The formation of new particles through condensation from the gas phase is an important source of atmospheric aerosols. The properties of the electrically neutral clusters formed in the very first steps of the condensation process are, however, not directly observable by experimental means. We present here electronic structure calculations on the hydrates of clusters of three molecules of sulfuric acid and three molecules of ammonia or dimethylamine. On the basis of the results of these new calculations together with previously published material we simulate the influence of hydration on the dynamic processes involved in particle formation. Most strongly affected by hydration and most important as a mediator for the effect on particle formation rates are the evaporation rates of clusters. The results give an estimate of the sensitivity of the atmospheric particle formation rate for humidity. The particle formation rate can change approximately two orders of magnitude in either direction due to hydration; the net effect, however, is highly dependent on the exact conditions.