Frustrated charge transfer in vibrationally inelastic Ar⁺+N₂ collisions via hard collision glory scattering

Collisional energy transfer via inelastic scattering, wherein part of the kinetic energy of colliding molecules is converted to internal excitation (electronic, vibrational, or rotational) or vice versa, plays a central role in many gaseous environments, from atmospheric and interstellar chemistry to combustion and plasmas^1,2,3,4,5. The advances in inelastic scattering have paralleled those in reactive scattering processes, providing complementary and in-depth understanding of the interaction potential energy surface (PES) between the colliding partners⁶. In recent years, the combination of high-resolution velocity-map imaging (VMI) and various electric and magnetic molecular manipulation methods with the crossed beam technique has greatly advanced the study of molecular inelastic scattering dynamics, particularly in the cold regime, with synergistic collaboration from high-level quantum calculations^7,8,9. Deep insights into the quantum natures, such as scattering resonances and interference effects, have been revealed for molecular inelastic scattering processes^{10,11,12,13,14,15}. Nevertheless, such advances have mainly been limited to collisions between neutral molecules, wherein various laser-based quantum state selective photoionization schemes with high-resolution VMI detection made the state-to-state scattering dynamics investigations possible. The experimental study of another type of important molecular collisions, namely collisional energy transfer processes between neutrals and charged species, has remained challenging (vide infra), particularly in the low collision energy regime (<10 eV)¹⁶.

Despite the challenges, significant advances have been achieved in recent years in the measurement of quantum state-to-state collisional energy transfer rates between ions and neutrals, thanks to the development of technologies for ion cooling and trapping. For example, Wester and coworkers successfully measured the rate coefficients for the transition from the first excited rotational level to the ground rotational level of the hydroxyl negative ion through collisions with helium, which has potential applications for preparing internally cold molecular ions¹⁷. Angle resolved differential cross sections for ion-molecule collisional energy transfer have also been measured at relatively high collision energies (>10 eV) using a conventional crossed beam setup with a rotating detector. Interesting collisional energy transfer dynamics were revealed, mainly between H⁺/H^- ions and small molecules like H₂, N₂, O₂, CO and so on^18,19,20,21. However, these measurements were limited to a narrow angular range in the forward scattering direction, the signal in the sideway and backward directions could not be detected due to instrumental limitations.

Recently, a combination of the crossed beam and H-atom Rydberg tagging time-of-flight methods was used to measure the angle resolved differential cross sections for the collisional energy transfer between high-n Rydberg H atom and small neutral molecules, firstly by Davis and coworkers²² and later by Yang and coworkers^23,24. Full angle and rovibrational state resolved differential cross sections were obtained by taking advantage of the fact that both colliding partners are neutral. However, because the electron in a high Rydberg state spends most of its time far from the ion core, it is often treated as a spectator to the collision process. Hence, the above experiments provide insights into the collisional energy transfer dynamics between H⁺ ions and small neutral molecules^22,23,24. However, the much shorter lifetimes of high-n Rydberg states of heavier atoms and molecules than the H atom limited the applicability of such an approach.

The crossed beam method has been routinely combined with the VMI technique to measure the full angle and quantum state resolved differential cross sections for reactive^25,26 and nonreactive^10,11,12,13 scattering between two neutral species, and more recently for reactive scattering between ions and neutrals^27,28,29,30. Although this approach provides the most detailed information about collisional dynamics, to our best knowledge, it has not so far been applied to study collisional energy transfer processes between ions and neutral molecules. There are two potential reasons for this. First, the energy spread and spatial size of the low-energy ion beam is difficult to control, and can be seriously perturbed by small fluctuations of any electric fields, which severely limits the experimental resolution. Second, the reactant ions and scattered product ions are the same chemical species in the collisional energy transfer process, while the former is usually 3–4 orders of magnitude more intense than the latter. Hence, the unambiguous detection of the scattered ions may be severely undermined.

For the collisional energy transfer between neutral molecules, it has long been accepted that the repulsive part of the interacting PES plays the dominant role, and this leads to the conventional wisdom that glancing collisions with large impact parameters are typically forward-scattered with low energy transfer, and hard collisions with small impact parameters are likely sideway- or backward-scattered with relatively efficient energy transfer⁶. Recently, several pioneering studies have found that the attractive part of PES could also play a major role, particularly at low energies, leading to quite different outcomes from those predicted by the textbook model of collisional energy transfer^31,32,33. The PES between ions and neutral molecules usually features long-range interaction and deep attractive wells, thus can result in distinct energy transfer properties from those observed between neutrals. A systematic study on the collisional energy transfer dynamics between ions and neutrals is thus highly desired, particularly with quantum states resolved.

The Ar⁺+N₂ system has served as a model for studying collisional charge-transfer dynamics for half a century^34,35,36,37. Our recent studies on the three-dimensional VMI crossed-beam apparatus showed that the charge-transfer dynamics strongly depends on the initial spin-orbit level of the Ar⁺ ion and the vibrational level of the N₂⁺ product, and the attractive part of the PES plays an important role in determining the rotational and angular distributions of the N₂⁺ product^29,30. This makes Ar⁺+N₂ an interesting candidate for studying the collisional energy transfer dynamics between ions and neutrals. Despite extensive previous studies on its charge-transfer dynamics, experimental investigations on the collisional energy transfer dynamics have been rare. Futrell and coworkers reported the only experimental differential cross section of the inelastic Ar⁺+N₂ scattering³⁷. Unfortunately, the measured vibrational populations of the inelastically scattered N₂ were not in agreement with theoretical calculations^38,39. A better understanding thus demands further investigations.

In this study, the recently constructed three-dimensional VMI crossed-beam apparatus^40,41 is used to measure the differential cross sections of the collisional energy transfer between spin-orbit state-selected Ar⁺ ions and N₂. The measurements are accompanied by full-dimensional trajectory surface hopping (TSH) calculations, which qualitatively reproduce the experimental observations. The combined experiment-theory study reported here provides unprecedently deep insights into the energy transfer dynamics of the Ar⁺+N₂ system and beyond.

Imaging of the inelastic Ar⁺+N₂ collision

Since the primary Ar⁺ ions are much more intensive than the inelastically scattered ones, a piece of black tape is used to cover the area corresponding to the primary Ar⁺ ions on the phosphoscreen to block their signals. However, strong fluorescence from the primary Ar⁺ ions hitting on the phosphoscreen can still leak out to be detected by the photomultiplier tube (PMT), which is much more intense than that due to the elastically and inelastically scattered Ar⁺ ions. Thus, accurate time-of-flight information is impossible to obtain, and only the conventional two-dimensional (2D) crushed VMI image of the scattered Ar⁺ ions could be collected. The crushed 2D VMI images for the inelastic Ar⁺+N₂ collision at the center-of-mass (COM) collision energy of 1.58 eV with the Ar⁺ ion prepared in the spin-orbit ground (²P_3/2) and excited (²P_1/2) levels are shown in Fig. 1a, d, respectively. The VMI images under the same experimental conditions but with the N₂ beam off are also collected and shown in Fig. 1b, e, respectively. By comparing the VMI images with and without the N₂ beam, it is clear that the long tails seen in all the VMI images are due to residual Ar⁺ ions from the primary ion beam, and the extra ions seen in Fig. 1a, d are due to the scattered Ar⁺ ions from collisions with the N₂ beam. The completely blank areas in all the VMI images represent the shape of the black tape used for blocking the primary Ar⁺ ion beam.

a The two-dimensional (2D) crushed VMI image for the inelastic collision between Ar⁺(²P_3/2) and N₂ at the COM collision energy of 1.58 eV; (b) the 2D crushed VMI image collected under the same experimental condition of (a) except that the N₂ molecular beam is off; (c) the integrated Ar⁺ speed distributions in the angular ranges of 90–135° (red) and 135–180° (black), which are obtained by reconstructing the bottom left quadrant of the VMI image (red box in a) using the MEVELER algorithm; (d) the 2D crushed VMI image for the inelastic collision between Ar⁺(²P_1/2) and N₂ at the COM collision energy of 1.58 eV; (e) the 2D crushed VMI image collected under the same experimental condition of (d) except that the N₂ molecular beam is off; (f) the integrated Ar⁺ speed distributions in the angular ranges of 90–135° (red) and 135–180° (black), which are obtained by reconstructing the bottom left quadrant of the VMI image (red box in d) using the MEVELER algorithm. The black concentric rings labeled with numbers in (a, b), and the black droplines in (c) represent the kinematic cutoffs for the corresponding vibrational levels of N₂, which are calculated assuming a collisional energy transfer process of Ar⁺(²P_3/2) + N₂ → Ar⁺(²P_3/2) + N₂(v′, J′); those in (d, e, f) are calculated assuming a collisional energy transfer process of Ar⁺(²P_1/2) + N₂ → Ar⁺(²P_3/2) + N₂(v′, J′). The red arrows in (b) represent the directions of the Ar⁺ and N₂ beams in the COM frame.

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Although the extreme forward region of the VMI images cannot be observed due to the intensive primary Ar⁺ beam, elastically and inelastically scattered Ar⁺ ions by the N₂ beam in the scattering angular range from ~70° to 180° can be clearly observed, as shown in Fig. 1a, d. To obtain the partial velocity distributions of the scattered Ar⁺ ions, the bottom left quadrants of the VMI images (red boxes in Fig. 1a, d), which are nearly free of disturbance from the intensive primary Ar⁺ beam, are analyzed and the corresponding three-dimensional velocity distributions are reconstructed by the Maximum Entropy Velocity Legendre Reconstruction (MEVELER) algorithm^42,43. The obtained velocity distributions of the scattered Ar⁺ ions in the angular ranges of 90–135° (red) and 135–180° (black) are presented in Fig. 1c, f, respectively, for the spin-orbit ground and excited Ar⁺ ions.

The black concentric rings labeled with numbers in the VMI images represent the kinematic cutoffs for the corresponding vibrational levels of the scattered N₂. For the collisions between the spin-orbit ground Ar⁺(²P_3/2) ion and N₂ as shown in Fig. 1a, the radii of the concentric rings are calculated assuming that only the rovibrational levels of N₂ are excited, while the spin-orbit level of Ar⁺ stays unchanged in the collision. As shown in Fig. 1a, c, the radius of the ring corresponding to N₂(v′=0) coincides with the edge of the VMI image of the scattered Ar⁺ ions, and the peak with the highest speed in the velocity distribution matches well with the v′=0 level of N₂, indicating that the collisional energy transfer process Ar⁺(²P_3/2) + N₂(v′′=0, J′′)→Ar⁺(²P_3/2) + N₂(v′, J′) should dominate. As a direct comparison, if the radii of the concentric rings are calculated assuming a collisional energy transfer process of Ar⁺(²P_3/2) + N₂(v′′=0, J′′)→Ar⁺(²P_1/2) + N₂(v′, J′), as shown in Supplementary Fig. 1, scattered Ar⁺ ions beyond the kinematic cutoff for N₂(v′=0) are clearly observed, indicating that the collisional spin-orbit excitation process should be minor. This observation is in qualitative agreement with the measurement by Futrell and co-workers³⁷, and with previous theoretical calculations^38,39.

For collisions between the spin-orbit excited Ar⁺(²P_1/2) ion and N₂ as shown in Fig. 1d, the radii of the concentric rings are calculated assuming that the spin-orbit excited Ar⁺(²P_1/2) ion is quenched to the ground spin-orbit level in the collision process, namely Ar⁺(²P_1/2) + N₂ → Ar⁺(²P_3/2) + N₂(v′, J′). As shown in Fig. 1d, f, the radius of the ring corresponding to N₂(v′=1) coincides with the main onset of the VMI image of the scattered Ar⁺ ions, and the peak with the highest speed in the velocity distribution matches well with the v′=1 level of N₂, indicating that N₂ should mainly be excited to the v′=1 vibrational level together with quenching of Ar⁺ from the spin-orbit excited ²P_1/2 level to the ground ²P_3/2 level. This observation is in accord with the previous theoretical calculations^38,39, which predicted that the process with simultaneous quenching of Ar⁺(²P_1/2) to Ar⁺(²P_3/2) and one quantum of N₂ vibrational excitation is efficient. As a comparison, the concentric rings are also calculated assuming a collisional energy transfer process of Ar⁺(²P_1/2) + N₂ → Ar⁺(²P_1/2) + N₂(v′, J′), as shown in Supplementary Fig. 2. It is seen that the radius of the ring corresponding to N₂(v′=0) coincides with the edge of the VMI image of the scattered Ar⁺ ions, indicating that the collisional energy transfer process Ar⁺(²P_1/2) + N₂ → Ar⁺(²P_1/2) + N₂(v′, J′) might not be negligible. This is confirmed by the TSH calculation as presented below. However, the resolution of the current experiment is not enough to resolve the kinematic cutoffs corresponding to the two processes Ar⁺(²P_1/2) + N₂ → Ar⁺(²P_3/2) + N₂(v′=1) and Ar⁺(²P_1/2) + N₂ → Ar⁺(²P_1/2) + N₂(v′=0).

Because individual vibrational levels are not resolved due to the accompanying high rotational excitation of the scattered N₂ as confirmed by the TSH calculation, and the extreme forward scattering is blocked, accurate determination of the vibrational population and the angular distribution of the scattered N₂ in each individual vibrational level is not feasible. Nevertheless, an interesting dynamic feature of the vibrational excitation and angular distribution of the scattered N₂ is clearly revealed by the collected VMI images. For collisions with the spin-orbit ground Ar⁺(²P_3/2) ions (Fig. 1a–c), the N₂ molecules scattered near θ ~ 180^o are mainly in the v’=0 vibrational level, and those scattered into the more forward region are excited to higher vibrational levels. This is evident in the Ar⁺ product velocity distributions as shown in Fig. 1c. The velocity distribution in the scattering angular range of 135–180° (black) features a single prominent peak assigned as the v’=0 vibrational level of N₂, while that in the scattering angular range of 90–135° (red) has a much broader distribution extending up to v’=3 vibrational level of N₂. In the forward hemisphere (scattering angle <90°), even more prominent vibrational excitation of N₂ can be clearly observed, as shown in Fig. 1a. For collisions with the spin-orbit excited Ar⁺(²P_1/2) ion, similar feature of the vibrational excitation and angular distribution is observed, where more rovibrational excitation of N₂ is clearly observed at smaller scattering angles, as shown in Fig. 1d, f. The observation that scattered products get more rovibrational excitation as the scattering angle decreases contradicts the conventional wisdom generally accepted for the inelastic collisional energy transfer process⁶.

Trajectory surface hopping calculations

To gain deeper insights into the collisional energy-transfer process of the Ar⁺(²P_3/2,1/2) + N₂ system, full-dimensional TSH calculations were performed. The potential energy curves of the relevant states at the collinear geometry with N₂ at its equilibrium geometry are shown in Fig. 2, while cuts of the three states along the N-N distance in the asymptote are displayed in the inset. The calculated transition probabilities into specific final spin-orbit levels of Ar⁺ and vibrational levels of N₂ for the collisions between Ar⁺(²P_3/2) and N₂ and between Ar⁺(²P_1/2) and N₂ are presented in Fig. 3a, b, respectively. To make a better comparison with the experiment, the corresponding transition probabilities in the backward hemisphere (scattering angle >90°) were also calculated, and shown in Fig. 3c, d, respectively. For the collision between Ar⁺(²P_3/2) and N₂, the most probable vibrationally inelastic channel without spin-orbit excitation is Ar⁺(²P_3/2) + N₂(v′=1), and the most probable vibrational channel with spin-orbit excitation is Ar⁺(²P_1/2) + N₂(v′=0), in qualitative agreement with the previous calculation based on the Landau-Zener-Stückelberg formalism³⁹. In the backward hemisphere, the most probable scattered channel is Ar⁺(²P_3/2) + N₂(v′=0) (Fig. 3c), in agreement with the experiment, as shown in Fig. 1a, c. For the collision between Ar⁺(²P_1/2) and N₂, the spin-orbit quenching process is quite efficient with the N₂(v′=1) channel more probable than the N₂(v′=0) channel, in qualitative agreement with previous calculations^38,39. In the backward hemisphere, the elastic channel Ar⁺(²P_1/2) + N₂(v′=0) dominates (Fig. 3d), which is in qualitative agreement with the experiment (Supplementary Fig. 2).

The inset depicts the asymptotic potentials as a function of the N-N distance (r).

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a The calculated state-to-state transition probabilities for the collisional energy transfer processes of Ar⁺(²P_3/2) + N₂ → Ar⁺(²P_3/2) + N₂(v′) (red) and Ar⁺(²P_3/2) + N₂ → Ar⁺(²P_1/2) + N₂(v′) (black) at the COM collision energy of 1.58 eV; (b) the calculated state-to-state transition probabilities for the collisional energy transfer processes of Ar⁺(²P_1/2) + N₂ → Ar⁺(²P_1/2) + N₂(v′) (red) and Ar⁺(²P_1/2) + N₂ → Ar⁺(²P_3/2) + N₂(v′) (black) at the COM collision energy of 1.58 eV; (c, d) presents the transition probabilities for the same processes as those in (a, b), respectively, but only signals in the backward hemispheres (scattering angle >90°) are counted.

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The calculated vibrationally resolved angular distributions of the N₂ product at 1.58 eV is presented in Fig. 4. For both Ar⁺(²P_3/2) and Ar⁺(²P_1/2), the elastic scattering channel dominates at all scattering angles. The most noticeable feature of the angular distributions is that all vibrationally excited N₂ (up to v’=3) are predominantly scattered into the forward region for both Ar⁺(²P_3/2) and Ar⁺(²P_1/2). This is in excellent agreement with the experimental measurements as presented earlier, where more rovibrational excitation of N₂ is clearly observed at smaller scattering angles. The rotational distributions and the correlations with the scattering angles for the N₂ product in various vibrational levels at 1.58 eV are also calculated and shown in Fig. 5. For Ar⁺(²P_3/2), the N₂(v’=0) product channel is mainly in the forward scattering direction with low rotational excitation. For higher vibrational levels of N₂, the scattered products exhibit interesting rotational excitation dynamics. Specifically, the N₂(v’=1) and N₂(v’=2) product channels have much hotter rotational distributions than the N₂(v’=0) channel, peaking at J’ = ~ 28, and are mainly scattered into the forward direction, as shown in Fig. 5b, c. For Ar⁺(²P_1/2), the correlation contour maps of the N₂(v’=2) product channel show similar features to the N₂(v’=1) and N₂(v’=2) product channels of Ar⁺(²P_3/2), as shown in Fig. 5f. Previously, high rotational excitation was also observed predominantly in the extreme forward scattering region in the N₂⁺(v’=2) product channel for the charge-transfer reaction between Ar⁺(²P_3/2) and N₂²⁹. This implies that the collisional charge-transfer and energy-transfer processes of the Ar⁺+N₂ system are closely related to each other, and the hard collision glory mechanism should also play an important role in the rovibrational energy transfer process between Ar⁺(²P_3/2,1/2) and N₂^29,32.

The calculated product angular distributions (DCSs) for the collisional energy transfer processes (a) Ar⁺(²P_3/2) + N₂ → Ar⁺(²P_1/2,3/2) + N₂(v′) and (b) Ar⁺(²P_1/2) + N₂ → Ar⁺(²P_{1/2, 3/2}) + N₂(v′) at the COM collision energy of 1.58 eV. The statistical error is given by \(\sqrt{({N}_{{total}}-{N}_{r})/{N}_{{total}}{N}_{r}}\), where N_r and N_total are numbers of reactive and total trajectories.

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The calculated correlation contour map between the N₂ product rotational excitation and the scattering angle for the collisional energy transfer process Ar⁺(²P_3/2) + N₂ → Ar⁺(²P_{1/2, 3/2}) + N₂(v′) at the COM collision energy of 1.58 eV: (a) N₂(v′=0), (b) N₂(v′=1), (c) N₂(v′=2); and the calculated correlation contour map between the N₂ product rotational excitation and the scattering angle for the collisional energy transfer process Ar⁺(²P_1/2) + N₂ → Ar⁺(²P_{1/2, 3/2}) + N₂(v′) at the COM collision energy of 1.58 eV: (d) N₂(v′=0), (e) N₂(v′=1), (f) N₂(v′=2).

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A careful analysis of the trajectories revealed that vibrational excitation of N₂ derives mainly from a frustrated charge transfer process, in which transient Ar+N₂⁺ species are formed. An exemplary trajectory is presented in Supplementary Fig. 3, in which the system undergoes a nonadiabatic hop to the Ar+N₂⁺ state, which has a very different N-N equilibrium distance, before hopping back to the Ar⁺+N₂ state. The N₂ vibrational excitation resulted in the first charge transfer, which is evidenced by the large oscillations in the N-N distance and has been extensively discussed in our earlier work^29,30, remains after the reverse charge transfer. To gauge the importance of this frustrated charge transfer mechanism, we calculated the probabilities of vibrationally excited states of N₂ that underwent charge transfer, and the values are listed in Supplementary Table 1. It is clear that almost all N₂ vibrational excitations are due to transient charge transfer. Such a mechanism has been noted before in several other collisional energy transfer systems; wherein strong charge transfer couplings exist between the two collisional partners^19,20,21,44.

Regarding the forward scattering for the vibrational excited N₂, shown in Fig. 4, we attribute it to the hard collision glory scattering (HCGS) mechanism³². As we discussed in our earlier charge transfer studies, the HCGS mechanism originates from the balance between the repulsive and attractive parts of the interaction potential. Specifically, a trajectory with a relatively small impact parameter is pulled into a strongly coupled collisional complex by the attractive region of the PES, undergoes vibrational excitation, and is then repelled by the repulsive region of the PES, resulting in a vibrationally excited product in the forward direction. Since the vibrational excitation in N₂ is dominated by the frustrated charge transfer mechanism, as alluded above, it is not surprising that these excited N₂ products are forward scattered. This is confirmed by examining trajectories in Supplementary Fig. 4.

Unexpected vibrational energy transfer in forward scattering has been observed before in several other collisional systems^18,20,31. In the inelastic H + D₂ collisions, Zare and coworkers observed that all the highly vibrationally excited D₂ products are strongly forward scattered, which they attributed to the strong attractive force when the H atom grazes the D₂ molecule due to the relatively deep potential well formed at the linear geometry on the PES³¹. Anomalous forward scattering in vibrational inelastic collision was also observed between ions and neutrals. One of the particularly notable examples is the inelastic scattering between the H⁺ ion and H₂, for which prominent vibrational excitation was observed in the extremely forward scattering region¹⁸. A bond dilution model was invoked to explain the observation, wherein the passing H⁺ ion strongly “dilutes” the H₂ bond by withdrawing electron density from it, and this stretches the bond to induce vibrational excitation⁴⁵. Although the above two examples share the same feature with the present experiment that highly vibrationally excited products are predominantly forward scattered, substantial differences exist between them. In the inelastic collisions of H + D₂ and H⁺ + H₂, the vibrational excitations are mainly from collisional trajectories with relatively large impact parameters corresponding to glancing collisions^31,45; while in the inelastic Ar⁺+N₂ collision studied here, the highly vibrationally excited N₂ products (v’ > 2) in the forward scattering are mainly from trajectories with relatively small impact parameters (b < 3 Å), as shown in Supplementary Fig. 5. Such HCGS mechanism has been identified in inelastic rotational energy transfer process³², and the current experiment showed for the first time that the HCGS mechanism can also play a major role in inelastic vibrational energy transfer processes, particularly between ions and neutrals. This unique behavior of vibrational excitation in the forward direction observed here is a combined consequence of HCGS and frustrated charge transfer. Deep potential wells are omnipresent on the interaction PESs between ions and neutrals, thus the HCGS mechanism could be quite common in many other inelastic ion-molecule collisions.

To our best knowledge, the present study represents the first crossed beam imaging experiment on the inelastic collisional energy transfer dynamics between ions and neutrals at relatively low collision energies. With further improvements, we would expect that such crossed beam imaging method can be applied for many other inelastic ion-molecule collisions, which are of utmost importance in many research fields, but systematic investigations and deep understandings are still lacking.

Experimental

The state-selected ion-molecule scattering apparatus used in the current study has been described in detail previously^40,41. The spin-orbit state selected Ar⁺(²P_3/2) and Ar⁺(²P_1/2) ions are produced by the (3 + 1) and (4 + 1) resonance-enhanced multiphoton ionization (REMPI) process, respectively. The REMPI photoionization scheme has been proven to be able to produce spin-orbit state selected Ar⁺(²P_3/2) and Ar⁺(²P_1/2) ions with quantum state purities better than 95%⁴⁶. The ultraviolet (UV) laser used for the REMPI process was generated by doubling the fundamental output of a dye laser (LiopTec, LIOPSTAR-E) pumped by the second-harmonic output of a 10-Hz YAG laser (Beamtech, Nimma-900). The UV laser was focused into the photoionization region by a plano-convex lens with a focal length of 150 mm, where it perpendicularly crosses with a supersonic beam of pure Ar generated by a pulsed valve (Parker, Series 9) running at 10 Hz and a backing pressure of ~4 atm. For Ar⁺(²P_3/2), the UV laser wavelength is set at 314.466 nm with a pulse energy of ~0.8 mJ; for Ar⁺(²P_1/2), the corresponding laser wavelength and pulse energy are 372.765 nm and ~7.5 mJ, respectively⁴⁶. To suppress the space charge effect and maintain a reasonable signal-to-noise level, ~200 Ar⁺ ions are produced in each pulse. The produced Ar⁺ ion beam is then accelerated to ~120 eV, and decelerated to the target kinetic energy before arriving at the reaction center. The focus and deceleration of the ion beam are achieved by applying proper voltages to the corresponding ion source electrodes⁴¹. In the center of the 3D VMI set-up (reaction center), the Ar⁺ ion beam crosses the supersonic molecular beam of N₂ at 90°, which is produced by a second general valve (Parker, Series 9). After collision, the three velocity components of the scattered Ar⁺ products are measured by the 3D VMI set-up⁴⁰. For each scattering image, ~100,000 product ions are collected.

It should be noted that the reactant ions and scattered products in the current experiment are the same species Ar⁺, thus cannot be separated from each other by the means of time-of-flight mass spectrometry. Furthermore, the primary Ar⁺ beam is 3–5 orders of magnitude more intensive than the scattered Ar⁺ ion. Therefore, it is necessary to block the primary ion beam when detecting the scattered ions. In the experiment, the primary reactant ions are mainly concentrated in the forward scattering region, and an opaque black tape is used to cover the corresponding area on the phosphoscreen, thus they are not detected by the camera. In this way, only scattered ions in the sideways and backward scattering regions are collected. Despite being blocked by the black tape, strong fluorescence from the primary reactant ion beam can still leak out to be detected by the PMT. The leaking-out signal is still much stronger than that from the scattered ions. This makes the accurate measurements of the time-of-flight of the scattered ions not feasible, thus only the conventional two-dimensional (2D) crushed VMI images of the scattered Ar⁺ ions could be obtained. The MEVELER method is then used for reconstructing the 3D velocity distributions of the scattered ions from the crushed 2D VMI images^42,43.

Theoretical

The PESs used for the theoretical calculations are adapted from the 5 × 5 empirical diabatic potential energy matrix (DPEM) of Candori et al.⁴⁷. To simplify the model, we only use three states, \({{{\rm{Ar}}}}^{+}({\scriptstyle{2}\atop}P_{3/2,1/2})+{{{\rm{N}}}}_{2}({X}^{1}{{{\Sigma }}}_{g}^{+})\), \({{{\rm{Ar}}}}^{+}({\scriptstyle{2}\atop} P_{1/2,1/2})+{{{\rm{N}}}}_{2}({X}^{1}{{{\Sigma }}}_{g}^{+})\), and \({{\rm{Ar}}}+{{{\rm{N}}}}_{2}^{+}({X}^{2}{{{\Sigma }}}_{g,\frac{1}{2}}^{+})\), as discussed in our recent work^29,30. In addition, Morse functions of N₂ and \({{{\rm{N}}}}_{2}^{+}\) are added to the corresponding PESs, with the explicit assumption that the vibrational degree of coordinate is decoupled with the other nuclear degrees of freedom in each diabatic state.

The fewest switches with time uncertainty (FSTU) method⁴⁸, as implemented in the ANT program⁴⁹, was utilized in the dynamics calculations. Nonadiabatic transitions were tracked in the adiabatic representation using the stochastic decoherence (SD) scheme⁵⁰ used with FSTU, while the gradV prescription⁵¹ was applied for all frustrated hops. The initial state of N₂ was specified by v′′=0, J′′ = 0, and the initial separation between the collision partners at 8 Å. trajectories was terminated once the two were separated by 10 Å, at which point the vibrational and rotational quantum numbers of the N₂ products were then determined, as outlined in our earlier work^29,30. The impact parameter (b) was sampled from a uniformly distributed random number ζ∈[0, 1], following b = b_maxζ^1/2, where b_max equals to the initial reactant separation between the collision partners (8.0 Å). The total numbers of trajectories for the ground and excited states of Ar⁺ + N₂ are 650,000 and 1000,000, respectively. Extensive tests were conducted to ensure convergence of the results.