Kinetics of collision-sticking processes between vapor molecules and clusters of low-volatility compounds govern the initial steps of atmospheric new particle formation. Conventional non-interacting hard-sphere models underestimate the collision rate by neglecting long-range attractive forces, and the commonly adopted assumption that every collision leads to the formation of a stable cluster (unit mass accommodation coefficient) is questionable for small clusters, especially at elevated temperatures. Here, we present a generally applicable analytical interacting hard-sphere model for evaluating collision rates between molecules and clusters, accounting for long-range attractive forces. In the model, the collision cross section is calculated based on an effective molecule–cluster potential, derived using Hamaker's approach. Applied to collisions of sulfuric acid or dimethylamine with neutral bisulfate–dimethylammonium clusters composed of 1–32 dimers, our new model predicts collision rates 2–3 times higher than the non-interacting model for small clusters, while decaying asymptotically to the non-interacting limit as cluster size increases, in excellent agreement with a collision-rate-theory atomistic molecular dynamics simulation approach. Additionally, we calculated sticking rates and mass accommodation coefficients (MACs) using atomistic molecular dynamics collision simulations. For sulfuric acid, a MAC ≈1 is observed for collisions with all cluster sizes at temperatures between 200 and 400 K. For dimethylamine, we find that MACs decrease with increasing temperature and decreasing cluster size. At low temperatures, the MAC ≈1 assumption is generally valid, but at elevated temperatures MACs can drop below 0.2 for small clusters.