The formation of carbonaceous and silicate precursor molecules to astrophysical dust grains is investigated. Using density functional theory (DFT) in combination with global optimization techniques, the ground-state binding energies of dust precursors are determined. These results are employed in atomistic nucleation theory (ANT) to predict the critical size and nucleation rates of molecular clusters that are likely to form in the environment of stellar outflows. Carbon grains are shown to have critical sizes fall on the locations of ground-state geometry transitions (chain-to-ring, ring-to-fullerene) with nucleation rates suppressed at large temperatures and enhanced at low temperatures. Silicate grains are modeled as Mg-rich olivine (Mg2SiO4)n. At large sizes, these clusters are found to be amorphous rather than crystalline. A dust growth model is developed alongside the results from ANT calculations. A chemical kinetics integration code is developed, which takes into account the formation of refractory cores from nucleation.