The formation of atmospheric aerosol particles through clustering of condensable vapors is an important contributor to the overall concentration of these atmospheric particles. However, the details of the nucleation process are not yet well understood and are difficult to probe by experimental means. Computational chemistry is a powerful tool for gaining insights about the nucleation mechanism. Here, we report accurate electronic structure calculations of the potential energies of small clusters made from sulfuric acid, ammonia, and dimethylamine. We also assess and validate the accuracy of less expensive methods that might be used for the calculation of the binding energies of larger clusters for atmospheric modeling. The PW6B95-D3 density-functional-plus- molecular-mechanics calculation with the MG3S basis set stands out as yielding excellent accuracy while still being affordable for very large clusters.