We present simulations of stable isothermal clouds exposed to ionizing radiation from a discrete external source, and identify the conditions that lead to Radiatively Driven Implosion and Star Formation. We use the Smoothed Particle Hydrodynamics code SEREN (Hubber et al. 2010) and the HEALPix-based photoionization algorithm described in Bisbas et al. (2009). We find that the incident ionizing flux is the critical parameter determining the evolution; high fluxes disperse the cloud, whereas low fluxes trigger star formation. We find a clear connection between the intensity of the incident flux and the parameters of star formation.