Field studies show that gas phase nucleation is an important source of new particles in the Earth's atmosphere. However, the mechanism of new particle formation is not known. The predictions of current atmospheric nucleation models are highly uncertain because the models are based on estimates for the thermodynamics of cluster growth. We have measured the thermodynamics for the growth and evaporation of small cluster ions containing H2SO4 and H2O, and incorporated these data into a kinetic aerosol model to yield quantitative predictions of the rate of ion-induced nucleation for atmospheric conditions. The model predicts that the binary negative ion H2SO4/H2O mechanism is an efficient source of new particles in the middle and upper troposphere. The ion-induced HSO4-/H2SO4/H2O mechanism does explain nucleation events observed in the remote middle troposphere, but does not generally predict the nucleation events observed in the boundary layer.