I will present a computational method for simulating the dynamics of atomic systems on time scales much longer than can be simulated with classical dynamics. In this method, possible reaction mechanisms available to the system are found with a minimum-mode following algorithm. Rates are estimated using harmonic transition state theory, and the system is propagated in time according to the kinetic Monte Carlo algorithm. The method can be run in parallel, and a distributed computing system has allowed us to simulate the deposition and growth of metal surfaces over experimental time scales using an embedded atom potential. Our algorithm is efficient enough to model the evolution of systems with ab-initio forces as well, for which I will show several examples, including metal cluster formation on oxide surfaces.