In this work, the authors developed an ‘analytical interacting hard sphere’ model based on an effective molecule-cluster potential using Hamaker’s approach. This model is verified by comparison with point particle molecular dynamics and atomistic MD simulations. Overall, I enjoy reading this work, especially the discussion on relevant time scales, which I believe helps clarify confusions on the cluster formation process. However, I’m a bit doubtful about the applicability of the proposed methods and how much difference it makes compared to current approaches of calculating enhancement factors.The manuscript can be published after the following comments have been addressed.

1. In the discussion of the enhancement factor, I’d like to see comparisons with previous works (such as the work by Sceats). By doing so the readers can have a quantitively understanding of the difference between the current work and previous ones and decide whether to implement proposed model.
2. Although from the text one can figure out how to apply the proposed model, it is better if a step by step procedure is given in the supplementary information, specifying at each step what technique is used and what quantities are calculated.
3. If one intends to do calculations for collision rates involving (SA)₁(DMA)₁ or other atmospherically relevant clusters, is it necessary calculate the interactions parameters with MD simulations? If this is the case, the applicability of the model is somewhat restricted.
4. How to proceed with the model if the clusters are heterogeneous containing several types of ‘monomers’?
5. Line 391: Some citations on the vibrational coupling between vapor molecules and clusters can be added here. For readers with no formal training in physical chemistry, this does not seem to be common knowledge.

Technical corrections:

In Fig. 4a, the horizontal white line in the middle should be removed.

Line 383: Revise this sentence. ‘When considering the quantum mechanical nature of the system, some high frequency intramolecular vibrations possess no, or at least significantly less, energy than k_BT/2 at finite temperature.’

This manuscript focuses on extending the “Central field approach” to collision rate calculations to monomer-cluster calculations.  It is somewhat dense- it took several readthroughs to fully understand manuscript.  However, in the end I found the manuscript well-written, thorough in its presentation (both of prior work and the present model), and I believe it to be a substantial contribution to the literature.  I only have a few remarks for the authors to consider in revision:

1. (General).  Recent trajectory calculation models (by the authors and others) have shown that the sticking rate is very weakly sensitive to temperature- at higher temperatures the Maxwell Boltzmann distribution is shifted to higher speeds, but the influence of potential interactions is diminished.  I suggest also including plots for fixed cluster size as a function of temperature, perhaps over a wider temperature range, to see what temperature dependencies result here.
2. (General). Can the approach be extended to non-pairwise potentials?  This was not clear to me in reading the manuscript how to do this.
3. Figure 3a. While I do not see anything wrong with showing the critical impact parameter for the Coulomb potential, for long range, Coulombically attractive collisions at atmospheric pressure, the free molecular assumption is not valid, and the method the authors are using will not work (this is the problem of ion-ion recombination:   doi: 10.5194/acp-22-12443-2022, doi: 10.1063/1.5144772)