坏速率形成的“局部”微分速率方程理论。SOHR方法使用的是“全局”化学途径。在模拟过程中，化学途径跟随一个化学片段，如“标记原子”，因为它在不同的物种之间跳跃，这是由于反应造成的。我们发现，如果列举了足够数量的这些化学途径，就可以定量地描述模型的全部化学性质。SOHR方法在名称上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方法可以通过求和足够的路径来产生收敛的定量解。拟议的研究有两个主要目标。首先，将SOHR方法的方法论进一步发展成为一种普遍适用的仿真工具。这涉及到引入一种迭代求解方法来获得路径概率。此外，图形搜索算法正在开发，以定位到产品的最重要的化学路线。第二个目标是用SOHR解释燃烧化学和表面催化中发现的化学机制。SOHR算法发现的化学途径作为产物形成的整体机制具有直接的物理意义。因此，可以在现实模型中探索诸如产物选择性、痕量物种形成和催化循环的出现等问题。该方法将应用于大型机制，如丙烷燃烧和甲醇-蒸汽重整反应在cu纳米颗粒催化剂上。

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.