Introduction

Understanding a chemical reaction demands detailed insight into how it evolves from reactants to products at an atomistic level. On a complex potential energy landscape, a reaction outcome depends on the pathways that connect reactants to products. Acid-base reactions, addition, elimination, and substitution are four well-known reaction types that cover most of the discussions in organic chemistry textbooks. Bimolecular nucleophilic substitution (SN2) is such a reaction that, over the years, has served as a prototype to unravel the atomistic dynamics, energetics, and reactivity of chemical reactions related to synthesis in organic and bio-chemistry1,2,3,4,5,6. Reactions of halide anions with methyl halides (X− + CH3Y → CH3X + Y−) represent the simplest model system for SN2 reactions. Many different direct reaction mechanisms such as stripping, rebound, and front-side attack, as well as indirect mechanisms as the roundabout, complex formation, barrier recrossing, and double inversion could be identified7,8,9,10,11,12.

Up to now the vast majority of chemical reaction dynamics are described using quasiclassical trajectory (QCT) simulations on multidimensional Born-Oppenheimer potential energy surfaces (PESs). Good agreement has been found for a variety of chemical reactions13,14,15,16,17,18. Quantum mechanical effects on the dynamics of the atomic nuclei on the Born-Oppenheimer PES have been a long-standing research topic19. They are, however, challenging to reveal and have so far only been identified in reaction processes with three or four light atoms20,21,22,23,24. Larger systems have only rarely been treated with full-dimensional quantum scattering calculations25. It is therefore difficult to assess in how far quantum effects, such as tunneling of light hydrogen atoms or quantum resonances due to discrete vibrational eigenstates, are effective in polyatomic reactions.

Isotopic substitution is an important approach for testing the validity of the Born-Oppenheimer surface in molecular spectroscopy. In reaction dynamics it allows one to search for effects not captured by QCT simulations. The effect of isotopic exchange is frequently discussed for reaction rates and is known as the kinetic isotope effect (KIE), defined as the ratio of the reaction rate coefficients for hydrogen versus deuterium-containing reactants. The KIE may occur through lowering of the zero-point energy (ZPE), which causes a reaction after deuterium replacement to require a different energy to cross a potential barrier and thereby renders it sensitive to the transition-state structure as well as the temperature26. In SN2 reactions, inverse KIEs (smaller than one) have been measured for a range of systems27,28,29. High-level quantum dynamics calculations have found both normal and inverse isotope effects for the H + CH4 reaction, which are explained by inefficient energy transfer between translational and vibrational motion30 that may bear similarities with negative-ion SN2 reactions.

Reaction dynamics under isotopic exchange have been studied for the neutral OH + CH4 system and its isotopic variants using the crossed molecular beam method31. A notable change in the stretching excitation for the deuterated system was observed, while the excitation in bending and other modes is not significant. This result suggested that isotopic exchange has ‘quite subtle’ effects on the product angular distributions and the secondary-KIE only affects the vibrational distribution of the water products31. These experimental results were theoretically supported by QCT calculations using an analytical full-dimensional PES32, which showed that QCT simulations had a better match with the experiment for the deuterated case. The conclusion was that due to the more ‘local’ character of the HOD stretching and less influence from tunneling, the reaction with the deuterated counterpart matches better with the QCT calculation than for H2O.

Quantum effects in reaction dynamics have also been explored by investigating the vibrational specificity of chemical reactions after exciting a single quantum of a selected vibrational mode33,34. The F− + CH3I collision system9,35,36,37 showed that the symmetric CH stretching vibration of the neutral acts as a spectator for the SN2 reactivity at a relative collision energy of 0.7 eV, while an enhancement has been observed with the increase in collision energy38,39. This ‘spectator’ mode character implies that this mode is weakly coupled to the reaction coordinate and does not influence the reactivity, while an overall enhancement has been observed for the proton transfer channel with CH stretching excitation40. Unlike most X− + CH3Y SN2 reactions, the pre-reaction complex is not co-linear in this case, but the F− first attaches to one of the three H-atoms36.

In this work we study the reaction dynamics of the nucleophilic substitution and deuteron transfer channels in the following reactions:

$$\,\,{{{{\rm{F}}}}}^{-}+{{{{\rm{CD}}}}}_{3}{{{\rm{I}}}}\to {{{{\rm{CD}}}}}_{3}{{{\rm{F}}}}+{{{{\rm{I}}}}}^{-}\,\,\,\,\,\Delta H=-1.96\,{{{\rm{eV}}}}$$
(1)
$${{{{\rm{F}}}}}^{-}+{{{{\rm{CD}}}}}_{3}{{{\rm{I}}}}\to {{{\rm{FD}}}}+{{{{\rm{CD}}}}}_{2}{{{{\rm{I}}}}}^{-}\,\,\Delta H=0.72\,{{{\rm{eV}}}},$$
(2)

where the enthalpies are taken from ref. 37, corrected for the ZPE of the deuterated species. The results are compared to recent data for the corresponding hydrogenated reactions39,40, as well as to QCT and quantum dynamics calculations. In this multifaceted comparison, we find quantitative agreement between experiment and QCT simulations for the deuterated reaction but distinct differences in the hydrogenated reaction. This allowed us to identify that non-classical effects modify the orbital angular momentum-dependent reaction dynamics for the hydrogenated reactant.

Results

The experimental energy- and angle-dependent differential scattering cross sections have been obtained for the anionic reaction products I− and CD2I− of the reactions (1) and (2) using a crossed-beam velocity map imaging spectrometer (see Methods section). We also present scattering data for the products of the reaction of fluorine anions with hydrogenated methyl iodide CH3I from previous publications39,40 for comparison with the deuterated measurements. The reactive scattering experiments have been conducted under single-collision conditions for collision energies Erel ranging from 0.7 to 2.3 eV with an average energy width of 180 meV (FWHM). The setup and the experimental procedures are described in the methods section. Full-dimensional QCT simulations and reduced-dimensional quantum scattering calculations, described in the methods section, are also presented. Throughout this article, reactive collisions of F− with CD3I will be referred to as the deuterated reaction, and with CH3I as the hydrogenated reaction.

SN2 reaction dynamics

Experimental results for the SN2 channel, reaction (1), are presented in Figs. 1 and 2. Figure 1 shows the angle- and velocity differential cross sections for the product I−. The first row of Fig. 1(a1–a4) presents three-dimensional velocity distributions of I− products from CD3I as a target molecule, projected onto the two-dimensional scattering plane. The second row (b1–b4) are iodide anions resulting from the isotopologue CH3I39. The outermost circles superimposed on each figure mark the kinematic cutoff for each dataset, representing the maximum velocity achievable given the conservation of energy and momentum in the reaction. The figures are represented in the center-of-mass frame of the collision. Reactant ions move from left to right in our chosen reference frame and the neutral reactant from right to left. This defines the forward direction for detected product ions on the left-hand side of each image.

Fig. 1: Measured differential scattering cross sections for the SN2 reaction.
figure 1

Row (a) depicts I− products resulting from F− + CD3I, while row (b) shows products from the hydrogenated reaction F− + CH3I [the data for panels b1, b2, and b4 are replotted from ref. 39]. The I− velocity distributions are depicted in the center-of-mass frame at four different relative collision energies ranging from 0.7 to 2.3 eV. The outermost rings mark the kinematic cutoff, representing the maximum velocity an I− can achieve at the given initial F− and CH3I/CD3I velocities. The dashed lines mark the segmentation of the images to quantify the contributions of different mechanisms due to (F)orward, (S)ideways, (I)ndirect, and (B)ack scattering (see supplementary information for details). The Newton diagram at the top depicts the relative orientation for the velocity vectors of both reactants and I−. Source data are provided as a Source Data file.

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We extracted the angular and internal energy distributions from the cross section data, as shown in Fig. 2. The first row (a1–a4) are velocity-integrated angular distributions of the product I− resulting from scattering of F− with CD3I (red) and CH3I (blue). The forward and backward directions are matched to the cross-sectional data, which is why the data is plotted as \(-\cos (\theta )\). The panels in the third row (c1–c4) in Fig. 2 represent experimentally obtained internal energy distributions of CD3F (red) and CH3F (blue) product molecules.

Fig. 2: Angular and internal energy distributions for the SN2 reactions of F− + CH3I (blue) and F− + CD3I (red) at different relative collision energies ranging from 0.7 to 2.3 eV.
figure 2

Row a: Velocity integrated angular distributions extracted from differential cross sections. Row b: Calculated quasi-classical trajectory (QCT) angular distribution of hydrogenated and deuterated SN2 type reactions. Row c: Derived internal energy distributions of the CH3F (blue) and CD3F (red) product molecules. Row d: Calculated (QCT) product internal energy distributions. Source data are provided as a Source Data file.

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Starting at the lowest collision energy of 0.7 eV, the deuterated system shows three distinct reaction mechanisms visible in the differential cross section and, more quantitatively, in the velocity-integrated angular distributions. These are: Direct backscattered products at higher velocities close to the kinematic cutoff, direct forward scattered products at intermediate and isotropically scattered products at low velocities. The umbrella-like signature in the backward hemisphere can be assigned to the direct rebound mechanism9,41, which corresponds to the classic textbook description of an SN2 reaction, where a Walden inversion takes place42. Back-scattered events like this require small impact parameter collisions5. At intermediate velocities, a direct forward scattering signature is visible on the left side of the images. These forward scattered events are characteristic of a stripping mechanism. Stripping mechanisms are large impact parameter events where the product is only slightly deflected8. Finally, at the lowest product velocities, isotropically scattered ions are observed. These are representative of an indirect mechanism, where the reactant ion and neutral form a complex that has longer lifetimes than one average rotation and dissociates statistically. The complex-forming mechanism coincides with slower products and therefore high internal excitation of the neutral CD3F. The internal energy distribution at 0.7 eV (Fig. 2, panel c1) shows that highly excited products emerging from indirect mechanisms are the preferred outcome at this collision energy.

We have quantified the contribution of each reaction mechanism for both deuterated and hydrogenated reactions at each collision energy (see Fig. 1 and supplementary information). The results with their estimated accuracies are presented in Table 1. At the lowest collision energy, isotropic scattering has the largest contribution with 51(9)% for the deuterated reaction. Forward scattered events have the lowest contribution with 17(4)%. The third mechanism, direct rebound, is found in 33(4)% of the events. At the higher collision energy of 1.2 eV, we are able to differentiate an additional reaction mechanism in the deuterated reaction. Here, products are observed that are deflected towards large sideways angles of near 90°, referred to as sideways scattering. Upon increasing the relative collision energy, the contribution of isotropic scattering, the dominant mechanism at low energies, decreases, while back-scattered direct rebound contribution increases. Direct sideways scattering remains roughly constant over the entire deuterated dataset. Forward scattered products nearly vanish at the highest collision energy.

Table 1 Different reaction mechanisms assigned to both deuterated and hydrogenated differential cross sections in the energy range of 0.7–2.3 eV
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To gain additional insight, we performed QCT simulations for the deuterated system and its isotopologue using a multidimensional potential energy surface37 (see Methods section). Computed angular and internal energy distributions at each collision energy are presented in the second row (b1–b4) and fourth row (d1–d4) of Fig. 2, respectively. Comparing experimental and theoretical results shows an excellent agreement in angular and internal energy distributions for the deuterated reaction, with all features being reproduced with high fidelity.

When turning to the hydrogenated case, the same reaction mechanisms as discussed above can be identified (see Table 1). A similar shift from indirect towards more direct dynamics is seen with increasing collision energy, with direct rebound and sideways scattering being the prevalent reaction mechanisms at higher energies. The hydrogenated scattering cross section shows significantly more direct forward scattering dynamics with a correspondingly reduced number of back-scattered events. Specifically, about 10% of counts in the hydrogenated case lead to additional forward scattering, while back-scattering sees on average about 10% less counts (see Table 1). This is also directly visible in the experimental angular distributions in Fig. 2, (a1–a4). In a direct comparison between the hydrogenated reaction (blue line) and the deuterated reaction (red line), the former clearly shows strong enhancement of forward scattering dynamics. The enhancement of forward scattering is also visible in the internal energy distribution for CH3F (blue) and CD3F (red). The hydrogenated system forms neutral products with higher internal excitation than its deuterated counterpart. This is illustrated by a visual comparison in panel c4 of Fig. 2. The deuterated reaction shows a clear bimodal structure through the shift towards more direct dynamics, where the first lower peak corresponds to products formed by the direct rebound mechanism and the second peak shows high internal product excitation through indirect mechanisms. The minimum in between is the internal energy range where we would expect CD3F products resulting from forward scattering. This is filled in the hydrogenated reaction and only a barely significant dip at large internal excitation is remaining.

The QCT calculations for the hydrogenated reaction also show an overall agreement with the measurement. But there is one important difference between experiment and theory: The strongly enhanced forward scattering mechanism is not reproduced in the simulations for CH3I. This is further discussed below.

Deuteron transfer reaction dynamics

We also present differential velocity- and angle-dependent cross sections for both deuteron and proton transfer reactions (reaction (2)), taken together with the SN2 data at the same relative collision energies, see Fig. 3. Panels (a1–a3) depict CD2I− products stemming from the deuteron transfer reaction F− + CD3I → DF + CD2I−, panels (b1–b3) show CH2I− product ions of the isotopologue. The experimental and simulated angular and internal energy distributions are shown in Fig. 4.

Fig. 3: Measured differential scattering cross sections for the proton (F− + CH3I) and deuteron transfer (F− + CD3I) reactions.
figure 3

Row (a) depicts CD2I− products, while row (b) shows CH2I− [the data for panels b1 and b3 are replotted from ref. 40]. The data are presented in the same manner as Fig. 1. Source data are provided as a Source Data file.

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Fig. 4: Angular and internal energy distributions for the proton transfer (blue) and deuteron transfer reactions (red) at different relative collision energies.
figure 4

The data are presented in the same manner as Fig. 2. Row a: Velocity integrated angular distributions extracted from differential cross sections. Row b: Quasi-classical trajectory (QCT) calculations simulating the angular distribution of both proton and deuteron transfer. Row c: Derived internal energy distributions Row d: Simulated (QCT) product internal energy distributions. Source data are provided as a Source Data file.

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Both CD2I− and CH2I− can be barely observed at a relative collision energy of 0.7 eV, which corresponds to the enthalpy of both reactions. As a consequence, the statistics are too low for meaningful analysis at this energy. The appearance of products close to threshold is due to the absence of a transition state barrier above the product energy43. While SN2 is the predominant reaction channel throughout all measured collision energies, the proton and deuteron transfer channels increase in relative strength at higher collision energies. The trend of both reactions is a shift from isotropically scattered events at low collision energy to purely forward scattered large-impact parameter events. This is in line with previous results on proton transfer40,44. Slight differences also appear in the data; there is slightly more forward scattering for proton transfer and, in contrast, more backward scattering for deuteron transfer.

Figure 4 also presents QCT simulations for comparison. Both angular and internal energy distributions show a very good agreement with the measured data. Notably, also the differences in the angular distribution for proton and deuteron transfer are correctly captured by the simulations.

Calculated reaction probabilities

Further information on the SN2 channel of the hydrogenated and deuterated reactions is obtained from reduced dimensional quantum scattering calculations. For this, the reaction is studied using the initial state-selected time-dependent quantum wave packet method on the same PES37 used for the QCT simulations (see Methods section and supplementary information for details). The CH3I moiety is assumed to maintain the C3v symmetry and six important degrees of freedom relevant to the SN2 reaction are treated explicitly. In addition to the scattering coordinate, these are the C-I stretching, CH3 symmetric stretching and umbrella bending modes, and the rotational degrees of freedom of CH3I.

The reaction probabilities as a function of total angular momentum, obtained from the quantum dynamics calculations, are plotted in Fig. 5, panels a–d, for the ground rovibrational states of CH3I and CD3I at the four studied collision energies. In the same figure also the opacity functions obtained from the QCT simulations for CH3I and CD3I are plotted. For both hydrogenated and deuterated reactions, the quantum dynamics results show very different reaction probabilities than the QCT results, in particular visibly larger probabilities for higher angular momenta. Between hydrogenated and deuterated reaction the quantum dynamics result differs by around a factor of two, while the QCT results differ by around 20%. Furthermore, for collision energies of 1.2 eV and above the quantum reaction probability vanishes for slightly smaller total angular momenta for the deuterated compared to the hydrogenated reaction. The integral cross sections (see Fig. S2) obtained by the quantum dynamics calculations are a factor of two larger than the QCT results for both hydrogenated and deuterated reactants, which is further discussed below. The experimental results at 0.7 and 1.0 eV35 (also shown in Fig. S2) lie in between the calculated values.

Fig. 5: Calculated opacity functions.
figure 5

Opacity functions for the hydrogenated (blue) and deuterated (red) SN2 reactions (F− + CH3I / CD3I) at four different collision energies (panels a: 0.7 eV, b: 1.2 eV, c: 1.5 eV, and d: 2.3 eV) using a quantum scattering approach (solid lines) and quasiclassical trajectories (dashed lines) as a function of the total angular momentum Jtot. Source data are provided as a Source Data file.

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Discussion

We observe a shift from direct backward to forward scattering when the deuterium atoms in the F− + CD3I reaction are isotopically substituted by hydrogen atoms, which we refer to as a dynamic isotope effect. The difference is found at all collision energies and the relative change is estimated to make up around 10% of observed events. QCT calculations can reproduce all features observed in the deuterated reaction with high fidelity, but do not fully reproduce the hydrogenated reaction. This deviation only occurs for the SN2 reactions. The measured proton and deuteron transfer channels also show differences, but these are in very good agreement with the QCT calculations. Here, the C-H or C-D bond is directly affected, which suggests a more subtle difference for the SN2 channel. Supposed that the discrepancy between experiment and simulation is due to the quasiclassical nature of the calculated trajectories, we can expect a quantum mechanical effect to be the cause for the difference. The dipole moments of CH3I and CD3I are almost the same (1.6406(4) D and 1.6507(4) D, respectively45). Therefore the long-range interactions with F− are very similar and cannot introduce an isotope effect. This statement is true for high angular momenta as well, because the reduced masses of the F− + CH3I/CD3I systems are also almost the same. Note that the measured total reaction rate coefficient for the title reaction at 300 K is close to the Langevin limit for both hydrogenated and deuterated reactions27, showing the absence of a KIE at room temperature. In contrast, the rate coefficient decreases far below the capture limit at collision energies above a few hundred meV35. This bodes well with the present findings of a much higher reaction probability for the hydrogenated reaction than for the deuterated reaction.

The quantum dynamics calculations show that the reaction probability is much larger at large orbital angular momentum than extracted from the QCT simulations, leading to an overall larger integral cross section by a factor of two compared to the QCT integral cross section. One way this can be explained is via the effective potential energy barrier, which increases as the impact parameter or, correspondingly, the total angular momentum increases. Although the SN2 reaction is intrinsically barrierless, it is mediated by the effective potential, defined as the sum of the potential energy and the centrifugal potential along the minimum energy path. The effect of the centrifugal barrier is expected to be maximal at the Walden-inversion barrier, where the intermolecular distance of the reactants is minimal. When the total angular momentum increases to a certain value (around 300ℏ) in the reaction, the effective potential energy barrier for the SN2 reaction becomes positive. The barrier height is essentially the same for the hydrogenated and the deuterated reactions due to the only slight difference in the reduced masses of the two systems. However, near and above the reaction threshold quantum tunneling may become relevant, which could explain the non-zero quantum reaction probability at the largest angular momenta relevant for the hydrogenated SN2 reaction, most visible at 1.2 eV collision energy, where the deuterated reaction probability already vanishes (see Fig. 5b). These large impact parameters are expected to preferentially lead to forward scattering, in qualitative agreement with the experimental observation for the hydrogenated reaction. Note, however, that the quantum dynamics calculations do not include the proton/deuteron transfer channel, which is smaller in probability than the substitution channel, but still of significant magnitude. It is therefore likely that some reactants that would undergo proton/deuteron transfer are drawn towards the SN2 product channel, enhancing unphysically the reactivity of the SN2 reaction. For the proton or deuteron transfer channel, due to the deep pre-reaction well and its endothermicity, it is unlikely that quantum tunneling plays a significant role.

The much higher density of states in the deuterated reaction could also facilitate more direct dynamics as more efficient vibrational coupling could shorten the lifetimes of intermediate complexes. For example, it has been seen that for the Cl− + CH3Cl system, the substitution of H by D decreases the barrier recrossing rate substantially due to the faster rate for intramolecular vibrational energy redistribution (IVR)46. If the vibrational coupling is reduced in the hydrogenated reaction that may not be fully captured in the QCT simulations, which tend to overestimate the rates for IVR in reaction complexes47,48.

In reactive scattering experiments of F− with vibrationally excited CH3I39,40, we have observed changes in the dynamics and reactivity after exciting the symmetric CH-stretching vibration in CH3I, which could also not be fully reproduced by QCT simulations49, using the same PES as in the present QCT calculations. This provides further evidence that the coupling of the vibrational modes in the hydrogenated reaction complex may be sensitive to the quantum mechanical density of states. In the future, full-dimensional quantum dynamics calculations are expected to resolve these differences. These are presently becoming possible for six-atomic systems, at least for zero total angular momentum and only two heavy atoms25. Alternatively, approximate quantum methods such as ring polymer molecular dynamics simulations50 may be useful to shed light on the identified quantum effects in nucleophilic substitution reactions.

In summary, we have obtained experimental differential cross sections for the reaction of F− + CD3I for both the SN2 and deuteron transfer pathways. These are compared to experimental data for the same pathways in the F− + CH3I reaction, full-dimensional QCT calculations for both pathways, and reduced-dimensional quantum scattering calculations for the SN2 channel using the same PES. The QCT calculations reproduce the experimental results for the deuterated reaction very well, but in the hydrogenated case the comparison highlights a clear difference in the differential cross sections. Backward scattered, direct rebound is shifted to forward scattering when moving from the deuterated to the hydrogenated nucleophilic substitution reaction. Whereas most features of the deuteron and proton transfer dynamics are captured by the QCT calculations, the enhanced forward scattering for the SN2 channel is not reproduced.

In the absence of an agreement with quasiclassical dynamics, this dynamic isotope effect is assigned to a quantum mechanical effect, which is qualitatively supported by quantum dynamics calculations in reduced dimensions. Compared to the deuterated reaction, these calculations show a slightly enhanced reaction probability of the hydrogenated reaction at large angular momenta, where the forward-scattering mechanism is favored. The preference of large angular momenta in the hydrogenated SN2 reaction over the deuterated one may be attributed to tunneling through a positive effective barrier in the hydrogenated case, formed from the sum of the Walden-inversion barrier, involving the umbrella motion of the hydrogen atoms in the CH3 unit, and the centrifugal potential.

Quantum dynamical effects, as found in the present case, may be more prevalent than currently expected given the success of QCT simulations to accurately describe gas phase chemical dynamics. With more and more high- or even full-dimensional quantum scattering calculations for reactions of polyatomic molecules, it will be an important task to search for such effects. This is particularly important for reactions where hydrogen atoms are involved, even if their involvement is only indirect as in the case of nucleophilic substitution.

Methods

Experiment

We employ velocity map imaging in a crossed-beam setup to record angle- and velocity dependent differential cross sections of reactive ion-molecule collisions9,51,52,53.

To create the reactant ions, a 10% mixture of NF3 seeded in argon is used as a precursor gas. A home-built cantilever piezo valve is used to produce F− ions via dissociative electron attachment in a pulsed plasma discharge. The average pulse length is varied between 30 and 80 μs at switched DC-voltages of around 700 V, depending on the stability of the ion signal. The ions are extracted perpendicularly to the initial direction in a Wiley-Mclaren-type electrode configuration for mass selection. An octupole radiofrequency ion trap is subsequently used to trap the ions along the experimental axis for tens of milliseconds. Helium buffer gas thermalizes the trapped ion ensemble to room temperature inside the trap, which reduces the energy spread of the ion beam. The ions are then extracted and decelerated to desired kinetic energies and crossed with a neutral beam of CH3I or CD3I in the interaction region of the spectrometer at a crossing angle in the laboratory frame of 60°. The laboratory kinetic energies, recorded with two-dimensional velocity map imaging, were tuned to between 1.1 and 3.0 eV, with about 160 meV FWHM. Combined with the neutral beam velocity, this led to relative collision energies between 0.7 and 2.3 eV with an average accuracy of 180 meV (FWHM).

The neutral beam is produced via supersonic expansion in a differentially pumped neutral beam chamber. For the hydrogenated (deuterated) reaction experiment a mixture of 5% methyliodine (methyliodine-D3) seeded in helium is used to create the neutral beam. To prevent clustering in the neutral beam and to avoid condensation inside the nozzle, a backing pressure of 0.7 bar on a heated nozzle at 60 °C was used for the neutral beam. The resulting neutral beam velocity, typically (1100 ± 100) m/s, is measured frequently during data acqusition using electron impact ionization and two-dimensional velocity map imaging, in order to identify possible velocity drifts. The setup is operated at a repetition rate of 20 Hz. Reaction products are mapped onto a time- and position sensitive detector. For each reactive event the recorded position and time information are transformed into a velocity vector and product mass in the center-of-mass frame.

From this velocity vector histograms of the scattering angle, the internal energy in the molecular product, and images of the differential cross section in the scattering plane are produced. The cross section images are plotted as a function of the velocity component parallel (vx) and perpendicular (vr) to the reactant’s relative velocity axis (see the Newton diagram in Fig. 1). Each entry is weighted with 1/vr to create an image that corresponds to a sliced image through the three-dimensional scattering distribution, such that isotropic scattering is representend by a homogeneous intensity.

Quasiclassical trajectory calculations

QCT computations were performed for the F− + CH3I and F− + CD3I reactions at 0.71, 1.20, 1.57, and 2.33 eV and 0.76, 1.10, 1.50, and 2.24 eV collision energies, respectively, using our own dynamics code and a recently-developed full-dimensional high-level ab initio analytical PES37. The initial distance of the reactants is \(\sqrt{{x}^{2}+{b}^{2}}\), where x = 30.0 bohr. The impact parameter b varies between 0.0 and \({b}_{\max }\), where the reaction probabilities vanish, with a step size of 0.5 bohr. The \({b}_{\max }\) values are 13.5(13.0), 11.5(11.5), 11.0(10.5), and 9.5(9.0) bohr for the F− + CH3I(CD3I) reactions at the above collision energies, respectively. The initial orientation of the reactants is random, and the trajectories are initiated from the vibrational ground states of the polyatomic reactants by setting their zero-point vibrational energies using standard normal-mode sampling54. The initial rotational angular momentum of the reactants is set to zero by standard modification of the velocities. Five thousand trajectories were run for each impact parameter-collision energy pair.

The cross sections of the reactions at different collision energies are obtained with a b-weighted numerical integration of the opacity functions. The scattering angle distribution of the products is calculated by binning the cosine of the included angle θ of the relative velocity vector of the reactants and that of the products into 10 equidistant bins, where backward scattering corresponds to \(\cos \theta=-1\).

Quantum scattering calculations

The six-dimensional model for the X + CH3Y system employed in this study has been presented previously48 (see Fig. S1 in the supplementary information). The 6D model Hamiltonian for the F− + CH3I reaction is written as (ℏ = 1),

$$\widehat{H}=\frac{-1}{2{\mu }_{R}}\frac{{\partial }^{2}}{\partial {R}^{2}}+\frac{{\left({\widehat{J}}_{{{{\rm{tot}}}}}-\widehat{J}\right)}^{2}}{2{\mu }_{R}{R}^{2}}+{\widehat{K}}_{{{{{\rm{CH}}}}}_{3}{{{\rm{I}}}}}^{{{{\rm{vib}}}}}+{\widehat{K}}_{{{{{\rm{CH}}}}}_{3}{{{\rm{I}}}}}^{{{{\rm{rot}}}}}+V(R,r,\rho,\gamma,\theta,\varphi ).$$
(3)

Here, R is the distance from the center of mass of CH3I to F−, r is the distance from the center of mass of CH3 to I. The symmetric CH stretching mode and the umbrella mode of the CH3 group are described by scaled-polar coordinates (ρ, γ), the rotation of CH3I in the body-fixed frame is described by the angles (θ, φ), and μR is the reduced mass of the F− + CH3I system. \({\widehat{J}}_{{{{\rm{tot}}}}}\) is the total angular momentum operator of the system and \(\widehat{J}\) is the rotational angular momentum operator of CH3I. \({\widehat{K}}_{{{{{\rm{CH}}}}}_{3}{{{\rm{I}}}}}^{{{{\rm{vib}}}}}\) and \({\widehat{K}}_{{{{{\rm{CH}}}}}_{3}{{{\rm{I}}}}}^{{{{\rm{rot}}}}}\) are the vibrational and rotational kinetic energy operators of CH3I, respectively. The last term V(R, r, ρ, γ, θ, φ) is the potential energy37. The operators are described in detail in the supplementary information.

The initial wave packet is constructed as the direct product of a localized wave packet G0(R) and the eigenfunction of CH3I specified by (n0, J0, k0, K0, p0), which represent the initial vibrational quantum number, initial rotational quantum number of CH3I, the projection of J0 on the C3v symmetry axis, the projection of Jtot on the body-fixed z-axis, and the parity of CH3I, respectively. G0(R) is chosen to be a Gaussian function,

$${G}^{0}(R)={\left(\pi {\delta }^{2}\right)}^{-1/4}\exp \left[\frac{-{\left(R-{R}_{0}\right)}^{2}}{2{\delta }^{2}}\right]\exp \left(-i\sqrt{2{\mu }_{R}{E}_{0}}R\right),$$
(4)

where R0 and δ are the center and width of the Gaussian function, and E0 is the mean collision energy. The wave packet is propagated using the split operator method55.