HOM cluster decomposition in APi-TOF mass spectrometers

Identification of atmospheric molecular clusters and measurement of their concentrations by APi-TOF mass spectrometers may be affected by systematic error due to possible decomposition of clusters inside the instrument. Here, we perform numerical simulations of decomposition in an APi-TOF and formation in the atmosphere of a set of clusters which involve a representative kind of highly-oxygenated organic molecule (HOM), with molecular formula C10H16O8. This elemental composition corresponds to one of the most common mass peaks observed in experiments on ozone-initiated autoxidation of 5 α-pinene. Our results show that decomposition is highly unlikely for the considered clusters, provided their bonding energy is large enough to allow formation in the atmosphere in the first place.

Cluster decomposition in the APi-TOF is one of the main sources of uncertainty in the measurements. Lack of accuracy for a quantitative estimate of decomposition for example makes it difficult to draw definitive conclusions on the presence (or absence) of certain molecular clusters in the atmosphere. Often the absence of observations of specific clusters by  has led to speculation about decomposition inside the mass spectrometer . Recently, a numerical model to study decomposition in the APi-TOF has been developed by Zapadinsky et al. (2018). The decomposition model has been tested on simple clusters involving one bisulfate anion and two sulfuric acid molecules, giving very good agreement with experimental results (Passananti et al., 2019).
The uncertainties on cluster concentration measurements by APi-TOF and the lack of a comprehensive understanding of 30 decomposition inside the instrument are the motivations of the present work. Here we use a theoretical model to study in detail the decomposition of clusters involving so-called Highly-Oxygenated organic Molecules (HOM), which have recently been identified as a key contributor to NPF (Bianchi et al., 2019). HOM are molecules formed in the atmosphere from Volatile Organic Compounds (VOC). Some VOC with suitable functional groups can undergo an autoxidation process involving peroxy radicals, generating polyfunctional low-volatility vapors (i.e. HOM) that subsequently condense onto pre-existing particles.

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HOM thus contribute to Secondary Organic Aerosol (SOA), which constitutes a significant fraction of the submicron organic aerosol mass and is known to affect the Earth's radiation balance (Jimenez et al., 2009;Donahue et al., 2009;Hallquist et al., 2009). Recent chamber experiments have shown that NPF induced by multicomponent systems, such as sulfuric acid, ammonia and HOM, could correctly reproduce the NPF events observed in boreal forest (Lehtipalo et al., 2018).
Our study involves a specific kind of representative HOM (C 10 H 16 O 8 ) in the APi. This elemental composition corresponds 40 to one of the most common mass peaks observed in experiments on ozone-initiated autoxidation of α-pinene, which also fulfills the "HOM" definition of Bianchi et al. (2019). The precise molecular structure was adopted from Kurtén et al. (2016), and corresponds to the lowest-volatility structural isomer of the three C 10 H 16 O 8 compounds investigated in that study. The structure of the molecule is shown in Fig. 1.
The main scope of this work is to determine to what extent we are able to perform measurements of atmospheric cluster 45 concentrations using APi-TOF mass spectrometers. More specifically, we want to determine whether decomposition can possibly be responsible for the lack of observations of some HOM-containing clusters in an APi-TOF. Basically, the formation

Method
The model computes the probability of fragmentation of a single negatively-charged cluster from a large number (⇡ 10 3 ) of independent stochastic realizations of its dynamics in the APi. The algorithm of the code is described by the simplified flowchart shown in Fig. 3. We give here a brief description. For detailed description see Zapadinsky et al [16].
The dynamics starts with the ionized cluster accelerating in the mass spectrometer under the e↵ect of an electric field generated by the electrodes inside the APi. While moving, a random time interval to the next collision is computed from the cumulative distribution function P coll (t), which expresses the probability to encounter a collision after a time t: Here, ⌥ is the collision frequency which depends on the cluster velocity v, while t = 0 is the moment when the previous collision occurred. Simultaneously, another   collision: where P frag is the fragmentation probability and k, the fragmentation rate constant, is the inverse of the statistical average of fragmentation time, which depends on the cluster excess energy E beyond its fragmentation energy threshold. The fragmentation time is interpreted as the time the cluster spends intact before fragmenting. The fragmentation rate constant is derived from equilibrium condition between fragmentation and recombination processes using the detailed balance condition [16]. At this point, if the time required by the cluster to escape from the simulated region of the mass spectrometer is less than both the collision

Method
The model computes the probability of fragmentation of a single negatively-charged cluster from a large number (⇡ 10 3 ) of independent stochastic realizations of its dynamics in the APi. The algorithm of the code is described by the simplified flowchart shown in Fig. 3. We give here a brief description. For detailed description see Zapadinsky et al [16].
The dynamics starts with the ionized cluster accelerating in the mass spectrometer under the e↵ect of an electric field generated by the electrodes inside the APi. While moving, a random time interval to the next collision is computed from the cumulative distribution function P coll (t), which expresses the probability to encounter a collision after a time t: Here, ⌥ is the collision frequency which depends on the cluster velocity v, while t = 0 is the moment when the previous collision occurred. Simultaneously, another random time interval is computed for the fragmentation event from a Poisson distribution, which corresponds to the time-dependent survival probability P surv after  where P frag is k, the fragme of the statist which depend beyond its fra fragmentation cluster spend fragmentation librium condi combination p condition [16 At this poi ter to escape mass spectrom 3 (a) (b) Figure 2. (a) The overlap between the decomposition and particle formation regions defines the range of decomposition energy at which both the events (decomposition in the APi-TOF and particle formation in the atmosphere) are allowed. (b) The two events are incompatible.
of clusters in the atmosphere (often referred to as "nucleation") is driven by the bigger stability of the cluster with respect to its separated molecular (and sometimes ionic) components (fragments). The degree of stability is given by the energy difference between the fragments and the cluster in their (electronic and rotational-vibrational) ground states, which is called either 50 reaction, binding or decomposition energy, and it is equal to the amount of energy necessary to decompose the cluster (or, viceversa, the amount of energy released by the clustering). Higher decomposition energy implies lower decomposition and evaporation rates, and thus higher net formation rates in the atmosphere. On the contrary, decomposition in the APi-TOF is enhanced when the decomposition energy decreases, since less energy is required to break the cluster. It is clear at this point that decomposition and new-particle formation ("nucleation") have opposite dependences on the cluster decomposition energy.

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For a given temperature and vapor concentration, two situations are possible ( Fig. 2): 1. There is a limited range of values for the decomposition energy which allows both decomposition in the APi-TOF, and particle formation in the atmosphere.
2. The smallest decomposition energy that allows particle formation in the atmosphere is still too large to permit decomposition in the APi-TOF.

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Here, we predict both an upper bound for decomposition energy necessary for decomposition in the APi-TOF, and a lower bound for new-particle formation in the atmosphere given realistic vapor concentrations. The former can be evaluated using the numerical model developed by Zapadinsky et al. (2018), while the latter is computed using the Atmospheric Cluster Dynamics Code (ACDC) (McGrath et al., 2012). In the present work the simulations on decomposition have been performed by a new C++ version of the decomposition code, which keeps the same basic algorithm but performs faster.

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Another purpose of this work is to analyze the dynamics of complex clusters in the APi, showing where and why the decomposition events take place.
In Section 2 we present the decomposition model. In Section 3 we show the main results on HOM cluster decomposition and we compare them with ACDC simulations. Finally, in Section 4, we present the conclusions.

Method
The model computes the probability of fragmentation of a single negatively-charged cluster from a large number (⇡ 10 3 ) of independent stochastic realizations of its dynamics in the APi. The algorithm of the code is described by the simplified flowchart shown in Fig. 3. We give here a brief description. For detailed description see Zapadinsky et al [16].
The dynamics starts with the ionized cluster accelerating in the mass spectrometer under the e↵ect of an electric field generated by the electrodes inside the APi. While moving, a random time interval to the next collision is computed from the cumulative distribution function P coll (t), which expresses the probability to encounter a collision after a time t: Here, ⌥ is the collision frequency which depends on the cluster velocity v, while t = 0 is the moment when the previous collision occurred.  collision: where P frag is the fragmentation probability and k, the fragmentation rate constant, is the inverse of the statistical average of fragmentation time, which depends on the cluster excess energy E beyond its fragmentation energy threshold. The fragmentation time is interpreted as the time the cluster spends intact before fragmenting. The fragmentation rate constant is derived from equilibrium condition between fragmentation and recombination processes using the detailed balance condition [16]. At this point, if the time required by the cluster to escape from the simulated region of the mass spectrometer is less than both the collision

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The model computes the probability of decomposition of a single negatively-charged cluster from a large number (≈ 10 3 ) of independent stochastic realizations of its dynamics in the APi. The algorithm of the code is presented in the simplified flowchart shown in Fig. 3. We give only a brief description of the algorithm here, for full details see Zapadinsky et al. (2018).
The dynamics starts with the ionized cluster accelerating in the mass spectrometer under the effect of an electric field generated by the electrodes inside the APi. While moving, a random time interval to the next collision is computed from the cumulative 75 distribution function P coll (t), which expresses the probability to encounter a collision after a time t: Here, Υ is the collision frequency which depends on the cluster velocity v, while t = 0 is the moment when the previous collision occurred. Simultaneously, another random time interval is computed for the decomposition event from a Poisson distribution, which corresponds to the time-dependent survival probability P surv after collision: where P dec is the decomposition probability and k, the decomposition rate constant, is the inverse of the statistical average of decomposition time, which depends on the cluster excess energy ∆E beyond its decomposition energy threshold. The decomposition time is interpreted as the time the cluster spends intact before decomposing. The decomposition rate constant is  and fragmentation times, the single realization is completed and the counting of intact clusters is increased by one (Fig. 4a). A second possibility is that the fragmentation time is smaller than collision and escape times, in which case the count of fragmented clusters is increased by one (Fig. 4b). Finally, as third possibility, the collision time may be the smallest, in which case a collision between the cluster and a carrier gas molecule takes place (Fig. 4c). The dynamics of the collision is described by a stochastic process, where random velocities for the carrier gas molecules are computed from the Maxwell-Boltzmann distribution. In this case, the motion of the gas molecules is considered as solely translational. During the collision, the kinetic energy of the two colliding objects is partially converted into the internal degrees of freedom of the cluster (vibrational and rotational modes), according to the microcanonical ensemble approach: any equally-energetic configuration of the system is equally-probable. The fundamental relation governing this statistics is given by the proportionality between the probability density function of energies for two di↵erent interacting degrees of freedom and their density of states: where ✏ i is the energy of mode i, ⇢ i is the density of states of mode i and the Dirac delta function ensures conservation of total energy E. After in-tegrating Eq. 3 on all the possible values can assume, we get the probability densit tion for ✏ a : Notice that this formula holds at equil This assumption is justified from the fa the energy transfer takes place at time much shorter than the time scale betwe consecutive collisions. Specifically, vibr vibrational energy exchange takes place i 10 13 -10 12 s, rotational-vibrational exch 10 11 s and collisions every 10 9 -10 5 s.
After collision, the energy is then redist between rotational and vibrational modes ing the same principle, and the dynamics from the acceleration of cluster.
The computation of the density of vib and rotational states requires to knowledg corresponding energy levels, which are co by the quantum chemistry program Ga using the PM7 semi-empirical method, is the newest and generally best semi-em method available in Gaussian [19]. We no while semi-empirical methods are unable t rately model the energetics of molecular ing, this is not a problem in the present st the binding/fragmentation energy is here as a freely variable parameter (i.e. the able PM7 binding energy is not actually The purpose of the PM7 optimizations a quency calculations is simply to provide tatively correct distribution of rotational brational energy levels. As vibrational with wavenumbers above 2500 cm 1 are s underestimated by the PM7 method, we h ther rescaled the frequencies following t tion suggested in Rozanska et al., 2014  derived from Phase Space Theory of chemical reactions (PST). Basically, it is determined by the ratio of the densities of states 85 of products to the densities of states of reactant, exploiting the detailed balance condition (Zapadinsky et al., 2018). This is a more rigorous derivation than RRKM theory, since the latter does not take into account angular momentum conservation in the decomposition process.
At this point, if the time required by the cluster to escape from the simulated region of the mass spectrometer is less than both the collision and decomposition times, the single realization is completed and the count of intact clusters is increased by 90 one (Fig. 4a). A second possibility is that the decomposition time is smaller than collision and escape times, in which case the count of decomposed clusters is increased by one (Fig. 4b). Finally, as third possibility, the collision time may be the smallest, in which case a collision between the cluster and a carrier gas molecule takes place (Fig. 4c).
The dynamics of the collision is described by a stochastic process, where random velocities for the carrier gas molecules are computed from the Maxwell-Boltzmann distribution. In this case, the motion of the gas molecules is considered as solely 95 translational. During the collision, the kinetic energy of the two colliding objects is partially transferred to the internal degrees of freedom of the cluster (vibrational and rotational modes), according to the microcanonical ensemble approach: any configuration of the system with the same energy is equally probable. The fundamental relation governing this statistics is given by the proportionality between the probability density function of energies for two different interacting degrees of freedom and their densities of states: where i is the energy of mode i, ρ i is the density of states of mode i and the Dirac delta function δ ensures conservation of total energy E. After integrating Eq. 3 over all the possible values that b can assume, we get the probability density function for a : Notice that this formula holds at equilibrium. This assumption is justified from the fact that the energy transfer takes place at time scales much shorter than the time scale between two consecutive collisions. Specifically, vibrational-vibrational energy exchange takes place in about 10 −13 -10 −12 s, rotational-vibrational exchange in 10 −11 s and collisions every 10 −9 -10 −5 s.
After collision, the energy is then redistributed between rotational and vibrational modes following the same principle, and the dynamics continues with the acceleration of the cluster in the electric field.

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In region IV, where the quadrupole is located, the cluster is subjected to additional acceleration in the transverse directions, because of the alternating electric field generated by the quadrupole. The dynamics is determined by the renowned Mathieu equation (Miller and Denton, 1986): where 115 a = 4eU with y one of the two transverse displacements from the quadrupole axis, t the time, e the elementary charge, U the DC component and V the AC amplitude of the electric potential, m the cluster mass, r 0 the half-distance between quadrupole rods, and ω the AC angular frequency.
The computation of the density of vibrational and rotational states requires the knowledge of the corresponding energy 120 levels, which are computed by the quantum chemistry program Gaussian, using the PM7 semi-empirical method, which is the newest and generally best semi-empirical method available in Gaussian (Frisch et al., 2016). We note that while semi-empirical methods are unable to accurately model the energetics of molecular clustering, this is not a problem in the present study, as the binding/decomposition energy is treated here as a freely variable parameter (i.e. the unreliable PM7 binding energy is not actually used). The purpose of the PM7 optimizations and frequency calculations is simply to provide a qualitatively correct 125 distribution of rotational and vibrational energy levels. As vibrational modes with wavenumbers above 2500 cm −1 are strongly underestimated by the PM7 method, we have further rescaled the frequencies following the relation suggested in Rozanska et al. (2014): The vibrational density of states is then computed using the harmonic approximation, which is most likely the biggest source of error in the evaluation of the cluster survival probability. (See Section 3 for a sensitivity analysis on the effect of varying the vibrational frequencies).  The vibrational density of states is then computed using the harmonic approximation, which is most likely the biggest source of errors in the evaluation of the cluster survival probability.
(See next section for a sensitivity analysis on the e↵ect of the varying the vibrational frequencies).

Results
The simulation region involves only a portion of the total length of the APi-TOF mass spectrometer. Specifically, the simulations take place in the most critical region, between the end of the first chamber and the second one, where the pressure values make fragmentation possible. Before this region the collisions are not energetic enough, while after the carrier gas is so sparse that no collision happens [16]. In Fig. 5 we have a sketch of the simulated region. We subdivide the simulation region into 5 sections with di↵erent electric field and pressure values. Region I is at the end of the first chamber, region II defines the interface between the first and the second chambers and regions III, IV and V are located in the second chamber of the APi. The pressure in the first region is P 1 , while in the regions III, IV and V it is P 2 . In the region II, where the skimmer is located, the pressure is treated as a gradient, changing continuously from P 1 to P 2 . The electric field takes di↵erent values in the regions I, III, IV and V , while in II it is set to zero.
The voltage and pressure configuration, defines the electric fields and the pressures in the APi chambers, used in the CLOUD10 ex iments, are the following: We will use this voltage configuration and t pressures in our simulations. It is importan notice here that the electric field takes very d ent values in di↵erent sections, up to 3 orde magnitude, which will a↵ect the fragmenta positions as we will see (Fig. 12). We ass low amplitude of the oscillating electric fie the quadrupole of region IV . In this regime transverse motion of the cluster is negligible does not a↵ect the fragmentation probabilit this study the cluster fragmentation energy is treated as a free parameter. This allows u explore the behaviour of cluster survival pr bility as a function of E f on a large energy ra Moreover, keeping E f as a variable is also u since its computation by quantum chemistry culations (especially low-level methods suc PM7 used here) is a↵ected by large errors.
The clusters studied here are formed by bisulfate anion, one sulfuric acid molecule an least one HOM molecule. The clusters are sumed to fragment by losing one HOM, as lows: (HSO 4 )(H 2 SO 4 ) n (HOM 10 ) m ! (HSO 4 )(H 2 SO 4 ) n (HOM 10 ) m 1 + (HOM with n = 1, 2, m = 1, 2, 3 and HOM 10 is structure shown in Fig. 1. Our specific ch for HOM is not unique: this is one among m potential HOM produced in the ↵-pinene + reaction. The compound chosen is broadly re sentative of autoxidation products as it cont both hydroperoxide, ketone and carboxylic groups. The clusters have been constructe first maximizing H-bonds between the H 2

Decomposition in the APi
The simulation of decomposition involves only a portion of the total length of the APi-TOF mass spectrometer. Specifically, the simulations take place in the most critical region, ranging from the end of the first to the end of the second chamber of the APi, where the pressure values make decomposition possible: at the beginning of the first chamber the collisions are not energetic enough, while in the third chamber the carrier gas is so sparse that no collision happens (Zapadinsky et al., 2018).

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In Fig. 5 we have sketched the simulated section of the instrument. We subdivide the simulated section into 5 regions with different longitudinal electric field and pressure values. Region I is at the end of the first chamber, region II defines the interface between the first and the second chambers and regions III, IV and V are located in the second chamber of the APi. The pressure in the first region is P 1 , while in the regions III, IV and V it is P 2 . In the region II, where the skimmer is located, the pressure changes continuously from P 1 to P 2 . The electric field takes different values in the regions I, III, IV and V, while in II it is set 145 to zero. The voltage and pressure configuration inside the APi chambers, used in the CLOUD10 experiments (Lehtipalo et al., 2018), is the following: -Ω = 1.3 MHz where V DC and V AC are the direct and alternating components of the quadrupole electric potential in region IV, while Ω is its radio frequency. We will use this voltage and pressure configuration in our simulations. It is important to notice here that the electric field takes very different values in different regions, varying over 3 orders of magnitude, which will greatly diversify the probability of decomposition at different locations.

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In this study the cluster decomposition energy E f is treated as a free parameter. This allows us to explore the behaviour of cluster survival probability as a function of E f over a large energy range. Moreover, keeping E f as a variable is also useful since its computation by quantum chemistry calculations (especially low-level methods such as PM7 used here) is affected by large errors.
The clusters studied here are formed by one bisulfate anion, one to two sulfuric acid molecules and one to three HOM 165 molecules. The clusters are assumed to decompose by losing one HOM, as follows: with n = 1, 2, m = 1, 2, 3 and HOM 10 is the structure shown in Fig. 1. Our specific choice for HOM is not unique: this is one among many potential HOM produced in the α-pinene + O 3 reaction. The compound chosen is broadly representative of autoxidation products as it contains both hydroperoxide, ketone and carboxylic acid groups. The clusters have been constructed 170 by first maximizing H-bonds between the HSO − 4 core ion and other molecules, and then maximizing other H-bonds without creating too much strain. We note that the cluster conformers obtained in this fashion are unlikely to correspond precisely to the global energy (or free energy) minima. However, this mainly affects the computed binding energy -which (as pointed out earlier) is not actually used in this study. For purposes of generating a representative ensemble of vibrational and rotational energy levels, the conformer generation approach used here is adequate.

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For each kind of cluster we performed several simulations at different E f . The simulated carrier gas is air, modelled to consist of 80% nitrogen and 20% oxygen.
The final survival probabilities P surv are shown in Fig. 6. As expected, P surv is monotonic with respect to E f . From these results we can identify a boundary at E f ≈ 25 kcal/mol beyond which decomposition is highly unlikely. The weakest bonds between non-hydrogen atoms in HOM molecules are likely to be the O−O bonds of peroxide or hydroperoxide groups. These 180 typically have bond dissociation energies around 35 -50 kcal/mol (Bach et al., 1996;Schweitzer-Chaput et al., 2015. Vinyl peroxide systems have much lower dissociation energies, but (with the exception of short-lived vinyl hydroperoxides generated in ozonolysis) these are unlikely to form in gas-phase oxidation processes. The threshold cluster decomposition energies reported here are thus much lower than the energies required to dissociate even the weakest covalent bonds in the HOM molecules.

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Larger clusters are found to decompose more easily. This can be understood looking at the probability density function (PDF) of vibrational energy at equilibrium at temperature T = 300 K (Fig. 7a) density of states of vibrational modes by the Boltzmann factor, and then renormalized: Larger clusters contain a higher number of bonds, which for fixed decomposition energy, will each increase the internal energy 190 of the cluster, because of the equipartition theorem. This leads to a higher probability to exceed the decomposition energy, even at equilibrium condition, i.e. in the absence of an electric field. Suppose, for example, E f = 20 kcal/mol. Fig. 7a shows that the smallest cluster has roughly 50% probability to have an internal energy higher than E f , while the biggest cluster is certainly at higher energy than E f , with an average near 50 kcal/mol. This effect is in part counterbalanced by the behaviour of decomposition rate constant as a function of cluster size. As we can see in Fig. 7b, the decomposition rate at fixed internal 195 energy tends to be smaller for larger clusters. Indeed, a larger number of bonds reduces the probability to find a large quantity of energy in a single bond.
The model requires as input parameters the vibrational and rotational frequencies of both the reactant and products from an external quantum chemistry program (in our case Gaussian 16). These input data are affected by errors that depend on the level of accuracy of the computational method. It is therefore interesting to study how errors in the inputs affect the 200 survival probability. For this reason, we generated new random frequencies from normal distributions centered at the original frequencies, with a standard deviation equal to 20% of their values. Fig. 8 shows the deviations of the survival probability for 10 different sets of input frequencies. Here we can see that, even with large errors in the input parameters (20%), the final results change by no more than 10%. These results demonstrate the low sensitivity of the model on deviations in the input frequencies, thus validating our use of rather crude approaches for both the quantum chemical calculations, and the conformer 205 generation.
Let us now analyze the locations where collisions take place in the APi. In particular, we are interested in the highest-energy collisions, which lead to decomposition. We dub them as fatal collisions. For this study we used the voltage configuration and pressures used in CLOUD10 and we collected data from 5000 realizations of (HSO − 4 )(H 2 SO 4 )(HOM 10 ) cluster dynamics at E f = 17.88 kcal/mol, corresponding to a survival probability P surv ≈ 50% (see Fig. 6).  (Fig. 9b), a sign of low-energy collisions despite the very strong electric field (7189 V/m). When the cluster moves to the region II, in the skimmer, we see a drop in collisions, reflecting the negative pressure gradient. Moreover, the absence 220 of electric field in this region makes fatal collisions very unlikely to happen (≈ 0.017% probability). In the region III, at the beginning of the second APi chamber, the pressure is low (2.96 Pa), and the cluster experiences few collisions. However, the strong electric field (804.9 V/m) leads to cluster acceleration and an increase of fatal collisions, about 0.4% of total collisions. The passage to region IV is characterized by a high speed of the cluster acquired in the previous region. This leads to a large number of decompositions, as shown in Fig. 9a. Subsequently, the cluster decelerates because of the very weak 225 electric field in this region (18.04 V/m). Since the cluster moves for a long distance at low velocities in region IV, the average probability of decomposition per collision drops to ≈ 0.05%. Finally, in the region V, the cluster accelerates again due to a strong electric field (1104 V/m), which is visible from the large increase of the probability of fatal collisions (≈ 2%). The cumulative survival probability of clusters as they travel through regions I to V is illustrated by the red dots in Fig. 10. The decomposition probabilities in each respective region are indicated by the histogram bars.

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Although the decomposition is mainly induced by the voltages applied between regions II and III as shown in Passananti et al. (2019), these results demonstrate that the decomposition takes place mainly in region IV (Fig. 9a). This is due to the large acceleration acquired by the cluster in region III, with subsequent possible collision at high energy in the beginning of the next region. These results are complementary to previous data reported in literature (Passananti et al., 2019;Lopez-Hilfiker et al., 2016) and help to define the terms "declustering voltages" as the voltages that induce decomposition (between the region II 235 and III) and the "declustering region" as the region of the APi where the decomposition takes place (region IV).
In region IV a quadrupole is used as ion guide in order to focus the cluster trajectories, through an alternating transverse electric field (Miller and Denton, 1986). For this reason, the cluster is also subjected to a transverse acceleration in addition to the longitudinal one, increasing the velocity and, consequently, the probability of decomposition. In order to separate the contributions to decomposition from the longitudinal and the transverse electric fields, we performed additional simulations 240 setting the quadrupole electric potential V AC = 0. In this situation the motion in the transverse directions is negligible (as in the other regions of the APi). The increase in the final survival probabilities can be seen in Fig. 11a, which shows a minor deviation from the case with V AC = 200 V. More specifically, Fig. 11b shows the slight reduction of decomposition probability within the quadrupole region when V AC = 0. Hence, with the present voltage configuration, the quadrupole voltage does not affect the probability of decomposition significantly.

Formation in the atmosphere
In parallel to the simulations on decomposition in the APi, we used the ACDC code (McGrath et al., 2012) to compute the concentrations of HOM 10 needed to provide a significant enhancement of new-particle formation rate in the atmosphere (details on ACDC simulations provided in Appendix A). Specifically, at given H 2 SO 4 monomer concentration and decomposition energy E f , we computed the concentration of HOM 10 at which the new-particle formation rate is increased by 1 cm −3 s −1 250 with respect to the pure sulfuric acid system (i.e. J sa+hom = J sa + 1 cm −3 s −1 ).  For Tommaso: I agree with length and almost fully agree with content of the description of ACDC simulation and figures 10&11 in the article. + Fig.10 I did not expect that you use figure from the email. + I did not see you use anywhere else SA and B, so we can change it also here to (HSO % ' ) and (H " SO % ) + change the information about generic ions (see below). + the definition of new particle formation rate improvement is slightly different Please, add some reference to SI which describes the whole simulation in great detail.  In the simulation, the formation rate J sa+hom corresponds to clusters growing out of (HSO − 4 )(H 2 SO 4 ) 4 (HOM 10 ) 0−3 or (HSO − 4 )(H 2 SO 4 ) 0−3 (HOM 10 ) 4 , as shown in Fig. 12a. The increment in the formation rate value here is indicative, and it serves as a reference for a reasonable NPF process in the atmosphere (Lehtipalo et al., 2018). The concentration of HSO − 4 is kept constant at 700 cm −3 , which corresponds to the steady-state concentration at the ions formation rate J ions = 4 cm −3 s −1 , 255 reproducing the galactic cosmic rays (GCR) conditions (Kirkby et al., 2016).
The HOM clusters are subsequently formed by collisions between bisulfate anions, sulfuric acid and HOM molecules. As we can see in Fig. 12b, the H 2 SO 4 and HOM 10 concentrations needed to provide the increment ∆J = 1 cm −3 s −1 decrease when the decomposition energy increases, reaching experimental conditions (e.g. non-nitrate HOM 10 and H 2 SO 4 concentrations measured in CLOUD experiment (Lehtipalo et al., 2018)) at E f > 30 kcal/mol, where HOM 10 and H 2 SO 4 concentrations 260 do not exceed 10 8 cm −3 . At this decomposition energy, decomposition in APi is negligible (P surv ≈ 1 in Fig. 6). Thus we can conclude that for the case of SA-HOM clusters, rapid formation in the atmosphere (given typical vapor concentrations) and significant decomposition in the APi are mutually incompatible situations (case b in Fig. 2).

Conclusions
In this work, we have presented the numerical results on decomposition inside an APi-TOF instrument of a specific class of 265 atmospheric clusters that involve sulfuric acid and HOM molecules. A previously reported low-volatility α-pinene ozonolysis product, with the molecular formula C 10 H 16 O 8 , was used as a representative HOM.
There are three main results from our simulations. First, decomposition of HOM clusters in the APi requires a range of cluster decomposition energies which is incompatible with efficient cluster formation in the atmosphere given sub-ppb vapor concentrations. This result has been obtained by computing the cluster survival probability in the APi as a function of its 270 decomposition energy, and then comparing the range of energies leading to decomposition with those needed to obtain a reasonably high new-particle formation rate in atmospheric conditions. The two ranges have no overlap -the highest energy allowing decomposition differs from the lowest energy allowing atmospheric new-particle formation by roughly 10 kcal/mol.
Observations of SA-HOM clusters in CLOUD experiments (Lehtipalo et al., 2018) validate the results of our model.
Our second main result is the identification of the locations of the highest-energy collisions that lead to decomposition of 275 SA-HOM clusters in the APi. The simulation shows that they are mainly localized in the quadrupole region (IV). This is due to the large velocity of the cluster acquired in the previous region (III), caused by the strong electric field. Moreover, our results show that the alternating field of the quadrupole in region IV has only a minor effect on decomposition probability.
As a third main result, we have shown that the model displays low sensitivity to changes in cluster vibrational and rotational frequencies. This feature allows us to obtain reliable results also with low-level input data (e.g. semi-empirical methods and 280 limited configurational sampling).
This study was performed for a small set of HOM clusters with particular functional groups (e.g. hydroperoxides, ketones), but in future similar simulations could be performed for other types of clusters, for example to assess whether they should be detectable in an APi-TOF or not, or whether they could possibly affect new-particle formation, despite not being directly detected.
Competing interests. The authors declare that they have no conflict of interests.