While atmosphere is known to contain a significant fraction of organic substance and the effect of acetic acid to stabilize hydrated sulfuric acids is found to be close that of ammonia, the details about the hydration of (CH3COOH)(H2SO4)2 are poorly understood, especially for the larger clusters with more water molecules. We have investigated structural characteristics and thermodynamics of the hydrates using density functional theory (DFT) at PW91PW91/6-311++G(3df,3pd) level. The phenomena of the structural evolution may exist during the early stage of the clusters formation, and we tentatively proposed a calculation path for the Gibbs free energies of the clusters formation via the structural evolution. The results in this study supply a picture of the first deprotonation of sulfuric acids for a system consisting of two sulfuric acid molecules, an acetic acid molecule, and up to three waters at 0 and 298.15 K, respectively. We also replace one of the sulfuric acids with a bisulfate anion in (CH3COOH)(H2SO4)2 to explore the difference of acid dissociation between two series of clusters and interaction of performance in clusters growth between ion-mediated nucleation and organics-enhanced nucleation.