Recently, we have shown that the binary homogeneous nucleation (BHN) of H2SO4 and H2O can be treated as a quasi-unary nucleation (QUN) of H2SO4 in the equilibrium with H2O vapor and have developed a kinetic H2SO4-H2O nucleation model, which simulates the dynamic evolutions of cluster distributions explicitly. In this paper we present improved and updated version of the QUN model, which has been modified through the incorporation of more rigorous thermodynamics of the cluster formation and the effect of the surface area of preexisting particles on nucleation rates. The difference in the model predictions of the improved and original QUN models is not dramatic; however, the improved QUN model is more consistent thermodynamically. The predicted BHN rates based on the QUN model are in good agreement with existing observations within the range of uncertainties. We also study the dependence of kinetic BHN rates on key input parameters and discuss the conditions in which the H2SO4-H2O homogeneous nucleation in the atmosphere may become significant. The nucleation rates look-up tables derived from the QUN model, which can be readily used to find the nucleation rates at given conditions, are presented. The look-up tables cover a wide range of key parameters that can be found in the ambient atmosphere, in the laboratory studies, and in the exhaust plumes. These look-up tables can be easily incorporated in multidimensional models to predict BHN rates, and they can be utilized directly for the analysis and interpretation of the observed nucleation events.