The abundance and basicity of a stabilizing base have shown to be key factors in sulfuric acid driven atmospheric new-particle formation. However, since experiments indicate that a low concentration of ammonia enhances particle formation from sulfuric acid and dimethylamine, which is a stronger base, there must be additional factors affecting the particle formation efficiency. Using quantum chemistry, we provide a molecular-level explanation for the synergistic effects in sulfuric acid-dimethylamine-ammonia cluster formation. Because of the capability of ammonia to form more intermolecular interactions than dimethylamine, it can act as a bridge-former in sulfuric acid-dimethylamine clusters. In many cluster compositions, ammonia is more likely to be protonated than dimethylamine, although it is a weaker base. By nanoparticle formation rate simulations, we show that due to the synergistic effects, ammonia can increase the particle formation rate by up to 5 orders of magnitude compared to the two-component sulfuric acid-amine system.