Efficient implementation of Cluster Expansion models in surface Kinetic Monte Carlo simulations with lateral interactions: Subtraction Schemes, Supersites and the Supercluster Contraction F. Hess. *J. Comp. Chem.* 40 (**2019**) 2664– 2676. 10.1002/jcc.26041

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### Overcoming the challenges of simulating surface reactions with complex interaction models

The complexity of first-principles-based Kinetic Monte Carlo (KMC) models to treat chemical reactions at surfaces has risen dramatically over the past few years. Lateral interactions have been disregarded in kinetic models of surface reactions for a long time, in part due to the inability to obtain reliable parameters from experiments, in part due to the belief that these interactions play only a minor role in the kinetics of surface reactions, and also, in part, due to the extensive computational effort associated with computing them on the level of electronic structure theory and simulating reactions with lateral interactions in KMC.

Lateral interactions in KMC simulations are often modeled in a Cluster Expansion (CE) Hamiltonian, where the total energy of the lattice and adsorption energies are represented as a sum of interaction clusters, where each cluster represents a pattern in which adsorbates are arranged on the surface, for instance, pairwise, three-body, four body, and larger clusters. The Cluster Expansion is, in principle, exact, but is always truncated in practical application due to constraints in the number of parameters that can be determined (and meaningfully fitted) on a first principles level, and in the evaluation of the Hamiltonian.

While lateral interaction models for surface coadsorbate systems 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 this additional computational cost 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. However, these challenges can be overcome by dedicated optimization strategies and we have made significant progress in developing new KMC algorithms using Cluster Expansion Hamiltonians. The code and benchmark have recently been released on Github and in a J. Comp. Chem. paper.

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