We demonstrate that the Langmuir–Hinshelwood formalism is an incomplete kinetic description and, in particular, that the Hinshelwood assumption (i.e., that adsorbates are randomly distributed on the surface) is inappropriate even in catalytic reactions as simple as A + A → A₂. The Hinshelwood assumption results in miscounting of site pairs (e.g., A*–A*) and, consequently, in erroneous rates, reaction orders, and identification of rate-determining steps. The clustering and isolation of surface species unnoticed by the Langmuir–Hinshelwood model is rigorously accounted for by derivation of higher-order rate terms containing statistical factors specific to each site ensemble. Ensemble-specific statistical rate terms arise irrespective of and couple with lateral adsorbate interactions, are distinct for each elementary step including surface diffusion events (e.g., A* + * → * + A*), and provide physical insight obscured by the nonanalytical nature of the kinetic Monte Carlo (kMC) method—with which the higher-order formalism quantitatively agrees. The limitations of the Langmuir–Hinshelwood model are attributed to the incorrect assertion that the rate of an elementary step is the same with respect to each site ensemble. In actuality, each elementary step—including adsorbate diffusion—traverses through each ensemble with unique rate, reversibility, and kinetic-relevance to the overall reaction rate. Explicit kinetic description of ensemble-specific paths is key to the improvements of the higher-order formalism; enables quantification of ensemble-specific rate, reversibility, and degree of rate control of surface diffusion; and reveals that a single elementary step can, counter intuitively, be both equilibrated and rate determining.

我们证明，Langmuir-Hinshelwood形式主义是不完整的动力学描述，尤其是，即使在像A + A→A _2这样的催化反应中，Hinshelwood的假设（即吸附物随机分布在表面上）也是不合适的。。Hinshelwood的假设导致对位点对（例如，A * –A *）的计数错误，并因此导致错误的速率，反应顺序和速率确定步骤的识别。Langmuir-Hinshelwood模型未注意到的表面物种的聚类和隔离是通过推导包含特定于每个站点集合的统计因子的高阶速率项来严格解决的。特定于集合的统计速率项不依赖于横向吸附物相互作用而与之耦合，对于包括表面扩散事件（例如，A * + *→* + A *）的每个基本步骤都是不同的，并且提供了因非分析性质而模糊的物理洞察力动力学蒙特卡罗（kMC）方法-高阶形式主义在数量上与之一致。Langmuir-Hinshelwood模型的局限性归因于错误的主张，即每个站点集合的基本步骤的速率相同。实际上，每个基本步骤（包括吸附物扩散）都以独特的速率，可逆性和与总反应速率的动力学相关性贯穿每个集合。显式动力学描述合奏特定路径是改进高阶形式主义的关键。能够量化整体特定速率，表面扩散的可逆性和速率控制程度；并揭示出，一个基本步骤可以直观地抵消，并且可以确定费率。每个基本步骤（包括吸附剂扩散）都以独特的速率，可逆性以及与总反应速率的动力学相关性贯穿每个集合。显式动力学描述合奏特定路径是改进高阶形式主义的关键。能够量化整体特定速率，表面扩散的可逆性和速率控制程度；并揭示出，一个基本步骤可以直观地抵消，并且可以确定费率。每个基本步骤（包括吸附剂扩散）都以独特的速率，可逆性以及与总反应速率的动力学相关性贯穿每个集合。显式动力学描述合奏特定路径是改进高阶形式主义的关键。能够量化整体特定速率，表面扩散的可逆性和速率控制程度；并揭示出，一个基本步骤可以直观地抵消，并且可以确定费率。