Highly oxidized organic molecules may play a critical role in new-particle formation within Earth's atmosphere along with sulfuric acid, which has long been considered as a key compound in this process. Here we explore the interactions of these two partners, using quantum chemistry to find the formation free energies of heterodimers and trimers as well as the fastest evaporation rates of (2,2) tetramers. We find that the heterodimers are more strongly bound than pure sulfuric acid dimers. Their stability correlates well with the oxygen to carbon ratio of the organics, their volatility, and the number of hydrogen bonds formed. Most of the stable trimers contain one sulfuric acid and two organics (1,2), whereas many (2,2) tetramers evaporate quickly, probably due to the stability of (1,2) clusters. This finding agrees with recent experimental studies that show how new-particle formation involving oxidized organics and sulfuric acid may be rate limited by activation of (1,2) trimers, confirming the importance of this process in the atmosphere.