在具有横向相互作用的表面动力学蒙特卡罗模拟中团簇膨胀模型的有效实现：减法方案、超位点和超团簇收缩
Efficient implementation of Cluster Expansion models in surface Kinetic Monte Carlo simulations with lateral interactions: Subtraction Schemes, Supersites and the Supercluster Contraction
摘要：
虽然表面反应的横向相互作用模型已经逐渐普及并在复杂性方面增长，但它们在化学动力学中的使用受到当前KMC算法的低性能的阻碍。在KMC模拟与横向相互作用的额外的计算成本的起源可以追溯到更精细的集群扩展哈密顿量，更广泛的速率更新，并相互作用的吸附物系统的基于速率目录的算法的不切实际。相反，有利于基于站点的算法，我们提出了三种方法来降低成本的KMC模拟：1。用一个较小的超团簇哈密顿量表示晶格能而不损失精度，2。采用减法方案来更新模拟中的关键量，所述关键量在反应事件期间仅经历小的局部变化，以及3.从一组已建立的方法中应用有效的搜索算法（超现场方法）。由此产生的算法是固定成本相对于实际的晶格尺寸和规模的横向相互作用的范围的平方的晶格网站的数量。包括复杂的横向相互作用模型的总增加成本小于3倍。由于有限的数值精度在实施中的实际问题进行了详细讨论，并提出了进一步的建议，为治疗远程横向相互作用。我们的结论是，虽然KMC模拟与复杂的横向相互作用模型是具有挑战性的，这些挑战可以通过修改已建立的变步长方法，采用超聚类，减法和超位点算法（SSS-VSSM）来克服。
英文摘要：
While lateral interaction models for reactions at surfaces have steadily gained popularity and grown in terms of complexity, their use in chemical kinetics has been impeded by the low performance of current KMC algorithms. The origins of the additional computational cost in KMC simulations with lateral interactions are traced back to the more elaborate Cluster Expansion Hamiltonian, the more extensive rate updating, and to the impracticality of rate-catalog-based algorithms for interacting adsorbate systems. Favoring instead site-based algorithms, we propose three ways to reduce the cost of KMC simulations: 1. Represent the lattice energy by a smaller Supercluster Hamiltonian without loss of accuracy, 2. employing Subtraction Schemes for updating key quantities in the simulation that undergo only small, local changes during a reaction event, and 3. applying efficient search algorithms from a set of established methods (Supersite Approach). The resulting algorithm is fixed-cost with respect to the number of lattice sites for practical lattice sizes and scales with the square of the range of lateral interactions. The overall added cost of including a complex lateral interaction model amounts to less than a factor 3. Practical issues in implementation due to finite numerical accuracy are discussed in detail, and further suggestions for treating long-range lateral interactions are made. We conclude that, while KMC simulations with complex lateral interaction models are challenging, these challenges can be overcome by modifying the established Variable Step Size Method by employing the Supercluster, Subtraction and Supersite algorithms (SSS-VSSM).
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