The dissocn. of methane and hydrogenation of at. carbon on the Ru(0001) surface are simulated via the Dynamic Monte Carlo method. First-principle quantum chem. calcns. are carried out to predict the binding energies and lateral interactions of adsorbed CHx species on the Ru(0001) surface. Subsequently, the DFT results are used to parametrize the interactions of these adsorbates on the surfaces. The lateral interactions are assumed to be pairwise additive. The DMC with lateral interaction is compared to a classical Mean Field description and DMC without lateral interactions. The inclusion of lateral interactions induces a radical change to the behavior of the simulation with an increase of the rate of dissocn. while the rate of hydrogenation...