Kinetic Monte Carlo Method: Mathematical Foundations and Applications for Physics of Low-Dimensional Nanostructures

Kinetic Monte Carlo simulations for heterogeneous catalysis: Fundamentals, current status, and challenges

“…[65][66][67] The KMC framework is specifically tailored to address the time-scale problem just discussed, and in doing so, it allows us to access the long time dynamics necessary to explore heterogeneously catalyzed reactions. 24,28,54,55,68 As its name indicates, KMC combines the Monte Carlo (MC) method with a kinetic approach that focuses on the time-scale of the barrier crossings and uses transition state theory (TST) 69 arguments to describe the statistics of the transitions between basins of the PES. Therefore, in contrast to traditional equilibrium MC simulations where the time variable is absent, 70,71 in KMC, the temporal evolution of the catalytic system is taken into account but just in a coarse-grained sense, namely the simulations pertain to the timescale of the barrier crossings rather than that of atomic vibrations, as in MD.…”

Aggregation of Size-Selected Oxide Clusters Deposited onto Au(111)

“…For a general description of using kMC for surface simulations, the reader is directed to several review papers on this topic. 38,39 The goal was to allow for flexible inputs of both energetic and system conditions to observe how these parameters influence the growth of dendritic structures.…”

“…A kinetic Monte Carlo (kMC) code was developed to simulate the aggregation of interacting particles on a 2D grid using realistic thermodynamic parameters that control diffusion and interparticle interactions. For a general description of using kMC for surface simulations, the reader is directed to several review papers on this topic. , The goal was to allow for flexible inputs of both energetic and system conditions to observe how these parameters influence the growth of dendritic structures.…”

“…The latter include energetics, e.g., diffusion barriers, barriers to intercluster bond formation, and intercluster binding energies, as well as experimental factors such as surface temperature and deposition rate. Some of the energetic quantities can be estimated from DFT calculations on isolated clusters and/or dimers and these can be used in larger scale kinetic Monte Carlo (kMC) simulations of particle motion and interactions that also include experimental variables. − In particular, 2D kinetic Monte Carlo (kMC) simulations that explicitly include energetics of particle diffusion and interparticle interactions have been used successfully to model the growth and morphology of surface species (atoms and molecules) deposited onto planar surfaces. − ,,− …”