Monte Carlo methods for the simulation of the dynamic behavior of surface reactions are developed, based on the chemical master equation. The methods are stated in a general framework which makes them applicable to a variety of models. Three methods are developed. A comparative analysis of the performance of the three methods, both theoretically and empirically, is included. ͓S1063-651X͑98͒08207-5͔
Results of dynamic Monte Carlo simulations of a model for CO oxidation on a reconstructing Pt͑100͒ surface are presented. A comparison is made between simulations that explicitly include surface diffusion of adsorbed CO and simulations without diffusion. Oscillatory behavior as well as spatio-temporal pattern formation are studied as a function of system size. In the absence of diffusion the amplitude of kinetic oscillations decreases with grid size and oscillations are not stable. Spatio-temporal patterns appear, as expected for an excitable medium. Such patterns become stabilized by structural substrate defects. The length scale of the patterns is in the order of 10-100 nm, the temporal period of the oscillations is around 200 seconds. Inclusion of diffusion stabilizes and synchronizes oscillations. Spatio-temporal features now appear with larger spatial dimensions.
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