Molecularly engineered deposition processes require computational algorithms that efficiently capture phenomena present at widely varying length and time scales. In this work, the island dynamics method was applied to simulation of kinetically-limited metal nucleation and growth by electrodeposition in the presence of additives. The model included additive kinetics, surface diffusion of adatoms, nucleation, and growth. The model was demonstrated for copper deposition in acid sulfate electrolyte containing [bis(3-sulfopropyl)disulfide], polyethylene glycol, and chloride. Simulation results were compared with kinetic Monte Carlo (KMC) calculations and found to be within 1% for fractional coverage values, and within 10% for nucleation density. The computational time was more than 10X faster than comparable KMC simulations over the range studied. The island dynamics algorithm was applied to the electrodeposition of a metal onto a substrate initially configured with an array of hemispherical seed clusters. It was found that the presence of chloride in the model additive system caused high densities of nuclei on the substrate surrounding the initial seed clusters, which led to the formation of a continuous thin metal film. Simulations carried out under low-chloride conditions resulted in the growth only of the initial seed clusters, without significant nucleation or thin film formation. Additional phenomena were explored by linking the molecular scale island dynamics algorithm to a continuum model that described the migration and diffusion in the diffusion layer near the electrode surface. The multiscale linkage allowed simulation of nucleation, growth, and additive chemistry under mass transport limited conditions, including the formation of nucleation exclusion zones surrounding growing nuclei. A two-step approach was used to calculate the spatial distribution of nucleation events on an electrode undergoing deposition by electrolysis under the influence of mass transport. The simulations were carried out by first, calculating the time-dependent concentration profiles in the vicinity of a hemispherical nucleus, then using the concentration profiles as boundary conditions for a surface simulation that relied on the island dynamics algorithm. The model additive system was found to uniformize the distribution of nuclei on the simulated surface, leading to a significant reduction in the size of nucleation exclusion zones.