Monte Carlo Algorithms for Complex Surface Reaction Mechanisms: Efficiency and Accuracy

A continuous-time Monte Carlo (CTMC) algorithm with lists of neighbors and local update (tree-type architecture) for simulating the dynamics and stationary pattern formation of complex surface reaction mechanisms is discussed. Two additional CTMC algorithms, often used in the literature, are also presented. The computational efficiency of these CTMC algorithms is compared to a null-event algorithm for the CO oxidation on a Pt(100) surface by direct numerical simulations. Furthermore, we have derived simple formulas for the real time advanced using the null-event algorithm and the CTMC with local update algorithm for the infinitely fast and finite CO oxidation kinetics as well as a unimolecular surface reaction. We have found that the proposed CTMC algorithm with classes and local update can be much faster than the traditional null-event algorithms by orders of magnitude, when stiffness occurs (rare event dynamics). In addition, we address the computational accuracy of Monte Carlo algorithms, due to limited resolution caused by finite lattice sizes, for key intermediate species in a complex reaction mechanism. It is shown that surface concentrations below the resolution of the lattice and corresponding reaction rates can accurately be calculated through the use of a time-weighted average of reaction rates.