In the kinetic Monte Carlo method is a stochastic approach for modeling a sequence of thermally activated events such that the likelihood of each event occurs is consistent with the rate of event. A typical KMC algorithm executes elementary events one after the other (one event at time) and generates a sequence of configurations and times to decide when the transitions between these configurations occur. This solves the master equation numerically: Where the sum over j runs over all neighbouring configurations of lattice site i and ?ji denotes the rate constant for adatom hops from i to j.
1.2 Reaction modelA simple model which describes a catalytic reaction between two different species A and B is used here. The catalyst surface is given by the two-dimensional integer lattice (system size of 100×100 was used for all calculations). The forces working on an atom or a molecule that adsorbs on a surface move it to well-defined positions on the surface, which correspond to minima in the potential energy.
The species A and B may diffuse from one site to another by overcoming energy barriers, given by ?EA and ?EB, respectively. The atoms are assumed to react with each other instantly when they occupy the same adsorption site. The product A-B formed will desorb from the catalyst surface and the site will be re-occupied by new atoms. Figure 1. Snapshots of reaction model, which consists of catalyst surface (single atomic layer) and atoms of A and B (pink and orange spheres), and reaction product (blue spheres) at kT = 1.0 This model assumes that the partial pressure can be modified to keep the total numbers of A and B constant at any time. In practice, coverages are variables of a differential equation system to be solved for.
Furthermore, all catalytic sites are considered to be equivalent in this case. However, it is not true in general: catalytic surface exposes a variety of sites with different coordination numbers, onto which adsorbates bind with different strengths.