State-correlated reaction dynamics unveiled in full from a single product-image measurement

Domain: physics
Published: 2025-11-25
Editorial outcome: major_revision

Abstract
Electron-or photoionization mass spectrometry coupled with product time-of-flight measurement is a universal detection scheme, which has been playing pivotal role in advancing our fundamental understanding of chemical reactions. This powerful detection scheme, however, usually does not provide the product state-specific information. Here, we propose a variant of universal detection with state-resolving capability by leveraging a three-dimensional velocity-map imaging detector with vacuum-ultraviolet photoionization probe. As demonstrated by a crossed-beam reaction of F+CH4 →CH3(v)+HF(v), both product vibrational branching and state-resolved angular distributions are simultaneously unveiled in a (v,v) pair-correlated manner from a single product-image measurement, which enables us to gain previously inaccessible insights. Comparisons with a six-dimensionality quantum dynamics calculation show excellent agreements, validating the approach. The proposed method is general and should open a new opportunity to gain deeper insights into many important complex chemical processes that are otherwise difficult to study.

Introduction
One of the fundamental goals of physical chemistry is to understand how a chemical transformation that invokes the breaking and forming of chemical bonds takes place. Reaction dynamics addresses this question from the molecular point of view, i.e., how the constituent atoms rearrange themselves in going from reactants to products1,2. The knowledge of product state and angular distributions has proven insightful in advancing our current understanding of chemical reactivity over the past decades. For instance, a statistical product state distribution and forward-backward symmetric angular distribution will strongly suggest an indirect complex-forming mechanism with a long-lived reaction intermediate3, whereas a non-statistical formation of a highly inverted product vibrational state distribution (or a hot translational energy release), usually accompanied by very anisotropic angular distributions, will be the imprint of a direct mechanism with the activated barrier lying early (or late) along the reaction pathway4.

Traditionally, two distinct experimental approaches have been developed to acquire such dynamical attributes. For the simple atom+diatom reaction, state-resolved detection of the diatomic product by laser spectroscopy, if applicable, suffices. Complex reactions, however, can lead to multiple product channels and often yield polyatomic products, whose detailed spectroscopic information, in most cases, might not be available. Then, a universal detection using either electron-impact5–7 or non-resonant one-photon ionization8–10 mass spectroscopic scheme becomes the method of choice. The time-of-flight measurements of the (neutral) products in this approach typically yield broad, featureless kinetic energy distributions, thus providing no product state information, except for the landmark work on F+H2 and its isotopic variants11. In other words, this general-purpose method trades the state-specificity for its universality—a dilemma of “seeing the forest but not trees”. Consequently, these two conventional approaches are generally conceived of applying to different classes of reactions depending on the availability of product spectroscopy.

Moreover, a polyatomic reaction often yields two molecular products. Then, even if the spectroscopic prerequisite of one product is fulfilled, the conventional spectroscopic methods would remain blind to the internal-state distributions of its coproduct. In order to uncover such a hidden information, a method combining the resonance-enhanced multiphoton ionization (REMPI) spectroscopy with high-resolution velocity map of the REMPI-tagged ions was developed12 to acquire, with the aid of energy and momentum conservations, the state-correlation between the concomitantly formed product pair in each individual reactive event13,14.

Despite the advance of this innovative method, the detailed information thus derived still suffers a significant shortcoming of being fragmentary, making it cumbersome to piece that information together for a bigger picture—a crucial aspect needed for a deeper understanding of chemical reactivity. As previously reported on the F+CD4 reaction, the umbrella-mode (v2) excited products CD3(v2=0, 1, 2, 3) were individually REMPI-tagged and imaged to reveal the concomitantly formed DF vibrational states of each individual CD3(v2) state—one at a time13,15. The resultant pair-correlated distribution of (v2(CD3), v(DF)), however, bore notable uncertainties of the relative REMPI detection sensitivities of each individually interrogated CD3(v2) state. [The notation of (v2(CD3), v(DF)) refer to the vibrational quantum states of two products, CD3 and DF, that are concomitantly formed in a single reactive event.] In addition, the information on other modes of excitation of CD3 was missing for either the lack of spectroscopic data or the weakness of REMPI signals, which, however, not necessarily reflects low reactivity. A similar experiment on the individual pair-correlated angular distribution of (v2(CH3), v(HF)) in F+CH4 was recently reported; though no attempt was made to obtain the pair-correlated vibrational branching16. Therefore, it is most pressing to develop an alternative detection scheme with two seemingly conflicting requirements of universality and state-specificity to quantitatively delineate the fuller picture of the reactivity.

In this work, we propose a general detection method with both universal and state-specific capabilities. We demonstrate, using the benchmark F+CH4 reaction, that complete product state and angular distributions can be simultaneously acquired in a pair-correlated manner from a single measurement, rendering more robust results possible without problematic calibrations of the detection sensitivities of different states by other state-specific methods. To attest the reliability of the experimental results, we also perform quantum dynamic calculation on a highly accurate full-dimensional potential energy surface. The comparisons between experiment and theory show remarkable agreements in nearly all aspects. Furthermore, the uncovered dynamical features enable us to pinpoint the angle‒angular momentum correlation being the key factor in governing the reactivity.

Results
A universal detection with product state-specificity
We achieved that by fully utilizing the unique feature of (ion) velocity-map imaging (VMI) of the recoiled products in a three-dimensional (3D) manner (Methods, Supplementary Fig. 1). By exploiting vacuum ultraviolet (VUV) one-photon ionization as a general probe, the widely used 2D image technique velocity-mapped those (ionized) products in the image plane x-y—regardless of their spatial locations of (x,y)—to a single spot on a position-sensitive detector17. By operating VMI under the soft-focusing condition (17.6 V/cm extraction field), the arrival time of the whole ion packet was stretched to about 300 ns, and at the same time, the temporal spreads of those ions with the same vz-speed but residing at different locations along the z-direction were greatly compressed through the space-focusing effect12,18,19. As such, the acquired imaging signals become insensitive to the finite scattering and ionization volumes, and thus the full product 3D velocity information can be faithfully mapped out.

The reaction of F+CH4 →CH3+HF was benchmarked for proof-of-concept demonstration. This reaction has been the subject of extensive studies over the past decades for its fundamental significance as a prototypical polyatomic reaction as well as its practical application in chemical lasers20–27. Dynamically, most of the prior works focused on the product state distributions of either CH3 or HF (refs. 23–26), except for more recent studies on the angular distributions through REMPI-tagged product pair-correlation measurements13–16. In this work, we used 118 nm (10.48 eV) photons to ionize CH3 products (ionization potential of 9.84 eV). One-photon ionization scheme has previously been employed in numerous studies of polyatomic reactions; no state-resolved features have ever been reported8–10. The implementation of the above 3D-VMI scheme, combined with time-sliced imaging (<20 ns gate-width) detection of the 3D velocity information of CH3+ at the center of the ion packet12, enables us to reveal all possible states of concomitantly formed product pairs of CH3 and HF. As will be presented below, the results from such universal and state-specific detection in turn give access to hitherto inaccessible information.

It has been shown that over the photon energy range of 10.2―11 eV, the CH3 photoionization cross-section appears to be independent of the umbrella-mode vibrational level (up to v2=2)28–31. This vibrational independency can be ascribed to the non-bonding nature of the highest-occupied molecular orbital (HOMO) of the CH3 ground state and structural resemblance of the final CH3+ state. Consequently, the Franck-Condon envelopes for photoionization would strongly favor the transitions that preserve both the vibrational mode and its quantum number28,30. Furthermore, because the 118 nm photon energy lies 0.64 eV above the ionization threshold, thus exceeding the autoionization regime, no strong vibrational dependence is expected. Thereby, we surmised that the present ionization scheme could serve as a universal probe with nearly uniform detection efficiency for the rovibrational states of CH3 products of our concern.

All essential dynamical attributes from a single image
Figure 1A presents the background-subtracted raw image of one-photon ionized CH3 products in the F+CH4 reaction at collision energy (Ec) of 2.4 kcal mol−1 (0.106 eV), for which the photochemical and discharge-generated spurious backgrounds have been subtracted (Supplementary Fig. 2). The distributions of previously reported (00, 3) and (00, 2) product pairs, obtained by REMPI-tagged ground-state CH3(00) products32, are clearly seen as labels b and h, respectively. Lying between them are a series of new ring-like features. Also shown in Fig. 1C are the relevant energetics of all product vibrational pairs (vCH3, vHF) of this work. Based on energy conservation, the nature of those ring-like features can readily be identified and assigned in red in Fig. 1C. Significantly, the vibrational excitation of CH3 products reside predominantly in the umbrella-mode (v2), with minor production of symmetric-stretching (v1) excitation and nearly null in the remaining modes of v3 (asymmetric stretch) and v4 (deformation)—clearly, a highly mode-selective reaction. The formation of CH3(v2=1) has been noted previously in a REMPI-tagged VMI experiment33. However, its relative reactivity could not be quantified at the time due to the unknown relative REMPI detection sensitivity of the 11-band.

The dynamics information encoded in Fig. 1A can be quantified after the density-to-flux correction12. Figure 2A presents the resultant product speed distribution P(u) over the 0o―90o angular range, where the multiple rings are better resolved. Also shown are two sparse features shaded in pink, which are the speed distributions of (00, 3) and (00, 2) acquired previously from an image with λ-scanning the Q-head of CH3(00) REMPI band32. As seen, both peaks match very well with the features b and h, respectively. Note an early symmetric profile of the (00, 3) pair and an asymmetric one with a long tail toward slower speeds for (00, 2). Presumably, such distinct shapes reflect that more energy is available for disposal into the two rotors (CH3 and HF) of the (00, 2) vibrational pair. By subtracting the pink-shaded distribution from the present P(u), the speed distributions of vibrationally excited CH3(vi) products are unveiled in Fig. 2B. Based on the energetic onset of each product pair (Fig. 2A) and referred to the extended tails of the (00, 3) and (00, 2) distributions, the profile of each individual vibrationally excited pair was then estimated and dissected from the congested distribution. The results are displayed as the blue dotted line in Fig. 2B. Once the shape of each component was determined, the product speed and translational energy distributions over the full angular range could then be uncovered by varying the magnitude of each individual vibrational component, while keeping its shape intact, till the observed total distributions were fitted. The results are presented in Fig. 2C, D, respectively.

Figure 3A summarizes the (pair) correlated vibrational branching fraction deduced from Fig. 2C or Fig. 2D in a 3D (vCH3, vHF)-matrix representation. We also perform a reduced six-dimensionality (6D) state-to-state quantum dynamics (QD) calculation34 on a highly accurate full-dimension neural network (NN) potential energy surface35. The 6D model (Methods: Theory) first constrains the non-reacting CH3 group within the C3V symmetry based on the eight-dimensional (8D) framework of Palma and Clary36, and then assumes that the CH3 group can rotate freely around its C3V symmetry axis and the CH bond length can be fixed at its equilibrium value in the reactant (2.06 bohr) to further reduce computational costs. Test calculations show that the 6D treatment yields reaction probabilities in good agreement with those of the 8D treatment. After including the effects of initial CH4 rotational states of this experiment at 8 K (Methods: Experiment), the QD results are displayed in Fig. 3B, for which only the v2 mode is explicitly considered. Remarkable agreements between experiment and theory are noted in nearly all aspects. For example, although the dominance of umbrella-mode excitation of CH3(v2) is intuitively anticipated, both experiment and theory show that the distribution of the v2-excitations, concomitantly formed with HF(v=2), peaks around v2=1—a rather mild excitation. Collectively, the umbrella-mode excitations account for ∽58% (theory) to ∽57% (experiment) of total reactive fluxes, an unprecedented and perhaps unexpected finding. Good agreements are also notable from the lower-dimension product state distributions of HF (in red, sum of all concomitantly formed CH3(vi) states for a given HF(v) state) and likewise CH3(vi) (in blue) displayed on the respective background. Such global agreements not only testify the experimental conjecture of uniform detection efficiencies of all CH3 internal states, but also validates that key dynamical feature can indeed be faithfully captured by the present theoretical 6D-approximation.

Figure 4 compares the experimental and theoretical correlated differential cross sections (CDCSs) at Ec = 2.4 kcal mol-1. This is the first 6D-QD calculation of state-to-state CDCSs for a six-atom reaction with dynamical resonances. As seen, both displays similar patterns showing strikingly distinct distributions for different product pairs. Nearly all product pairs feature a sharp forward structure, for which the theoretical prediction appears significantly sharper. Two plausible mechanisms could account for such distinctive forward peaking: A classical slowing-down (or time-delay) mechanism of trajectories over the centrifugally shifted barrier in large impact-parameter collisions37, and the contribution from a resonance-mediated pathway that has been suggested as the dominant reaction mechanism at lower Ec, particularly for the formation of HF(v=3)33,38. As shown in Supplementary Fig. 3, the initial CH4 rotational excitation significantly lowers the HF(v=3) branching fraction, implicating a negative impact on the resonance pathway. Thereby, the discrepancies in the forward peaks, the imprint of the resonance pathway, would be reduced if the reactants CH4(j=1, 2) were also included in the calculation. More significantly, the overall distribution evolves from being predominantly forward peaking for (00, 3) to exhibiting marked sideways scattering for (2, 2), and then to essentially backward-scattered (00, 2). Such a systematic trend follows closely with exoergicity of the product pair (Fig. 1C), with the internally hotter pair recoiled mainly in the forward direction and the least (internally) energetic pair shifted to backward scattering.

Mechanistic origin: angle-angular momentum correlation
Two factors could be at work for this prominent recoil energy dependency of angular distributions. As alluded to earlier, the reaction of F+CH4 proceeds predominantly by a resonant tunneling mechanism at low Ec ≤ 1 kcal mol−1 (ref. 33). At Ec = 2.4 kcal mol−1 the direct abstraction mechanism prevails with minor contribution from the resonance pathway32,38–41. This is a highly exoergic, heavy-light-heavy reaction with a somewhat bent, yet highly fluxional, F‒H‒C transition-state geometry35,42. For a light-atom transfer reaction, both the initial and final orbital angular momenta, l and l’, are mainly carried by the orbital motions of two heavy particles. On inertial grounds l and l’ are strongly coupled, leading to l≈l’ or li ≈ l’i for the ith vibrational pair1,2. The conservation of angular momentum dictates Jtotal = l+jCH4 = l’+jCH3+jHF. The initial rotational angular momentum of CH4, jCH4, is negligibly small for a supersonically expanded beam at the rotational temperature of ∽8 K (ref. 43). Therefore, jCH3+jHF must be small, in line with experimental finding of small rotational energy disposal of 1.5 kcal mol−1 (Method: Energy disposal) and 6D-QD results that both rotors exhibit low excitations with distributions peaking around j≈2 (Supplementary Fig. 4). Since l’=m’u’b’, where m’ denotes the reduced mass of two products, u’ is the recoiling speed and b’ the impact parameter of the departing products. In a direct near-collinear scattering process, smaller b’ tend to associate with smaller b, thus prefers backward scattering. In keeping with l’≈l, a more exoergic product pair with faster speed u’, e.g., (2, 1) or (0, 2), must recoil with smaller b’, i.e., preferentially in the backward direction. Likewise, the channel recoiled with small translational energy, such as (00, 3), will be mostly forward-scattered. The key factor in governing this kinematic correlation between angle and orbital angular momentum seems to be the energetics—irrespective of product vibrational modes—in accord with the observed trend.

The above kinematic consideration, rooted in the A+BC reaction, should hold for the newly formed H‒F bond (Supplementary Fig. 5). The CH3-moiety is not directly involved in bond cleavage and formation. Yet, the mere fact that about 57% of total reactive fluxes are channeled into umbrella-excited CH3 products attests to the strong coupling of the umbrella motions of CH3 to the reaction coordinate; thus, CH3-moiety is not an innocent spectator and cannot be regarded as a pseudo-atom. To understand the mechanistic origin of the observed umbrella-mode excitation and its dynamical attributes, we first note that the breaking C‒H bond is always directed away from (and uniformly distributed around) the center-of-mass of CH4, which lies on the C-atom. This site-specific consideration leads to the notion of peripheral dynamics44,45 for the present reaction, whose transition-state features a reactant-like structure with elongated F‒H bond and slightly distorted umbrella angles (∽107o) from the tetrahedral angle (109.5o) of CH4 35,42.

For the large impact-parameter or high-l collisions (the grazing collisions), the force along the line-of-centers (i.e., the incident F-atom to the C-atom) will be weak, exerting little distortion to the reactant-like transition-state structure. As the H-atom is abstracted with vibrational-excited HF scattered forward, the pyramidal CH3-moiety at transition state flattens abruptly to the planar CH3 product structure, resulting in mildly umbrella-excited CH3 products. On the other hand, for the low-l collisions (the head-on collisions), the line-of-centers force imparted by the incident F-atom is stronger, which attracts a H-atom under attack, causing the remaining CH3-moiety flattened gradually until the rupture of attacked C‒H bond, and thus leads predominantly to the backward-scattered ground-state CH3 products. This qualitatively explains the observed correlation that low umbrella-excited CH3 prefers backward scattering, whereas higher umbrella-excited CH3 yields more in the sideway and forward directions. A theoretical inspection on how the umbrella motion of CH3-moiety evolves along the reaction path (Supplementary Fig. 6) confirm this classical physical picture.

It is worth noting that the proposed interpretation can also account for a recently reported center-barrier reaction of D+CH4 (ref. 46) and H+CH4/CD4 (ref. 47). where the umbrella angle at the transition state is 103o (ref. 48). Hence, like the present reaction, the ground state-pair (00, 0) is expected to be scattered more backward than the umbrella-excited pair (2, 0), as experimentally observed. More elaborative QD wave-packet analysis led to the same conclusion46. As for the reversed behavior in the late-barrier Cl+CH4 reaction, i.e., the ground state CH3 products tend to be scattered more in the forward hemisphere (Supplementary Fig. 7), it can again be comprehended within this angle-angular momentum correlation framework. This is because that compared to the low-l collisions, the high-l collisions induce weaker distortion to the product-like transition-state structure, which features an early planar CH3-moiety; leading to more forward-scattered ground-state CH3 products. Putting together, with the consideration of the entire transition-state structure (meaning both the active X‒H‒C site and the spectator CH3 moieties), this angle-angular momentum correlation provides a conceptually appealing framework for understanding diverse dynamic behaviors of a host of direct reactions. The mechanistic insight proposed herein in turn serves as a vivid example to illustrate how the product dynamical attributes are controlled by the transition-state structure49.

Methods
Experiment
Supplementary Fig. 1 depicts the crossed-beam setup used in this work12,50,51. It consisted of two rotatable pulsed molecular beams and a fixed detector assembly housed in a vacuum chamber. The F-atom beam was generated by a pulsed high-voltage discharge of 5% F2 seeded in a pulsed supersonic expansion of Ne at 6 atm. The CH4 beam was also produced by pulsed supersonic expansion of neat CH4 at 6 atm and characterized by a rotational temperature of 8 K, i.e., the initial j-state distribution of nj=0 : nj=1 : nj=2 = 0.31: 0.54: 0.15 (ref. 43). Both beams were collimated by double skimmers and crossed in a differentially pumped scattering chamber; collision energy (Ec) was tuned by varying the intersection angle of the two molecular beams.

To interrogate the reaction products, non-resonant one-photon ionization of CH3 radicals was employed using 118 nm photon that was produced by the third harmonic generation scheme of a third harmonics YAG laser (355 nm) in a cell filled with ∽11 Torr of Xe (ref. 50). The CH3+ thus generated was then guided by a set of specially designed ion-optics and velocity-mapped in a three-dimensional manner onto the image detector consisting of gated-MCP, phosphor, and CCD camera12,51. The center-sliced image was then recorded by a computer for data analysis (Supplementary Fig. 2).

Image analysis
To retrieve the state-resolved angular distributions, or the CDCSs, from the overlapped image features, a two-step data analyses were performed. First, we tested how each individual CDCS will be affected by the sampling annulus with different widths or the u-ranges. As shown in Supplementary Fig. 8 samplings of three different annular widths (the right panels) exert little effect on the resultant CDCSs (the left panels). With that, we then proceeded to disentangle the “contaminations” from the proximate peaks for each given product pair to recover the ‘best-estimated’ CDCS. Based on the red-shaded slabs in the right-middle panel in Supplementary Fig. 8 for the respective product pair, we analyzed the angular distribution over the corresponding u-range. The results are presented as the black line in Supplementary Fig. 9, which encompasses both the desired distribution and the contamination from the adjacent product pairs. Due to the asymmetric P(u) profiles, the position and width of each desired pair were chosen so that it would capture its main peak with contaminations mainly from the lower speed part of the adjacent pair to the right and the long tail of the (00, 2) pair. The extent of contamination can be estimated from the overlapped flux or the area. Starting from the right, (00, 2), the overlap-corrections were then performed progressively one-by-one towards the left. The results are presented as the red lines in Supplementary Fig. 9, which represent our “best-estimated” CDCSs. Tests were also performed for somewhat different choices of u-slabs to ensure the consistency of the results.

Energy disposal
Conservation of energy can be expressed as Etotal = ‒ΔH + Ec = V(CH3+HF) + R(CH3+HF) + T(CH3-HF), where ΔH is the heat of reaction (‒31.82 kcal mol−1), V(CH3+HF) (or R(CH3+HF)) denotes the averaged energy deposited into two product vibrators (or rotors), and T(CH3-HF) is the averaged kinetic energy release of the departing products. Experimentally, the product speed distribution was measured; thus T(CH3-HF) can be deduced from Fig. 2D, 6.1 kcal mol−1 or a fractional translational energy release fT = 0.178. The vibrational energy disposal V(CH3+HF) can be derived from the normalized pair-correlated distribution presented in Fig. 3A, V(CH3+HF) = 26.7 kcal mol−1 or fV = 0.778. Notably, most of the available energy is deposited into the vibrational motions of the newly formed HF bond (fV(HF) = 0.71), in line with Polanyi’s rule for a highly exoergic atom+diatom reaction with an early barrier4. The conservation of energy, fT + fV + fR = 1.0, will then lead to fR = 0.044 or a low value of 1.5 kcal mol−1 for the combined energies of two rotors R(CH3+HF). In view of relatively large rotational constants of two products (BCH3 ∽ 9.6 cm−1, CCH3 ∽ 4.7 cm−1, and BHF ∽ 19 cm−1), small values of jCH3+jHF are then expected.

Theory: Reduced dimensional state-to-state quantum dynamics calculation
The reduced dimensional model employed in the time-dependent wave packet (TDWP) calculations here was the free-torsion seven-dimensional (FT-7D) model we proposed for the X+YCZ3 → XY+CZ3 reaction in 2013 (ref. 34), by assuming that the CZ3 group can rotate freely with respect to its C3V symmetry axis (Supplementary Fig. 10). With the bond length of CH fixed at its equilibrium value in reactant (2.06 bohr) because it essentially does not change during the reaction, the number of the degrees of freedom included in the calculation was reduced to six. We used the multiple-step reactant−product decoupling (MRPD) method52,53 to obtain the state-to-state information. We carried out state-to-state calculations covering all the total angular momentum Jtotal from 0 to 60 to converge the ICS and DCS for the initial ground state reaction for collision energies up to 0.1 eV. The state-to-state ICS for the initial CH4 rotational excitation were obtained using the weight-inclusive J-shifting method41, by including results for Jtotal = 0, 20, 40, and 60. The impacts of reactant rotations to CICSs are summarized in Supplementary Fig. 3.

Numerical parameters used in the 6D-QD calculation
The numerical parameters used in reactant Jacobi coordinates are as following: A total number of 280 sine basis functions covering a range from 3.0 to 19.8 bohrs were used for R with 110 grid points in the interaction region. For the r dimension, 70 basis functions were used in the range of [1.0, 9.0] bohrs in the interaction region, while six basis functions were used in the asymptotic region. The number of basis functions for the umbrella motion was 16. The rotational basis functions were constrained by the parameters, Jmax=164, lmax=140, jmax=24. The center of the prepared Gaussian wave packet was located at R0 = 18.0 bohrs, with the width of δ = 0.2 bohr, and the central energy of Ec = 0.15 eV. For total angular momentum Jtotal = 0, we propagated the wave packets for 150,000 a.u. of time with a time step of 10 to converge the reaction probabilities. The absorption potential on the r coordinate for the MRPD calculation takes the form

Vp(r) = C(r-r0)^n

with r0 = 6.5 a.u., Δr = 2.5 a.u., C = 0.04, and n = 1.5. To minimize the computational cost, the coordinate transformation is carried out at every eight propagation time steps. Continuous propagation in the product Jacobi coordinates only involves a total number of 300 sine functions for the translational coordinate in a range of [3.0, 21.0] bohrs and seven vibrational basis functions for HF bond. The number of basis functions for the umbrella motion was 11. The rotational basis functions were constrained by the parameters, J0max=54, l0max=30, and j0max=24. A dividing surface is placed at R0 = 15.5 bohr to extract S matrix elements. The number of K’-blocks included in the product calculation increases with the total angular momentum, from 1 for Jtotal = 0, up to 7 for Jtotal = 60.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The authors investigate the reaction dynamics of F + CH4 in a joint experimental and theoretical study. They use crossed beam velocity map imaging in combination with one photon ionization by a VUV photon from a free electron laser. This combination allows them to record product state specific differential cross sections which they term correlated differential cross sections. They complement the experimental results by high level quantum dynamics simulations. They find a remarkable agreement between experiment an theory. The study is well executed and the experimental and theoretical data is convincing and support the arguments made by the authors (once one understands them) but the presentation in the manuscript is not at the same level as the data or its analysis. The study might be suitable for publication in Nature Communications after major revisions of the data presentation and the manuscript.\n\nThere is little to no discussion on prior studies, experimental or theoretical, on the reaction except for the experimental one done by the authors before. They should take more care about this and I find this not up to common standards.\n\nThe reaction has been studied by part of the authors using the same (according to extended data Fig 1) except for the ionization scheme used for the CH3 radical. In earlier studies REMPI was used and each state was investigated in its own experiment whereas now different product states can be monitored in the same experimental run, respectively image. The authors highlight the new experimental capabilities as a major breakthrough but give surprisingly little experimental details.\n\nI find the language used throughout the manuscript unnecessarily fanciful and little to forward for me. A simpler language would help with understanding because I was often confused reading the manuscript. This is a starting with the abstract. What is the conventional perception the authors allude to throughout the manuscript? The use of “all-important” is not followed by an explanation as to why? The authors give bold statements and arguments but then these are very unspecific or lack facts and numbers. They state on page 5 that the present experiment has a “significantly higher resolution” but there are no numbers given: neither on the reactant beam uncertainties, the collision energy or the product velocity spread or the specs of the VUV beam. Only the temperature of the CH4 is given as 8K in conjunction with the angular momentum discussion.\n\nThe discussion on the importance or not importance of a prior found dynamical resonance to the presented data interpretation is so convoluted that it almost seems like dropping a key word. It requires the caption of Extended Data Fig. 3 and the SI to understand. The manuscript should stand by itself. The whole paragraph somehow reads backwards. I need several attempts to make some sense of it. And I am still not sure if I got right in the end: The dynamical does not play a significant role in for the present study, right? If my interpretation of the paragraph is correct, why put so\n\nFigure 1\nI consider the background subtracted image not really a difference image. Part of the authors referred to experiments with and without vibrationally excited reactant to difference images. This is a real difference image. Background subtraction needs to done and properly explained (as done here) but it is no difference image.\n\nI am missing a legend in figure 1A and 1B for the scaling for the color schemes used in the histograms. Is it linear or logarithmic, absolute or normalized? Why use the same line shape and color for two different kinematic cut-offs? Please make them distinguishable.\n\nPage 5, first full paragraph\nThe first sentence is really confusing and long. What is a “recoiled velocity”?\n\nFigure 7\nThe width of the used fitting functions and the significance of the relative contributions cannot be validated because no energy spread is given. Why use km/s as unit?\n\nPage 8, Line 2\nCan the authors please indicate why part of the image they are evaluating? In figure 1 only 0° and 180° are indicated. For experts is obvious but not for a general chemistry audience.\n\nPage 8, Line 15\nThe authors refer to “proper scaling” what is scaled how and why? More information is needed.\n\nFigure 3A\nWhat is the unit for the “correlated ICS” given that the data comes from a crossed beam experiment and the associated velocity map image. The data is not really an integral cross section but rather a relative branching ratio of the different product channels and should be labeled as such. Is there an error associated to it?\n\nPage 11 Line 22\nI do not understand the sentence. Something is missing. The authors should check if “auto-correction” did some unintended corrections.\n\nPage12, Line 9\n“does not directly invoke in bond cleavage and formation”\nPlease check wording.\n\nPage 12, Line 15+16\nI do not understand the meaning of this sentence in relation to reaction centers, respectively dynamics. The authors might want to check the language.\n\nPage 12, Line 26\nShouldn’t that be forward scattered CH3 when the HF is scattered backward. Also see next sentence. I guess something got mixed up.", "reviewer_2": "The authors (and others) have previously carried out extensive studies on the dynamics of the reaction F + CH → CH + HF\n4 3\nand deuterated analogs, in which they have probed CH products in their vibrational ground state and in various umbrella-\n3\nmode (ν ) vibrationally excited states (v = 0, 1, 2, 3) via REMPI and velocity-map imaging. These studies have revealed the\n2 2\npair-correlated scattering distributions of the CH with various vibrational states of the HF (or HD) coproduct. The present\n3\nstudy extends this work by using VUV photoionization at 118 nm as a universal probe to enable simultaneous detection of\nall rovibrational states of CH formed in the chemical reaction. The new experimental results are interpreted with the help of\n3\ncomprehensive six-dimensional quantum dynamics simulations.\n\nIn addition to the product channels previously characterised, the paper identifies, and importantly, quantifies contributions\nfrom asymmetric-stretch (ν ) excited CH products. These have been observed before using REMPI detection, but one-\n1 3\nphoton ionisation makes it much more straightforward to determine the relative contributions from different product channels.\nThe authors present product state distributions and pair-correlated angular distributions in excellent agreement with the\ntheoretical predictions, and provide a detailed commentary on the mechanisms leading to the observed angular scattering.\n\nThis is a comprehensive, generally well-written, and very high quality piece of work, which fills in some additional dynamical\ndetails for the benchmark F + CH reaction. However, I was extremely surprised at the number of times the authors stated\n4\nthe novelty of their 118 nm universal ionization approach, given that this ionization method, as well as universal ionization\nusing other VUV wavelengths, has been used in velocity-map imaging studies in a number of different laboratories for well\nover a decade. A few examples of which I am immediately aware include Fan et al, J. Chem. Phys., 123, 204301 (2005),\nAshfold et al, J. Phys. Chem. Lett, 8, 3440 (2017), Gardiner et al, Phys. Chem. Chem. Phys., 17, 4096 (2015), Lipciuc et al, J.\nChem. Phys., 147, 013941 (2017), and various other papers from these and other groups, but I am sure there are numerous\nothers. None of this previous work was mentioned or referenced in the manuscript. In my view, this is the one major\nshortcoming of the paper as it stands. There are also a few minor typos, etc, that the authors may want to correct in a revised\nversion of the manuscript.\n\n1. Abstract: remove the initial ‘The’. Also, “electron-impact ionization” is now usually referred to simply as “electron\nionization”.\n2. Page 3, line 13: “a state-resolved detection” should just be “state-resolved detection”.\n3. Page 11, line 8: lines 8-11 could do with a small amount of rewording, for clarity, e.g. “Thereby, the discrepancies in the\nforward peaks, the imprint of the resonance pathway, would be reduced if the reactants CH4(j = 1,2) were also included in\nthe calculation. More significantly, the overall distribution evolves from being predominantly forward peaking for (0 ,3) to\n0\nexhibiting marked sideways scattering for (2 ,2), and then to essentially backward-scattering for (0 ,2).”\n2 0\n4. Page 11, line 16: “recoiled-energy” should be “recoil energy”\n5. Page 12, line 9: I am not sure what the authors mean by “The CH -moiety does not directly invoke in bond cleavage and\n3\nformation”. Do they mean that the CH is not directly involved in bond cleavage and formation?\n3\n6. Page 12, line 11: should be “...products attests to the strong coupling...”\n7. Page 12, line 15: I am not sure what the authors mean when they say that the transferred H atom “is always sprouting away”\nfrom the centre of mass of CH . Are they just referring to the chemical structure of CH ? If so, it might be clearer to say\n4 4\nthat the breaking C-H bond is always directed away from the centre of mass of CH , which lies on the C atom. However, I\n4\nfind it difficult to think of an example in which a breaking bond would not be pointing away from the centre of mass of the\nmolecule within which it resides, so perhaps the authors could find a clearer way of making their point in this regard, perhaps\nwith the aid of a diagram?", "reviewer_3": "The VUV single photon ionization method has been well known as a soft and universal product detection scheme, while universal detection has been linked with no product state specificity all the time previously. In this study, Pan et al. demonstrated an experiment combining the universality of VUV photoionization for the reaction product detection and the high velocity resolution achievable in a three-dimensional VMI which can handle relatively large reaction or ionization volumes of the reaction products, and they achieved universality and state-specificity for product detection simultaneously. They successfully mapped out almost all the important product pair-correlated dynamical attributes of the prototypical polyatomic reaction F + CH4 → CH3(vi) + HF(v) from a single product image. Six-dimensionality quantum dynamics calculations are performed and found to be able to reproduce nearly all the aspects observed in the experiment, and have provided new insights into this important prototypical polyatomic reaction. Such a method is a very useful addition to the community of reaction dynamics, and can be definitely used in the studies of many other reactions, I thus recommend its publication in Nature Communications. The whole paper is very nicely presented, and I only have two comments for the authors to consider.\n\n1. The universal VUV single photoionization detection is an important addition to the product state-specific detection method, and can provide most of the time qualitative information for the full dynamical picture. However, its ability may not be overstated. In the study of the F + CH4 → CH3(vi) + HF(v), one of the reasons why it is very successful is that the products are all rotationally cold, which enables the resolve of the pair-correlated vibrational distributions. For reaction products with significant rotational excitation, the complete resolve will become difficult. At the same time, previous state-specific studies also play an important role in analyzing the data in this study. I thus believe that the proper combination of the universal and state-specific methods would become a powerful method in studying reaction dynamics in the future, as demonstrated in this study.\n\n2. For the last paragraph on page 12, a classical physical picture is described to explain the “observed correlation that low umbrella-excited CH3 prefers backward scattering, whereas higher umbrella-excited CH3 yields more in the sideway and forward directions.” Two points that may need be explained a little more: first, it seems that both the large and small impact collisions involve the flatten motion of the CH3 moiety, while one results in the umbrella vibrational excitation, and the other dose not? Second, the above picture only applies to processes within the same HF vibrational excitation, for example, for HF=3, the products are mainly forward scattered, even though the umbrella motion of CH3 is not excited. Is it possible to make it clearer why this picture strongly depends on the excitation of the co-product HF?", "reviewer_4": "The authors describe, implement, and test a VMI experiment capable of what they call “universal” state-resolved product selection. The well-studied F + CH4 system is considered, and the experiment is shown to resolve product states of CH3 alongside HF. The instrument is validated against quantum dynamics, which on its own is a substantial achievement of the work.\n\nThe demonstration given here is notable and, in my opinion, is appropriate for publication in a high-impact journal. Unfortunately, some awkward English and rushed descriptions make this short paper difficult to understand in places. I would specifically suggest improving the English in the abstract and elaborating on key discussion points. As written, the reader needs to already be familiar with VMI studies of this system to understand the paper.\n\nFor example, the notation of the observed state pairs, e.g., (23, 2), are not explicitly explained and instead must be inferred.\nI would suggest clarifying what aspects of the new design are responsible for the breakthrough here. The earlier work did not get information for all the vibrational levels of CH3 at once, like here, but I wasn’t sure why. Likewise, is there additional information in this experiment, as compared to earlier “3D” VMI studies on this system, or is the advance here that the information is gathered more directly?\n\nFinally, I wondered if plots like Fig. 1A could be produced from the calculations?"}, "author_response": "Author responses to the reviewers’ reports on NCOMMS-25-55690-T\nReviewer #1 (Remarks to the Author):\nThe authors investigate the reaction dynamics of F + CH4 in a joint experimental and theoretical study.\nThey use crossed beam velocity map imaging in combination with one photon ionization by a VUV\nphoton from a free electron laser. This combination allows them to record product state specific\ndifferential cross sections which they term correlated differential cross sections. They complement the\nexperimental results by high level quantum dynamics simulations. They find a remarkable agreement\nbetween experiment an theory. The study is well executed and the experimental and theoretical data is\nconvincing and support the arguments made by the authors (once one understands them) but the\npresentation in the manuscript is not at the same level as the data or its analysis. The study might be\nsuitable for publication in Nature Communications after major revisions of the data presentation and\nthe manuscript.\n[Reply]: Thank you for the positive comments about our works. We will try to improve our\npresentation in the revision to match up with the data and analysis. By the way, there may be a\nmisunderstanding that the VUV photon used in this work was generated by a third-harmonics process,\nnot from a free electron laser.\nThere is little to no discussion on prior studies, experimental or theoretical, on the reaction except for\nthe experimental one done by the authors before. They should take more care about this and I find this\nnot up to common standards.\n[Reply]: Yes, there is a very long list of experimental and theoretical literatures on this benchmark\nreaction over the past decades because of both fundamental and technological (e.g., chemical laser)\nrelevance. It will take at least a long paragraph just to glance over them without detailed descriptions.\nThus, in this short communication only the most relevant aspects (product state-resolved angular\ndistributions) to the present work are discussed. Discussion on many of those earlier literatures can be\nfound in the cited publications of this work. A sentence has been added on page 5, line 6 to call\nattention of readers.\nThe reaction has been studied by part of the authors using the same (according to extended data Fig 1)\nexcept for the ionization scheme used for the CH3 radical. In earlier studies REMPI was used and\neach state was investigated in its own experiment whereas now different product states can be\nmonitored in the same experimental run, respectively image. The authors highlight the new\nexperimental capabilities as a major breakthrough but give surprisingly little experimental details.\n[Reply]: That is not really a new capability, but rather a realization of the potential (or the feature) of\nour experimental setup and an execution to its current limit. This key feature (capable of achieving\nspace-focusing effect at the same time of 2D VMI) was explicitly elaborated. To be clear, we rewrite\nthat part, starting from page 4, line 29 to page 5, line 4. In retrospect, the potential of the present\napproach for achieving both universal and state-specific detection of crossed-beam scattering products\nis so obvious that we were surprising that no one, including ourselves, has made serious attempts over\npast years.\nI find the language used throughout the manuscript unnecessarily fanciful and little to forward for me.\nA simpler language would help with understanding because I was often confused reading the\nmanuscript. This is a starting with the abstract. What is the conventional perception the authors allude\nto throughout the manuscript? The use of “all-important” is not followed by an explanation as to why?\nThe authors give bold statements and arguments but then these are very unspecific or lack facts and\n1\nnumbers. They state on page 5 that the present experiment has a “significantly higher resolution” but\nthere are no numbers given: neither on the reactant beam uncertainties, the collision energy or the\nproduct velocity spread or the specs of the VUV beam. Only the temperature of the CH4 is given as\n8K in conjunction with the angular momentum discussion.\n[Reply]: Thanks for the comments. The abstract is rewritten in the revision. The ‘conventional\nperception’ referred to the common belief in the community that the universal detection is usually\nlinked with no product state specificity. To be clear, we now replace the wording of ‘the conventional\nperception’ by a short sentence in plain language in the abstract.\nWe thought that “all-important” is apparent in the present context: In a typical chemical dynamics\nstudy, all important attributes are manifested in the product state- and angle-resolved distributions,\nwhich is revealed simultaneously by a single measurement in this study.\nAs for “significantly higher resolution”, the data speaks for itself: The structural ring-like features of\numbrella-mode excited CH products can clearly be identified as presented in Figs. 1 and 2. Those\n3\nfeatures are the convoluted results of all those instrument factors mentioned. And this observation is\nunprecedented, testifying higher resolution. Nevertheless, we now rewrite the paragraph (page 5, lines\n7-13), and that wording is deleted.\nThe discussion on the importance or not importance of a prior found dynamical resonance to the\npresented data interpretation is so convoluted that it almost seems like dropping a key word. It requires\nthe caption of Extended Data Fig. 3 and the SI to understand. The manuscript should stand by itself.\nThe whole paragraph somehow reads backwards. I need several attempts to make some sense of it.\nAnd I am still not sure if I got right in the end: The dynamical does not play a significant role in for\nthe present study, right? If my interpretation of the paragraph is correct, why put so\n[Reply]: Yes, we believe that dynamical resonance does not play a significant role at the present\ncollisional energy, which has explicitly been mentioned on page 11, lines 22-23: “At E = 2.4 kcal\nc\nmol-1 the direct abstraction mechanism prevails with minor contribution from the resonance\npathway.”\nThe ‘signature” of resonance in this reaction is mainly manifested in the HF(v = 3) attributes, i.e., its\nbranching fraction and forward peak. However, as discussed in the text (page 11, line 6), a classical\nmechanism could also contribute to those attributes. Unfortunately, it is difficult to quantify the\nrelative contributions of two mechanisms (classical time-delay and quantum resonance). In addition,\nas shown in Extended Data Fig. 3, the QM results indicate that the initial CH rotational excitation\n4\nsignificantly reduces the HF(v = 3) branching fraction, which we interpret as evidence that resonance\nis suppressed for the j=1 and 2 states. Considering that the experimental rotational temperature is 8 K\n(nj=0 : nj=1 : nj=2 = 0.31 : 0.54 : 0.15), dynamical resonance should not play a significant role at the\npresent collisional energy. Please note that although the theoretical forward scattering appears sharper\nthan the experimental observations, the forward peak typically yields smaller contribution to total flux\nbecause of the solid angle factor. As such, a very sharp forward peak could only amount to small\nreactive flux.\nFigure 1\nI consider the background subtracted image not really a difference image. Part of the authors referred\nto experiments with and without vibrationally excited reactant to difference images. This is a real\ndifference image. Background subtraction needs to done and properly explained (as done here) but it is\nno difference image.\n[Reply]: The point is well taken. The word of ‘background subtracted image’ is used in the revision.\nIs it linear or logarithmic, absolute or normalized? Why use the same line shape and color for two\ndifferent kinematic cut-offs? Please make them distinguishable.\n[Reply]: The scaling for the color schemes is now added to Figs. 1A and 1B, as well as Extended Data\nFig. 2.\nWe are not sure what you refer to; two red circles in Fig. 1A? If so, we now use two different colors.\nPage 5, first full paragraph\nThe first sentence is really confusing and long. What is a “recoiled velocity”?\n[Reply]: We now make the paragraph more concise, and hopefully it is more readable.\nThe wording is now changed to “3D velocity information”.\nFigure 7\nThe width of the used fitting functions and the significance of the relative contributions cannot be\nvalidated because no energy spread is given. Why use km/s as unit?\n[Reply]: There is no Figure 7. We assume that you mean page 7, Figure 2 (?).\nAs explained in the text (page 8, lines 6-12), we used an independent measurement of λ-scanning the\nQ-head of CH (00) REMPI band (the pink-shaded one in Fig. 2A), which included all apparatus\n3\n0\nfunctions, as a guide for the fitting functions to dissect the vibrational contributions. We believe that is\nbest way one can analyze such a congested distribution. To be clear, we reword the sentences (page 8,\nlines 14-20).\nOur measurement is in the speed domain, so the data is best analyzed in terms of speed, not in energy.\nPage 8, Line 2\nCan the authors please indicate why part of the image they are evaluating? In figure 1 only 0° and\n180° are indicated. For experts is obvious but not for a general chemistry audience.\n[Reply]: As stated in the text (page 8, line 5), the ring-like features in that angular range (see Fig 1A)\nare more apparent, thus more informative as to the vibrationally excited states. It then makes sense to\nstart with that range. Once the vibrational shapes in that portion are determined, the full angular\ninformation can be obtained by scaling (up or down) each individual vibrational component, while\nkeeping the shape intact, to fit the observation. For clarity, we rephrase the sentences (page 8,\nlines 14-20).\nPage 8, Line 15\nThe authors refer to “proper scaling” what is scaled how and why? More information is needed.\n[Reply]: See the above reply.\nFigure 3A\nWhat is the unit for the “correlated ICS” given that the data comes from a crossed beam experiment\nand the associated velocity map image. The data is not really an integral cross section but rather a\nrelative branching ratio of the different product channels and should be labeled as such. Is there an\nerror associated to it?\n[Reply]: Agreed. The experimental figure axis is now relabeled as “vibrational branching fraction”.\nThe actual error is difficult to quantify. It mostly comes from how well the fitting is to the observed\ndistribution. Judging from what presented in Fig. 2, the room for further adjustments seems limited. So,\nFig. 3 represents our “best” estimate for comparing with theoretical results.\nI do not understand the sentence. Something is missing. The authors should check if “auto-correction”\ndid some unintended corrections.\n[Reply]: We are not sure about what this comment specifically referred to. Nonetheless, we rephrase\nthe sentence (page 11, line 26); hopefully, it will clarify your concerns.\nPage12, Line 9\n“does not directly invoke in bond cleavage and formation”\nPlease check wording.\n[Reply]: We rephrase the sentence as “The CH -moiety is not directly involved in bond cleavage and\n3\nformation.”\nPage 12, Line 15+16\nI do not understand the meaning of this sentence in relation to reaction centers, respectively dynamics.\nThe authors might want to check the language.\n[Reply]: We rephrase the sentence as “the breaking C‒H bond is always directed away from (and\nuniformly distributed around) the center-of-mass of CH , which lies on the C atom.” (page 12, lines\n4\n17-19).\nPage 12, Line 26\nShouldn’t that be forward scattered CH3 when the HF is scattered backward. Also see next sentence. I\nguess something got mixed up.\n[Reply]: What you stated is a traditional way used in the community. However, this view will depend\non which product (CH or HF) is measured or referred to, and it could cause some confusion when\n3\ndifferent people talk about the dynamics from different views. For instant, stripping mechanism\nusually yields forward scattering, whereas rebound dynamics is associated with backward scattering.\nThen, seeing forward scattered CH will argue a stripping mechanism, but the backward scattered HF\n3\nwill then suggest a rebound mechanism; an obvious dilemma. The situation could be more confusing\nwhen one is thinking of the angular distribution of concomitantly formed product state-pair (v , v ),\nCH3 HF\nas the present case. This apparent paradox can be reconciled if one always views forward-scattering as\nthe direction of the scattered product with respect to where it is from. For instance, CH must come\n3\nfrom CH and HF from the F-atom (note that the directions of F-atom and CH are opposite to each\n4 4\nother in the center-of-mass frame), so that the forward-scattering will always convey the same\ndynamical behavior (say, stripping mechanism) irrespective of HF or CH products.\nThe authors (and others) have previously carried out extensive studies on the dynamics of the reaction\nF + CH → CH + HF and deuterated analogs, in which they have probed CH products in their\n4 3 3\nvibrational ground state and in various umbrella-mode (ν ) vibrationally excited states (v = 0, 1, 2, 3)\n2 2\nvia REMPI and velocity-map imaging. These studies have revealed the pair-correlated scattering\ndistributions of the CH with various vibrational states of the HF (or HD) coproduct. The present study\n3\nextends this work by using VUV photoionization at 118 nm as a universal probe to enable\nsimultaneous detection of all rovibrational states of CH formed in the chemical reaction. The new\n3\nexperimental results are interpreted with the help of comprehensive six-dimensional quantum\ndynamics simulations.\nquantifies contributions from asymmetric-stretch (ν ) excited CH products. These have been observed\n1 3\nbefore using REMPI detection, but one-photon ionisation makes it much more straightforward to\ndetermine the relative contributions from different product channels. The authors present product state\ndistributions and pair-correlated angular distributions in excellent agreement with the theoretical\npredictions, and provide a detailed commentary on the mechanisms leading to the observed angular\nscattering.\nThis is a comprehensive, generally well-written, and very high quality piece of work, which fills in\nsome additional dynamical details for the benchmark F + CH reaction. However, I was extremely\n4\nsurprised at the number of times the authors stated the novelty of their 118 nm universal ionization\napproach, given that this ionization method, as well as universal ionization using other VUV\nwavelengths, has been used in velocity-map imaging studies in a number of different laboratories for\nwell over a decade. A few examples of which I am immediately aware include Fan et al, J. Chem.\nPhys., 123, 204301 (2005), Ashfold et al, J. Phys. Chem. Lett, 8, 3440 (2017), Gardiner et al, Phys.\nChem. Chem. Phys., 17, 4096 (2015), Lipciuc et al, J. Chem. Phys., 147, 013941 (2017), and various\nother papers from these and other groups, but I am sure there are numerous others. None of this\nprevious work was mentioned or referenced in the manuscript. In my view, this is the one major\nshortcoming of the paper as it stands. There are also a few minor typos, etc, that the authors may want\nto correct in a revised version of the manuscript.\n[Reply]: Yes, VUV one photoionization method is a well-established soft/universal detection scheme.\nWe are fully aware of huge amounts of literatures. In fact, it has been mentioned on page 3, line 17,\nand some relevant prior works on crossed-beam scattering were cited as refs. 8-10.\nOur message is more on the non-resonant one-photon ionization probe, rather than on a specific\nwavelength, say 118 nm. We chose 118 nm photon to probe CH mainly because of its feature of\n3\npotentially state-independent ionization efficiency, which will be one of the prime considerations for\nfuture application to any other system. Of course, easy generation of 118 nm also helps; many other\nVUV lasers at different wavelengths can also serve as probe but will be more involved to generate\nthem.\nThe suggested publications concern instead photodissociation studies using 118 nm, which admittedly\nare mostly missing here not because of their unimportance, but rather considering the focus of this\nreport (crossed-beam reactions). Nonetheless, we did discuss the photoionization detection of CH in\n3\nlength about its sensitivity and quoted refs. 20-22. In that regard, we now gratefully add the suggested\nwork by Gardiner et al in 2015 as ref. 23, which has unfortunately escaped our attention in the initial\nsubmission. We appreciate the reviewer for calling our attention to it.\n1. Abstract: remove the initial ‘The’. Also, “electron-impact ionization” is now usually referred to\nsimply as “electron ionization”.\n[Reply]: Thanks, reword them accordingly.\n2. Page 3, line 13: “a state-resolved detection” should just be “state-resolved detection”.\n[Reply]: Thanks, correct it accordingly.\n3. Page 11, line 8: lines 8-11 could do with a small amount of rewording, for clarity, e.g. “Thereby, the\ndiscrepancies in the forward peaks, the imprint of the resonance pathway, would be reduced if the\nreactants CH4(j = 1,2) were also included in the calculation. More significantly, the overall\n5\ndistribution evolves from being predominantly forward peaking for (0 ,3) to exhibiting marked\n0\nsideways scattering for (2 ,2), and then to essentially backward-scattering for (0 ,2).”\n2 0\n[Reply]: Thanks, correct it accordingly.\n4. Page 11, line 16: “recoiled-energy” should be “recoil energy”\n[Reply]: Thanks, correct it accordingly.\n5. Page 12, line 9: I am not sure what the authors mean by “The CH -moiety does not directly invoke\n3\nin bond cleavage and formation”. Do they mean that the CH is not directly involved in bond cleavage\n3\nand formation?\n[Reply]: Thanks, correct it accordingly.\n6. Page 12, line 11: should be “...products attests to the strong coupling...”\n[Reply]: Thanks, correct it accordingly.\n7. Page 12, line 15: I am not sure what the authors mean when they say that the transferred H atom “is\nalways sprouting away” from the centre of mass of CH . Are they just referring to the chemical\n4\nstructure of CH ? If so, it might be clearer to say that the breaking C-H bond is always directed away\n4\nfrom the centre of mass of CH , which lies on the C atom. However, I find it difficult to think of an\n4\nexample in which a breaking bond would not be pointing away from the centre of mass of the\nmolecule within which it resides, so perhaps the authors could find a clearer way of making their point\nin this regard, perhaps with the aid of a diagram?\n[Reply]: Thanks, see also the comments by Reviewer #1. We now rephrase the sentence as “the\nbreaking C‒H bond is always directed away from (and uniformly distributed around) the\ncenter-of-mass of CH , which lies on the C atom.” (page 12, lines 17-19).\nThe VUV single photon ionization method has been well known as a soft and universal product\ndetection scheme, while universal detection has been linked with no product state specificity all the\ntime previously. In this study, Pan et al. demonstrated an experiment combining the universality of\nVUV photoionization for the reaction product detection and the high velocity resolution achievable in\na three-dimensional VMI which can handle relatively large reaction or ionization volumes of the\nreaction products, and they achieved universality and state-specificity for product detection\nsimultaneously. They successfully mapped out almost all the important product pair-correlated\ndynamical attributes of the prototypical polyatomic reaction F + CH4 → CH3(vi) + HF(v) from a\nsingle product image. Six-dimensionality quantum dynamics calculations are performed and found to\nbe able to reproduce nearly all the aspects observed in the experiment, and have provided new insights\ninto this important prototypical polyatomic reaction. Such a method is a very useful addition to the\ncommunity of reaction dynamics, and can be definitely used in the studies of many other reactions, I\nthus recommend its publication in Nature Communications. The whole paper is very nicely presented,\nand I only have two comments for the authors to consider.\n[Reply]: Thanks for the positive comments. Our messages are clearly conveyed.\n1. The universal VUV single photoionization detection is an important addition to the product\nstate-specific detection method, and can provide most of the time qualitative information for the full\n6\ndynamical picture. However, its ability may not be overstated. In the study of the F + CH4 → CH3(vi)\n+ HF(v), one of the reasons why it is very successful is that the products are all rotationally cold,\nwhich enables the resolve of the pair-correlated vibrational distributions. For reaction products with\nsignificant rotational excitation, the complete resolve will become difficult. At the same time, previous\nstate-specific studies also play an important role in analyzing the data in this study. I thus believe that\nthe proper combination of the universal and state-specific methods would become a powerful method\nin studying reaction dynamics in the future, as demonstrated in this study.\n[Reply]: We fully agreed. No detection scheme is perfect in all aspects for all reactions, and every\nprobe scheme will end up with some compromises, depending on what one would like to achieve. We\nbelieve the F+CH reaction is not the only one suitable for the present approach. We have several other\n4\nclasses of reactions in mind. Our intention is instead to alert the community about the possibility that a\nuniversal probe can also work as state-specific detection for some reactions by fully utilizing the\n3D-VMI detection.\nAs stated in the end of conclusions (page 14, lines 18-21), attentive readers may also realize that the\ncombination of the present non-resonant one-photon ionization and widely used REMPI scheme\nshould really be the way to go. One may first do one-photon ionization VMI. Once the big picture has\nbeen sketched, one can always zoom in the details if necessary or when the required high-resolution\nREMPI information becomes available.\n2. For the last paragraph on page 12, a classical physical picture is described to explain the “observed\ncorrelation that low umbrella-excited CH3 prefers backward scattering, whereas higher\numbrella-excited CH3 yields more in the sideway and forward directions.” Two points that may need\nbe explained a little more: first, it seems that both the large and small impact collisions involve the\nflatten motion of the CH3 moiety, while one results in the umbrella vibrational excitation, and the\nother dose not? Second, the above picture only applies to processes within the same HF vibrational\nexcitation, for example, for HF=3, the products are mainly forward scattered, even though the\numbrella motion of CH3 is not excited. Is it possible to make it clearer why this picture strongly\ndepends on the excitation of the co-product HF?\n[Reply]: First, as presented in the paragraph starting from line 22 of page 12, the difference between\nthe large and small impact parameter collisions is the magnitudes of the line-of-center force, which\ndistorts the pyramidal geometry of CH moiety to different extent as the C-H is ruptured to form HF.\ngeometry yields v -excited CH coproducts. For small impact parameter collision, the incoming\n2 3\nF-atom pushes the attached H-atom and the central C-atom moves inward, gradually flattening the\nCH moiety. As HF bounces backward, the relaxation of gradually flattening CH moiety yields less\n3 3\nv -excitation.\nangular distribution is mainly governed by the angle-angular momentum correlation. Qualitatively,\nF+CH can be approximated as a simpler three-atom system if only the newly-formed HF product is of\n4\nconcern. On the other hand, unlike A + BC reaction, the structure of the CH moiety at the transition\n3\nstate and how it changes to product will also be at work, which can be comprehended by the\nline-of-centers argument in the paragraph starting from line 22 on page 12, as well as the elaborations\ngiven above. Although the above two arguments underpinning the dynamical behaviors for HF(v) and\nCH (v ) cannot be completely decoupled, we believe that the formation of HF bond will be prime\n3 2\ndriving force and this early-barrier transition state with elongated H-F bond (line 20 on page 12) will\nalways favor highly vibrational-excited HF products scattered in the forward direction, as evidenced\n7\nby Supplementary Fig. 5: HF(v=3) is predominantly forward scattered and HF(v=1) is mostly\nbackward scattered, only HF(v=2) exhibits angular distribution spread over a wide range of angles for\ndeciphering the coincidently formed CH (v ) components. To emphasize the importance of the entire\n3 2\ntransition state structure, we rephrase the sentences starting from line 16 to 21 on page 13. Of course,\nthe collision energy of this work is too low to produce much concomitantly umbrella-excited CH with\nenough (v (CH ), v =3) or (v (CH ), v =1) could be formed and analyzed.\n2 3 HF 2 3 HF\nReviewer #4 (Remarks to the Author):\nThe authors describe, implement, and test a VMI experiment capable of what they call “universal”\nstate-resolved product selection. The well-studied F + CH4 system is considered, and the experiment\nis shown to resolve product states of CH3 alongside HF. The instrument is validated against quantum\ndynamics, which on its own is a substantial achievement of the work.\nThe demonstration given here is notable and, in my opinion, is appropriate for publication in a\nhigh-impact journal. Unfortunately, some awkward English and rushed descriptions make this short\npaper difficult to understand in places. I would specifically suggest improving the English in the\nabstract and elaborating on key discussion points. As written, the reader needs to already be familiar\nwith VMI studies of this system to understand the paper.\n[Reply]: Thanks for the positive comments about this work.\nIn the revision we tried to improve our writings in various places including the abstract, and elaborated\nsome statements. We hope the revision is more readable to the general readers.\nFor example, the notation of the observed state pairs, e.g., (23, 2), are not explicitly explained and\ninstead must be inferred.\n[Reply]: It is now explained in the revision, page 6, line 17 (in the caption for Fig. 1 C).\nI would suggest clarifying what aspects of the new design are responsible for the breakthrough here.\nThe earlier work did not get information for all the vibrational levels of CH3 at once, like here, but I\nwasn’t sure why. Likewise, is there additional information in this experiment, as compared to earlier\n“3D” VMI studies on this system, or is the advance here that the information is gathered more\ndirectly?\n[Reply]: The key of this work is to fully utilize the space-focusing capability as elaborated on page 4,\nline 29 to page 5 line 4. See also the above reply to Reviewer #1: “In retrospect, the potential of the\npresent approach to achieving both universal and state-specific detection of crossed-beam scattering\nproducts is so obvious that we were surprising that no one, including ourselves, has made serious\nattempts over past years.”\nAll previous works used REMPI to probe CH vibrational states, one at a time. Because of the\n3\ndisparate REMPI sensitivities, it is difficult to piece that information together to get a full dynamics\npicture. The present approach probes all CH states simultaneously with nearly uniform detection\n3\nsensitivities, and thus can uncover previously inaccessible information. For example, product\nvibrational branching fractions (which requires to know the relative sensitivities when detecting\ndifferent vibrational states) reveal that the ground-state CH products account for, unexpectedly, mere\n3\n40% of reactivity—despite being the most prominent feature in REMPI spectra. Most reactive fluxes\nare instead channeled into umbrella-excited CH with little or negligible amounts for three other\n3\n8\nvibrational modes, etc. The ability of both universal and state-specific detection also allows us to\nunveil the angle-angular momentum correlation in the reaction, and extend to whole class of X+CH\n4\nreactions.\nFinally, I wondered if plots like Fig. 1A could be produced from the calculations?\n[Reply]: We are not sure such a plot will add more information. All dynamical attributes extractable\nfrom Fig. 1A are already presented in Figs. 2-4 and compared with corresponding theoretical\ncalculations in a quantitative manner. Such a plot from theory seems redundant and will be a\nqualitative comparison at best (besides, it needs to be convoluted first by density-to-flux correction for\na direct comparison with Fig. 1A).\n9"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors answered my questions and cleared up some confusion. The changes to the text make the manuscript easier to understand. The manuscript is suitable for Nature Communications. Maybe, the authors want to consider some minor comments:\n\nIn the abstract and on page 5 they refer to “previously inaccessible insights”. Why not state at this point what was previously inaccessible more plainly. The wording works in the abstract but on page five it reads strange with the kind of left confused at as to what is new- The answer is only given later on page6.\n\nI now understand the author’s use of forward and backward in the relative frame of reference. Maybe readers would benefit from an addition of the relative orientation of the incident beams with respect to the scattering angle as indicated in figure1.\n\nI find “all-important” a presumptuous phrase to use. Why use it at all? For me, it adds nothing to the paper but confusion because it has no direct scientific meaning.\n\nA comment:\nIn the authors refer to space and length of the communication with respect to the limited number of references to earlier studies. Length might be an argument, number of allowed references is not. The author guidelines state that up to 70 references are allowed or considered reasonable. The current number of references is 44 (three more than in the original submission). I still think this is a major point to consider. The authors do not need to write a “review” style introduction but the references to prior studies on either the reaction studies or the methodology are limited.", "reviewer_2": "The authors have responded comprehensively to the suggestions of the referees, and amended their manuscript accordingly. Assuming the other referees are in agreement, I believe that the paper is now suitable for publication in Nature Communications.", "reviewer_3": "The authors have addressed all my comments in proper ways, I thus recommend its publication in Nature Communications in its current form."}, "author_response": "Author responses to the reviewers’ reports on NCOMMS-25-55690A\nReviewer #1 (Remarks to the Author):\nThe authors answered my questions and cleared up some confusion. The changes to the\ntext make the manuscript easier to understand. The manuscript is suitable for Nature\nCommunications. Maybe, the authors want to consider some minor comments:\n\n[Reply] Thanks for the positive feedback.\n\nIn the abstract and on page 5 they refer to “previously inaccessible insights”. Why not state\nat this point what was previously inaccessible more plainly. The wording works in the\nabstract but on page five it reads strange with the kind of left confused at as to what is\nnew- The answer is only given later on page6.\n\n[Reply] We found that it will be too involved to explain “what is new” at that point. That\nis the reason for the original statement on Page 5, Line 27: “As will be presented (Note:\nchange now from “shown”) below, the results from such universal and state-specific\ndetection in turn give access to hitherto inaccessible information.”\n\nI now understand the author’s use of forward and backward in the relative frame of\nreference. Maybe readers would benefit from an addition of the relative orientation of the\nincident beams with respect to the scattering angle as indicated in figure1.\n\n[Reply] We are delighted that we are in line with each other. As suggested, Fig. 1 is\nmodified.\n\nI find “all-important” a presumptuous phrase to use. Why use it at all? For me, it adds\nnothing to the paper but confusion because it has no direct scientific meaning.\n\n[Reply] Two most important information can be derived from the chemical dynamics\nstudies are the product state and angular distributions. Traditionally, these two attributes in\nreactions beyond the simple A + BC system are, unfortunately, acquired by very different\nand usually non-compatible detection schemes. The approach proposed in this work\nenables simultaneously acquiring both dynamical attributes in a single measurement, and\nthus providing “all-important” information. We originally used “all-important” simply as a\nplain statement to reflect this fact, and when checking the dictionary, this phrase also does\nnot sound presumptuous. Nonetheless, we now change “all-important” to “all essential”,\nand we welcome any suggestion for a better phrase to use here.\n\nA comment:\nIn the authors refer to space and length of the communication with respect to the limited\nnumber of references to earlier studies. Length might be an argument, number of allowed\nreferences is not. The author guidelines state that up to 70 references are allowed or\nconsidered reasonable. The current number of references is 44 (three more than in the\n1\noriginal submission). I still think this is a major point to consider. The authors do not need\nto write a “review” style introduction but the references to prior studies on either the\nreaction studies or the methodology are limited.\n\n[Reply] We now elaborate a bit about prior works on Page 5. Lines 17-21 (reproduced\nbelow), and some relevant new references 20-27 are cited.\n\n“This reaction has been the subject of extensive studies over the past decades for its\nfundamental significance as a prototypical polyatomic reaction as well as its practical\napplication in chemical lasers20-27. Dynamically most of prior works focused on the\nproduct state distributions of either CH or HF (refs 23-26), except more recent studies on\n3\nthe angular distributions through REMPI-tagged product pair-correlation\nmeasurements13-16.”\n\nReviewer #2 (Remarks to the Author):\nThe authors have responded comprehensively to the suggestions of the referees, and\namended their manuscript accordingly. Assuming the other referees are in agreement, I\nbelieve that the paper is now suitable for publication in Nature Communications.\n\n[Reply] Thanks for the suggestions and comments which make the paper better.\n\nReviewer #3 (Remarks to the Author):\nThe authors have addressed all my comments in proper ways, I thus recommend its\npublication in Nature Communications in its current form.\n\n[Reply] Thanks for the suggestions and comments which make the paper better.\n2"}]

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