A consistent hierarchy of generalized kinetic equation approximations to the master equation applied to surface catalysis.
A consistent hierarchy of generalized kinetic equation approximations to the master equation applied to surface catalysis.
复制标题
适用于表面催化的主方程的广义动力学方程近似的一致层次结构。
作者：
G. Herschlag;S. Mitran;G. Lin
我们开发了一个层次逼近主方程的系统，表现出平移不变性和有限范围的空间相关性。层次结构中的每个近似都是一组常微分方程，这些常微分方程考虑了不同晶格距离的空间相关性；假设整个系统将具有有限的空间相关性，因此层次结构中的模型的行为将接近整个系统的行为。我们在一维和二维数值例子的背景下提供了这种收敛的证据。考虑较短空间相关性的层次结构中的较低层次显示比一维系统的传统动力学蒙特卡罗方法（KMC）快三个数量级，同时预测与KMC方法相似的系统动力学和稳态。然后，我们在二维模型上测试了CO在RuO2上氧化的层次结构（110），表明层次结构的低阶截断有效地捕获了基本的系统动力学。通过考虑考虑较长空间相关性的层次结构中的模型序列，连续模型预测可用于建立误差估计的经验近似值。该层次可以被认为是一类广义的现象学动力学模型，因为层次的每个元素都近似于主方程，并且层次中的最低层次与简单的现有现象学动力学模型相同。
We develop a hierarchy of approximations to the master equation for systems that exhibit translational invariance and finite-range spatial correlation. Each approximation within the hierarchy is a set of ordinary differential equations that considers spatial correlations of varying lattice distance; the assumption is that the full system will have finite spatial correlations and thus the behavior of the models within the hierarchy will approach that of the full system. We provide evidence of this convergence in the context of one- and two-dimensional numerical examples. Lower levels within the hierarchy that consider shorter spatial correlations are shown to be up to three orders of magnitude faster than traditional kinetic Monte Carlo methods (KMC) for one-dimensional systems, while predicting similar system dynamics and steady states as KMC methods. We then test the hierarchy on a two-dimensional model for the oxidation of CO on RuO2(110), showing that low-order truncations of the hierarchy efficiently capture the essential system dynamics. By considering sequences of models in the hierarchy that account for longer spatial correlations, successive model predictions may be used to establish empirical approximation of error estimates. The hierarchy may be thought of as a class of generalized phenomenological kinetic models since each element of the hierarchy approximates the master equation and the lowest level in the hierarchy is identical to a simple existing phenomenological kinetic models.