Modelling approaches for atmospheric iondipole collisions: allatom trajectory simulations and central field methods
 ^{1}Institute for Atmospheric and Earth System Research / Physics, Faculty of Science, University of Helsinki, P.O. Box 64, FI00014, Finland
 ^{2}Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, 92 Weijin Road, Tianjin 300072, China
 ^{1}Institute for Atmospheric and Earth System Research / Physics, Faculty of Science, University of Helsinki, P.O. Box 64, FI00014, Finland
 ^{2}Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, 92 Weijin Road, Tianjin 300072, China
Abstract. Iondipole collisions can facilitate the formation of atmospheric aerosol particles, and play an important role in their detection in chemical ionization mass spectrometers. Conventionally, analytical models, or simple parametrizations, have been used to calculate rate coefficients of iondipole collisions in the gas phase. Such models, however, neglect the atomistic structure and charge distribution of the collision partners. To determine the accuracy and applicability of these approaches at atmospheric conditions, we calculated collision cross sections and rate coefficients from allatom molecular dynamics collision trajectories, sampling the relevant range of impact parameters and relative velocities, and from a central field model using an effective attractive interaction fitted to the longrange potential of mean force between the collision partners. We considered collisions between various atmospherically relevant molecular ions and dipoles, as well as charged and neutral dipolar clusters. Based on the good agreement between collision cross sections and rate coefficients obtained from molecular dynamics trajectories and a generalized central field model, we conclude that the effective interactions between the collision partners are isotropic to a high degree, and the model is able to capture the relevant physicochemical properties of the systems. In addition, when the potential of mean force is recalculated at the respective temperatures, the central field model exhibits the correct temperature dependence of the collision process. The classical parametrization by Su and Chesnavich [J. Chem. Phys., 76, 5183–5185, 1982], which combines a central field model with simplified trajectory simulations, is able to predict the collision rate coefficients and their temperature dependence quite well for molecular systems, but the agreement worsens for systems containing clusters. Based on our results, we propose the combination of potential of mean force calculation and central field model as a viable and elegant alternative to brute force sampling of individual collision trajectories over a large range of impact parameters and relative velocities.

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The requested preprint has a corresponding peerreviewed final revised paper. You are encouraged to refer to the final revised version.

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The requested preprint has a corresponding peerreviewed final revised paper. You are encouraged to refer to the final revised version.
 Preprint
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 Final revised paper
Journal article(s) based on this preprint
Ivo Neefjes et al.
Interactive discussion
Status: closed

RC1: 'Comment on egusphere202293', Kai Leonhard, 16 May 2022
General comments:
The present work describes molecular Dynamics (MD) simulations of collisions of molecules / clusters and ions and the determination of collision rate constants from these simulations as well as from theory, using analytical equations with different approximations. The study increases our understanding of the validity range and limitations of these approximations.
Specific comments:
Eq 11: to my understanding, β_{L} is the rate constant for the collision of an ion with a polarizable molecule and β_{SC} that for an ion with a polarizable dipolar molecule. Hence, I would expect that K should approach one for μ_{d} (and hence x) approaching 0, but it seems to be 0.025. Please comment on this behaviour.
I find the description of the equilibration process difficult to follow (lines 222233). There is a statement “The collision partners were first separately equilibrated for 50 ps using a Langevin thermostat with a damping factor of 0.1 ps. During the equilibration, both the centerofmass motion of each collision partner and the angular momentum of the total system were removed … Both collision partners were then given a velocity along the xdirection” If they are equilibrated separately (i.e. in separate simulations), both fragments should not have any rotational angular momentum. I have the impression rather “together, but separated with a large distance” is meant. If the latter is the case, have you checked the correct distribution of rotational angular momenta? Only a check of the energy distribution is mentioned. This this is a scalar and the angular momentum is a vector, therefore this may not be sufficient.
Line 261: “The centerofmass distance criterion for a successful collision was determined for each system by taking the distance at which the value of the PMF was 5kBT (∼ 0.13 eV at 300 K) higher than its minimum,” There are two such distances, right and left from the minimum. Which one have you chosen?
Line 270, Discarding and adding new trajectories in case of dissociation: Is that the correct procedure? To me, it would seem most appropriate to define 3 outcomes of the encounters: no collision, association, and dissociation of an existing dimer. Then one would use the total number of trajectories in the denominator for each of the rate calculations. This would seem in line with what is done in Master Equation calculations for barrierless reactions. Please comment on the justification for your approach.
Line 279: What do you mean by “small oscillations in the interaction energy”?
Can you specify statistical uncertainties, for the MD results, e.g. in table 2?
Technical comment:
Figs 4 and 5: The Circles to not show up on my Adobe Acrobat on android, but they do on windows.

RC2: 'Comment on egusphere202293', Anonymous Referee #1, 06 Jul 2022
This manuscript explores the collision dynamics of eight iondipole systems using potential of mean force (PMF) calculations and molecular dynamics (MD) simulations. Collision probability maps are obtained by MD to determine the dynamic collision cross sections. The collision rate coefficient results obtained by PFM and MD are compared to the classic Su and Chesnavich and the LangevinGioumousisStevenson models.
The manuscript is in general well written and well organized and manages to provide an understanding of the conditions that PMF calculations and central field models can be used reliably for the determination of the collision rate coefficient.To further improve the manuscript, I suggest adding a comment on how long the clusters are traced after collision, i.e. what is the lifetime of the clusters shown here. In addition, the value of the probability, P(v,b), at which the dynamic collision cross sections of Fig. 4(eh) and Fig. 5(eh) were obtained by MD, should be provided.

AC1: 'Author response on egusphere202293', Ivo Neefjes, 14 Jul 2022
We greatly thank both referees for their helpful insights and constructive feedback. We have provided pointbypoint responses to each of their comments in separate response letters to each referee. These response letters have been added as a single supplement to this comment.
Interactive discussion
Status: closed

RC1: 'Comment on egusphere202293', Kai Leonhard, 16 May 2022
General comments:
The present work describes molecular Dynamics (MD) simulations of collisions of molecules / clusters and ions and the determination of collision rate constants from these simulations as well as from theory, using analytical equations with different approximations. The study increases our understanding of the validity range and limitations of these approximations.
Specific comments:
Eq 11: to my understanding, β_{L} is the rate constant for the collision of an ion with a polarizable molecule and β_{SC} that for an ion with a polarizable dipolar molecule. Hence, I would expect that K should approach one for μ_{d} (and hence x) approaching 0, but it seems to be 0.025. Please comment on this behaviour.
I find the description of the equilibration process difficult to follow (lines 222233). There is a statement “The collision partners were first separately equilibrated for 50 ps using a Langevin thermostat with a damping factor of 0.1 ps. During the equilibration, both the centerofmass motion of each collision partner and the angular momentum of the total system were removed … Both collision partners were then given a velocity along the xdirection” If they are equilibrated separately (i.e. in separate simulations), both fragments should not have any rotational angular momentum. I have the impression rather “together, but separated with a large distance” is meant. If the latter is the case, have you checked the correct distribution of rotational angular momenta? Only a check of the energy distribution is mentioned. This this is a scalar and the angular momentum is a vector, therefore this may not be sufficient.
Line 261: “The centerofmass distance criterion for a successful collision was determined for each system by taking the distance at which the value of the PMF was 5kBT (∼ 0.13 eV at 300 K) higher than its minimum,” There are two such distances, right and left from the minimum. Which one have you chosen?
Line 270, Discarding and adding new trajectories in case of dissociation: Is that the correct procedure? To me, it would seem most appropriate to define 3 outcomes of the encounters: no collision, association, and dissociation of an existing dimer. Then one would use the total number of trajectories in the denominator for each of the rate calculations. This would seem in line with what is done in Master Equation calculations for barrierless reactions. Please comment on the justification for your approach.
Line 279: What do you mean by “small oscillations in the interaction energy”?
Can you specify statistical uncertainties, for the MD results, e.g. in table 2?
Technical comment:
Figs 4 and 5: The Circles to not show up on my Adobe Acrobat on android, but they do on windows.

RC2: 'Comment on egusphere202293', Anonymous Referee #1, 06 Jul 2022
This manuscript explores the collision dynamics of eight iondipole systems using potential of mean force (PMF) calculations and molecular dynamics (MD) simulations. Collision probability maps are obtained by MD to determine the dynamic collision cross sections. The collision rate coefficient results obtained by PFM and MD are compared to the classic Su and Chesnavich and the LangevinGioumousisStevenson models.
The manuscript is in general well written and well organized and manages to provide an understanding of the conditions that PMF calculations and central field models can be used reliably for the determination of the collision rate coefficient.To further improve the manuscript, I suggest adding a comment on how long the clusters are traced after collision, i.e. what is the lifetime of the clusters shown here. In addition, the value of the probability, P(v,b), at which the dynamic collision cross sections of Fig. 4(eh) and Fig. 5(eh) were obtained by MD, should be provided.

AC1: 'Author response on egusphere202293', Ivo Neefjes, 14 Jul 2022
We greatly thank both referees for their helpful insights and constructive feedback. We have provided pointbypoint responses to each of their comments in separate response letters to each referee. These response letters have been added as a single supplement to this comment.
Peer review completion
Journal article(s) based on this preprint
Ivo Neefjes et al.
Ivo Neefjes et al.
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