Introduction

Chemical reactions typically proceed through the minimum energy path (MEP), where a conventional transition state (TS) characterizing the breaking of old bonds and the formation of new bonds play an important role. This MEP mechanism has been widely employed to predict rates, reactivity, and selectivity. However, the recently discovered roaming pathway deviates from the traditional MEP1,2,3,4,5. Instead of proceeding through a well-defined transition state, frustrated bond cleavage leaves part of the molecule with insufficient energy to escape. This fragment orbits the remaining portion of the molecule until it encounters a reactive site, ultimately forming the products via intramolecular abstraction. Furthermore, an unstable complex may form a temporary free radical that roams until it finds an opportunity to abstract atoms and form molecular products. This revelation underscores the intricate and unpredictable nature of chemical reactions, prompting further investigation into the underlying mechanisms that govern their behavior.

Since the initial discovery of the roaming mechanism in the photodissociation of H2CO, evidence for this mechanism has been identified across numerous unimolecular dissociation systems and several bimolecular reactions6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29. In most cases, these roaming pathways play a minor role in the overall reactivity, indicating that chemical processes predominantly adhere to the traditional pathways dictated by MEP or transition states. A notable exception is the photodissociation of acetaldehyde3,25, where the roaming pathway accounts for approximately 84% of the total reactivity, producing CH4 and CO via a mechanism in which the CH3 fragment roams and ultimately abstracts a hydrogen atom from HCO. For the photodissociation of NO3, both ground-state and excited-state roaming pathways were revealed for the unimolecular dissociation of products O2 + NO5. Recently, roaming in highly excited-states of SO2 was reported in leading to the excited-state products of O2 and S, which gives rise to roughly one-half of total yield of O2(a1Δg)26. In addition to the unimolecular dissociation, roaming mechanisms in bimolecular reactions might present even more intriguing characteristics9,12,17,20,23,24,27,28,29. For instance, roaming in the H + HCO → H2 + CO reaction was found to play an important role29. A collision-induced roaming mechanism has been proposed for the H + C2H4 → C2H3 + H2 reaction, which exhibits distinct product angular and energy distributions compared to the complex-mediated roaming20. Quantum manifestations of roaming in the MgH + H → Mg + H2 reaction were investigated by quantum scattering calculations12. In addition, the roaming mechanism has also been observed in barrierless bimolecular exothermic reactions, such as those involving chlorine (Cl) atoms and propene or isobutene14,27,28. Nevertheless, in all cases studied thus far, direct abstraction via a traditional transition state remains the dominant mechanism for bimolecular reactions. Consequently, the extent to which the roaming mechanism contributes to bimolecular reactions remains an open question.

The reaction of chlorine atoms with acetylene is recognized as a significant atmospheric process, serving both as a removal pathway for acetylene in the marine and polar troposphere and as a sink for halogen atoms in the lower stratosphere30,31,32,33. Numerous experimental studies have measured the association rate of a chlorine atom to acetylene molecule (Cl + C2H2 → C2H2Cl) across a range of low to moderate temperatures, reflecting conditions relevant to its atmospheric role31,32,33,34,35,36,37,38,39. Under atmospheric pressure, Cl-atom addition to the acetylene and stabilization of the adduct by collisions will dominate. However, despite the importance of this process, theoretical investigations of the Cl + C2H2 reaction remain relatively limited40,41,42. The stationary-point geometries were calculated using different level of ab initio theory for both the association Cl + C2H2 → C2H2Cl and H-abstraction Cl + C2H2 → C2H + HCl41. Zhang et al. calculated the association pathway by unified variable-reaction-coordinate and reaction-path variational transition-state theory42. The computed rate constants for this radical molecule association reaction were in good agreement with some of experimental results. However, the hydrogen abstraction reaction Cl + C2H2 → C2H + HCl was not addressed, probably due to the complicated electronic structure calculations and a higher reaction barrier of roughly 30 kcal/mol. These previous studies leave open questions regarding the true mechanism of the Cl + C2H2 reaction and the prevalence of roaming pathways in bimolecular reactions.

Here we report a full-dimensional dynamics study for the Cl + C2H2 reaction at collision energies ranging from 30 kcal/mol to 60 kcal/mol, based on an accurate, global, machine-learning potential energy surface (PES) covering both hydrogen abstraction and association reaction channels. Our calculations provide strong evidence that the reaction predominantly proceeds via the roaming mechanism, leading to the formation of HCl and C2H, with direct abstraction via the traditional transition state being negligible. In addition to the dominant Cl-atom roaming pathway, H-atom roaming is also found, although this is also a minor pathway. The dominance of the roaming mechanism over the conventional transition state mechanism is an important supplement to existing reaction rate theory.

Results

Full-dimensional potential energy surface

We developed a global, highly accurate full-dimensional potential energy surface (PES) for the Cl+C2H2 reaction using the fundamental invariant neural network (FI-NN) approach43,44,45,46, which was based on ~70,000 high-level UCCSD(T)-F12a/aug-cc-pVTZ energy data points. The FI-NN approach was proposed by our group in relation to the PIP47,48 and PIP-NN49 approaches, which can provide enhanced efficiency for larger molecular systems with more identical atoms by minimizing the number of input invariants and reducing the computational time required for evaluating potential energy. Details for getting initial ab initio database and fitting process are given in the Supplementary Information. The final fitted PES has a root-mean-square error (RMSE) of 11.39 meV over all configurations up to 6 eV, which is very accurate for a complicated multichannel reaction. More details about the fitting errors of all configurations, optimized geometries, and harmonic frequencies of stationary points obtained from the PES and ab initio calculations are provided in Supplementary Figs. 1 and 2 and Supplementary Table 1, respectively. Excellent agreement between the PES and ab initio results is clearly shown, so indeed the goal of obtaining a precise fit for the PES has been achieved.

Figure 1 presents a comprehensive schematic potential energy diagram for the stationary configurations along the minimum-energy paths of the Cl + C2H2 reaction. The labeled energies are calculated relative to the Cl + C2H2 fragments, including vibrational zero-point energies. The diagram demonstrates excellent agreement between the PES and the direct ab initio value. The collision of Cl with C2H2 can endothermically lead to both the HCl + C2H and H + C2HCl products. For the HCl + C2H channel, there is a single accessible pathway via the transition state TS1, with a barrier of 30.8 kcal/mol, where the hydrogen atom from the acetylene molecule is directly abstracted by the colliding chlorine atom. In the Cl + C2H2 → H + C2HCl reaction, three isomers with distinct energies are identified in the deep well of around 18 kcal/mol. The I1 complex, an essential intermediate formed via TS2 after the collision, is located at 18.1 kcal/mol below the Cl + C2H2 asymptote. The I1 complex can transition to the I2 complex via TS4 or to the I3 complex by overcoming a very high barrier of approximately 25.8 kcal/mol (TS3) through H atom migration. Both I1 and I2 complexes can eventually decompose into H + C2HCl fragments via TS5 (about 28.5 kcal/mol), while I3 decomposes via TS6 (about 26.1 kcal/mol). The complicated potential energy diagram with various intermediates poses a challenge to figure out the unique and true mechanism of the Cl + C2H2 reaction.

Fig. 1: A complete schematic potential energy diagram for the stationary configurations on the minimum-energy paths of the Cl + C2H2 reaction.
figure 1

The label energies are calculated relative to the fragment Cl + C2H2 (with vibrational zero-point energies). The energy shown in parentheses is from UCCSD(T)-F12a/AVTZ calculations, and the unit of energies is kcal/mol.

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Full-dimensional reaction dynamics simulations

To gain a deep understanding of the reaction mechanisms, we performed extensive quasi-classical trajectory (QCT) calculations based on the accurate, full-dimensional PES. The acetylene molecule was initially set in the ground rovibrational state, and roughly 50 million trajectories were run for each collision energy to converge the product angular and energy distribution, at the collision energies of 30–60 kcal/mol. Further computational details are provided in the Supplementary Information. The dynamics calculations based on the PES indicate that the cross-section for the HCl + C2H product channel (~0.018 Å2) is nearly three times as large as that of the Cl + C2H2 → ClC2H2 → H + C2HCl reaction (~0.006 Å2) at the collision energy of 60 kcal/mol. However, as shown in Fig. 1, the barrier height for the formation of HCl + C2H products is even higher than that of H + C2HCl, relative to the reactants. This unexpected behavior in the dynamics suggests the existence of alternative reaction pathways for the Cl + C2H2 → HCl + C2H reaction.

Chlorine-roaming and Hydrogen-roaming dynamics

Full-dimensional dynamics simulation reveals that the reaction does not follow the well-established direct abstraction mechanism via transition state TS1 for Cl + C2H2 → HCl + C2H, which is unexpected in this endothermic reaction. Instead, two different pathways leading to the C2H + HCl fragments were identified, characterized as chlorine roaming (Cl-roaming) and hydrogen roaming (H-roaming). The Cl-roaming pathway involves the frustrated dissociation of the C2H2Cl adduct into a chlorine atom and acetylene, with the partially detached chlorine atom roaming around the acetylene molecule and finally abstracting a hydrogen atom from it. In the H-roaming pathway, the partially detached hydrogen atom migrates around the C2HCl intermediate to abstract the chlorine atom, resulting in the formation of HCl.

Two sets of nine frames for the representative trajectories of the Cl-roaming and H-roaming mechanisms are given in Fig. 2a, b, respectively. In Fig. 2a, the formation of a short-lived C2H2Cl adduct is observed following the attack of an incoming Cl atom on acetylene. The collision makes the Cl-C bond vibrationally excited, thus the unstable C2H2Cl is formed. Then the Cl atom begins to depart and roam without fully dissociating, which finally picks up a hydrogen atom with an orientation favorable for abstraction to form HCl. This collision-induced Cl-roaming mechanism, involving a short-lived C2H2Cl adduct, efficiently transfers collision energy to the vibrational excitation of the C–H bond in acetylene, which facilitates the self-abstraction to form HCl and C2H products. Additionally, the Cl-roaming mechanism involving a long-lived C2H2Cl complex plays an important role in the overall reactivity as well. In contrast, in the H-roaming pathway shown in Fig. 2b, the Cl atom migrates between the two carbon atoms of the vibrationally excited C2H2Cl adduct, allowing sufficient time for the activation of a hydrogen atom. The H atom then detaches and abstracts the Cl atom, resulting in the formation of HCl and C2H fragments. Two animations of Cl-roaming and H-roaming trajectories are provided in the Supplementary Movies 1and 2, respectively.

Fig. 2: Snapshots of two roaming pathways at the reaction time indicated (fs).
figure 2

a Snapshots for the Chlorine-roaming pathway, b Snapshots for the Hydrogen-roaming pathway. The unit of the internuclear distances is (Å).

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Differential cross-sections

The distributions of the reaction time for the Cl + C2H2 → C2H + HCl reaction at the collision energy of 60 kcal/mol are illustrated in Fig. 3a. Reaction time is defined as the duration time for a reactive trajectory to progress from the reactant side to the product side, with the distance between two fragments reaching up to 6.0 Bohr. From the figure, it can be observed that the Cl-roaming pathway comprises a dominant portion of the total distribution, while direct abstraction represents a very small proportion, and the H-roaming pathway contributes the least. Consequently, we have enlarged the displays of direct abstraction and the H-roaming pathway in the inset for detailed discussion and analysis. The dominant Cl-roaming pathway shows three prominent peaks (labeled A, B, and C). Peak A (~103 fs) performs only slightly longer reaction time than the direct abstraction pathway, while Peak B (~133 fs) is close to Peak A, suggesting that the short-lived complexes are present in both of the two peaks. The reaction time for Peak C together with a long tail distribution indicates a long-lived complex forming process. In the H-roaming pathway, the observed fluctuations in the distribution indicate the presence of both long-lived and short-lived complexes along this pathway. In contrast, the reaction time for direct abstraction via the conventional transition state is very short, with a peak at ~58 fs. As shown, the contribution from the direct abstraction channel is negligible. One animation of direct abstraction trajectory is provided in the Supplementary Movie 3.

Fig. 3: Dynamics information for the reaction time and scattering angular distributions.
figure 3

a The distribution of the reaction time (ps) of the trajectories of Cl + C2H2 → HCl + C2H at the collision energy of 60 kcal/mol. b The scattering angular distribution of HCl product relative to the direction of the incoming Cl atom, resulting from the three peaks of Cl-roaming pathway in the reaction time distribution. c The scattering angular distribution of HCl product relative to the direction of the incoming Cl atom for Cl-roaming, H-roaming pathways, and direct abstraction. d 3D polar plot for the product translational energy and angular distributions from the Cl-roaming.

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For further analysis, Fig. 3b shows the angular distribution of the HCl product relative to the incoming Cl atom for the three peaks in the Cl-roaming pathway, which also reflects the different processes in the Cl-roaming reaction. For Peak A, the pronounced sideways and backward scattering distributions correspond to the very short reaction time associated with the collision-induced Cl-roaming mechanism at small impact parameters. It describes a nearly inelastic collision where, once the unstable C2H2Cl adduct forms, the Cl atom quickly bounces back and picks up an H atom within a very short period. The snapshots of this typical backward scattering trajectory are provided in Supplementary Fig. 3a. The relatively small impact parameter of such trajectories is a crucial factor contributing to the side and backward scattering distribution.

While Peak B also corresponds to a short reaction time due to the formation of a short-lived adduct, its angular distribution exhibits a forward scattering feature due to large impact parameters. The snapshots presented in Fig. 2a illustrate a typical Cl-roaming process, where the collision between chlorine and carbon leads to significant vibrational excitation of the C-Cl bond. This results in the Cl atom dissociating first, followed by the self-abstraction of a hydrogen atom. In contrast, Peak C corresponds to the migration of the Cl atom from the initially attacked carbon atom to the other carbon atom in the C2H2Cl adduct, as shown in Supplementary Fig. 3b. This migration allows the roaming Cl atom to abstract an H atom from the other side of the carbon, leading to a Cl-roaming pathway characterized by predominantly forward scattering. As the reaction time increases beyond 280 fs, the reaction exhibits characteristics of a typical complex-forming reaction before Cl-atom roaming. Such a complex-mediated Cl-roaming mechanism leads to near forward-backward scattering symmetry. Thus, with contributions from all four components, the overall Cl-roaming pathway predominantly displays forward scattering, along with additional contributions from sideways and backward scattering, as shown in Fig. 3b.

A clear comparison of the scattering angular distribution of HCl relative to the direction of the incoming Cl atom in Fig. 3c shows that the Cl + C2H2 → C2H + HCl reaction occurs almost exclusively via the Cl-atom roaming pathway, with negligible contributions from both the direct abstraction and H-atom roaming pathways. However, the corresponding angular distributions for the H-atom roaming and direct abstraction pathways, plotted at an appropriate scale, are shown in Supplementary Fig. 4a. In the H-roaming pathway, the complex-forming process takes more time, leading to a loss of memory regarding the initial approach direction. As a result, the scattering angle distributions for the H-roaming pathway tend to exhibit near-symmetry between forward and backward directions. In contrast, the direct abstraction pathway is characterized by a prominent forward-sideways scattering intensity, indicative of direct stripping via TS1.

Figure 3d presents a 3D polar plot illustrating the product translational energy and angular distributions for the Cl-roaming pathway, offering deeper insights into the partitioning of total available energy and the relationship between the initial and final velocity vectors. The pronounced forward-scattering peak at low kinetic energies is due to energy conservation, where products with higher internal excitation correspond to lower kinetic energies. The 3D plots for the H-roaming pathway and direct abstraction, shown in Supplementary Fig. 4b, c, further demonstrate that the products of both roaming pathways exhibit lower translational energy compared to those from direct abstraction, due to the formation of long-lived intermediates.

Product translational energies

The product translational energy distributions, P(ET), for the Cl + C2H2 → C2H + HCl reaction at a collision energy of 60 kcal/mol are shown in Fig. 4a, b. In the Cl-roaming pathway, the peak of P(ET) is around 16.5 kcal/mol, with an average translational energy of approximately 15.7 kcal/mol, accounting for 49% of the total available energy (about 31.8 kcal/mol). The slightly lower energy available for translation results from the formation of a rovibrationally excited complex. Similarly, the average translational energy of the H-roaming pathway, involving a long-lived intermediate, accounts for 52.6% of the total available energy. The slightly higher fraction of translational energy in the H-roaming pathway does not significantly affect the proportion of energy allocated to translation, reflecting the similar dynamics of intermediate formation and energy distribution as compared with the Cl-roaming pathway. In contrast, the direct abstraction pathway shows a peak at much higher energy of ~30 kcal/mol. The average translational energy of 26 kcal/mol represents a larger fraction (82%) of the total available energy. More energy is transferred to the translational motion of products in the direct abstraction pathway, because the intermediate complex is not formed.

Fig. 4: Dynamics information for the energy distributions.
figure 4

a The relative translational energy distributions of C2H + HCl for the Direct, Cl-roaming and H-roaming pathways at the collision energy of 60 kcal/mol. b is the same as (a), except for only two pathways, Direct and H-roaming. c The distributions of the internal energy of C2H, P(EI), for the Cl + C2H2 → C2H + HCl reaction during the Direct, Cl-roaming, and H-roaming pathways at the collision energy of 60 kcal/mol. d is the same as (c), except for only two pathways, Direct and H-roaming.

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Product rovibrational energies

The corresponding internal energy distributions of C2H, denoted as P(EI), are shown in Fig. 4c, d. The peak of P(EI) is around 15.0 kcal/mol for both the Cl-roaming and H-roaming pathways, but only about 5.0 kcal/mol for the direct abstraction pathway. The C2H products formed via the Cl-roaming and H-roaming pathways exhibit higher internal energies due to the formation of the C2H2Cl intermediate. This highlights the critical role of intramolecular energy redistribution in the roaming pathways. In contrast, the internal energy distributions of the HCl product from both roaming and direct abstraction pathways are quite similar, with peaks near 10.0 kcal/mol for all pathways, as shown in Supplementary Fig. 5. This similarity arises from the nature of the roaming pathways, which involve the self-abstraction of an H atom by Cl.

Roaming versus direct abstraction

To investigate the role of roaming pathways at various collision energies, we present the integral cross sections for the Cl-roaming, H-roaming, and direct abstraction pathways in Fig. 5, with the corresponding branching ratios shown in Table 1. As the collision energy increases, the cross sections for both the roaming and direct abstraction pathways increase. Notably, the cross-section for the Cl-roaming pathway is nearly two orders of magnitude larger than that of the direct abstraction pathway, indicating its overwhelming dominance in the Cl + C2H2 → C2H + HCl reaction. Furthermore, the H-roaming pathway becomes comparable to the direct abstraction pathway at collision energies exceeding 50 kcal/mol. Although the branching fraction for the Cl-roaming pathway decreases slightly with increasing collision energy, it remains the dominant mechanism, accounting for 97% of the total yield at 60 kcal/mol. The overall roaming mechanism, encompassing both Cl-roaming and H-roaming, accounts for approximately 99% of the total yield across a wide range of collision energies. This suggests that the reaction proceeds almost exclusively via the Cl-roaming pathway. Consequently, rate constants for the Cl + C2H2 → C2H + HCl reaction may be inaccurately represented if only the direct abstraction pathway through TS1 is considered, posing a challenge to conventional rate theory.

Fig. 5: Integral cross-section.
figure 5

Integral cross-sections for the roaming and direct abstraction pathways at collision energies of 30, 40, 50, and 60 kcal/mol, respectively.

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Table 1 Branching ratios
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Discussion

Full-dimensional dynamics simulations based on an accurate, global PES reveal that the Cl + C2H2 → C2H + HCl reaction does not proceed through the conventional direct abstraction mechanism via the transition state TS1, as previously understood. Instead, two mechanistic pathways—chlorine roaming (Cl-roaming) and hydrogen roaming (H-roaming)—were identified as dominant contributors to the product formation. These roaming pathways showcase complex intermediate formations and energy redistribution processes that differ significantly from the traditional direct abstraction approach. The Cl-roaming mechanism is characterized by the formation of a short-lived C2H2Cl adduct, followed by the partial dissociation of the chlorine atom, which then roams around the acetylene molecule and abstracts a hydrogen atom to form HCl. This pathway is highly efficient in transferring collision energy into the vibrational excitation of the C–H bond, thereby facilitating the self-abstraction process. The H-roaming mechanism, on the other hand, involves the partial detachment of a hydrogen atom, which migrates around the C2HCl intermediate before abstracting the chlorine atom to form the final products.

The analysis of reaction times and product angular distributions further underscores the dominance of the Cl-roaming pathway. At a collision energy of 60 kcal/mol, Cl-roaming contributes the most to the total reaction yield, accounting for nearly 97% of the product distribution, while the contributions from the H-roaming and direct abstraction pathways are comparable. At lower collision energies, the fraction of roaming rises to nearly 100%. Three distinct peaks in the reaction time distribution suggest the presence of both short-lived and long-lived complexes along the Cl-roaming pathway, with significant forward and sideways-backward scattering features. These features are indicative of varying impact parameters and complex-forming behaviors that govern the overall dynamics of the roaming processes. Interestingly, the roaming pathways exhibit a different energy partitioning pattern compared to direct abstraction. Products from the Cl- and H-roaming pathways show lower translational energy but higher internal energy, reflecting the role of complex in redistributing energy. In contrast, the direct abstraction pathway yields products with higher translational energy and lower internal energy due to the absence of complex formation.

This study highlights the critical role of roaming mechanisms in bimolecular reactions involving heavy atoms like chlorine. The dominance of the Cl-roaming pathway challenges the conventional understanding of the Cl + C2H2 → C2H + HCl endothermic reaction, where the direct abstraction mechanism via a transition state was previously thought to be the primary channel in this reaction. The findings also suggest that neglecting roaming mechanisms in theoretical models may lead to inaccuracies in rate constant predictions. The implications of this research extend to a broader understanding of reaction dynamics, where nontraditional pathways like roaming can have significant impacts on reaction outcomes.

It is worth noting that we have not discussed the non-reactive collisions, but the energy-transfer processes involved are worthy of further study in the future. Because the isomerization energy between acetylene and vinylidene is estimated to be around 43.53 ± 0.15 kcal, this non-reactive pathway might also be involved at high collision energies.

The dominance of roaming pathways in the reaction mechanism can be attributed to the formation of unstable C2H2Cl complexes, which act as pre-roaming intermediates. These complexes arise due to the attractive regions of the PES, facilitating the roaming process before the final bond formation. This behavior underscores the critical role of the PES topology in guiding reaction pathways, especially in systems involving complex intermediates. The calculated rate constant by variational transition-state theory for the association of Cl with C2H2 exceeded experimental values by approximately a factor of 242, likely due to re-crossing effects at higher temperatures. The association involves much lower energy conditions, and the energy landscape and conditions differ from those of the current reaction. In future work, we could investigate the dynamics and kinetics for the association of Cl with C2H2 on our PES using full-dimensional simulations. This would provide a deeper understanding of the interplay between the PES and roaming dynamics for describing such complex reactions.

Methods

Potential energy surface

The global, accurate, full-dimensional PES for the Cl + C2H2 reaction was developed by the FI-NN fitting approach43,44,45,46, based on a total of 67,292 high-level UCCSD(T)-F12a/AVTZ energies points. The ab initio calculations are challenging for the C2H2Cl system due to difficulties in converging to the correct electronic states. To address this, initial guesses were based on neutral, anion and cation species for each configuration, resulting in a reasonably smooth potential surface50. A total of 16 FIs with a specific maximum order of 3 are taken as the inputs of network, using permutational symmetry of AB2C2. The structure of the fitting network is 16-50-50-1 and the weight is 3451. To further reduce random errors, the final PES is obtained by averaging the results of the five best FI-NN fittings. The overall fitting error is only 11.39 meV across an energy range of approximately 6 eV, as determined by the root mean square error (RMSE). This low error value highlights the accuracy of the PES, confirming its reliability for dynamics simulations and predictive analysis for this system. The PES developed in this work is given as the Supplementary Data 1.

QCT calculations

Standard QCT calculations for the Cl + C2H2 reaction were performed on the FI-NN PES with analytical forces, covering collision energies from 30 to 60 kcal/mol, with the C2H2 reactant initially in the ground rovibrational state. The initial coordinates and momenta of C2H2 were determined through random sampling, with adjustments made to ensure that the total angular momentum of C2H2 was zero. The vibrational energies of acetylene were set to zero-point energies (ZPEs) using standard normal mode sampling. The trajectories were then simulated using the Velocity-Verlet integration algorithm, with a time step of 0.2 fs and a maximum simulation time of 120 ps. Each trajectory was terminated when any two fragments reached a separation of 18.0 Bohr. In total, approximately 50 million trajectories were run to gather converged dynamical information.