Crossed beam polyatomic reaction dynamics: recent advances and new insights

Huilin Pan a, Kopin Liu *ab, Adriana Caracciolo c and Piergiorgio Casavecchia *c
aInstitute of Atomic and Molecular Sciences (IAMS), Academia Sinica, P.O. Box 23-166, Taipei, 10617, Taiwan. E-mail:
bDepartment of Physics, National Taiwan University, Taipei, 10617, Taiwan
cDipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, 06123 Perugia, Italy. E-mail:

Received 14th August 2017

First published on 23rd November 2017

Over the past ten years or so, great advances in our understanding of the dynamics of elementary (bimolecular) polyatomic reactions in the gas-phase have occurred. This has been made possible by critical improvements (a) in crossed molecular beam (CMB) instruments with rotating mass spectrometric detection and time-of-flight analysis, especially following the implementation of soft ionization (by tunable low energy electrons or vacuum-ultraviolet synchrotron radiation) for product detection with increased sensitivity and universal detection power, and (b) in REMPI-slice velocity map ion imaging (VMI) detection techniques in pulsed CMB experiments for obtaining product pair-correlated information through high-resolution measurements directly in the center of mass system. The improved universal CMB method is permitting us to identify all primary reaction products, characterize their formation dynamics, and determine the branching ratios (BRs) for multichannel non-adiabatic reactions, such as those of ground state oxygen atoms, O(3P), with unsaturated hydrocarbons (alkynes, alkenes, dienes). The improved slice VMI CMB technique is permitting us to explore at an unprecedented level of detail, through pair-correlated measurements, the reaction dynamics of a prototype polyatomic molecule such as CH4 (and isotopologues) in its ground state with a variety of important X radicals such as F, Cl, O, and OH. In this review, we highlight this recent progress in the field of CMB reaction dynamics, with an emphasis on the experimental side, but with the related theoretical work, at the level of state-of-the-art calculations of both the underlying potential energy surfaces and the reaction dynamics, noted throughout. In particular, the focus is (a) on the effect of molecular complexity and structure on product distributions, branching ratios and role of intersystem crossing for the multichannel, addition–elimination reactions of unsaturated hydrocarbons with O atoms, and (b) on the very detailed dynamics of the abstraction reactions of ground-state methane (and isotopologues) with atoms (F, Cl, O) and diatoms (OH), with inclusion of also rotational mode specificity in the vibrationally excited methane reactions.

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Huilin Pan

Huilin Pan received her doctoral education in the group of Prof. Xueming Yang from Dalian Institute of Chemical Physics, Chinese Academy of Sciences. She is currently a postdoctoral research fellow in the Institute of Atomic and Molecular Sciences, working with Prof. Kopin Liu. Her research interests focus on gas-phase reaction dynamics, especially on understanding and controlling the detailed dynamics of the elementary steps in physical and chemical processes.

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Kopin Liu

Kopin Liu is a Distinguished Research Fellow at the Institute of Atomic and Molecular Sciences of Academia Sinica in Taiwan, an Academician of Academia Sinica, and an elected Fellow of APS, RSC, and TWAS. His research activity focuses on molecular-beam studies of chemical dynamics, for which he has been recognized by a number of honors, including the 1st Presidential Science Prize of Taiwan (2001), the Alexander von Humboldt Research Award (2011), the International Symposium on Molecular Beams Award (2013), and the R. B. Bernstein Award (2014).

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Adriana Caracciolo

Adriana Caracciolo obtained her Master's degree in Chemistry from Alma Mater Studiorum University in Bologna working with Assimo Maris and Sonia Melandri in the group of Prof. Walter Caminati. She is currently a doctoral student at the Department of Chemistry, Biology and Biotechnology of the University of Perugia, under the supervision of Prof. Piergiorgio Casavecchia and Prof. Nadia Balucani. Her research is focused on gas-phase reaction dynamics by the crossed molecular beam technique with mass spectrometer detection, in particular on reactions involved in combustion chemistry and astrochemistry.

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Piergiorgio Casavecchia

Piergiorgio Casavecchia is Full Professor of Physical Chemistry at the Department of Chemistry, Biology and Biotechnology of the University of Perugia in Italy, and coordinator of the PhD School in Chemical Sciences. His research activity focuses on crossed molecular beam studies of chemical reaction dynamics, for which he has been recognized with a number of honors, including the Polanyi Medal (2008), the International Symposium on Molecular Beams Award (2015), a Journal of Physical Chemistry A Festschrift special issue (2016, with colleague Antonio Laganà), and the Doctorate Honoris Causa from the University of Rennes 1 (2017).

1. Introduction

Since the advent of quantum mechanics, chemists have dreamed to understand how elementary chemical reactions actually occur. Our current understanding of the microscopic (i.e., at the atomic/molecular level) dynamics of elementary (bimolecular) reactions in the gas-phase is due to synergistic experimental and theoretical efforts over many decades. Experimentally, studies of reaction dynamics are typically carried out under single-collision conditions, which can be achieved using molecular beam techniques or pump–probe, time-resolved laser spectroscopic methods.1 In particular, crossed molecular beam (CMB) techniques, coupled to laser methods, can allow us to determine the state-to-state reactive differential cross section (DCS), which is (almost – see Section 3.8) the most detailed observable that can be measured for a bimolecular reaction.1–5 Since the 1970s, much experimental and theoretical endeavors have been devoted to a detailed understanding of simple, prototype reactions involving three-atoms, of the abstraction type such as H + H2,2,6,7 F + H2,8–10 Cl + H211–13 and O(3P) + H214 (and isotopic variants), and of the insertion type such as O(1D) + H2,15 N(2D) + H2,16 C(1D) + H2,17,18 and S(1D) + H219,20 (and isotopic variants). For this kind of systems the state-to-state DCS can be calculated by rigorous quantum mechanical (QM) methods, including non-adiabatic (i.e., spin–orbit and electronic) effects, on accurate ab initio potential energy surfaces (PESs), and this has permitted us to perform very detailed comparisons between experiment and theory.21–23 The same approach has also been extended to some four-atom reactions (OH + H2,24–26 CN + H2,27 OH + CO,28,29 F + H2O30,31), although at a lower level of detail. This progress is continuing up to the present days32 with the experimental exploration of also vibrational excitation of reactions such as F + H2(v)33 and Cl + H2(v)34 (and isotopologues), and is backed up by theoretical calculations which are corroborating the experimental findings and allowing their detailed understanding, including the observation of pronounced resonance phenomena.35–37 All this has led to the conclusion that the three-atom reactive scattering problem is essentially solved and fully understood, with the four-atom problem on its way to a nearly full understanding as well.

Notably, over the past 15 years, following on the progress in experimental and computational capabilities, the attention of researchers has widened up very significantly to encompass the detailed dynamics of also polyatomic (i.e., involving more than four-atoms) elementary reactions. Among these, several classes of systems have been tackled with considerable success: (a) direct, abstraction type reactions involving essentially one product channel, such as X + CH4 → HX + CH3 (and isotopic variants) (X = H, F, Cl, OH);38,39 (b) indirect, insertion type, multichannel reactions, such as X + CH4 [X = O(1D),40–43 N(2D),44 C(1D),45 and S(1D)]46 leading to at least two main competitive product channels (HX + CH3 and H + CH3X); (c) indirect, insertion type, multichannel reactions, such as X + saturated/unsaturated hydrocarbons [X = O(1D),47 N(2D),48–50 and S(1D)]51 leading to several competitive product channels; (d) indirect addition–elimination reactions, such as those of ground state carbon atoms, C(3P),52–55 boron atoms, B(2P),56 and radicals (such as CN,57–59 CH,60,61 C2H,62–64 C6H5,65–67 SiH68) with unsaturated hydrocarbons, leading mainly to the H-displacement channel; and (e) indirect addition–elimination reactions, such as those of ground state oxygen atoms, O(3P), with unsaturated hydrocarbons, which lead to a large variety of product channels and involve strong non-adiabatic effects (intersystem crossing – ISC).69,70 Reviews have been also published on CMB studies of abstraction reactions of F and Cl atoms with organic molecules by velocity map imaging detection71,72 and of boron and carbon atoms addition reactions with unsaturated hydrocarbons in the low collision energy regime by LIF or REMPI detection.73 Besides their fundamental interest, these studies on polyatomic reactions are of relevance in areas of practical interest, ranging from combustion- and atmospheric- to astro-chemistry.

In this review, we cover two main classes of reactions, namely class (a) and (e) mentioned above, which have revealed the richest and more complex dynamics and for which the strong progress has relied critically on recent experimental advances. Specifically, advances in CMB instruments with rotating mass spectrometric (MS) detection and time-of-flight (TOF) analysis, following the implementation of soft ionization (by tunable low energy electrons74–76 or vacuum-ultraviolet (VUV) synchrotron radiation77–81) for product detection with increased sensitivity and universal detection power, have permitted us to identify all primary reaction products, characterize their formation dynamics, and determine the branching ratios (B.R.s) for multichannel reactions, such as the multichannel non-adiabatic reactions of ground state oxygen atoms O(3P) with unsaturated hydrocarbons (alkynes, alkenes, dienes),69,70,82 a long-standing problem for more than 50 years. At the same time, progress in REMPI-slice velocity map ion imaging (VMI) detection techniques in pulsed CMB experiments has permitted us to obtain product pair-correlated information, through high-resolution measurements of integral and differential cross sections directly in the center of mass system, and hence to explore, at an unprecedented level of detail, the reaction dynamics of a prototype polyatomic molecule such as CH4 (and isotopologues), in its ground state and also in selected excited vibrational states, with a variety of important radicals, such as F(2P), Cl(2P), O(3P), and OH(2Π).36,38,83,84 The progress in the above two experimental techniques can be seen as complementary towards a deeper, more insightful understanding of chemical reactivity, the very heart of chemistry. In Section 2, we shall focus on the effect of molecular complexity and structure on product distributions, branching ratios and role of intersystem crossing in the addition–elimination multichannel reactions of unsaturated hydrocarbons (alkynes, alkenes, and dienes) with O(3P). In Section 3, we shall focus on the very detailed dynamics of the abstraction reactions of vibrational ground-state methane with atoms (F, Cl, O) and diatoms (OH), with inclusion of also rotational mode specificity in the vibrationally excited methane reactions.

2. Primary products, branching ratios and intersystem crossing in polyatomic reactions

The CMB scattering technique with universal MS detection, based on hard (i.e., 70–200 eV) electron ionization (EI) and TOF analysis, has proven to be a powerful technique for exploring the dynamics of bimolecular reactions and, since its introduction,85 has played a central role in the development of the field.4,47,52,86–92 However, when applied to the investigation of multichannel reactions involving polyatomic molecular/radical reactants and products, such as hydrocarbon molecules/radicals, it has shown a serious limitation due to the problem of dissociative ionization that occurs in the EI source of the MS detector. This problem usually prevents the identification of most of the primary reaction products because many ion signals at the masses of interest are typically obscured by ion signals, at the same mass-to-charge (m/z) ratio, coming from dissociative ionization of interfering species (elastically/inelastically scattered reactants, products, and background gases).

A turning point, which has permitted us to overcome this problem (see the next section), has been the implementation of soft EI (in our laboratory)69,70,74–76 and soft PI (photo-ionization) by VUV synchrotron radiation (in other laboratories)55,77–81 in CMB experiments. It should be noted that this technique is the only one that can probe all different products on the same footing, which is essential for identifying the primary products and determining their branching ratios. The systematic CMB studies of the multichannel nonadiabatic reactions of O(3P) with unsaturated hydrocarbons performed in our laboratory over the past 10 years have become possible only by exploiting soft EI70 (the soft EI or PI approach has been central for also studying some product channels of other multichannel radical + molecule54,55,67,76 and radical + radical69,93,94 reactions). The aim of this review is, however, not that of giving a comprehensive survey of those studies (still continuing today), but rather of examining the main results, emphasizing what we have learnt, and highlighting the opportunities offered by the soft ionization approach. We shall focus on the reactions of O(3P) with the simplest (containing two and three carbon atoms) alkynes, alkenes and dienes. These reactions are not only of great interest in important practical areas ranging from combustion-chemistry82,95–98 to astro-chemistry,99–101 but they are also of fundamental relevance since they can be considered prototypical reactions occurring via the widespread addition–elimination mechanism and may exhibit a pronounced nonadiabaticity, namely ISC from the entrance triplet to the underlying singlet PES, that can open up other reaction channels not accessible on the triplet PES. The key features of the reaction profiles of this class of reactions are illustrated in a simplified manner in Fig. 1. In general these reactions proceed via numerous intermediates and exhibit a variety of competing product channels. The identification of all product channels, the elucidation of their mechanism and dynamics of formation, the determination of their relative yields (B.R.s) and the characterization of the role of ISC, possibly as a function of translational energy (temperature), are of central importance in the field of chemical reaction dynamics (kinetics) and combustion; however, this has always represented a challenging task.

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Fig. 1 Schematic representation of reaction profiles for a generic reaction of O(3P) with an unsaturated hydrocarbon featuring intersystem crossing (ISC) between triplet and singlet PES. The increasing stability of the initial triplet intermediate (formed from the electrophilic attack of the O atom to the preferred carbon of the unsaturated bond) in going from alkenes to alkynes and to dienes is indicated.

High-level electronic structure calculations of minima, maxima (transition states), and product energetics of the relevant PESs, and statistical RRKM/ME (Rice–Ramsperger–Kassel–Marcus/Master equation) calculations of branching ratios, with inclusion of nonadiabatic effects, have nowadays become possible for most of these polyatomic reactions and contribute very substantially to characterize the reaction dynamics/kinetics, especially when carried out in synergy with experiment. Recently, it has also become possible to compare the experimental results with accurate dynamical predictions from QCT-SH (quasiclassical trajectory-surface hopping) dynamical calculations on coupled triplet/singlet PESs, taking ISC into account.102 These theoretical studies will be noted throughout.

In the following, we first highlight in Section 2.1 the power of soft ionization for identifying the primary products and determining the B.R.s. In Section 2.2 the dynamics of O(3P) reactions with the two simplest alkynes will be summarized as an example of how the product distribution and the extent of non-adiabaticity (ISC) vary dramatically when an H atom is replaced by a CH3 group. Section 2.3 will examine how ISC increases strongly in passing from the O(3P) reaction with the simplest alkyne to that with the simplest alkene, and then how it decreases significantly in going from a two-C to a three-C alkene. Section 2.4 will highlight the dramatic increase in the extent of ISC in going from a 3-C alkene (propene) to the prototype 3-C diene/cumulene (propadiene, also known as allene). Section 2.5 will try to examine and rationalize the observed trends of product distributions and extent of ISC with the variation of molecular complexity and molecular structure. A synergistic experimental/theoretical approach in these studies has provided new insights and permitted a better understanding of the experimental findings and the achievement of a detailed comprehension of the reaction mechanisms.

2.1 Crossed-beams with soft electron-ionization MS detection

The basic methodology of CMB reactive scattering experiments with MS detection and TOF analysis was established long ago.85–88 Here, we briefly remind the observables of this technique, the information obtained, and the critical features of the recently implemented soft EI for product detection. The main aspects of the Perugia CMB apparatus (a schematic is shown in Fig. 2a) have been described in detail elsewhere.4,22,69,88 Briefly, two supersonic beams of the reactants are crossed at a fixed angle of 90° (45° and 135° are also possible) in a high-vacuum chamber and the reaction products are detected as a function of laboratory (LAB) scattering angle and time (using TOF analysis) by an EI quadrupole MS detector kept in a ultra-high-vacuum (UHV), triply differentially pumped chamber which is rotatable in the reactant plane around the collision center.
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Fig. 2 (a) Schematics of a CMB apparatus with a rotatable universal EI MS detector and TOF analysis.69 (b) Velocity vector diagram defining the experimental kinematics of a bimolecular multichannel reaction. Circles delimit the maximum velocity that the indicated product (case of O + propene at Ec = 9.3 kcal mol−1)103 can attain if all available energy is channelled into translation. (c) Flux (velocity-angle) contour map of the (C2H4) product of a channel (that leading to C2H4 + CO) of a bimolecular reaction (O + allene).104 Bottom: Schematics of the general procedure: from product LAB angular and TOF distributions to product CM angular and translational energy distributions for each reaction channel, to product branching ratios (B.R.s) (see text). Reproduced (a) from ref. 69 with permission from Royal Society of Chemistry, copyright 2009, (b) and (c) from ref. 103 and 104, respectively, with permission from American Chemical Society, copyright 2015 and 2012, respectively.

Fig. 2b depicts the velocity vector diagram of a typical experiment (O + propene103) defining its kinematics and showing how the different (actually detected) reaction products are confined, by energy and momentum conservation, within a given angular and velocity range in the LAB and CM (center-of-mass) frames. From measurements in the LAB of the product intensity as a function of the scattering angle Θ (the laboratory angular distribution, N(Θ)), and the product intensity as a function of Θ and arrival time t (TOF spectra, N(Θ, t)), we retrieve the product differential cross section (DCS) in the CM frame, ICM(θ, u), via the relation NLAB(Θ, v) = ICM(θ, u)v/u2 (where v and u are product LAB and CM velocities, respectively, and θ is the CM angle).4,5,87 The ICM(θ, u), or rather the ICM(θ, ET′) (where ET′ is the product translational energy), is commonly factorised into the product of an angular, T(θ), and a translational energy, P(ET′), distribution. Analysis of the LAB data is performed by forward convoluting tentative T(θ) and P(ET′) distributions over the experimental conditions. When multiple reaction channels contribute to the signal at a given detected m/z ratio, as in the systems discussed here, a weighted total CM DCS, ICM(θ, ET′)total, reflecting the various possible contributions is used in the data analysis of the LAB distributions recorded at a specific m/z, that is, ICM(θ, ET′)total = Σiwi × [T(θ) × P(ET′)]i, with the parameter wi representing the relative contribution of the integral cross section of the ith channel.70 For each product the final result is a velocity-angle flux contour map of the product, ICM(θ, u); Fig. 2c, for instance, shows the image ICM(θ, u) of the C2H4 product of the C2H4 + CO channel from the reaction O(3P) + CH2CCH2 (allene).104 The T(θ) and P(ET′) functions, synthesized in ICM(θ, u), for a given reaction channel contain all the information about the reaction dynamics of that channel.

Once the origin of the various ion signals is sorted out from the experimental data, the relative cross sections of two generic products, σi and σj, can be derived from the relative apparent cross sections σappi and σappj (i.e., the wi weight obtained from the best-fit analysis of the LAB data), the estimated ionization cross section σioni and σionj, and the fraction of the two specific products, fi and fj, appearing at the given m/z ratio, taking into account the quadrupole transmission: σi/σj = (σappi/σappj)(σionj/σioni)(fj/fi).70 The derived product branching ratios [(B.R.)i = σi/σtotal] have uncertainties ranging from ±20% to ±50%, depending on the channel.

In a CMB experiment with hard EI MS detection, if elastically/inelastically scattered particles as well as inherent detector and/or main chamber effusive background signals occur at the same m/z ratio of the reactive signal one seeks to measure, the problem is usually so serious to make the experiment impossible, because especially elastically scattered signals are typically at least two orders of magnitude larger than reactive signals (see, for instance, Fig. 3), and the latter cannot be recovered. The dissociative ionization problem has limited for decades the application of the technique to detailed studies of polyatomic multichannel reactions such as those discussed here. In these cases it is, in fact, necessary to suppress (or at least mitigate) the dissociative ionization of reactants, products and background gases which may critically interfere with product detection. For suppressing (or at least mitigating) the interfering signals the solution is to use soft ionization and this can be achieved by both soft EI69,74–76 or soft PI.55,77–81 Pioneering work exploiting soft ionization techniques was reported already in the 1970s; in some cases, soft PI using fixed frequency gas lamps105,106 or soft EI using tuneable low-energy electrons107 was used both in flow reactor kinetic experiments with MS detection and in rudimentary crossed beam experiments with effusive beams and a fixed MS detector.105–107 However, only 30 years later this kind of studies became practical when were implemented (i) continuous or pulsed CMB experiments with a rotatable MS detector and TOF analysis using low-energy tuneable electrons (see, for instance, Fig. 3-bottom panel)69 or tuneable VUV synchrotron radiation,81 respectively (in some cases also fixed-frequency VUV laser radiation67,91), and (ii) time-resolved flow kinetic experiments with MS detection using tuneable VUV synchrotron radiation.108,109

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Fig. 3 TOF spectra at Θ = 34° for the O(3P) + C2H4 reaction at Ec = 12.9 kcal mol−1 recorded at m/z = 14 using (top) hard (60 eV) and (bottom) soft (17 eV) electron ionization.69 Top panel: Signal is coming nearly exclusively from dissociative ionization of elastically/inelastically scattered C2H4 reagent. Bottom: Signal is coming exclusively from the reaction (note the relative scales: the reactive signal is only about 1% of the elastic signal); the heavy solid line is the total TOF distribution of reactively scattered signals calculated from the best-fit product CM translational energy and angular distributions for the indicated contributing five product channels. Reproduced from ref. 69 with permission from Royal Society of Chemistry, copyright 2009.

2.2 O(3P) + alkynes (CH[triple bond, length as m-dash]CH and CH3C[triple bond, length as m-dash]CH)

Detailed CMB studies on the O(3P) reaction with the alkyne prototype, ethyne (acetylene), and with the next in the series, propyne (methyl-acetylene), have revealed that elongating the hydrocarbon chain by substituting an H atom with a CH3 group leads to a dramatic change in the product distribution and extent of ISC.
2.2.1 O(3P) + CH[triple bond, length as m-dash]CH. Studies at three different Ec's (8.2, 9.8, and 13.0 kcal mol−1) of the O(3P) + ethyne reaction110 confirmed the occurrence of only two product channels:
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and established their B.R. of 0.79 ± 0.05 and 0.21 ± 0.05, respectively, independent of Ec. Notably, the spin-forbidden pathway:
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was found to be negligible. These studies superseded the pioneering CMB work on this system performed in Berkeley in the late 1980s using hard EI.111

Fig. 4 exemplifies the two detected HCCO and CH2 products (via their angular (a) and TOF (b) distributions), the reaction kinematics (via the velocity vector diagram and the limiting circles of the two different products), and a simplified diagram of the relevant triplet and singlet C2H2O PESs (c). Clean detection of CH2 was made possible by soft EI.69,74,110

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Fig. 4 (a) HCCO and CH2 product LAB angular distributions from the O(3P) + C2H2 reaction at Ec = 9.5 kcal mol−1.74 The Newton diagram of the experiment shows the circles delimiting the maximum velocity that the indicated products can attain assuming all available energy channeled into product translation. (b) Exemplary TOF spectra of m/z = 41 (HCCO) and m/z = 14 (CH2) products. At an electron energy of 17 eV the dissociative ionization of the HCCO product at 13CH+ and C2H2 reagent at 13CH+ and CH2+ is completely suppressed, so all m/z = 14 signal is from the CH2 reaction product. (c) Schematics of the triplet (red) and singlet (blue) PESs for C2H2O with seam of ISC, product channels and their route of formation, and experimental B.R.s indicated. Reproduced (a and b) from ref. 74 and adapted (c) from ref. 112 with permission from American Institute of Physics, copyright 2004, and American Chemical Society, copyright 2006, respectively.

The B.R.s derived from the CMB results are nicely in line (actually coincide) with those obtained in the most recent and accurate kinetics determinations at 300 K (see ref. 110) (corresponding to Ec of about 1 kcal mol−1) and with those predicted from theoretical calculations,112 based on statistical rate theory and master equation analysis as well as on dynamical QCT-SH calculations on-the-fly on coupled triplet/singlet ab initio PESs.113 All this confirms that the B.R.s for O + C2H2 are essentially temperature independent. Notably, the latter calculations,113 which predict a B.R. of 0.21 for the CH2 + CO channel, also found the formation of a small fraction (B.R. ≈ 0.07) of channel (1c), suggesting that ISC in this reaction, if occurs at all, is minor.

The reaction mechanism sees the electrophilic attack of the O atom to the unsaturated bond of ethyne (Fig. 4c) with the formation of a relatively stable (by −50 kcal mol−1)112 triplet HCCHO intermediate which can undergo C–H bond cleavage to H + HCCO (ketyl) or isomerize by 1,2-H shift to 3CH2CO (triplet ketene) followed by fast C–C bond dissociation to 3CH2 + CO. Both pathways occur on the triplet PES and are characterized by a sizeable exit barrier, as suggested by the shape of the experimental P(ET′) distributions and corroborated by the PES calculations.112,113 The negligible or very low probability of ISC can be traced back to a low probability of triplet → singlet crossing for this light system with a limited number of internal degrees of freedom and consequently a relatively short lifetime (estimated to be ≈15 ps at T = 1000 K and ≈4 ps at T = 2000 K),112 consistent with the observed, somewhat forward biased CM angular distribution (osculating complex mechanism).110 Theoretical work has suggested that the absence of a significant ISC in O(3P) + C2H2 with respect, for instance, to O(3P) + C2H4 (see below) can be attributed to faster (non-statistical) decomposition of the chemically activated triplet HCCHO adduct and a slower ISC on account of the HCCHO triplet and singlet surface crossing seams being restricted to a narrower geometry range.112

2.2.2 O(3P) + CH3C[triple bond, length as m-dash]CH. Things were found to change dramatically in O(3P) + propyne.114,115 Here the O atom has two possible sites of electrophilic attack: to the terminal or central C of the unsaturated bond (see Fig. 5, portraying the schematics of the ab initio triplet and singlet C3H4O PESs).114,115 Attack on the central C forms a triplet diradical, 3CH3COCH (with a stability of about −53 kcal mol−1 with respect to reactants), that can lead to CH3 displacement via a significant exit barrier (B.R. = 0.10). On the other hand, attack to the terminal C forms an isomeric triplet intermediate, 3CH3CCHO, of similar stability which can evolve toward several pathways: (a) H-displacement via a small exit barrier (B.R. = 0.04), (b) isomerization to 3CH2CHCHO followed by CC bond cleavage to C2H3 (vinyl) + HCO (formyl), and (c) ISC to (i) 1CH3CCHO followed by very rapid isomerization to 1CH2CHCHO (acrolein) and leading to H2 elimination (B.R. = 0.01) and C2H3 + HCO formation, and/or to (ii) 1CH3CHCO (methylketene) which can lead barrierless to 1CH3CH + CO and, via a high exit barrier, to 1C2H4 + CO, for a total B.R. of CO formation of 0.74.
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Fig. 5 Potential energy diagram (schematic) illustrating the main stationary points on the triplet (red solid lines) and singlet (blue dashed lines) PESs for the O(3P) + propyne reaction.114,115 Only the main observed product channels are indicated with their exothermicity, route of formation and experimental branching ratios. The two seams of intersystem crossing following terminal and central C atom attack by the O atom are indicated as ISC1 and ISC2, respectively. Adapted from ref. 115 with permission from American Chemical Society, copyright 2016.

Fig. 6a portrays the velocity vector diagram with the limiting circles within which the observed reaction products are confined in a CMB study at Ec = 9.2 kcal mol−1. Fig. 6b shows the data sensitivity to a channel (H2 elimination) at the level of B.R. = 0.01. Fig. 6c depicts the angular and TOF distributions at m/z = 26 (one of the detected masses):114 here, with respect to the heavy CH3CCO (methyl-ketyl radical, detected at the daughter ion C2H2+) from the H displacement channel and which has a N(Θ) centered at the CM angle and the N(Θ, t) TOF distributions centered at the CM velocity, the lighter C2H4 product (detected at the same C2H2+ daughter ion) from the strongly exothermic CO + C2H4/CHCH3 channel occurring via ISC1 (see Fig. 5) is much more broadly distributed in angle and its TOF distribution is much faster than that of CH3CCO because of energy and linear momentum conservation.

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Fig. 6 (a) Velocity vector diagram with superimposed circles delimiting the maximum CM velocity of the various detected products (indicated) of the O(3P) + propyne reaction at Ec = 9.2 kcal mol−1 (see Fig. 5 for product channels).114 (b) TOF distribution at m/z = 53 recorded at the CM angle and enlargement. The main broad peak corresponds to the CH3CCO product from the H displacement channel (B.R. = 0.04), while the fast shoulder is attributed to the CH2CCO product from the H2 elimination channel (B.R. = 0.01).114 (c) LAB angular (top panel) and TOF (bottom panel) distributions at m/z = 26. The contributing product channels at this mass are indicated. Reproduced (a and b) and adapted (c) from ref. 114 with permission from American Chemical Society, copyright 2016.

As can be seen in Table 1, in contrast to O + ethyne, in O + propyne the H channel yield decreases dramatically from 79% to 4%, because new competitive channels become accessible to the initial triplet intermediate, including ISC (see Fig. 5). The experimental B.R. for the vinyl + HCO channel is 0.11, which according to theory arises from both triplet (1/5) and singlet (4/5) PES.115 Notably, in contrast to the O + C2H2 reaction, CO formation results to be the dominant product channel (B.R. = 0.74), to a large extent (B.R. = 0.58) occurring via ISC.115

Table 1 Experimental branching ratios of the two simplest O + alkyne reactions at Ec ∼ 10 kcal mol−1. The extent of ISC is obtained by adding together the triplet (T) PES (italicized) and singlet (S) PES (bold) yields114,115
Reaction channel O + HCCH B.R. O + CH3CCH B.R.
H H + HCCO 0.79 (T) H + CH3CCO 0.04 (T)
CH3 CH3 + HCCO 0.10 (T)
CO CH2 + CO 0.21 (T) C2H4/CHCH3 + CO 0.16(T), 0.58 (S)
HCO HCO + C2H3 0.02 (T), 0.09 (S)
H2 CHCCO + H2 0.01 (S)
Extent of ISC 0% 68 ± 20%

Interestingly, recent kinetic studies at 300 K with synchrotron radiation gave very similar B.R.s for O + propyne, with the exception that the CO channel is somewhat smaller (but within the error bars in agreement with the above CMB results) and the C2H3 + HCO channel is significantly larger.116 The extent of ISC at 300 K is estimated to be ∼84% ± 14%, slightly larger than the values (68% ± 20%) at Ec = 9.2 kcal mol−1; however, within the error bars it can be concluded that ISC remains essentially constant with T, with a slight tendency to decrease with increasing T, as also observed for O + C2H4 and O + propene (see the next section). It is noteworthy that statistical RRKM/ME calculations on coupled triplet/singlet PESs corroborate these findings at both 300 K and the Ec of the CMB study, confirming that CO formation (via ISC) is by far the main channel, while the H and CH3 channels (both coming from the triplet PES) are of the order of 4% and 10%, respectively.115 All this shows that a variety of channels (five) are significant in O(3P) + propyne and, in particular, that ISC plays a very important role, in contrast of what occurs in O + C2H2. This can be ascribed to the longer lifetime of the initial triplet CH3CCHO intermediate with respect to HCCHO, due to the much higher density of states and triplet/singlet crossing seams extended over a wider geometry range.115 These factors determine overall a dramatically higher probability of ISC in O + propyne with respect to O + ethyne, because multiple nonadiabatic passages are facilitated (see Section 2.5).

2.3 O(3P) + alkenes (CH2[double bond, length as m-dash]CH2 and CH3–CH[double bond, length as m-dash]CH2)

Moving from the reactions with alkynes to those with alkenes, for both two-C and three-C containing species the number of possible product channels increases considerably, because alkenes contain a larger number of H atoms with different carbon hybridization.
2.3.1 O + ethene. The O(3P) + C2H4 reaction is a fundamental oxidation step in combustion and is proto-typical of reactions in which oxygen adds to double bonds; it can also be considered as a prototypical polyatomic nonadiabatic multichannel reaction, which as such has been very extensively investigated both experimentally and theoretically.102,117–122 The PES of O + ethene (see Fig. 7d) is more complex than that of O + ethyne (Fig. 4c). As for other reactions of O(3P) with unsaturated hydrocarbons, decomposition of the initial triplet adduct via spin-allowed reaction channels on the triplet PES competes with ISC which opens up a set of spin-forbidden reaction channels on the ground-state singlet PES. Again, the two PESs may also lead, in some cases, to the same bimolecular products, but via different intermediates, pathways, and transition states. Also for O(3P) + C2H4 the overall product branching is therefore a sensitive function of the ISC rate.
image file: c7cs00601b-f7.tif
Fig. 7 (a) Dots: LAB angular distributions measured at m/z = 15 using soft EI (17 eV) for the O(3P, 1D) + C2H4 reaction at Ec = 8.4 kcal mol−1.102 The separate contributions arising from the CH3 + HCO and the H + CH2CHO channels to the calculated global LAB angular distributions are shown. Light black line: CH2CHO from O(3P). Blue line: CH3 from O(3P). Red line: CH3 from O(1D). (b) Newton diagram showing the circles that delimit the angular range and center-of-mass speed for the indicated products.102 (c) TOF distribution at m/z = 15 recorded at Θ = 30°.102 (d) Potential energy diagram (schematic) illustrating the main stationary points on the triplet (red solid lines) and singlet (blue dashed lines) PESs for the O(3P) + ethene reaction.102,120 Only the main observed product channels are indicated with their exothermicity, route of formation, and experimental branching ratios. The seam of ISC is highlighted. Reproduced (a, b and c) and adapted (d) from ref. 102, 102 and 120, respectively, with permission from United States National Academy of Sciences, copyright 2012, and American Chemical Society, copyright 2005.

After the pioneering work in Lee's group in the late 1980s,117 CMB experiments with soft EI at two different Ec's (8.4 and 13.7 kcal mol−1) were instrumental in elucidating the dynamics of this reaction.102,118,119 Complementary work at lower Ec (Ec ∼ 3 kcal mol−1) was carried out in pulsed CMB experiments with soft PI by synchrotron radiation.81 From product LAB angular and TOF distribution measurements (Fig. 7a and c show exemplary data), angular and translational energy distributions in the CM system were obtained for the five observed exothermic competing reaction channels leading to H + CH2CHO, H + CH3CO, CH3 + HCO, CH2 + H2CO, and H2 + CH2CO. Table 2 summarizes the derived B.R.s and compares them with those derived from kinetic studies both at 300 K and in the range 300–900 K, as well as with the results of dynamical calculations. It was found that at Ec = 8.4 kcal mol−1 formation of CH3 + HCO is the major channel (B.R. = 0.34 ± 0.09), followed by H + CH2CHO (vinoxy) (B.R. = 0.30 ± 0.06). Formation of methylene + formaldehyde (CH2 + H2CO) in large amounts (B.R. = 0.20 ± 0.05) was also observed unambiguously. In addition, it was established that formation of molecular products, CH2CO + H2, is also a sizeable channel (B.R. = 0.13 ± 0.04) and, for the first time, it was shown that a small fraction of acetyl radicals is also formed (B.R. = 0.03 ± 0.01). Notably, at 300 K, formation of formaldehyde had been initially determined in the amount of about 6%,123,124 but very recent kinetic studies from 300 up to 900 K (at p = 1–8 Torr) have found that the H2CO B.R. is already 0.17 ± 0.03 at 300 K and remains essentially constant at the higher temperatures.122 The latter kinetic study corroborates the CMB findings that the product B.R.s do not vary significantly with temperature (Ec). The finding that at Ec's corresponding to typical combustion temperatures of about 800–1300 K formation of formaldehyde, an important pollutant, is a very important channel in this prototypical O + alkene reaction led to the conjecture that this may have been the case in also O + other terminal alkene reactions, such as those with propene103 and 1-butene.125 This indeed was confirmed both experimentally and theoretically (see also below).103,125 Notably, very recent statistical calculations predict that the formaldehyde channel at very high temperature (2000 K) accounts for 50% of the overall reaction yield.121

Table 2 Product branching ratios of the O(3P) + C2H4 reaction from kinetics and dynamics studies
Reference Products ISC (%)
CH2CHO vinoxy CH2 methylene CH3CO acetyl CH2CO ketene CH3 methyl
a See ref. 118. b Ref. 102 and 118. c Ref. 119. d Ref. 122.
Kineticsa (300 K) (Ec ≈ 0.9 kcal mol−1) 0.39 ± 0.10 0.06 ± 0.03 0.019 ± 0.001 0.53 ± 0.04 55
CMB (Ec = 8.4 kcal mol−1) 0.30 ± 0.06b 0.20 ± 0.05 0.03 ± 0.01 0.13 ± 0.04 0.34 ± 0.09 50
QCT-SH calc's (Ec = 8.4 kcal mol−1)b 0.28 0.08 0.10 0.05 0.49 64
CMB (Ec = 13.7 kcal mol−1)c 0.33 ± 0.07 0.22 ± 0.04 0.02 ± 0.01 0.13 ± 0.03 0.31 ± 0.08 47
Kinetics (300–900 K)d 0.31 ± 0.05 0.17 ± 0.03 ≤0.05 0.53 ± 0.09 55

Interestingly, the derived B.R.s (Table 2) indicate that ISC plays an important role in this reaction, since the formation of HCO, H2 and CH3CO, which account for about 50% of the overall reaction yield, can only be rationalized assuming that ISC between triplet and singlet PESs is occurring very efficiently. Yet, the ISC extent, which is very much larger than for O + ethyne (where B.R. ≈ 0), is significantly lower than for O + propyne at comparable Ec (B.R. = 0.69 ± 0.20). This may not be surprising because the extent of ISC can be connected to the lifetime of the initial triplet intermediate and its stability is only −22 kcal mol−1 for O + ethene against –50 kcal mol−1 for O + propyne.

The elucidation of the reaction dynamics was assisted by synergic full-dimensional QCT-SH calculations of the reactive DCS on coupled ab initio triplet/singlet PESs.102,118,119 Both experiment and theory find almost an equal contribution from the triplet and singlet PES to the reaction, with a clear tendency of the degree of ISC to decrease slightly with increasing Ec and with theory somewhat overestimating the extent of ISC (see Table 2). Theory and experiment also agree at the level of angular distributions and translational energy distributions for the three primary radical channel products H + CH2CHO, CH3 + HCO, and CH2 + H2CO.118 The good agreement between theory and experiment indicates that QCT-SH calculations, using reliable coupled multidimensional PESs, can yield accurate dynamical information for polyatomic multichannel reactions in which ISC plays an important role.

Another point of interest certainly is whether in moving from a two-C alkene to a three-C alkene the extent of ISC increases strongly, as in the alkyne series, or not. The investigation of O + propene was very enlightening in this regard.

2.3.2 O + propene. The reaction of O(3P) with the next alkene of the series is characterized by a higher complexity than for the prototype reaction with ethene because of the significantly larger number of atoms involved and a wider variety of possible reaction intermediates (see the schematic of the triplet and singlet PESs portrayed in Fig. 8).103 Again, two possible sites of O addition are now possible, with the terminal C (the less substituted one) being the favored site for electrophilic attack. Notably, the H-displacement channel can now originate from both possible triplet intermediates. From LAB angular and TOF measurements at different m/z ratios five different reaction channels were identified and characterized. Exemplary LAB data are depicted in Fig. 9. In particular, it was possible to discriminate between the two different H displacement channels, leading to aldehyde (CH3CHCHO, methylvinoxy) and keto (CH3COCH2) radical products.103 From the data (Fig. 9) one can also notice the clear observation of formaldehyde (at m/z = 30),126 and methyl and vinoxy (at m/z = 15), as well as of methyl-ketene (CH3CHCO) from the H2 elimination channel. The CMB B.R.s were corroborated by synergistic ab initio calculations of the triplet and singlet PESs and RRKM/ME computations of B.R.s with inclusion of ISC.103
image file: c7cs00601b-f8.tif
Fig. 8 Potential energy diagram (schematic) illustrating the main stationary points on the triplet (red solid lines) and singlet (blue dashed lines) PESs for the O(3P) + propene reaction.103 Only the main observed product channels are indicated with their exothermicity, route of formation and experimental branching ratios. The two seams of intersystem crossing following terminal and central C atom attack by the O atom are indicated as ISC1 and ISC2, respectively. Modified from ref. 103 with permission from American Chemical Society, copyright 2015.

image file: c7cs00601b-f9.tif
Fig. 9 LAB angular distributions at m/z = 56, 55, 29, and 15 and TOF distributions at m/z = 55, 30, 29, and 15 for the O(3P) + propene reaction at Ec = 9.3 kcal mol−1.103 The solid black curves represent the total calculated distributions when using the best-fit CM functions. The separate contributions to the calculated global LAB angular and TOF distributions are indicated with the formula of the corresponding product. Reproduced (left panel) and modified (right panel) from ref. 103 with permission from American Chemical Society, copyright 2015.

Table 3 compares the product B.R.s of O + propene with those of O + ethene at a comparable Ec. The most relevant results can be summarized as follows.

Table 3 Experimental branching ratios of the two simplest O + alkene reactions (T = triplet PES, S = singlet PES) at Ec ∼ 9 kcal mol−1. The extent of ISC is obtained by adding together the triplet (T) (italicized) and singlet (S) (bold) yields103,119
Reaction channel O + CH2[double bond, length as m-dash]CH2 B.R. O + CH3–CH[double bond, length as m-dash]CH2 B.R.
(1) The H channel in the O + CH3CHCH2 reaction is much less important than in O + C2H4 (12% versus 32%).(2) The CH3 channel is of comparable importance in the two systems (32%).(3) The H2CO channel in O + propene is even more important than in O + C2H4 (44% versus 20%).
H H + CH2CHO 0.30 (T) H + CH3CHCHO 0.07 (T)
H H + CH3CO 0.03 (S) H + CH3COCH2 0.05 (T)
CH3 CH3 + HCO 0.34 (S) CH3 + CH2CHO/CH3CO 0.20(T), 0.12(S)
H2CO CH2 + H2CO 0.20 (T) CHCH3/C2H4 + H2CO 0.44 (T)
H2 H2 + CH2CO 0.13 (S) CH3CHCO + H2 0.03 (S)
C2H5 C2H5 + HCO 0.09 (S)
ISC 50% 24%

The importance of the CH3 and H2CO channels is established also at 300 K from kinetic studies with synchrotron radiation.127 Interestingly, the H2CO channel is an important channel also in the O(3P) reaction with the next member of the alkene series, namely 1-butene, where the B.R. was very recently found to be about 0.25.125 Notable is also the fact that the H channel continues to decrease in relative importance in going from C2H4 to C3H6 to 1-C4H8, while the CH3 channel remains an important channel (the main channel in O + 1-butene125).

Particularly important is the fact that the H2CO channel has never been observed experimentally in O(3P) + C3H6 at combustion temperatures, nor considered to be important, although early works105,107 found that some H2CO is formed also at room temperature. Its inclusion in combustion kinetics models may affect the model outcomes.

2.4 O(3P) + dienes (CH2[double bond, length as m-dash]C[double bond, length as m-dash]CH2)

It is interesting to examine also the O(3P) reaction with the prototype of dienes, namely propadiene (allene), and compare it with the three-C alkene and alkyne reactions. This is for two reasons: on one side, allene is an isomer of propyne, so its comparative study with respect to propyne permits us to explore the product distribution and extent of ISC as a function of molecular structure; on the other side, it allows us to explore the effect of multiple double bonds on the O(3P) dynamics with unsaturated hydrocarbons, by comparing its reaction dynamics with that of propene. Furthermore, from the overall comparative study of the above two-C and three-C unsaturated hydrocarbons we can examine in a more comprehensive manner the effects of molecular complexity and structure on the product distributions and extent of ISC (see Section 2.5).

From LAB angular and TOF distributions measured at m/z = 53, 29, 27, 26 and 14 (see Fig. 10) for O(3P) + allene at Ec = 9.4 kcal mol−1 we were able to identify and characterize five competing product channels.104 As can be seen in Fig. 10 even at 17 eV in the data at m/z = 29, 27 and 26 there is a significant contribution arising from the dissociative ionisation of the CH2[double bond, length as m-dash]C–CHO product, the channel which appears as the dominant one in the LAB reference frame. Nevertheless, product intensity is clearly visible at LAB angles which are outside the angular range amenable to the H displacement channel. The shapes of the additional contributions in the m/z = 29, 27, 26 and 14 angular distributions are quite different, implying different signal sources. The TOF analysis allowed us to disentangle the various contributions at a given m/z. While the m/z = 53 TOF spectrum is unimodal, the other spectra have a pronounced structure with two or three peaks. From the best-fit product angular and translational energy distributions for the various channels and their relative weight wi, it has been possible to derive the B.R.s for the five most important channels: C2H4 + CO (77%), H2CO + C2H2 (9.1%), HCO + C2H3 (6.2%), CH2CO + CH2 (6.5%), CH2COCH + H (1.5%). While the last two channels take place on the triplet PES, the first three channels can only be formed from the singlet PES, after ISC has taken place (see the schematic of the triplet and singlet PESs128 in Fig. 11 highlighting all the observed channels, with the experimental B.R.s also indicated). Therefore, the CMB study indicates that the O + allene reaction is dominated by ISC (estimated to be >90%). The experimental B.R.s are corroborated by the ab initio and RRKM calculations of Nguyen et al.,128 although ISC has not been included in the statistical calculations.

image file: c7cs00601b-f10.tif
Fig. 10 LAB angular and TOF distributions at m/z = 53, 29, 27, 26, and 14 for the O(3P) + allene reaction at Ec = 9.4 kcal mol−1.104 The solid black curves represent the total calculated distributions when using the best-fit CM functions. The separate contributions to the calculated global LAB angular and TOF distributions are indicated with the formula of the corresponding product. Reproduced from ref. 104 with permission from American Chemical Society, copyright 2012.

image file: c7cs00601b-f11.tif
Fig. 11 Potential energy diagram (schematic) illustrating the main stationary points on the triplet (red solid lines) and singlet (blue dashed lines) PESs for the O(3P) + allene reaction.128 Only the main observed product channels are indicated with their exothermicity, route of formation, and experimental branching ratios. The seam of intersystem crossing following central C atom attack by the O atom is indicated. Modified from ref. 128 with permission from American Chemical Society, copyright 2006.

As can be seen from Fig. 11 oxygen addition to the central C atom (with a barrier height of 0.9 kcal mol−1) leads to the formation of the very stable (−70 kcal mol−1) CH2COCH2 diradical (oxyallyl) that, according to RRKM calculations, preferentially dissociates into CH2 + CH2CO, if the system remains on the triplet PES.128 Triplet oxyallyl, however, can also undergo ISC to the singlet PES and singlet oxyallyl easily isomerizes to cyclopropanone which in turn, because of its high internal energy content, under collision-free conditions undergoes fragmentation, by large preference, to the products CO + C2H4, which is the main reaction channel. Once jumped to the singlet PES, other products such as H2CO + C2H2 can also be formed. In contrast, O addition to one of the terminal C atoms leads to the formation of a much less stable (−22 kcal mol−1) intermediate, O–CH2–C–CH2 (entrance barrier height 1.34 kcal mol−1), which can easily fragment into CH2–C–CHO + H or, after some rearrangements, into C2H3 + HCO. The two initial addition intermediates can isomerize to each other and the complete scheme of the PES is quite complex (see Fig. 11).128

It is particularly interesting to compare the results for the two isomeric reactions O(3P) + allene and O(3P) + propyne. The experimental data for the two systems show numerous similarities, but also significant differences. In particular, the overall extent of ISC is significantly larger for O + allene (more than 90%) with respect to O + propyne (about 70%). In fact, the yield of the H and CH3 forming channels (both coming from the triplet PES) in O + allene is about three times smaller than for the corresponding triplet channels in O + propyne. This is likely due to the fact that for O + propyne there are more facile routes to H and CH3 elimination on the triplet PES.115 Furthermore, the probability of ISC is higher in O + allene because the triplet and singlet oxyallyl curves are very close, within a few kcal mol−1, for all CCC angles (the triplet–singlet splitting in oxyallyl is only 1 kcal mol−1),128 while in O + propyne the main viable route to ISC is via nonadiabatic transition from the triplet to the singlet CH3CCHO ketocarbene intermediates (resulting from the O attack to the terminal carbon atom) which are significantly separated in energy.115 Note also that the initial triplet intermediate is significantly more stable (−70 kcal mol−1) for O + allene (Fig. 11) than for O + propyne (−53 kcal mol−1) (Fig. 5).

Another very interesting aspect that emerged from the comparison between the reaction dynamics of these isomeric reactions is the experimental and theoretical evidence that, under single-collision conditions, the dominant product channel in both cases leads to CO formation. However, the co-products are singlet ethylidene (1CH3CH) in the case of O + propyne and singlet ethylene (C2H4) for O + allene.129 By comparing similarities and differences between pathways and energy barriers in the PES it was possible to rationalize the observations.129 The C3H4O triplet PESs can be accessed through the addition of O to either the central or terminal C of the triple (double) bond of propyne (allene). As can be seen in the schematic of Fig. 12, following O attack to the (most favored) terminal C atom of propyne, ISC occurs readily, leading to the very stable methylketene intermediate, which can dissociate either to CH2CH2 + CO via a tight transition state or, preferably, barrierless to 1CH3CH + CO, with isomerization to cyclopropanone being unfavored because of a very high barrier. In contrast, following O attack to the (most favored) central C atom of allene, triplet oxyallyl is formed which readily undergoes ISC to singlet oxyallyl that in turn rapidly isomerizes to cyclopropanone almost exclusively; its isomerization to methylketene is highly unfavored because of a high energy barrier. Cyclopropanone, because of its high energy content, readily undergoes ring-opening, H migration, and C–C bond rupture through a loose transition state to C2H4 + CO. These results settled a long-standing issue on whether ethylidene is actually formed in the O(3P) + propyne reaction, and suggest that formation of CO + alkylidene biradicals may be a common mechanism in O(3P) + alkyne reactions, in contrast to formation of CO + alkene molecular products in the corresponding isomeric O(3P) + diene reactions, either in combustion or in other gaseous environments.129 These findings, which are of fundamental significance, may have implications for improved combustion models. Notably, it was predicted129 that the so far neglected 1CH3CH + CO channel is among the main reaction routes also when the C3H4O singlet PES is accessed from the OH + C3H3(propargyl) entrance channel, and these two radical species play a key role in many combustion systems.

image file: c7cs00601b-f12.tif
Fig. 12 Potential energy diagrams (schematic) illustrating reactants, stationary points, and main products on the singlet C3H4O PESs. Blue lines: O + propyne; red lines: O + allene. Blue and red solid lines mark the preferential pathways to 1CH3CH and C2H4 products from methylketene and cyclopropanone, respectively, in the two isomeric cases. Reproduced from ref. 129 with permission from American Chemical Society, copyright 2016.

2.5 Dependence of intersystem crossing on molecular complexity and structure

It is instructive to take a panoramic look at the results obtained on the reaction dynamics of O(3P) with the simplest alkynes, alkenes and dienes. One can notice several aspects:

(i) The H-displacement channel is the most important channel in O + ethyne (B.R. = 0.79), but decreases strongly when going to propyne (B.R. = 0.04). It is also one of the two most important channels in O + ethene (B.R. = 0.30–0.33), but it decreases very significantly with the lengthening of the alkene chain: B.R. = 0.12 in O + propene and of the order of a few percent in the four-C alkene 1-butene125 and cumulene 1,2-butadiene.130 It is also minor in O + allene (B.R. = 0.015).

(ii) The methyl forming channel is particularly relevant in the reactions with alkenes. In fact, it is one of the two main channels in O + ethene (B.R. = 0.34), and remains very important also with the higher alkenes O + propene (B.R. = 0.32) and O + 1-butene125 (B.R. ∼ 0.4).

(iii) Another important channel in the reactions with alkenes is the formaldehyde forming channel which is the third largest channel in O + ethene (B.R. = 0.20), becomes the most important one in O + propene (B.R. = 0.44), and remains very important also in O + 1-butene125 (B.R. ∼ 0.25). The great relevance of this channel in all the O + terminal alkene reactions is perhaps the major novelty in terms of identity of the large variety of reaction products in these systems. It is noteworthy that this channel is dominantly formed from the triplet PES.

(iv) Vinoxy is also an important reaction product with all alkenes, from being one of the two major ones with ethene (B.R. = 0.30–0.33) to an important one with also the higher alkenes propene (B.R. > 0.2) and 1-butene (B.R. ∼ 0.2).125

(v) The B.R. of the CO channel is 0.2 in O + ethyne, but rises to more than 0.7 in O + propyne. On the other hand, CO is not formed in O + alkenes (except for a very small fraction by 3-body dissociation),103 but again is the major channel in O + allene (B.R. ≈ 0.8) and also in O + 1,2-butadiene (B.R. ≈ 0.5).130

(vi) The H2 elimination channel appears to occur in nearly all reactions, except with ethyne and allene, on the singlet PES via ISC, but it is always the smallest channel, on the order of a few percent, which is not surprising considering that usually it involves 3- or 4-center molecular elimination over a very high exit barrier.

Interestingly, the main reaction channels with propyne, propene and allene are C–C bond breaking channels and that means that the 3-carbon chain of the hydrocarbon (either alkyne, alkene or diene) is not maintained when attacked by atomic oxygen. This similarly occurs with four-C unsaturated hydrocarbons125,130 and also with ethene, the only exception being ethyne.

It was initially noted that the extent of ISC increases very significantly in going from ethene (∼50%) to allene (>90%), thus suggesting that it might increase with increasing molecular complexity. But we have seen that this is not the case with propene (neither with 1-butene). However what is very different between ethene and propene on one side and allene on the other side is that following O attack to the central C of allene a very stable triplet diradical is formed, CH2COCH2 (oxyallyl), which is strongly stabilized by resonance (about −70 kcal mol−1) and which does not have the equivalent in the alkene reactions. In contrast, O attack to the terminal C of allene leads to a triplet intermediate which has a stability (−22 kcal mol−1) similar to that existing with alkenes. This makes it difficult to extrapolate the extent of ISC along a series, because what actually determines the extent of ISC is the competition between dissociation of the initial triplet intermediate to products on the triplet PES and ISC, but this is determined by the details of the underlying PESs.

It should be noted that from theoretical calculations103,115 it appears that the nonadiabatic coupling matrix elements are rather similar (∼30–35 cm−1) for the O + alkene and O + alkyne systems under examination, that is, the probability of nonadiabatic transition on a single triplet → singlet passage is rather similar in the various systems; however, what can be (very) different is the number of times that the crossings are traversed and the longer the complex lifetime the higher the overall probability of ISC.

In order to shed further light on the role of ISC it is useful to correlate the extent of ISC with the relative stability of the triplet reaction intermediate(s) in the various systems. It can be noted that the relative stability of the initial triplet adduct in O + propene (−23.7 kcal mol−1) (Fig. 8) is very similar to that in O + ethene (−24.0 kcal mol−1) (Fig. 7d), so one may expect a comparable extent of ISC in the two cases. But, surprisingly, the extent of ISC in O + propene is lower (24%) than in O + ethene (50%) at comparable Ec, and this presumably is because a very significant fraction of the reactive flux goes from the more abundant CH3CHCH2O triplet intermediate (from the terminal C attack) to the 3CH3CH + H2CO products (see Fig. 8), a reaction channel whose equivalent in the O(3P) + C2H4 reaction is 3CH2 + H2CO (see Fig. 7d). In addition, also other channels become accessible on the triplet PES in O + propene (CH3 can be formed also on the triplet PES in O + propene, while only via ISC in O + ethene).

Comparisons of the CMB B.R.s with those from the recent kinetics studies at 300 K with synchrotron radiation116 and from RRKM/ME statistical predictions have provided information on the variation of B.R.s with Ec also for the O + propene reaction.103 ISC is found to decrease from about 60% at 300 K (Ec ≈ 1 kcal mol−1) (experiment: 84%) to about 20% (experiment: 24%) when Ec increases to about 9 kcal mol−1. This decrease is more pronounced than observed in O + propyne.114,115 A similar, but much less pronounced trend of ISC with Ec was also observed in the related O(3P) + C2H4 system.102,118,119 These trends in all systems have been confirmed by statistical calculations. Therefore, these results indicate that ISC does not necessarily always increase with increasing molecular complexity, but it appears, expectedly, to have temperature (Ec) dependence.

It is interesting and useful to look at Fig. 1 again and focus on the three-carbon alkene, alkyne and diene species for which we have a more complete data set and which best exemplify a three-C unsaturated hydrocarbon polyatomic molecule. If we look at the extent of ISC versus the stability of the triplet intermediate formed following the electrophilic addition of the O atom to the most favored C of the unsaturated bond (the terminal one for O + propyne and O + propene, while the central one for O + allene), we note an extremely simple and very interesting trend which is clearly expressed in the graph depicted in Fig. 13. As can be seen the extent of ISC grows linearly with increasing stability of the triplet intermediate, for a given Ec (∼9 kcal mol−1). A similar trend can also be observed for O + propyne and O + propene at 300 K from the kinetics and also theoretical results; notably, at 300 K the extent of ISC is somewhat higher than at Ec = 9 kcal mol−1 (corresponding to about 900 K) for both propyne (84 ± 14% versus 69 ± 17%)114–116 and propene (33 ± 7% versus 24 ± 6%).103,127 Unfortunately, B.R.s from kinetic experiments and/or statistical calculations with inclusion of ISC are not yet available for O + allene. Statistical calculations of B.R.s tell us that, on the contrary, the extent of ISC decreases strongly at very high T (for instance, for O + propyne the percentage of ISC is calculated to be 85% at 300 K and 2% at 2250 K).115 So, similar nearly linear trends (with possibly different slopes) can be expected to hold even at higher temperatures (Ec). It will certainly be interesting to examine in the near future the shape of the graph for the four-carbon alkene (1-butene), alkyne (1-butyne) and diene (1,2-butadiene) series. It should be noted that the two-C unsaturated hydrocarbons (ethyne and ethene) constitute peculiar cases and do not fit in the trend of Fig. 13, actually revealing an opposite trend, with ISC being ∼ 0 in O + ethyne and ∼50% in O + ethene.

image file: c7cs00601b-f13.tif
Fig. 13 Extent of ISC versus energy (stability) of the initial triplet O-unsaturated hydrocarbon intermediate. Solid circles with error bars refer to the series of three-C containing alkene, alkyne and diene at Ec ∼ 9 kcal mol−1. The straight line is drawn through the data point to guide the eye.

The higher the stability of the triplet intermediate (−70 kcal mol−1 for oxyallyl) the longer its lifetime is. Therefore, for long lifetimes of the triplet intermediate the chemically activated, vibrating triplet adduct can access the triplet → singlet crossing region many times, resulting in an increased transition probability and ISC rate.

Going back to Fig. 1, we can argue that the rate of ISC for a given temperature (collision energy) is determined by the competition between decomposition of the initial triplet intermediate to the various triplet channels and ISC, and that the ISC rate increases with increasing stability (and hence lifetime) of the triplet intermediate. The stability increases in going from alkenes to alkynes and to dienes (see Fig. 1, 5, 8 and 11), and therefore the extent of ISC increases in going from propene to propyne and to allene (see Fig. 13), as experimentally observed and theoretically corroborated. Similarly, the extent of ISC is expected to increase in going from 1-butene to 1-butyne, and to 1,2-butadiene.

These CMB studies, backed by theoretical calculations, not only have established the primary products and B.R.s for this important class of reactions, which is the most useful information for combustion modelers, but from the elucidation of the detailed reaction dynamics new insights into the reaction mechanism and role of ISC have also been gained.

3. Product pair correlation in polyatomic reactions

The combination of laser spectroscopy with crossed molecular beam scattering techniques has proven invaluable for interrogating the nascent rovibrational state distribution of reaction products,1 complementary to the traditional approach of using the universal, mass-spectroscopic detection method highlighted in Section 2. Thanks to the multiplexity nature of the VMI technique,131–135 past 20 or so years have witnessed tremendous advances in that area,136 which enables nowadays almost routine measurements of the state-resolved differential cross sections and often even in the product state pair-correlated manner with an unprecedented level of detail.38,137,138 This short review is not intended to give a comprehensive survey of those works, but rather showcases a few examples to highlight the salient features and the exciting opportunities afforded by this powerful and versatile approach. Specifically, we shall focus on the abstraction reactions of methane with atoms and diatoms. The key features of the reaction profiles for four of such reactions are depicted in Fig. 14. Compared to the indirect addition–elimination reactions presented in Section 2, where multiple product channels are possible and the reaction path of each channel often involves one or more potential wells, the profiles shown here are considerably simple. On the other hand, the reactions of methane with different radicals exhibit diverse energetics, barrier heights and locations as can be seen, thus, offering a great opportunity to explore how these factors affect polyatomic reactivity. In addition, treating the methyl moiety as a pseudo-atom, this series of reactions provide an enlightening contrast to the analogous, simpler atom + diatom reactions. The deeper insights gained from these benchmark studies could be instrumental in guiding our thinking for a wider range of more complex reaction systems. Because several recent reviews have already discussed various aspects of the impacts of reactant's vibrations on polyatomic reaction dynamics,83,84,139–142 here we will minimize the overlaps in scope by only focusing on the rotational-mode specificity in the vibrationally excited reactions and by exemplifying a few hitherto unobserved, fascinating phenomena in the ground-state reactions.
image file: c7cs00601b-f14.tif
Fig. 14 Schematic representation of the reaction profiles of four H-atom abstraction reactions along the reaction coordinate. All energetics are roughly scaled according to the available experimental results, and the locations of the barriers are in keeping with the ab initio calculations. Note the diversity of the heat of reaction, the barrier height and its location. Modified from ref. 83 with permission from American Institute of Physics, copyright 2015.

In the following, we will first introduce the concept of product pair correlation in Section 3.1. In Section 3.2 an example will be given to illustrate the capability of the pair-correlated measurement to decipher multiple chemical reactions recorded in a single product image. Sections 3.3–3.5 demonstrate how the pair-correlated results can lead to the discoveries of a number of intriguing dynamics phenomena in polyatomic reactions, such as the reactive resonance (Section 3.3), the reactive rainbow (Section 3.4), and the mode-correlation between the paired products (Section 3.5). The last three sections of 3.6–3.8 are devoted to an episode that spans over the past 5–6 years, trying to unravel the rotational-specific effects of either reactants or products. In a broader perspective, our conceptual understanding or the physical picture of reaction dynamics at the molecular level seemed to take a fresh twist whenever a new type of experiment that was aimed at removing another layer of “averaging” had been performed. How our thinking evolved and new insights were gained, as well as the lessons learnt along the way might be inspiring to others in the community. As the saying goes, in a fundamentally creative field, the satisfaction or fun comes from the chase, not the catch.

3.1 Product pair correlation

The knowledge of product state and angular distributions in the atom + diatom reaction has played a pivotal role in advancing our basic understanding of chemical reactivity over the past decades.1 As we move towards more complex reactions with polyatomic molecules, often two molecular products are formed. The conventional spectroscopic methods become handicapped in that measuring the product distributions of one species is blind to the distributions of its coproduct; yet, the two products must be formed together as a colliding pair from each individual reactive event. To this end, a time-sliced VMI technique was developed to provide the desired coincident information of the two product distributions,134,143 Whereas the method is capable of revealing the coincident information, it is experimentally distinct from the conventional coincidence-detection technique, for which the two (or multiple) concomitantly formed products (usually ions) are simultaneously detected for each single event. To avoid confusion, the method was then coined the product-pair correlation measurement,38,134,143 more precisely, the quantum state-correlation of a product-pair in a single, collisional event.

In terms of probability theory, what this method measures is the joint or conditional probability distributions P(ni, mj) of the quantum states, ni and mj, of the two products.38,144 For example, in the reaction of F + CD4 → DF(v) + CD3(v1v2v3v4), where only the vibrational modes/quantum states of products are considered, the measured distribution of P(v, vi) gives the pair-correlated probability for finding a DF vibrator coincidently formed in state v when a CD3 oscillator is in state vi from the same reactive event. The conventional product state distribution P(v) or P(v′) is simply the sum of P(v, vi) according to P(v) = ∑viP(v, vi); likewise, for P(vi). A matrix is a convenient way to represent the joint probability distribution; say, for v = 0, 1, 2 and 3, and vi = v1, v2, v3 and v4, the matrix will be 4 × 4 = 16 in dimension, which is clearly much larger than the combination of the two uncorrelated information, v + vi = 4 + 4 = 8. Obviously, one cannot retrieve the full P(v, vi) matrix elements from the information of P(v) and P(vi) alone even if both are available.

The basic idea to experimentally realize the pair-correlation measurement is by virtue of energy and linear momentum conservations of a collisional process.1 For the above F + CD4 reaction, the former leads to

Ec − ΔHrx = EDF(v) + ECD3(vi) + ET′,(2)
where for simplicity the rotational energies of the two molecular products are neglected, Ec is the collisional energy, ΔHrx denotes the heat of reaction, and ET′ gives the product recoil energy. The conservation of linear momentum in the center-of-mass frame requires mDFvDF + mCD3vCD3 = 0. Then, one can write
ET′ = 1/2[mCD3(mDF + mCD3)/mDF]v2CD3(3)
If one performs an experiment at a well-defined Ec and manages to detect one of the products, say CD3, in a state-specific manner, from eqn (2) one is left with two undetermined quantities, EDF(v) and ET′. If one goes one step further by simultaneously measuring the velocity vCD3 of the state-tagged CD3(vi) products, then from eqn (2) and (3), the desired quantum state-correlated information of the DF coproduct can be uncovered, with sufficient kinetic energy resolution, from the measured CD3-speed distribution.

The time-sliced VMI technique is one of the powerful methods to implement the above idea in the laboratory. Fig. 15 presents the schematics of the apparatus used in the first demonstration of the product pair-correlation measurement.134,143 The crossed molecular beam technique was employed to control Ec and a resonance-enhanced multiphoton ionization (REMPI) scheme to state-selectively detect one of the products. The REMPI-tagged ions were then recorded by a time-sliced velocity-mapped image, which provided sufficient velocity resolution to directly reveal the desired pair-correlated vibrational distributions of the (undetected) coproduct.

image file: c7cs00601b-f15.tif
Fig. 15 Schematic illustration of (a) a source-rotatable, crossed beam apparatus equipped with (b) a time-sliced velocity map imaging detector. The infrared (IR) laser can be either directed via a multipass ring reflector (not shown) just in front of a skimmer for efficient pumping of vibrationally excited reactants or sent directly to the crossed-beam scattering region to prepare aligned, excited reactants. Abbreviation: ICCD, intensified charge-coupled device; MCP, microchannel plate; PC, personal computer; PCO, camera; TOF, time of flight; UV-REMPI, ultraviolet resonance-enhanced multiphoton ionization. Modified from ref. 84 with permission from Annual Reviews, copyright 2016.

Illustrated in Fig. 16 are four images of the state-selected CD3(0 v2 0 0) products in the F + CD4 reaction at Ec = 5.37 kcal mol−1.143 The successive ring-like structures on each image correspond to the concomitantly formed DF(v) coproducts, starting with v = 4 as the inner-most feature that has the smallest radius (or the least recoil energy) and followed by v = 3, 2, etc. outwards. The intensity around each ring gives an immediate impression about the preferred scattering direction of the (pair) correlated differential cross section (CDCS). It is truly remarkable to observe such a rich variety of CDCS of each product-pair from the very same chemical reaction. The intriguing dynamics features revealed so vividly in this first reported pair correlation measurement still await theoretical interpretation. We note in passing that a very promising theoretical treatment – a QCT calculation with the results analyzed in a quantum spirit – of the pair-correlated distributions for the ground-state product-pair of this reaction has recently been reported.145 Extension to simulate the results shown in Fig. 3 could be most rewarding.

image file: c7cs00601b-f16.tif
Fig. 16 CD3 product state-resolved flux-velocity contour maps from the F + CD4 → DF + CD3(0 v2 0 0) reaction at Ec = 5.37 kcal mol−1. The intensities of four contours are not normalized to one another. The successive rings on each image correspond to the labeled vibrational states of the coincident DF product. Reproduced from ref. 143 with permission from American Association for the Advancement of Science, copyright 2003.

3.2 An example of probing several reactions at once

The power of pair-correlated measurement is not limited to unveiling some hitherto undetected or otherwise lost dynamics information as illustrated above. It can also be utilized to study several reactions occurring simultaneously from a single image. A good example is the report on the Cl + CH2D2 reaction,146 for which two major product channels, CH2D(00) + DCl(v) and CHD2(00) + HCl(v), are anticipated. Fig. 17(a) shows the raw images of the CH2D(00) products probed by the REMPI 000-band at four Ec's. Besides the dominant features that can readily be recognized as the labeled (v = 0) and (v = 1), the images also exhibit a few more extra, unexpected features. These faint features are concentric as the dominant ones, indicating that they all arise from the same Cl + CH2D2 reaction; otherwise, the center of the ring-like feature should be offset due to different mass combination; see eqn (2) and (3). Since only the vibrational ground state of CH2D products was selectively detected by REMPI, the remaining possible sources are from the two reactants, Cl and CH2D2. After the image analysis, indeed all features can be identified, on energetic grounds, as the results of four distinct reactions. They are labeled as (v = 0) for Cl + CH2D2(00) → CH2D(00) + DCl(v = 0), (v = 1) for Cl + CH2D2(00) → CH2D(00) + DCl(v = 1), (v = 0) for Cl + CH2D2 (vbend = 1) → CH2D(00) + DCl(v = 0), and (v = 1)* for Cl*(2P1/2) + CH2D2(00) → CH2D(00) + DCl(v = 1). Similar results were evident for abstracting the H-atom to form the CHD2(00) products.146 It is a delightful surprise that the reactivity of the minor species in the molecular beams, Cl*(2P1/2) and CH2D2(vbend = 1), could be clearly revealed by mere inspection of the pair-correlated raw images.
image file: c7cs00601b-f17.tif
Fig. 17 (a) Representative time-sliced raw images of the CH2D(00) products at four different collision energies as indicated. The state labelings correspond to (v = 0) for Cl + CH2D2(00) → CH2D(00) + DCl(v = 0), (v = 1) for Cl + CH2D2(00) → CH2D(00) + DCl(v = 1), (v = 0) for Cl + CH2D2 (vbend = 1) → CH2D(00) + DCl(v = 0), and (v = 1)* for Cl*(2P1/2) + CH2D2(00) → CH2D(00) + DCl(v = 1). (b) Effect of low-lying hot bands of CH2D2 reactants on the observed images. The upper panel displays the CH2D (00) product images at two different CH2D2 pulsed valve temperatures. The molecular beam intersection angles were adjusted slightly so that the two images were acquired at the same Ec = 5.8 kcal mol−1. The analysis of product speed distributions is presented in the lower panel. The two vertical arrows mark the maximal speeds from reactions with the ground-state (the inner) and bend-excited (the outer) reactants, respectively. For ready comparison, the intensities of two distributions are normalized by the peaks from the ground-state reaction (the slow component); significantly enhanced faster component at higher temperature is clearly displayed. Reproduced from ref. 146 with permission from American Institute of Physics, copyright 2006.

The assignments of the reactions with CH2D2(vbend = 1) and/or Cl*(2P1/2) brought up another interesting aspect. It is known that supersonic expansion will not cool the vibrational degree of freedom as effectively as the translational and rotational ones. The reactant CH2D2 has nine vibrational modes and five of them are low-frequency modes: CD2 scissor (1033 cm−1), CH2 rock (1090 cm−1), CH2 wag (1234 cm−1), CH2 twist (1333 cm−1), and CH2 scissor (1436 cm−1). The first two lower frequency modes, presumably more populated in the supersonic beam, contain merely ≲0.5 kcal mol−1 more energy than the spin–orbit energy (881 cm−1) of Cl*(2P1/2). Because of the energetic proximity of the two possible reactants CH2D2(vbend = 1) and Cl*(2P1/2), the product image may not have sufficient resolution to unambiguously differentiate their contributions. The unequivocal evidence came from a separate experiment using a heated CH2D2 beam.146Fig. 17(b) shows the results of the DCl(v) + CH2D(00) channel in a back-to-back experiment at different source temperatures of the CH2D2 beam, while maintaining the same Ec = 5.8 kcal mol−1. As seen, raising the CH2D2 nozzle temperature clearly enhanced the faster-recoiled component. Since the Cl-beam remained intact, this proved the assignment of that extra feature to the reaction of Cl + CH2D2(vbend = 1). Quantitative data analysis led to a vibrational enhancement factor of ∼3 for bend-excited CH2D2 reactions. This factor is virtually the same as the factors obtained in the analogous, bend-excited CH4/CD4/CHD3 + Cl reactions.147–149 It is worth noting that the excitation of bend-excited reactants can either promote or suppress the reactivity – depending on the collisional energy and varying with the reactions – very different behaviors were seen in the reactions of methane with F and O(3P) atoms.150–153

3.3 Reactive resonances in polyatomic reactions

Replacing the reactant CD4 by CHD3 in the F + CD4 reaction results in two distinct product channels, HF + CD3 and DF + CHD2. A series of detailed studies provided unequivocal fingerprints for reactive resonances (or quantum dynamical resonances) in both the integral cross section (ICS) and the CDCS.154,155 More significantly, closer comparisons of the dynamics attributes of the two isotopic channels suggest a plausible occurrence of a facile “isomerization” process between two structurally distinct [F–D–CHD2] and [F–H–CD3] transient resonant complexes in the transition state region.

Fig. 18 shows the excitation functions (i.e., the collisional energy dependency of the ICSs) of the two dominant paired-channels, (a) HF(v′) + CD3(00) and (b) DF(v′) + CHD2(00). Vastly different Ec-dependency is noted; perhaps, more intriguing are the unusual features in the low energy region.154 A prominent step-structure at Ec ≲ 1 kcal mol−1 is seen for the HF + CD3(00) product channel – a reminiscence of the resonance fingerprint observed in the simpler and well-studied F + HD → HF + D reaction.156–158 Yet, a concurrent kink-feature for the DF + CHD2(00) channel is also notable, in sharp contrast to the analogous F + HD → DF + H reaction whose excitation function displays a normal behavior of a typical activated reaction.156 It is unlikely to be coincidental that two isotopic product channels display unusual features at the same Ec in their excitation functions. Rather, this observation strongly suggests that these two features arise from the same mechanistic origin. To shed more light, Fig. 18(c) compares some of the state-resolved CDCSs of the two isotopic channels in a three-dimensional representation of the angular distribution dσ/d(cos[thin space (1/6-em)]θ) against θ and Ec.155 Broadly speaking, the general patterns of the two least exoergic products, HF(v = 3) and DF(v = 4), are alike in that both are dominated by oscillatory sharp-forward structures, similar to that observed in the resonant reaction of F + HD → HF(v = 3) + D.158 Totally different patterns are displayed for the next exoergic products, HF(v = 2) and DF(v = 3). Yet, both again exhibit a pattern strikingly similar to that in F + HD → HF(v = 2) + D.157,158

image file: c7cs00601b-f18.tif
Fig. 18 Presented are the excitation functions of (a) F + CHD3 → HF(v′) + CD3(00) and (b) F + CHD3 → DF(v′) + CHD2(00), respectively. The vibrational state-specific excitation functions for the HF and DF coproducts are also shown. The lines are to guide the eyes. The relative cross sections of the two isotopic channels have been normalized to each other, except the unknown REMPI-detection sensitivity factors. The dashed blue line near Ec ∼ 1.2 kcal mol−1 indicates the energy at which both the step and kink occur concurrently. Modified with permission from ref. 154. (c) Three-dimensional plot of dσ/d(cos[thin space (1/6-em)]θ) against θ and Ec showing the evolution of the product angular distributions, in the F + CHD3 reaction, with the increase in collisional energy for the product pairs of HF(v = 3) + CD3(00) and HF(v = 2) + CD3(00) in the upper panels, and of DF(v = 4) + CHD2(00) and DF(v = 3) + CHD2(00) pairs in the lower panels. Modified from ref. 155 with permission from Taylor & Francis, copyright 2010.

Taken together, one is led to a tantalizing proposition that both isotopic channels are mediated by the same reactive resonance states. This conjecture then raises an interesting question: imagining that the initial attack of the F atom can in principle be either at the H-atom or at the D-atom end of the CHD3 molecules, the resonance states associated with these two collisional geometries should be different. How can they manifest themselves as the same resonance states in the observed product attributes? A plausible scenario was further proposed,155 which invoked a facile isomerization process occurring between the two structurally distinct transient resonance states in the transition state region. And the rate of isomerization (or conformational change) must be faster than the rate of decomposition of resonant complexes.

Sighting reactive resonances in other polyatomic reactions have subsequently been reported, both experimentally36,159,160 and theoretically.161–167 What makes the reactive resonance special, compared to the other resonances, is that it is quasi-bound even along the reaction coordinate on a totally repulsive Born–Oppenheimer PES.3,36 Its very existence – no matter how fleeting it is – or the trapping mechanism, which requires attractive forces, is dynamical in origin. In many ways, it behaves like a stable, ordinary molecule with all vibrational degrees of freedom approximately assignable. From this view, it may not be too surprising that the observed resonance phenomena are often accompanied by various competing intra-molecular processes within the resonant complex, such as the isomerization in this case155 or the intramolecular vibrational redistributions in the F/Cl + CH4 reactions.159,160 Clearly, this is an intrinsic dynamics aspect unique to polyatomic reactions and beyond the prototypical atom + diatom reaction.36 A deeper understanding of dynamical resonance in polyatomic reactions will not only add an entirely new dimension to the concept of reactive resonance, but also provide an illuminating roadmap to bridge many of the well-established concepts in unimolecular dynamics to bimolecular reactivity.

3.4 Reactive rainbow

The rainbow phenomenon has long been established in elastic collisions of particles1 and in rotational energy transfer processes.168–170 In elastic collisions the interplay of the attractive and repulsive forces deflects the collisional trajectories from a range of impact parameters (b) into the same scattering angle θ, resulting in a constructive interference between the scattering amplitudes from different paths and consequently yielding a buildup of the scattering intensity or a bulge near the rainbow angle. In contrast, the rotational energy transfer processes involve two scattering variables, i.e., b and γ (the impact angle of the rotor axis with respect to the initial relative velocity vector k), as well as two observables, in θ and Δj (the change of the rotational states). Therefore, a rotational rainbow can in principle occur either from a potential well – a potential rainbow as in the elastic case – or from the orientation of the rotor – an orientation rainbow. As the rotational inelasticity is necessarily induced by the anisotropic interactions, an orientation rainbow is expected to prevail. Indeed, many of the key features observed in rotational rainbow can be understood by a simple hard-ellipsoid model,168–170 in which the attractive potential is entirely neglected and the rotational rainbow arises from trajectories of different b and γ accumulating into the same scattering θ or in certain Δj. The significance of observing these scattering rainbows lies in the fact that the rainbow characteristics are very sensitive to the interaction potential, whose key features – the well depth and location for elastic rainbow, and the shape of the ellipsoid or the anisotropy of the interaction for rotational rainbow – can often be captured and well-modeled from the observed rainbow features.

A recent report on the F + CH3D(v = 0) → CH2D(00) + HF(v = 3) reaction discovered a similar bulge-feature in the product pair-correlated angular distribution as the elastic/rotational rainbow scatterings.171Fig. 19 summarizes the observation at three different Ec's. The experiments were performed by detecting the ground vibrational states of CH2D(00) in two different ways: either by scanning the probe laser wavelength to detect all rotational states or by fixing the wavelength at the REMPI-peak to interrogate only few lower rotational states of CH2D(00). The concomitantly formed HF distributions were then revealed from the CH2D state-tagged images. Both modes of operation yielded nearly identical distribution (the black curves) including the feeble shoulder near 50° at Ec = 4.3 kcal mol−1, indicative of the independency of the probed rotational distributions of the CH2D(00) state. We note in passing that the shoulder feature would have escaped from being sighted, had one summed up all CDCSs, i.e., in terms of just the CH2D(00) state-resolved angular distribution – not in the product-pair manner.

image file: c7cs00601b-f19.tif
Fig. 19 Correlated angular distributions in the F + CH3D → HF(v = 3) + CH2D(00) reaction by two different ways of probing the CH2D(00) products, λ-peak (upper) and λ-scan (lower). The black curve is for the total component, and the red (blue) curve is for the faster (slow) speed component. Note the distinct bulges of the faster-speed component of HF(v = 3) at Ec = 4.3 kcal mol−1, as indicated by the red arrows near the scattering angle of 50°. The bulges were detected under both probes – the low rotational excitation of CH2D(00) for λ-peak and the entire rotational distribution of CH2D(00) for λ-scan, suggesting that this abnormal angular structure is associated with only the low-j states of HF(v = 3) products. Reproduced from ref. 171 with permission from American Chemical Society, copyright 2016.

Therefore, the observed shoulder must reflect the rotational-specific angular distributions of the HF(v = 3) coproduct. The image resolution was unfortunately not sufficient to resolve the individual rotational state. Nonetheless, as shown in Fig. 19, when one partitioned the recoiled speed distribution for HF(v = 3) into two parts – a fast and a slow component, a distinct “bulge” feature in the correlated angular distributions appeared only for the faster one at Ec = 4.3 kcal mol−1. By virtue of energy conservation, the fast (slow) component corresponds to rotationally colder (warmer) HF(v = 3) products. The puzzling questions are: Why is the bulge occurring only for low-jHF states? Why is it dependent on the Ec? And what is its mechanistic origin?

A systematic investigation led to the proposition that the observed bulge could be a manifestation of the reactive rainbow phenomenon.171 Further heuristic considerations of the relevant kinematics suggested that three conditions need to be met for this phenomenon to occur: (1) the reaction possesses a vibrationally adiabatic well, (2) the reactive scattering behaves elastically for certain specific product channels, and (3) the collisional energy should be high enough, rendering significant reactivity from the large-b collisions. In retrospect, similar “bulge” structures were noted earlier in the isotopically analogous F + CD4 and F + CHD3 reactions;143,172 they were termed “rainbow-like” features at the time, but without further investigations.

What makes the above proposition intriguing is that the inferred rainbow (or bulge) is for a bond breaking and forming event. And, by analogy to the other isotopically substituted reactions of F + CH4 (ref. 160) and CHD3 (Section 3.3), the presence of reactive resonances in F + CH3D is anticipated.36 If the observed bulge is indeed theoretically proven to be a rainbow, then it may open a new window to probe the adiabatically dynamic well that supports reactive resonances. So far, all scattering experiments aimed at detecting reactive resonance are performed at low Ec (near the threshold) with the undulatory structures in ICS and/or DCS as the possible signatures for quasi-bound metastable states.36 By way of contrast, the presence of a dynamic well could manifest itself as rainbow scattering instead at significantly higher Ec and even if the quasi-bound resonance states lie below the reactant asymptote, which will render the direct access to those states by low-energy collisions impossible, no matter how low. Moreover, detecting the reactive rainbow could be particularly appealing for larger chemical systems, for which the presence of numerous, transient resonances (instead of a few isolated resonance states in the simple atom + diatom system) is probably the norm.36,165 Owing to the lifetime broadening, those transient resonance states are expected to be heavily overlapped in energy. In terms of reaction dynamics, it might be more informative to directly characterize the properties of the dynamic well, rather than trying to resolve the overlapping, broad resonance states.

The study of F + CH3D reaction is the first experimental attempt to identify and characterize the rainbow phenomena in any chemical reaction. Unfortunately, at present it remains unclear as to how to quantitatively retrieve the key properties of the underlying dynamic potential well from the observed “bulge” structure. Further theoretical developments in establishing the correlation between the well property and bulge structure – similar to the elastic and rotational rainbow cases – will be particularly insightful in guiding future experiments.

3.5 Mode correlation between the polyatomic product pairs

So far, nearly all reported product pair-correlation experiments are of the atom + CH4 (and isotopologues) reactions, for which the products are methyl radical + HX (X: atom). The methyl radical product has multiple vibrational modes, offering the opportunity to study the mode-specific chemistry. The only exception is a series of reports on the reactions of OH/OD + CH4/CD4/CHD3.173–175 In this seven-atom reaction, both products, water and methyl, can be formed in different vibrational modes. Recall that different vibrational modes of a molecule signify distinct concerted motions of the constituent atoms. If one now envisions the transition state as a collective of motion of all atoms in the chemically strong interaction region, then the correlation between the internal motions of the coincident product pairs – the mode correlation – could be the imprint of the atomic motions in the transition state region, thus lightening the paths by which the chemical transformation occurs.

Fig. 20 exemplifies two raw images of the (a) CD3(v = 0) and (b) CD3(v2 = 2) products from the OH + CD4 → HOD + CD3 reaction at Ec = 16.2 kcal mol−1, where the notation of v2 denotes the umbrella vibrational mode of CD3 products.174 Two images display distinct and complicated patterns. The resultant product speed distributions, along with another two at lower Ec, are presented in Fig. 20(c). The state labeling in the figure corresponds to the quantum number of the three HOD vibrational modes of (vODvbendvOH) with the fundamental frequencies of (2720, 1400, 3360) in cm−1. Several observations are worth noting. (1) The correlated HOD products are formed almost exclusively with excitations in the OD stretch and its combination mode with bend. The absence of OH stretch-excited HOD, such as (001) and (002), implies that the old (reactant) OH bond acts as a spectator in the reaction, in good accordance with a recent theoretical result that the OH bond length remains unchanged throughout the course of the reaction.176–179 (2) The correlated distribution of HOD in concomitance with the ground-state CD3(v = 0), the upper panels in (c), is dominated by the overtone excitation of the OD stretching mode (200) and followed by the excitations in (100) and (110). This general pattern compares favorably to the HOD state distribution in the simpler OH + D2 → HOD + D reaction reported at lower Ec = 6.6 kcal mol−1,25 indicative of the spectator nature of the CD3-moiety when formed in the ground vibrational state. (3) When CD3(v2 = 2) was probed, however, the correlated HOD distribution changes dramatically. The dominant state shifts downward to (100). Similar anti-correlation in the quantum excitation of the paired product-vibrators was also observed for DF + CD3 in the F + CD4 reaction.143,144 And (4) more remarkable is the significant increase in the excitation of the combination-mode (110) of HOD coproducts in concomitance with CD3(v2 = 2) – a clear demonstration of the mode-correlation of the product pairs. In other words, the preferred mode-excitation of one product (the HOD here) depends on the specific mode-excitation of the coincidently formed coproduct (CD3). Unlike the stretching vibrations, both the CD3 umbrella (v2) and the HOD bending motions are nonlocalized and involve the concerted amplitudes of three or more atoms. We surmised that the observed mode-correlation could be the imprint of the distinct collective motions of all atoms in the vicinity of the transition state region, leading to the different product pairs.

image file: c7cs00601b-f20.tif
Fig. 20 Two representative time-sliced raw images of the (a) CD3(v = 0) and (b) CD3(v2 = 2) products from the OH + CD4 → CD3 + HOD reaction at Ec = 16.2 kcal mol−1. The probed REMPI bands are labeled and the Newton diagram overlaid. The forward/backward background appearing at two beam velocities was experimentally verified and discarded in data analysis. (c) Four P(u) distributions in the OH + CD4 → CD3(0 v2 0 0) + HOD(vODvbendvOH) reaction are exemplified. The upper panels are for the ground-state CD3 product and the lower two for the first overtone of umbrella-mode (v2) excited CD3. The dotted line gives the contribution from each labeled level and the solid line represents the resultant fit. Distinct patterns are readily observed for the two different CD3 states, whereas only minor differences are noted for the same CD3 state at different collision energies. Reproduced from ref. 174 with permission from American Chemical Society, copyright 2005.

3.6 Product rotational-mode specific reactivity

All the above examples, as well as most of the reports on the methane reactions, have been focused on interrogating only the vibrational motions of the methyl products. Because of the signal-to-noise consideration, the Q-head of a REMPI band of the methyl radical was universally exploited to acquire the image, and often by fixing the probe laser wavelength at the peak of the Q-head for convenience. It was noticed early on that different modes of operation – fixing the probe laser wavelength at the Q-peak or scanning the wavelengths over the entire Q-head – actually yielded subtly different results, in particular on the resulting vibrational branching ratios of the coproducts.154,155 A few systematic studies have since then been devoted to shedding more light on such rotational probe effects.180,181

Fig. 21 (top) presents a (2 + 1) REMPI spectrum of the vibrational ground state of CD3 products in the reaction of F + CD4 → CD3(v = 0, N) + DF(v) at Ec = 5.37 kcal mol−1.180 Clearly, the Q-head dominates the spectrum, and the intensities of the rotationally resolved O, P, R, and S branches are merely a few percentages of the Q-head intensity. Despite that, the N-resolved images could still be obtained, as exemplified in the bottom-left panel. Fig. 21 (bottom, right) summarizes the dependence of the correlated DF vibrational branching on the N-quantum number of the probed CD3(v = 0, N) products.181 In view of the comparably small rotational constant (B ≅ 4.8 cm−1) and a relatively narrow range of N-distributions of CD3(v = 0) products,182 such dramatic N-dependency is quite astonishing. Similarly, distinct N-dependent angular distributions of the DF(v) coproducts were noted (not shown).181 Since the rotational distribution of CD3(v = 0) is dominated by the low N-states in F + CD4 and fixing the probe laser wavelength at the peak of the Q-head preferentially samples the low N-states (N ≅ 1–6),181 the rotational probe-bias effect in this case turned out to be rather minor. Nevertheless, this detailed study serves as a cautious note for future studies of other reactions.

image file: c7cs00601b-f21.tif
Fig. 21 (top) REMPI spectra in the vicinity of the origin band 000 of the CD3 products from the F + CD4 reaction at Ec = 5.37 kcal mol−1. A circularly polarized light was used to suppress the Q-head intensity by more than ten-fold,180,181 which otherwise (when a linearly polarized laser was used) overwhelms the low-N features of the other rotational branches. (lower, left) Four raw images of CD3(v = 0, N) from the F + CD4 reaction. The probed rotational transitions, as indicated in the upper spectra, are S(1)/R(4), R(3), O(7), and O(11) for panels (a), (b), (c) and (d), respectively. (lower, right) Dependence of the correlated DF vibrational branching on the rotational quantum number N of the CD3(v = 0) products. Modified from ref. 181 with permission from American Institute of Physics, copyright 2006.

In contrast to the above example, the same rotational probe-bias can sometimes end up exerting enormous effects on interpreting the result. We encountered such a case in the study of the Cl + CHD3(v1 = 1) reaction. One of the aims of that study is to quantify the rate promotion by the reactant's vibrational excitation. The experiment exploited an infrared (IR) laser to prepare CHD3 with one-quantum excitation of the C–H stretching mode (v1 = 1), and compared the resultant stretch-excited reactivity to that of the ground-state reaction (i.e. IR-off) using the imaging technique.183 At a fixed Ec, vibrationally enhanced reactivity was observed. Similar results were found in other isotopically analogous methane + Cl reactions.184,185 The picture changed, however, when the efficacies of reactant's vibration versus translation were compared on the basis of the equivalent amount of total energy. At low Ec (≲4 kcal mol−1), translation is more effective in promoting the reaction than stretch-excited vibration motion. At higher Ec, the rate-enhancement factor by CH stretching excitation is not mode specific, being comparable to that obtained by adding the same amount of the translational energy184 – contrary to what one would have anticipated from Polanyi's rules for this late-barrier reaction.186

This surprising result has been under theoretical scrutiny since then.187,188 A QCT calculation on a highly accurate ab initio PES showed nearly quantitative agreement with experiment.187 Later, a reduced-dimensionality quantum dynamics (QD) calculation was performed on the same PES, yielding preferential vibrational enhancement factors of about four-fold larger than the experimental results; in other words, the approximate quantum result qualitatively corroborates Polanyi's rules.188

To reconcile the above QD theory–experiment discrepancy, it was noticed that the theoretical calculations included all rotational states of CD3(v = 0) products,187,188 whereas the experimental results referred to CD3(v = 0, low-|NK〉) products for fixing the probe laser wavelength at the peak of the Q-head.183 If that is the source of discrepancy, then it implies that the stretch-excited reaction must yield rotationally warmer CD3(v = 0) products than the ground-state reaction. Shown in Fig. 22 (left) are the CD3(v = 0) REMPI spectra over the Q-head at three different Ec's.189 Indeed, the IR-on spectra are more red-shaded (i.e., more rotational excitation) than the IR-off spectra. Repeating the product image experiment again by scanning the probe laser wavelength over the entire Q-head yielded the vibrational enhancement factor in line with the approximate QD result.189 This shows how sensitive and significant the product rotational-probe effect can be in this reaction, which would lead to an erroneous conclusion183 if not properly accounted for.

image file: c7cs00601b-f22.tif
Fig. 22 (left) (2 + 1) REMPI spectra, IR-off (black) and IR-on (red) of the CD3(v = 0) products from the Cl + CHD3 reaction at three Ec. The IR-on spectra appear more red-shaded than the IR-off spectra; the vertical blue-dashed line is to guide the eyes. Reproduced with permission from ref. 189. (right) Dependency of relative reactivity on the rotational state of CHD3(v1 = 1). At each Ec, the reactivity of the rotational ground state, |00〉 excited via the P(1) branch, is set to unity. The error bar represents the statistical uncertainty from repeated experiments, encompassing the propagated errors from the IR-excitation efficiency measurements. The IR-excited rotational states are labeled by |JK〉. Note the higher reactivity with increasing J and the change of the relative reactivity between R(0) and Q(1) for Ec < 2 kcal mol−1 – reversing the K-propensity. Reproduced from ref. 191 with permission from American Chemical Society, copyright 2015.

3.7 Rotational mode specificity of the reactant

Interestingly, the quantitative agreement just mentioned actually raised another intriguing question. The initial rotational state in the theoretical calculations is the rotational ground state |JK〉 = |00〉,187,188 whereas experimentally the R(1) branch of the CHD3(v1 = 1 ← 0) transition was used, resulting in the rotational states of |JK〉 = |20〉 and |2 ± 1〉 for the vibrationally excited CHD3(v1 = 1) reactants.183,189 In other words, the comparison between experiment and theory was made on a different footing. How will different rotation states of the reactant affect the reactivity?

This question then led to a series of systematic investigations by exploiting several different rotational branches in preparing the vibrationally excited CHD3(v1 = 1) reactants.190,191Fig. 22 (right) summarizes the dependency of the Cl + CHD3(v1 = 1) reactivity on the initial rotational states |JK〉. A marked reactant's rotational-mode specificity is clearly seen. In particular, the state of |20〉 + |2 ± 1〉 (the initial states in experiments183,189) is two-fold more reactive than the rotational ground-state |00〉 (the initial state in theoretical calculations187,188), implicating that the apparent theory–experiment agreement on the vibrational enhancement factor presented in Section 3.6 is fortuitous.

More intriguing is the other experimental finding that despite the distinct reactivity dependency on the initial rotational states (Fig. 22, right), the more detailed distributions are essentially invariant, as shown in Fig. 23 for the product speed distributions.191 These observations seem to defy the conventional wisdom that a measurement with less averaging should reveal more of the dynamic details, making the subtle difference more apparent. A “loss-of-memory” mechanism was then postulated to rationalize these unexpected results.191,192 The mechanism invokes a stepwise process: the initial step is governed by the capability of reactants to attain the transition state, which depends on the initial rotational state. Once the barrier is surmounted, however, the memory of the initial rotation is lost and the product distributions are primarily controlled by the ensuing transition-state dynamics – the second step.

image file: c7cs00601b-f23.tif
Fig. 23 The CD3(v = 0) product speed distributions at Ec from 1 kcal mol−1 to 6 kcal mol−1. At each Ec, the results of four different rotational branches are normalized to the same total intensities. On energetic grounds, the slow and fast peaks correspond to the HCl(v = 1) and HCl(v = 0) coproducts, respectively. Obviously, little reactant rotational-state dependencies are discernible. Reproduced from ref. 191 with permission from American Chemical Society, copyright 2015.

3.8 Controlling the collisional geometry – stereochemistry

Although the “loss-of-memory” mechanism seems reasonable in accounting for the observed rotational-mode specificity of reactants, it was inferred on the basis of the scattering results with unpolarized (or the randomly distributed) reactants. Since the rotational-mode specificity is conceived to be intimately related to the stereo-specific reactivity – the two specificities can be regarded as the two sides of a coin83,193 – will the inferred mechanism be the full story?

A series of more tale-telling polarization scattering experiments casted some doubts on the relevance or validity of the above loss-of-memory mechanism.194–198 The new set of experiments not only selected the ro-vibraionally excited reactant CHD3(v1 = 1, |JK〉), but also controlled the collisional geometry by exploiting the polarization of the IR excitation laser. After a rather elaborated data acquisition and analysis,195,199 a complete set of polarization-dependent differential cross sections in a product pair-correlated manner were obtained for the first time for any chemical reaction. The significance of those experiments lies in the fact that even the (conventional) state-to-state differential cross section still involves considerable averaging over an entire range of collisional impact parameters and the orientation distribution of the bond axis under attack. Such seemingly inevitable averaging is what Herschbach called the “forbidden fruit” back in 2006.200 The knowledge of a complete set of polarization-dependent differential cross sections might be the key step to unfold such averaging.196 Here, to shed more light on the above loss-of-memory mechanism, we shall just focus on two particular and chemically more intuitive collision geometries.

It has been shown194,196 that the experimental geometry with the IR-polarization direction εIR lying parallel to k physically corresponds to an end-on (‖) attack in the center-of-mass collision frame. On the other hand, when k is parallel to the IR propagation direction, the IR-aligned C–H bond will necessarily lie in a plane perpendicular to k, i.e., a side-on (⊥) attack.196Fig. 24 (upper panels) presents, under these two polarization configurations, the raw difference images (i.e., with the contributions of the ground-state reaction signals being subtracted) of the CD3(v = 0) products from the Cl + CHD3(v1 = 1, |10〉) reaction at Ec = 8.6 kcal mol−1.197 The sharp forward (0°) peak in the inner ring with a slower speed is ascribed, on energetic grounds, to the concomitantly formed HCl(v = 1) products, whereas the outer ring to HCl(v = 0). The general appearances of the two images are strikingly different. Not only the forward-peak intensity of HCl(v = 1) appears extremely sensitive to the reagent alignment, but also the angular distribution of HCl(v = 0) shows a dramatic change from backward scattering (the ‖ approach) to sideways dominance (the ⊥ attack). Such a strong variation on collisional geometries attests enormous steric effects in this reaction. Similar stereo-specificity has also been observed at lower Ec.194–196,199

image file: c7cs00601b-f24.tif
Fig. 24 Imaging the dynamical outcomes in the reaction of Cl + CHD3(v1 = 1) at Ec = 8.6 kcal mol−1. The excited CHD3(v1 = 1) reactants were aligned via two different rotational branches and each with two distinct collisional geometries. Presented are the raw difference (with the IR-off signals subtracted) images of the probed CD3(00) products for the IR polarization axis (εIR) or the reactive C–H bond being directed either along (left, the ‖-geometry) or perpendicular (right, the ⊥-geometry) to the scattering axis k. The forward scattering angle θ = 0° denotes the initial CHD3 beam direction in the center-of-mass coordinate system. The sharp forward peak in the inner ring with a slower speed is assigned to the HCl(v = 1) product channel, whereas the outer ring is ascribed to HCl(v = 0). Modified from ref. 197 with permission from American Institute of Physics, copyright 2016.

However, when the Q(1) branch transition (Fig. 24, lower panels), instead of R(0), was used to excite the CHD3(v1 = 1) reactants, a very different picture emerged: the product images are much less sensitive to the IR polarization direction, indicative of a substantially smaller steric effect.197 IR-excitations by the two rotational branches, R(0) and Q(1), correspond respectively to the reactions of Cl + aligned-CHD3(v1 = 1, |10〉) and Cl + aligned-CHD3(v1 = 1, |1 ± 1〉). In other words, the two excited reactants have the same J = 1 but differ in how they rotate in the molecule-fixed frame: a tumbling motion for K = 0 and a spinning rotation for K = ±1. Quantum mechanically, these two types of rotation yield distinct C–H bond axis distributions – even though the C–H bond axis is preferentially aligned along εIR in both cases for being a parallel band – in the molecule-fixed frame and subsequently in the space-fixed (or the scattering) frame.197,198 As a result, whereas the unpolarized speed and angular distributions of the two reactions are nearly identical, their respective anisotropic distributions are distinct, exhibiting vastly different K-dependent stereo-specificity.197 Hence, the origin of the aforementioned loss-of-memory phenomenon (Section 3.7) could be traced to the stereo-averaging over all possible collisional geometries in an experiment with unpolarized reagents – instead of the memory-loss of the initial K-selection as originally conjectured.191,192

The message from this series of studies of the benchmark Cl + CHD3(v1 = 1) reaction (Sections 3.7 and 3.8) should be loud and clear: after all, a more detailed measurement indeed uncovers finer dynamics – one just needs to go one step further, i.e., beyond the state-to-state level in this case, by examining the state-resolved stereo-requirement. Last but not least, as said once,3 “In a sense, the close comparison between experiment and theory marks just the beginning of physical understanding.” The “correct” mechanistic interpretation of the observed results, either experimentally or theoretically, can be challenging and sometimes rather elusive, at least not as unambiguous as one might have initially conceived.

4. Conclusions and outlook

We have reviewed recent advances in our understanding of polyatomic reaction dynamics, based on improvements in the experimental approaches used for the measurements of reactive DCSs. The attentive readers may notice that using the soft-ionization, universal CMB technique, this review covers only the reactions of O(3P) with various, systematically selected organic molecules, and for pair-correlated studies only the reactions of methane with different atoms/radicals are touched upon. Despite these rather limited scopes, the richness of chemistry is already clearly manifested and many interesting findings are vividly unveiled with significant, new insights being gained. We can partition the current challenges and achievements in polyatomic reaction dynamics into two main streams:

(i) Polyatomic reactions that cannot be studied at the state-resolved level, such as those involving more than 5–6 atoms and which exhibit a large variety of product channels, only partially known, such as the reactions discussed in Section 2. When you study an elementary polyatomic reaction that involves complex molecular/radical reactants and products and can have many competitive product channels, you address different questions than when you study a simpler reaction at the state-resolved level. These question are:

(a) What are the reaction products?

(b) What is their dynamics of formation?

(c) What are the branching ratios of all significant channels?

For this type of reactions the CMB studies highlighted in Section 2 represent the current state-of-the-art; in this case, critical has been the implementation of soft ionization detection.

We can conclude that the classic CMB technique with soft EI69,74–76 or PI55,77–81 MS detection and TOF analysis has recently truly become universal, featuring both high power and versatility. Indeed, using this technique it is possible to tackle nearly all kind of bimolecular neutral–neutral reactions, including reactions between two radicals, because you can probe all possible product channels on the same footing, which is essential, for instance, to derive branching ratios.

The work on the O(3P) reactions with the prototype two-C and three-C containing unsaturated hydrocarbons discussed here is expected to facilitate the elucidation of the reaction mechanisms also in systems involving larger (having four or more carbon atoms) alkynes, alkenes, and dienes (cumulenes) as well as conjugated dienes (such as 1,3-butadiene). Besides deepening our understanding of chemical reactivity, these studies offer an important bridge between CMB dynamics and thermal kinetics, and provide valuable information for improving combustion and astrochemistry models.

It will certainly be interesting and useful to extend CMB studies of atomic oxygen reactions to higher unsaturated hydrocarbons, such as 1-pentene and 1-hexene, including cyclic ones (such as cyclopentene and cyclohexene), and also to aromatics (such as benzene, toluene, phenol, anisole, etc.) and possibly hetero-aromatics (such as pyridine and pyrimidine, which are prototypes of nucleobases). Other classes of polyatomic reactions (both multichannel and one-channel) involving different radical reactants can be studied as well using this approach. For instance, soft PI with tunable synchrotron VUV radiation has recently permitted to explore, by measuring TOF spectra and photoionization-efficiency spectra in CMB experiments, the formation of polyynes HC2n+2H (n = 1–4) (HC4H, HC6H, HC8H, and HC10H) (observed in interstellar/circumstellar media and combustion processes) from the H-displacement reactions of C2nH radicals with C2H264 and of C2n+1H2 species (n = 1–4) (C3H2, C5H2, C7H2, and C9H2), which are important intermediates in the syntheses of large carbonaceous molecules, from the H-displacement reactions of CH, C3H, C5H, and C7H radicals with C2H2.61

Regarding future developments in the studies of multichannel polyatomic reaction dynamics, we should mention the great potential of complementary new detection techniques, such as those based on tunable VUV free electron laser sources201 for soft ionization in CMB/MS experiments, that should permit gaining significantly in VUV photon flux with respect to the current third generation synchrotron light sources81 and fixed VUV table-top lasers,67 thus allowing for greater detection efficiency. Complementary contributions can also be expected from techniques that are best suited for simple systems, such as the H-atom and O-atom Rydberg tagging technique, which is highly specific and sensitive to the H(D) forming channels202 and O(3Pj) products,203 and the REMPI/ion imaging technique72,143 if suitable and efficient REMPI schemes will become available for relatively simple polyatomic molecules/radicals, something which is within reach. This would allow one to deepen further the understanding of the dynamics of some of the channels of a complex multichannel reaction.

(ii) Polyatomic reactions that can be probed at the state-to-state level. The cases discussed in Section 3 represent a few illuminating examples and constitute the current state-of-the-art. These works will set the stage for the next step in the investigation at the state-resolved level of a polyatomic chemical reaction. Crucial is the capability of obtaining pair-correlated information, which is a new concept and something that is not needed for a 3-atom reaction. To achieve this the intuitively simple yet powerful experimental methodology discussed in Section 3 has proven as the best and most suitable approach so far.

The prerequisite to carry out the product pair-correlation measurement is a sensitive laser spectroscopic detection scheme for one of the reaction products. All pair-correlated measurements up to now have been limited to reactions with methane (and its isotopologues) by probing the methyl products ever since the first demonstration of this method in 2003.143 To further advance our basic understanding of polyatomic reaction dynamics, it is essential to go beyond the methane-family reactions. In that regard, the most pressing experimental challenge is to explore and develop the suitable REMPI scheme to detect other species (many of them are spectroscopically known) for different classes of reactions. Conceivably, the reaction complexity will increase and the multiple product channels likely occur. Yet it might offer the opportunity to address the questions of site specificity and the effects of the functional group on the pair-correlated reactivity. Such information can complement nicely the more global results obtained by the universal CMB approach as illustrated in Section 2, and thus deepen our fundamental understanding of more complex chemical reactions.

We wish to close this review by mentioning the successful application of the ion imaging technique to the investigation in crossed beams, at an unprecedented level of detail, also of the important class of ion–molecule204 and ion–radical205 bimolecular reactions. In the field of reaction dynamics a new area of rising interest is that of cold reactive collisions (i.e., at very low collision energies). This usually involves CMB experiments with very small crossing angles of the two reactant beams, tuned to similar velocities, and REMPI detection,20 or CMB experiments with Stark or Zeeman decelerated beams, using ion imaging detection, which have proven very successful for high-resolution inelastic scattering studies,206,207 but that are expected to be extendable to reactive scattering of suitable reactant molecular/radical species, such as NO, NH3 and OH. Another interesting prospect is the study of the reaction dynamics of selected molecular conformers with atoms/radicals in crossed beams, following on the demonstration of very significant effects in the reaction of supersonic beams of spatially separated (by strong electric fields) 3-aminophenol conformers with cold Ca+ ions (velocity and spatially defined in a Coulomb crystal at the center of an ion trap).208 Finally, roaming reactions are also a topic of great interest, after the clear observation of pronounced roaming effects in photodissociation processes and unimolecular reactions.209 Although so far a clear search for roaming effects in bimolecular reactions has eluded clear direct experimental observation (a first example is given by the addition–elimination reaction of Cl atoms with butenes210), we may expect that with the current and future progress in CMB methods and detection techniques the observation of roaming dynamics in reactive scattering may become within reach in the near future.

Conflicts of interest

There are no conflicts of interest to declare.


KL acknowledges the funding from Academia Sinica and the Minister of Science and Technology of Taiwan (MOST-105-2113-M-001-019-MY3). PC acknowledges financial support over the years by the Italian “Ministero Istruzione, Università e Ricerca – MIUR” (FIRB and PRIN projects) and current funding from the ‘‘Fondazione Cassa Risparmio Perugia – Italy” (Project code: 2015.0331.021 Scientific and Technological Research) and the University of Perugia (‘‘Fondo Ricerca di Base 2014”).


  1. R. D. Levine, Molecular Reaction Dynamics, Cambridge University Press, 2005 Search PubMed.
  2. L. Schnieder, K. Seekamp-Rahn, J. Borkowski, E. Wrede, K. H. Welge, F. J. Aoiz, L. Banares, M. J. D’Mello, V. J. Herrero, V. Saez Rabanos and R. E. Wyatt, Science, 1995, 269, 207–210 CAS.
  3. K. Liu, Annu. Rev. Phys. Chem., 2001, 52, 139–164 CrossRef CAS PubMed.
  4. P. Casavecchia, Rep. Prog. Phys., 2000, 63, 355–414 CrossRef CAS.
  5. P. Casavecchia, K. Liu and X. Yang, in Tutorials in Molecular Reaction Dynamics, ed. M. Brouard and C. Vallance, Royal Society of Chemistry Publishing, Cambridge, UK, 2010, ch. VI, pp. 167–213 Search PubMed.
  6. S. A. Harich, D. Dai, C. Wang, X. Yang, S. D. Chaok and R. T. Skodje, Nature, 2002, 419, 281–284 CrossRef CAS PubMed.
  7. H. Gao, M. Sneha, F. Bouakline, S. C. Althorpe and R. N. Zare, J. Phys. Chem. A, 2015, 119, 12036–12042 CrossRef CAS PubMed.
  8. D. M. Neumark, A. M. Wodtke, G. N. Robinson, C. C. Hayden and Y. T. Lee, J. Chem. Phys., 1985, 82, 3045–3066 CrossRef CAS.
  9. X. Yang, Phys. Chem. Chem. Phys., 2011, 13, 8112–8121 RSC ; and refs. therein.
  10. M. Qiu, Z. Ren, L. Che, D. Dai, S. A. Harich, X. Wang, X. Yang, C. Xu, D. Xie, M. Gustafsson, R. T. Skodje, Z. Sun and D. H. Zhang, Science, 2006, 311, 1440–1443 CrossRef CAS PubMed.
  11. M. Alagia, N. Balucani, L. Cartechini, P. Casavecchia, E. H. van Kleef, G. G. Volpi, F. J. Aoiz, L. Bañares, D. W. Schwenke, T. C. Allison, S. L. Mielke and D. G. Truhlar, Science, 1996, 273, 1519–1522 CAS.
  12. D. Skouteris, D. E. Manolopoulos, W. Bian, H.-J. Werner, L.-H. Lai and K. Liu, Science, 1999, 286, 1713–1716 CrossRef CAS PubMed.
  13. X. Wang, W. Dong, C. Xiao, Z. Ren, D. Dai, X. Wang, P. Casavecchia, X. Yang, B. Jiang, D. Xie, D. H. Zhang, H.-J. Werner and M. H. Alexander, Science, 2008, 322, 573–576 CrossRef CAS PubMed.
  14. S. A. Lahankar, J. Zhang, K. G. McKendrick and T. K. Minton, Nat. Chem., 2013, 5, 315–319 CrossRef CAS PubMed.
  15. X. Liu, J. J. Lin, S. Harich, G. C. Schatz and X. Yang, Science, 2000, 289, 1536–1538 CrossRef CAS PubMed.
  16. N. Balucani, L. Cartechini, G. Capozza, E. Segoloni, P. Casavecchia, G. G. Volpi, L. Banares, F. J. Aoiz, P. Honvault and J.-M. Launay, Phys. Rev. Lett., 2002, 89, 013201 CrossRef PubMed.
  17. N. Balucani, G. Capozza, L. Cartechini, A. Bergeat, R. Bobbenkamp, P. Casavecchia, F. J. Aoiz, L. Bañares, P. Honvault, B. Bussery-Honvault and J.-M. Launay, Phys. Chem. Chem. Phys., 2004, 6, 4957–4967 RSC.
  18. Z. Shen, H. Ma, C. Zhang, M. Fu, Y. Wu, W. Bian and J. Cao, Nat. Commun., 2017, 8, 14094 CrossRef CAS PubMed.
  19. S.-H. Lee and K. Liu, J. Phys. Chem. A, 1998, 102, 8637–8640 CrossRef CAS.
  20. M. Lara, S. Chefdeville, K. M. Hickson, A. Bergeat, C. Naulin, J.-M. Launay and M. Costes, Phys. Rev. Lett., 2012, 109, 133201 CrossRef PubMed.
  21. F. J. Aoiz, L. Banares and V. J. Herrero, J. Phys. Chem. A, 2006, 110, 12546–12565 CrossRef CAS PubMed ; and references therein.
  22. N. Balucani, G. Capozza, F. Leonori, E. Segoloni and P. Casavecchia, Int. Rev. Phys. Chem., 2006, 25, 109–163 CrossRef CAS.
  23. D. H. Zhang and H. Guo, Annu. Rev. Phys. Chem., 2016, 67, 135–158 CrossRef CAS PubMed ; and references therein.
  24. M. Alagia, N. Balucani, P. Casavecchia, D. Stranges, G. G. Volpi, D. C. Clary, A. Kliesch and H.-J. Werner, Chem. Phys., 1996, 207, 389–409 CrossRef CAS.
  25. B. R. Strazisar, C. Lin and H. F. Davis, Science, 2000, 290, 958–961 CrossRef CAS PubMed.
  26. C. Xiao, X. Xu, S. Liu, T. Wang, W. Dong, T. Yang, Z. Sun, D. Dai, X. Xu, D. H. Zhang and X. Yang, Science, 2011, 333, 440–442 CrossRef CAS PubMed.
  27. J. H. Wang, K. Liu, G. C. Schatz and M. T. Horst, J. Chem. Phys., 1997, 107, 7869–7875 CrossRef CAS.
  28. A. Laganà, E. Garcia, A. Paladini, P. Casavecchia and N. Balucani, Faraday Discuss., 2012, 157, 415–436 RSC.
  29. J. Li, J. Chen, D. H. Zhang and H. Guo, J. Chem. Phys., 2014, 140, 044327 CrossRef PubMed.
  30. A. M. Zolot and D. J. Nesbitt, J. Chem. Phys., 2008, 129, 184305 CrossRef PubMed.
  31. H. Song, S.-Y. Lee, Y. Lu and H. Guo, J. Phys. Chem. A, 2015, 119, 12224–12230 CrossRef CAS PubMed.
  32. For a collection of recent advances, see for example, Special Issue: Dynamics of Molecular Collisions XXV: Fifty Years of Chemical Reaction Dynamics, J. Phys. Chem. A, 2015, 119, 11949–12586.
  33. T. Yang, L. Huang, T. Wang, C. Xiao, Y. Xie, Z. Sun, D. Dai, M. Chen, D. Zhang and X. Yang, J. Phys. Chem. A, 2015, 119, 12284–12290 CrossRef CAS PubMed.
  34. T. Yang, J. Chen, L. Huang, T. Wang, C. Xiao, Z. Sun, D. Dai, X. Yang and D. H. Zhang, Science, 2015, 347, 60–63 CrossRef CAS PubMed.
  35. X. Yang and D. H. Zhang, Acc. Chem. Res., 2008, 41, 981–989 CrossRef CAS PubMed.
  36. K. Liu, Adv. Chem. Phys., 2012, 149, 1–46 CAS.
  37. Z. Ren, Z. Sun, D. H. Zhang and X. Yang, Rep. Prog. Phys., 2017, 80, 026401 CrossRef PubMed.
  38. K. Liu, Phys. Chem. Chem. Phys., 2007, 9, 17–30 RSC.
  39. H. Pan, J. Yang, Q. Shuai, D. Zhang, W. Zhang, G. Wu, D. Dai, B. Jiang, D. Zhang and X. Yang, J. Phys. Chem. A, 2014, 118, 2426–2430 CrossRef CAS PubMed.
  40. J. J. Lin, J. Shu, Y. T. Lee and X. Yang, J. Chem. Phys., 2000, 113, 5287–5301 CrossRef CAS.
  41. Q. Shuai, H. Pan, J. Yang, D. Zhang, B. Jiang, D. Dai and X. Yang, J. Chem. Phys., 2012, 137, 224301 CrossRef PubMed.
  42. H. Pan, J. Yang, D. Zhang, Q. Shuai, D. Dai, G. Wu, B. Jiang and X. Yang, J. Chem. Phys., 2014, 140, 154305 CrossRef.
  43. H. Kohguchi, Y. Ogi and T. Suzuki, Phys. Chem. Chem. Phys., 2011, 13, 8371–8378 RSC.
  44. N. Balucani, A. Bergeat, L. Cartechini, G. G. Volpi, P. Casavecchia, D. Skouteris and M. Rosi, J. Phys. Chem. A, 2009, 113, 11138–11152 CrossRef CAS PubMed.
  45. F. Leonori, D. Skouteris, R. Petrucci, P. Casavecchia, M. Rosi and N. Balucani, J. Chem. Phys., 2013, 138, 024311 CrossRef PubMed.
  46. C. Berteloite, S. D. Le Picard, I. R. Sims, M. Rosi, F. Leonori, R. Petrucci, N. Balucani, X. Wang and P. Casavecchia, Phys. Chem. Chem. Phys., 2011, 13, 8485–8501 RSC.
  47. X. Yang, Phys. Chem. Chem. Phys., 2006, 8, 205–215 RSC ; and refs. therein.
  48. N. Balucani, F. Leonori, R. Petrucci, M. Stazi, D. Skouteris, M. Rosi and P. Casavecchia, Faraday Discuss., 2010, 147, 189–216 RSC.
  49. N. Balucani, D. Skouteris, F. Leonori, R. Petrucci, M. Hamberg, W. D. Geppert, P. Casavecchia and M. Rosi, J. Phys. Chem. A, 2012, 116, 10467–10479 CrossRef CAS PubMed.
  50. S.-H. Lee, C.-H. Chin, W.-K. Chen, W.-J. Huang and C.-C. Hsieh, Phys. Chem. Chem. Phys., 2011, 13, 8515–8525 RSC.
  51. F. Leonori, R. Petrucci, N. Balucani, P. Casavecchia, M. Rosi, D. Skouteris, C. Berteloite, S. D. Le Picard, A. Canosa and I. R. Sims, J. Phys. Chem. A, 2009, 113, 15328–15345 CrossRef CAS PubMed.
  52. R. I. Kaiser, Chem. Rev., 2002, 102, 1309–1358 CrossRef CAS PubMed.
  53. A. M. Mebel and R. I. Kaiser, Int. Rev. Phys. Chem., 2015, 17, 21564–21575 Search PubMed.
  54. F. Leonori, R. Petrucci, E. Segoloni, A. Bergeat, K. M. Hickson, N. Balucani and P. Casavecchia, J. Phys. Chem. A, 2008, 112, 1363–1379 CrossRef CAS PubMed.
  55. C.-H. Chin, W.-K. Chen, W.-J. Huang, Y.-C. Lin and S.-H. Lee, Icarus, 2013, 222, 254–262 CrossRef CAS ; and references therein.
  56. N. Balucani, F. Zhang and R. I. Kaiser, Chem. Rev., 2010, 110, 5107–5127 CrossRef CAS PubMed.
  57. L. C. L. Huang, O. Asvany, A. H. H. Chang, N. Balucani, S. H. Lin, Y. T. Lee, R. I. Kaiser and Y. Osamura, J. Chem. Phys., 2000, 113, 8656–8666 CrossRef CAS.
  58. C. J. Bennett, S. B. Morales, S. D. Le Picard, A. Canosa, I. R. Sims, Y. H. Shih, A. H. H. Chang, X. Gu, F. Zhang and R. I. Kaiser, Phys. Chem. Chem. Phys., 2010, 12, 8737–8749 RSC.
  59. F. Leonori, K. M. Hickson, S. D. Le Picard, X. Wang, R. Petrucci, P. Foggi, N. Balucani and P. Casavecchia, Mol. Phys., 2010, 108, 1097–1113 CrossRef CAS.
  60. R. I. Kaiser, X. Gu, F. Zhang and P. Maksyuntenko, Phys. Chem. Chem. Phys., 2012, 14, 575–588 RSC.
  61. Y.-L. Sun, W.-J. Huang and S.-H. Lee, Phys. Chem. Chem. Phys., 2016, 18, 2120–2129 RSC.
  62. D. S. N. Parker, F. Zhang, P. Maksyutenko, R. I. Kaiser and A. H. H. Chang, Phys. Chem. Chem. Phys., 2011, 13, 8560–8570 RSC.
  63. D. S. N. Parker, R. I. Kaiser and A. M. Mebel, Chem. Soc. Rev., 2014, 43, 2701–2713 RSC.
  64. Y.-L. Sun, W.-J. Huang and S.-H. Lee, J. Phys. Chem. Lett., 2015, 6, 4117–4122 CrossRef CAS PubMed.
  65. R. I. Kaiser, D. S. N. Parker, M. Goswami, F. Zhang, V. V. Kislov, A. M. Mebel, J. Aguilera-Iparraguirre and W. H. Green, Phys. Chem. Chem. Phys., 2012, 14, 720–729 RSC.
  66. T. Yang, D. S. N. Parker, B. B. Dangi, R. I. Kaiser, V. V. Kislov and A. M. Mebel, J. Phys. Chem. A, 2014, 118, 4372–4381 CrossRef CAS PubMed.
  67. D. R. Albert and H. F. Davis, Phys. Chem. Chem. Phys., 2013, 15, 14566–14580 RSC.
  68. T. Yang, B. B. Dangi, A. M. Thomas and R. I. Kaiser, Chem. Phys. Lett., 2016, 654, 58–62 CrossRef CAS.
  69. P. Casavecchia, F. Leonori, N. Balucani, R. Petrucci, G. Capozza and E. Segoloni, Phys. Chem. Chem. Phys., 2009, 11, 46–65 RSC.
  70. P. Casavecchia, F. Leonori and N. Balucani, Int. Rev. Phys. Chem., 2015, 34, 161–204 CrossRef CAS , and references therein.
  71. S. Greaves, R. Rose and A. Orr-Ewing, Phys. Chem. Chem. Phys., 2010, 12, 9129–9143 RSC.
  72. B. Joalland, Y. Shi, A. D. Estillore, A. Kamasah, A. Mebel and A. G. Suits, J. Phys. Chem. A, 2014, 118, 9281–9295 CrossRef CAS PubMed ; and refs. therein.
  73. M. Costes and C. Naulin, Phys. Chem. Chem. Phys., 2010, 12, 9154–9164 RSC.
  74. G. Capozza, E. Segoloni, F. Leonori, G. G. Volpi and P. Casavecchia, J. Chem. Phys., 2004, 120, 4557–4560 CrossRef CAS PubMed.
  75. P. Casavecchia, G. Capozza, E. Segoloni, F. Leonori, N. Balucani and G. G. Volpi, J. Phys. Chem. A, 2005, 109, 3527–3530 CrossRef CAS PubMed.
  76. P. Casavecchia, G. Capozza and E. Segoloni, in Modern Trends in Chemical Reaction Dynamics: Experiment & Theory (Part II), ed. X. Yang and K. Liu, Adv. Series in Phys. Chem., World Scientific, Singapore, 2004, ch. 7, vol. 14 Search PubMed.
  77. X. Yang, J. Lin, Y. T. Lee, D. A. Blank, A. G. Suits and A. M. Wodtke, Rev. Sci. Instrum., 1997, 68, 3317–3326 CrossRef CAS.
  78. N. Hemmi and A. G. Suits, J. Chem. Phys., 1998, 109, 5338–5343 CrossRef CAS.
  79. H. F. Davis, J. Shu, D. Peterka and M. Ahmed, J. Chem. Phys., 2004, 121, 6254–6257 CrossRef PubMed.
  80. C. C. Wang, J. Shu, J. J. Lin, Y. T. Lee and X. Yang, J. Chem. Phys., 2002, 117, 153–160 CrossRef CAS.
  81. S.-H. Lee, W.-K. Chen and W.-J. Huang, J. Chem. Phys., 2009, 130, 054301 CrossRef PubMed.
  82. N. Balucani, F. Leonori and P. Casavecchia, in Cleaner Combustion, Green Energy and Technology, ed. F. Battin-Leclerc, et al., Springer-Verlag, London, 2013, ch. 22, pp. 577–606 Search PubMed.
  83. K. Liu, J. Chem. Phys., 2015, 142, 080901 CrossRef PubMed.
  84. K. Liu, Annu. Rev. Phys. Chem., 2016, 67, 91–111 CrossRef CAS PubMed.
  85. Y. T. Lee, J. D. McDonald, P. R. LeBreton and D. R. Herschbach, Rev. Sci. Instrum., 1969, 40, 1402–1408 CrossRef CAS.
  86. Y. T. Lee, Science, 1987, 236, 793–798 CAS.
  87. Y. T. Lee, in Atomic and Molecular Beam Methods, ed. G. Scoles, Oxford University Press, New York, 1987, vol. 1, pp. 553–568 Search PubMed.
  88. M. Alagia, N. Balucani, P. Casavecchia, D. Stranges and G. G. Volpi, J. Chem. Soc., Faraday Trans., 1995, 91, 575–596 RSC.
  89. J. J. Lin, S. Harich, Y. T. Lee and X. Yang, Rev. Sci. Instrum., 1998, 69, 1642–1646 CrossRef CAS.
  90. P. Casavecchia, N. Balucani and G. G. Volpi, Annu. Rev. Phys. Chem., 1999, 50, 347–376 CrossRef CAS PubMed.
  91. A. Willis, H. U. Stauffer, R. Z. Hinrichs and H. F. Davis, Rev. Sci. Instrum., 1999, 70, 2606–2614 CrossRef.
  92. J. J. Schroden and H. F. Davis, in Modern Trends in Chemical Reaction Dynamics: Experiment and Theory (Part II), ed. X. Yang and K. Liu, Adv. Series in Phys. Chem., World Scientific, Singapore, 2004, ch. 5, vol. 14 Search PubMed.
  93. F. Leonori, N. Balucani, G. Capozza, E. Segoloni, D. Stranges and P. Casavecchia, Phys. Chem. Chem. Phys., 2007, 9, 1307–1311 RSC.
  94. N. Balucani, F. Leonori, A. Bergeat, R. Petrucci and P. Casavecchia, Phys. Chem. Chem. Phys., 2011, 13, 8322–8330 RSC.
  95. W. C. Gardiner, Jr., Gas-phase combustion chemistry, Springer-Verlag, New York, NY, 2000 Search PubMed.
  96. J. A. Miller, M. J. Pilling and J. Troe, Proc. Combust. Inst., 2005, 30, 43–88 CrossRef.
  97. D. L. Baulch, C. T. Bowman, C. J. Cobos, R. A. Cox, Th. Just, J. A. Kerr, M. J. Pilling, D. Stocker, J. Troe, W. Tsang, R. W. Walker and J. Warnatz, J. Phys. Chem. Ref. Data, 2005, 34, 757–1397 CrossRef CAS.
  98. R. J. Cvetanovic, J. Phys. Chem. Ref. Data, 1987, 16, 261–326 CrossRef CAS.
  99. A. Occhiogrosso, S. Viti and N. Balucani, Mon. Not. R. Astron. Soc., 2013, 432, 3423–3430 CrossRef CAS.
  100. M. Dobrijevic, E. Hebrard, J. C. Loison and K. M. Hickson, Icarus, 2014, 228, 324–346 CrossRef CAS.
  101. L. M. Lara, E. Lellouch, M. Gonzales, R. Moreno and M. Rengel, Astron. Astrophys., 2014, 566, A143 CrossRef.
  102. B. Fu, Y.-C. Han, J. M. Bowman, L. Angelucci, N. Balucani, F. Leonori and P. Casavecchia, Proc. Natl. Acad. Sci. U. S. A., 2012, 109, 9733–9738 CrossRef CAS PubMed.
  103. F. Leonori, N. Balucani, V. Nevrly, A. Bergeat, S. Falcinelli, G. Vanuzzo, P. Casavecchia and C. Cavallotti, J. Phys. Chem. C, 2015, 119, 14632–14652 CAS.
  104. F. Leonori, A. Occhiogrosso, N. Balucani, A. Bucci, R. Petrucci and P. Casavecchia, J. Phys. Chem. Lett., 2012, 3, 75–80 CrossRef CAS.
  105. J. R. Kanofsky and D. Gutman, Chem. Phys. Lett., 1972, 15, 236–239 CrossRef CAS.
  106. J. R. Kanofsky, D. Lucas, F. Pruss and D. Gutman, J. Phys. Chem., 1974, 78, 311–316 CrossRef CAS.
  107. B. Blumenberg, K. Hoyerman and R. Sievert, Sixteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, PA, 1976, pp. 841–852 Search PubMed.
  108. C. A. Taatjes, N. Hansen, D. L. Osborn, K. Kohse-Höinghaus, T. A. Cool and P. R. Westmoreland, Phys. Chem. Chem. Phys., 2008, 10, 20–34 RSC.
  109. D. L. Osborn, P. Zou, H. Johnsen, C. C. Hayden, C. A. Taatjes, V. D. Knyazev, S. W. North, D. S. Peterka, M. Ahmed and S. R. Leone, Rev. Sci. Instrum., 2008, 79, 104103 CrossRef PubMed.
  110. F. Leonori, N. Balucani, G. Capozza, E. Segoloni, G. G. Volpi and P. Casavecchia, Phys. Chem. Chem. Phys., 2014, 16, 10008–10022 RSC.
  111. A. M. Schmoltner, P. M. Chu and Y. T. Lee, J. Chem. Phys., 1989, 91, 5365–5373 CrossRef CAS.
  112. T. L. Nguyen, L. Vereecken and J. Peeters, J. Phys. Chem. A, 2006, 110, 6696–6706 CrossRef CAS PubMed.
  113. K. Rajak and B. Maiti, J. Chem. Phys., 2014, 140, 044314 CrossRef PubMed.
  114. G. Vanuzzo, N. Balucani, F. Leonori, V. Nevrly, S. Falcinelli, A. Bergeat, D. Stranges, P. Casavecchia and C. Cavallotti, J. Phys. Chem. A, 2016, 120, 4603–4618 CrossRef CAS PubMed.
  115. I. Gimondi, C. Cavallotti, G. Vanuzzo, N. Balucani and P. Casavecchia, J. Phys. Chem. A, 2016, 120, 4619–4633 CrossRef CAS PubMed.
  116. J. D. Savee, S. Borkar, O. Welz, B. Sztáray, C. A. Taatjes and D. L. Osborn, J. Phys. Chem. A, 2015, 119, 7388–7403 CrossRef CAS PubMed.
  117. A. M. Schmoltner, P. M. Chu, R. J. Brudzynski and Y. T. Lee, J. Chem. Phys., 1989, 91, 6926–6936 CrossRef CAS.
  118. B. Fu, Y.-C. Han, J. M. Bowman, F. Leonori, N. Balucani, L. Angelucci, A. Occhiogrosso, R. Petrucci and P. Casavecchia, J. Chem. Phys., 2012, 137, 22A532 CrossRef PubMed.
  119. N. Balucani, F. Leonori, P. Casavecchia, B. Fu and J. M. Bowman, J. Phys. Chem. A, 2015, 119, 12498–12511 CrossRef CAS PubMed.
  120. T. L. Nguyen, L. Vereecken, H. J. Hou, M. T. Nguyen and J. Peeters, J. Phys. Chem. A, 2005, 109, 7489–7499 CrossRef CAS PubMed.
  121. X. Li, A. W. Jasper, J. Zádor, J. A. Miller and S. J. Klippenstein, Proc. Combust. Inst., 2017, 36, 219–227 CrossRef CAS.
  122. J. Morin and Y. Bedjanian, J. Phys. Chem. A, 2016, 120, 9063–9070 CrossRef CAS PubMed.
  123. Y. Endo, S. Tsuchiya, C. Yamada, E. Hirota and S. Koda, J. Chem. Phys., 1986, 85, 4446 CrossRef CAS.
  124. U. Bley, P. Dransfeld, B. Himme, M. Koch, F. Temps and H. G. Wagner, 22nd Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA, 1988, pp. 997–1006 Search PubMed.
  125. A. Caracciolo, G. Vanuzzo, N. Balucani, D. Stranges, C. Cavallotti and P. Casavecchia, Chem. Phys. Lett., 2017, 683, 105–111 CrossRef CAS.
  126. C. Cavallotti, F. Leonori, N. Balucani, V. Nevrly, A. Bergeat, S. Falcinelli, G. Vanuzzo and P. Casavecchia, J. Phys. Chem. Lett., 2014, 5, 4213–4218 CrossRef CAS PubMed.
  127. J. D. Savee, O. Welz, C. A. Taatjes and D. L. Osborn, Phys. Chem. Chem. Phys., 2012, 14, 10410–10423 RSC.
  128. T. L. Nguyen, J. Peeters and L. Vereecken, J. Phys. Chem. A, 2006, 110, 12166–12176 CrossRef CAS PubMed.
  129. G. Vanuzzo, N. Balucani, F. Leonori, D. Stranges, S. Falcinelli, A. Bergeat, P. Casavecchia, I. Gimondi and C. Cavallotti, J. Phys. Chem. Lett., 2016, 7, 1010–1015 CrossRef CAS PubMed.
  130. A. Caracciolo, G. Vanuzzo, S. Tanteri, D. Stranges, N. Balucani, C. Cavallotti and P. Casavecchia, XXVII International Symposium on Molecular Beams, Nijmegen, NL, 25–30 June 2017, Book of Abstracts, p. 80.
  131. D. W. Chandler and P. L. Houston, J. Chem. Phys., 1987, 87, 1445–1447 CrossRef CAS.
  132. A. T. J. B. Eppink and D. H. Parker, Rev. Sci. Instrum., 1997, 68, 3447–3484 CrossRef.
  133. C. R. Gebhardt, T. P. Rakitzis, P. C. Samartzis, V. Ladopoulos and T. N. Kistopoulos, Rev. Sci. Instrum., 2001, 72, 3848–3853 CrossRef CAS.
  134. J. J. Lin, J. Zhou, W. Shiu and K. Liu, Rev. Sci. Instrum., 2003, 74, 2495–2500 CrossRef CAS.
  135. D. Townsend, M. P. Minitti and A. G. Suits, Rev. Sci. Instrum., 2003, 74, 2530–2539 CrossRef CAS.
  136. For a collection of recent advances, see for example, Special Topic: Developments and Applications of Velocity Mapped Imaging Techniques, J. Chem. Phys., 2017, 147(1).
  137. D. Townsend, W. Li, S. K. Lee, R. L. Gross and A. G. Suits, J. Phys. Chem. A, 2005, 109, 8661–8674 CrossRef CAS PubMed.
  138. M. N. R. Ashfold, N. H. Nahler, A. J. Orr-Ewing, O. P. J. Vieumaire, R. L. Toomes, T. N. Kistopoulos, I. A. Garcia, D. A. Chestakov, S.-M. Wu and D. H. Parker, Phys. Chem. Chem. Phys., 2006, 8, 26–53 RSC.
  139. F. F. Crim, Acc. Chem. Res., 1999, 32, 877–884 CrossRef CAS.
  140. F. F. Crim, J. Phys. Chem., 1996, 100, 12725–12734 CrossRef CAS.
  141. R. N. Zare, Science, 1998, 279, 1875–1879 CrossRef CAS PubMed.
  142. H. Gao and K. Liu, Chem. Sci., 2016, 7, 3992–4003 RSC.
  143. J. J. Lin, J. Zhou, W. Shiu and K. Liu, Science, 2003, 300, 966–969 CrossRef CAS PubMed.
  144. J. J. Lin, J. Zhou, W. Shiu and K. Liu, Phys. Chem. Chem. Phys., 2006, 8, 3000–3006 RSC.
  145. J. Espinosa-Garcia, L. Bonnet and J. C. Corchado, J. Phys. Chem. A, 2017, 121, 4076–4092 CrossRef PubMed.
  146. Y.-T. Wu and K. Liu, J. Chem. Phys., 2006, 129, 154302 CrossRef PubMed.
  147. J. Zhou, J. J. Lin, B. Zhang and K. Liu, J. Phys. Chem. A, 2004, 108, 7832–7836 CrossRef CAS.
  148. B. Zhang, K. Liu, G. Czako and J. M. Bowman, Mol. Phys., 2012, 110, 1617–1626 CrossRef CAS.
  149. J. Zhou, B. Zhang, J. J. Lin and K. Liu, Mol. Phys., 2005, 103, 1757–1763 CrossRef CAS.
  150. G. Czako, Q. Shuai, K. Liu and J. M. Bowman, J. Chem. Phys., 2010, 133, 131101 CrossRef PubMed.
  151. F. Wang and K. Liu, J. Phys. Chem. Lett., 2011, 2, 1421–1425 CrossRef CAS.
  152. F. Wang and K. Liu, J. Phys. Chem. A, 2013, 117, 8536–8544 CrossRef CAS PubMed.
  153. B. Zhang and K. Liu, J. Phys. Chem. A, 2005, 109, 6791–6795 CrossRef CAS PubMed.
  154. J. Zhou, J. J. Lin and K. Liu, J. Chem. Phys., 2004, 121, 813–818 CrossRef CAS PubMed.
  155. J. Zhou, J. J. Lin and K. Liu, Mol. Phys., 2010, 108, 957–968 CrossRef CAS.
  156. R. T. Skodje, D. Skouteris, D. E. Manolopoulos, S.-H. Lee, F. Dong and K. Liu, J. Chem. Phys., 2000, 112, 4536–4552 CrossRef CAS.
  157. R. T. Skodje, D. Skouteris, D. E. Manolopoulos, S.-H. Lee, F. Dong and K. Liu, Phys. Rev. Lett., 2000, 85, 1206–1209 CrossRef CAS PubMed.
  158. S. H. Lee, F. Dong and K. Liu, J. Chem. Phys., 2006, 125, 133106 CrossRef PubMed.
  159. B. Zhang and K. Liu, J. Chem. Phys., 2005, 122, 101102 CrossRef PubMed.
  160. W. Shiu, J. J. Lin and K. Liu, Phys. Rev. Lett., 2004, 92, 103201 CrossRef PubMed.
  161. G. Nyman and J. Espinosa-Garcia, J. Phys. Chem. A, 2007, 111, 11943–11947 CrossRef CAS PubMed.
  162. T. Chu, X. Zhang, L. Ju, L. Yao, K.-L. Han, M. Wang and J. Z. H. Zhang, Chem. Phys. Lett., 2006, 424, 243–246 CrossRef CAS.
  163. T. Chu, K. Han and J. Espinosa-Garcia, J. Chem. Phys., 2009, 131, 244303 CrossRef PubMed.
  164. H. F. von Horsten and D. C. Clary, Phys. Chem. Chem. Phys., 2011, 13, 4340–4356 RSC.
  165. D. Schapers and U. Manthe, J. Phys. Chem. A, 2016, 120, 3186–3195 CrossRef PubMed.
  166. D. Wang and G. Czako, J. Phys. Chem. A, 2013, 117, 7124–7130 CrossRef CAS PubMed.
  167. R. Martinez, M. Gonzalez, P. Defazio and C. Petrongolo, J. Chem. Phys., 2007, 127, 104302 CrossRef PubMed.
  168. J. M. Bowman, Chem. Phys. Lett., 1979, 62, 309–311 CrossRef CAS.
  169. W. Schepper, U. Ross and D. Beck, Z. Phys. A: At. Nucl., 1979, 290, 131–141 CrossRef CAS.
  170. H. J. Korsch and R. Schinke, J. Chem. Phys., 1981, 75, 3850–3859 CrossRef CAS.
  171. H. Pan and K. Liu, J. Phys. Chem. A, 2016, 120, 6712–6718 CrossRef CAS PubMed.
  172. J. Zhou., J. J. Lin and K. Liu, J. Chem. Phys., 2003, 119, 8289–8296 CrossRef CAS.
  173. B. Zhang, W. Shiu, J. J. Lin and K. Liu, J. Chem. Phys., 2005, 12, 131102 CrossRef PubMed.
  174. B. Zhang, W. Shiu and K. Liu, J. Phys. Chem. A, 2005, 109, 8983–8988 CrossRef CAS PubMed.
  175. B. Zhang, W. Shiu and K. Liu, J. Phys. Chem. A, 2005, 109, 8989–8993 CrossRef CAS PubMed.
  176. J. Espinosa-Garcia and J. C. Corchado, Theor. Chem. Acc., 2015, 134, 1–10 CrossRef CAS.
  177. J. Espinosa-Garcia and J. C. Corchado, J. Phys. Chem. A, 2016, 120, 1446–1453 CrossRef CAS PubMed.
  178. L. Bonnet, J. C. Corchado and J. Espinosa-Garcia, C. R. Chim., 2016, 19, 571–578 CrossRef CAS.
  179. J. Li and H. Guo, J. Chem. Phys., 2015, 143, 221103 CrossRef PubMed.
  180. J. Zhou, W. Shiu, J. J. Lin and K. Liu, J. Chem. Phys., 2004, 120, 5863–5866 CrossRef CAS PubMed.
  181. J. Zhou, W. Shiu, J. J. Lin and K. Liu, J. Chem. Phys., 2006, 124, 104309 CrossRef PubMed.
  182. J. Zhou, J. J. Lin, W. Shiu, S.-C. Pu and K. Liu, J. Chem. Phys., 2003, 119, 2538–2544 CrossRef CAS.
  183. S. Yan, Y.-T. Wu, B. Zhang, X.-F. Yue and K. Liu, Science, 2007, 316, 1723–1726 CrossRef CAS PubMed.
  184. J. Riedel, S. Yan and K. Liu, J. Phys. Chem. A, 2009, 113, 14270–14276 CrossRef CAS PubMed.
  185. H. Kawamata and K. Liu, J. Chem. Phys., 2010, 133, 124304 CrossRef PubMed.
  186. J. C. Polanyi, Acc. Chem. Res., 1972, 5, 161–168 CrossRef CAS.
  187. G. Czako and J. M. Bowman, Science, 2011, 334, 343–346 CrossRef CAS PubMed.
  188. Z. Zhang, Y. Zhou, D. H. Zhang, G. Czako and J. M. Bowman, J. Phys. Chem. Lett., 2012, 3, 3416–3419 CrossRef CAS PubMed.
  189. F. Wang, J.-S. Lin, Y. Cheng and K. Liu, J. Phys. Chem. Lett., 2013, 4, 323–327 CrossRef CAS PubMed.
  190. R. Liu, F. Wang, B. Jiang, G. Czako, M. Yang, K. Liu and H. Guo, J. Chem. Phys., 2014, 141, 074310 CrossRef PubMed.
  191. F. Wang, H. Pan and K. Liu, J. Phys. Chem. A, 2015, 119, 11983–11988 CrossRef CAS PubMed.
  192. H. Pan, Y. Cheng and K. Liu, J. Phys. Chem. A, 2016, 120, 4799–4804 CrossRef CAS PubMed.
  193. R. D. Levine, J. Phys. Chem., 1990, 94, 8872–8880 CrossRef CAS.
  194. F. Wang, J.-S. Lin and K. Liu, Science, 2011, 331, 900–903 CrossRef CAS PubMed.
  195. F. Wang, K. Liu and T. P. Rakitzis, Nat. Chem., 2012, 4, 636–641 CrossRef CAS PubMed.
  196. F. Wang and K. Liu, Chin. J. Chem. Phys., 2013, 26, 705–709 CrossRef CAS.
  197. F. Wang and K. Liu, J. Chem. Phys., 2016, 145, 144305 CrossRef PubMed.
  198. F. Wang and K. Liu, J. Chem. Phys., 2016, 145, 144306 CrossRef PubMed.
  199. F. Wang, J.-S. Lin and K. Liu, J. Chem. Phys., 2014, 140, 084202 CrossRef PubMed.
  200. D. R. Herschbach, Eur. Phys. J. D, 2006, 38, 3–13 CrossRef CAS.
  201. X. Yang, work in progress, personal communication.
  202. X. Yang, Int. Rev. Phys. Chem., 2005, 24, 37 CrossRef CAS ; and references therein.
  203. C. Lin, M. F. Witinski and H. F. Davis, J. Chem. Phys., 2003, 119, 251–255 CrossRef CAS.
  204. J. Meyer and R. Wester, Annu. Rev. Phys. Chem., 2017, 68, 333–353 CrossRef CAS PubMed.
  205. L. Pei, E. Carrascosa, N. Yang, S. Falcinelli and J. M. Farrar, J. Phys. Chem. Lett., 2015, 6, 1684–1689 CrossRef CAS PubMed.
  206. A. von Zastrow, J. Onvlee, S. N. Vogels, G. C. Groenenboom, A. van der Avoird and S. Y. T. van de Meerakker, Nat. Chem., 2014, 6, 216–221 CrossRef CAS PubMed.
  207. S. Y. T. van de Meerakker, H. L. Bethlem, N. Vanhaecke and G. Meijer, Chem. Rev., 2011, 112, 4828–4878 CrossRef PubMed.
  208. Y.-P. Chang, K. Dlugolecki, J. Küpper, D. Rösch, D. Wild and S. Willitsch, Science, 2013, 342, 98–101 CrossRef CAS PubMed.
  209. J. M. Bowman and A. G. Suits, Phys. Today, 2011, 64, 33–37 CrossRef CAS.
  210. B. Joalland, Y. Shi, A. G. Suits and A. M. Mebel, Nat. Commun., 2014, 5, 4064–4067 CAS.

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