An ab initio-based kinetic Monte Carlo algorithm was developed to simulate the direct decomposition of NO over Pt and different PtAu alloy surfaces. The algorithm was used to test the influence of the composition and the specific atomic surface structure of the alloy on the simulated activity and selectivity to form N-2. The apparent activation barrier found for the simulation of lean NO decomposition over Pt(100) was 7.4 kcal/ mol, which is lower than the experimental value of 11 kcal/mol that was determined over supported Pt nanoparticles. Differences are likely due to differences in the surface structure between the ideal (100) surface and supported Pt particles. The apparent reaction orders for lean NO decomposition over the Pt(100) substrate were calculated to be 0.9 and -0.5 for NO and O-2 respectively. Oxygen acts to poison Pt. Simulations on the different Pt-Au(100) surface alloys indicate that the turnover frequency goes through a maximum as the Au composition in the surface is increased, and the maximum occurs near 44% An. Turnover frequencies, however, are dictated by the actual arrangements of Pt and An atoms in the surface rather than by their overall composition. Surfaces with similar compositions but different alloy arrangements can lead to very different activities. Surfaces composed of 50% Pt and 50% Au (Pt-4 and Au-4 surface ensembles) showed very little enhancement in the activity over that which was found over pure Pt. The Pt-Pt bridge sites required for NO adsorption and decomposition were still effectively poisoned by atomic oxygen. The well-dispersed Pt(50%)AU(50%) alloy, on the other hand, increased the TOF over that found for pure Pt by a factor of 2. The most active surface alloy was one in which the Pt was arranged into "+" ensembles surrounded by Au atoms. The overall composition of this surface is Pt56.2%Au43.8%. The unique "+" ensembles maintain Pt bridge sites for NO to adsorb on but limit 02 as well as NO activation by eliminating next-nearest neighbor Pt-bridge sites. The repulsive interactions between two adatoms prevent them from sharing the same metal atoms. The decrease in the oxygen coverage leads to a greater number of vacant sites available for NO adsorption. This increases the NO coupling reaction and hence N-2, formation. The inhibition of the rate of N? formation by 0, is therefore suppressed. The coverage of atomic oxygen decreases from 53% on the Pt(100) surface down to 19% on the ensemble surface. This increases the rate of N, formation by a factor of 4.3 over that on pure Pt. The reaction kinetics over the "+" ensemble Pt56.2%Au43.8%, surface indicate apparent reaction orders in NO and oxygen of 0.7 and 0.0, respectively. This suggests that oxygen does not poison the PtAu "+" alloy ensemble. The activity and selectivity of the PtAu ensembles significantly decrease for alloys that go beyond 60% Au. Higher coverages of An shut down sites for NO adsorption and, in addition, weaken the NO and 0 bond strengths, which subsequently promotes desorption as well as NO oxidation. The computational approach identified herein can be used to more rapidly test different metal compositions and their explicit atomic arrangements for improved catalytic performance. This can be done "in silico" and thus provides a method that may aid high-throughput experimental efforts in the design of new materials. The synthesis and stability of the metal complexes suggested herein still ultimately need to be tested.