Imaging a Resonance-Dominant Polyatomic Reaction: F + CH3D

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Spectroscopy and Photochemistry; General Theory

Imaging a Resonance-Dominant Polyatomic Reaction: F + CHD # CH(v = 2) + DF(v) 3

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Surjendu Bhattacharyya, Sohidul Mondal, and Kopin Liu J. Phys. Chem. Lett., Just Accepted Manuscript • Publication Date (Web): 06 Sep 2018 Downloaded from http://pubs.acs.org on September 6, 2018

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The Journal of Physical Chemistry Letters

J. Phys. Chem. Lett. (Manuscript ID: jz-2018-02517v)

Imaging a Resonance-Dominant Polyatomic Reaction: F + CH3D → CH3(v2 = 2) + DF(v) Surjendu Bhattacharyya,† Sohidul Mondal,† and Kopin Liu*,†,≠ †

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Institute of Atomic and Molecular Sciences (IAMS), Academia Sinica, P. O. Box 23-166, Taipei, Taiwan, 10617 Department of Physics, National Taiwan University, Taipei, Taiwan, 10617 Email: [email protected]

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ABSTRACT The title reaction was studied in a crossed-beam scattering experiment at the collisional energy (Ec) ranging from 0.46 to 4.53 kcal mol-1. Using a time-sliced velocity-imaging technique, both the paircorrelated integral and differential cross sections were measured. On the basis of the observed structures in state-specific excitation functions and the patterns in the Ec-evolution of product angular distributions, we inferred that the title reaction proceeds predominantly via a resonance-mediated pathway, in contrast to the previous findings in the isotopically analogous reactions where the alternative direct abstraction pathway often dominates the reactivity. Despite the complexity of numerous scattering resonances involved in this six-atom reaction, extending our understanding of the isolated resonance in the analogous benchmark F + HD (H2) reaction enables us to propose the plausible mechanistic origins for the formation as well as the decay of the complicated overlapped resonances.

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Reactive (or Feshbach) resonance here refers to a transiently formed, short-lived species produced while a chemical reaction is occurring.1-4 What makes reactive resonance intriguing is that it is quasibound even along the reaction coordinate on a totally repulsive Born-Oppenheimer potential energy surface (PES).3 Although the activated intermediate situates in the continuum and has sufficient total energy to break apart, it can be temporarily trapped as a vibrationally excited compound state so that the bond rupture will be delayed at a particular resonant energy. In many ways, one could regard the reactive resonance as a metastable species―similar to that encountered in a complex-forming reaction with the potential well―with all internal degrees of freedom assignable to approximate quantum numbers even in the transition state region.1 However, its very existence, no matter how fleeting it is or the trapping mechanism that requires attractive forces, is quantum dynamical in origin. The key to understanding a reactive resonance and how it affects the chemical reactivity lies on the underlying mechanisms of its formation and of the decay of the quasi-bound states.1,3 For a three-atom system, there are three internal degrees of freedom. Often only a few isolated resonance states exist at low energy, as evidenced in the F + HD and F + H2 reactions,5,6 for which the energy width of the metastable compound state is smaller than the energy level spacing. Detailed quantum dynamics calculations and theoretical analysis can be carried out to elucidate the nature of the compound states for deeper insights. As the reaction system becomes larger, total energy can be stored and distributed in many available internal degrees of freedom, and thus numerous resonance states become accessible. Conceivably, those states overlap with each other in energy, leading to a cluster (or a manifold) of overlapped resonances or even into the overlapping resonance regime when the widths of the resonances exceed the energy spacing.7-10 The nature of the reactive resonance then becomes complicated in that the assignment of the zeroth-order quantum numbers of each individual mode of excitation can be ambiguous.



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Nevertheless, observations of reactive resonances, both experimentally11-15 and theoretically,16-19 in the reactions of F- and Cl-atom with methane (and its isotopologues) have been reported. Then, the more sensible and insightful question to ask here should, perhaps, be the identification of the characteristic nuclear motions (rather than the quantum number assignments) that facilitate the formation and the decay of the manifold of overlapped (or the overlapping) resonances. Prior studies examined either the total reactivity (by theory)16-19 or that of the dominant ground-state methyl products (from experiment),11-15 the observed dynamical attributes usually comprise a significant fraction of direct abstraction component that could interfere with that from a resonance-mediated pathway. To unravel the complexity of the overlapped (or overlapping) resonances, it is thus desirable to scrutinize a reaction with minimal contribution from the direct abstraction pathway. Reported here seems to be one of such cases. The crossed-beam, product-imaging set up was essentially the same as that described in previous reports.20-22 In brief, two doubly-skimmed pulsed beams, a discharge-generated F-atom beam (a mixture of 5% F2 in Ne at 6 atm.) and a neat CH3D beam (6 atm.), were crossed in a differentially pumped chamber. After collisions, numerous product channels of CH3(v) and CH2D(v) were detected. In this work, we focus on the umbrella-mode excited CH3(v2 = 2, or 22) product channel. Besides detecting the CH3(22) + DF(v = 1‒4) pairs, the formation of a combination-band excited CH3(2241) products was also identified. [The relevant energetics is shown in Fig. S1.] The methyl products were probed by a (2+1) resonance-enhanced multiphoton ionization (REMPI) method via the CH3( 2 20 and 2 20 411 ) bands and recorded by a time-sliced, velocity imaging technique.20 To ensure an unbiased detection of the vibrationally excited CH3 products, the probe-laser wavelength was scanned back and forth over the REMPI band while the image was acquired.21,22 [Fig. S2 shows a REMPI spectrum and the wavelengthscanned range.] The collision energy (Ec) was varied by changing the molecular-beam intersection angle in this source-rotatable machine, covering Ec from 0.46 to 4.53 kcal mol-1. 4 ACS Paragon Plus Environment

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Figure 1 exemplifies the time-sliced raw images of CH3(22) products at six different Ec’s. By conservation of energy, the well-resolved ring-like image features can be assigned to the concomitantly formed DF(v) coproducts, as labeled. A closer inspection also reveals some faint signal adjacent to the DF(v = 3) ring. Energetically, it corresponds to products with additional 3-4 kcal mol-1 of internal energy to the DF(v = 2) coproducts, which thus excludes the reaction from the spin-orbit excited F (2P1/2) ＊

reactant that has only additional Eso = 1.15 kcal mol-1. Previous studies indicated that bendingexcitations of methane reactants can enhance the reaction rate with F-atom,22-25 which would also fulfill the energetic requirement. The hot-band experiments22 were then performed and, to our surprise, we found that the bend-excited CH3D reactants did not yield notable rate promotion in forming the CH3(22) products (see Fig. S3). Alternatively, this additional image feature could arise from a product state associated with another REMPI band that spectroscopically overlaps with the targeted CH3( 2 20 ) band. Taking the vibrational frequencies from a recent report,26 the only plausible REMPI vibronic transition that can simultaneously fulfill the requirements of both the spectral overlap and the needed product internal energy is the combination band of CH3( 2 20 411 ). We then tentatively assigned the additional ring feature as the (2241, 2) product pair in Fig. 1. The image analysis follows the previous procedure,20 the resultant product speed distribution dσ/du and angular distribution dσ/d(cosθ) for the images shown in Fig. 1 are presented in Figure 2 (a) and (b), respectively. The dominance of the (22, 3) pair at all Ec is clearly noted in Fig. 2(a), and the intensity of the (22, 2) pair increases with increasing Ec. Both the (22, 4) and (22, 1) pairs are small and observable only at higher Ec’s. Also indicated by the red curve is the estimated contribution from the (2241, 2) pair, which roughly amounts to about 9 ± 3 % of the total intensity of the (22, v) pairs (Fig. S4). In the remaining analysis and discussion, we shall focus only on the (22, v) results.



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Fig. 2(b) presents the pair-correlated angular distributions. The total angular distributions are obviously dominated by the (22, 3) pair, which displays remarkably distinct variation with Ec. The (22, 2) pair, so as (22, 1), is predominantly backward-scattered. By way of contrast, the (22, 4) pair that has an energetic threshold of 3.6 kcal mol-1 shows a prominent glory-like forward-peaking distribution. We note in passing that no sign of bulge can be sighted in any of these DCSs, which is in stark contrast to the recently reported ground-state CH2D(00) + HF(v) channel, yet entirely consistent with the proposed criteria for forming the reactive rainbow.21 In this study a total of twelve images were acquired and analyzed over the Ec range of 0.46‒4.53 kcal mol-1. Following the procedure detailed previously27 and with the (2241, 2) contribution removed, the Ec-dependence of the relative integral cross section (ICS) for the CH3(22) + DF(v) product pairs―the correlated excitation functions―were measured and shown in Figure 3(a). The most striking aspect is the very significant reactivity near the threshold and it is almost entirely derived from a single channel of (22, 3). Even at the higher Ec, the (22, 3) pair still accounts for more than two-third of total reactivity. The shape of the (22, 3) excitation function also appears unusual: nearly Ec-independent except for a small rising near Ec ~ 2 kcal mol-1, followed by a slow decline. In contrast, the excitation functions for the other pairs, in particular (22, 2), show the behavior for a typical activated reaction with a threshold near 0.5 kcal mol-1. Fig. 3(b) shows the vibrational branching fraction of the DF(v) coproducts. Clearly, the fraction is dominated by v = 3 and 2―a highly inverted vibrational distribution as anticipated by Polanyi’s rule for a newly formed D-F bond in an early-barrier reaction.28 The CH3(22) product was probed and the average product translational energy release 〈ET〉 can be obtained from the measured dσ/du distribution (Fig. 2(a)). Once the vibrational branching ratio of the DF coproducts is determined, so does the average DF vibrational energy 〈VDF〉, the average rotational energy 〈ER〉 of both products can then be deduced by virtue of energy conservation. Fig. 3(c) depicts the Ec-dependences of the energy disposals. As Ec 6 ACS Paragon Plus Environment

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increases, 〈ER〉 remains constant and 〈ET〉 increases. However, a clear decrease of 〈VDF〉 is also notable. In other words, the increase in product kinetic energy release is more than the additional initial kinetic energy, which appears at variance with the previous findings of ΔEc Δ〈ET〉 in the other isotopically analogous reactions.12,22,29 The latter is kinematically anticipated for a collinear-dominant reaction with the mass combination of heavy + light-heavy (due to the small mass-weighted skew angle that facilitates the inertia coupling between the two scaled coordinates). At first glance the present energy disposal seems odd. However, recalling that the premise for the ΔEc Δ〈ET〉 correlation lies on a direct abstraction reaction mechanism,28 the observed clear deviation of such correlation would perhaps suggest the dominance of an indirect (a resonance-mediated reaction, vide infra) pathway in the title reaction. It has been demonstrated that an informative way to reveal microscopic reaction mechanism and reactive resonance is to examine the three-dimensional plot of dσ/d(cosθ) against both θ and Ec,1,3,14,15,22,29 for which each state-resolved angular distribution dσ/d(cosθ) (Fig. 2(b)) is normalized to the corresponding ICS shown in Fig. 3(a). Figure 4 shows the results. The (22, 4) pair with the least kinetic energy release displays a prominent forward peak once it is energetically open. The most abundant (22, 3) pair exhibits rich structures: a distinct ridge in the backward hemisphere at lower Ec and turning abruptly towards sideway around Ec ~ 2 kcal mol-1 and onwards. At the same time, a forward feature oscillating with Ec can readily be noted. Significantly, this Ec-evolving pattern bears striking similarity to that previously reported for the F + HD → HF(v = 3) + D reaction at low Ec.30-32 The pattern in the latter reaction has been ascribed unequivocally to be the fingerprint of a resonancemediated mechanism.2,30,33 It is worth noting that despite such similarity in their general appearances, the detailed underpinnings for an isolated resonance reaction and that for overlapped resonances could have different origins. In the former case it arises from different partial waves and their interferences of the



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same (vibrational) resonance state as Ec is varied,30-33 whereas in the latter case additional interferences between the overlapped resonant states might also partake. As for the (22, 2) and (22, 1) pairs, both display a distinct backward swath―a typical pattern attributed to a direct rebound mechanism30,34―superimposed with some peaking structures. The small backward peaks for the (22, 1) pairs at Ec ~ 3 kcal mol-1 might be the artifact from the poor signal-tonoise ratios. The backward peaking feature for (22, 2) at Ec ~ 2 kcal mol-1, on the other hand, appears significant enough to distinguish it from the remaining backward swath in terms of reaction pathways. As a result, the total angular distribution for the F + CH3D → CH3(22) + DF reaction encompasses three prominent patterns: a backward-scattered swath at higher Ec―indicative of a direct abstraction pathway, a distinct ridge evolving with Ec, and an oscillatory forward-peaking feature. The latter two, as just mentioned, can be regarded as the characteristic fingerprints for a resonance-mediated pathway. In conjunction with the vibrational branching fraction shown in Fig. 3(b), we surmise that the title reaction is dominated by the reactive resonance, which accounts for more than two-third of reactivity even at higher Ec up to about 4.5 kcal mol-1. Although sightings of reactive resonances in F + methane (and its isotopologues) have been reported,11-13 those prior studies concerned the ground-state methyl products, for which the direct abstraction pathway makes significant contributions to the observed attributes. The current reaction, albeit a less abundant channel of CH3(22) + DF, appears to offer a better opportunity to reveal the nature of the resonances. However, as alluded to early, the complexity of resonances in this six-atom reaction remains very challenging. In a recent report Schӓpers and Manthe found about 60 resonance states of the F•CH4 complex with energies below the reactant asymptote.35 With the computed dissociation energy of 170 cm-1, the average density of states is about 0.35 states per cm-1. Clearly, the numbers of the quasibound states invoked in a scattering experiment will be even more. Nevertheless, we believe that extending our understanding of the resonances in the simpler benchmark F + HD (H2) reaction could 8 ACS Paragon Plus Environment

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offer clues as to the plausible origins for the formation and the decay of the complicated overlapped resonances. We start by noting that the vibrational-adiabatic model has been proven to be a conceptually appealing framework for understanding the nature of the reactive resonance.3,13-15 Within this model, Figure 5 depicts a picturesque representation of what we envisioned for the present reaction. Ignoring the long-range van der Waals interactions, the Born-Oppenheimer PES (with the zero-point energy corrected) exhibits a low barrier (~ 0.8 kcal mol-1) without any potential well.35-38 By using the reaction path Hamiltonian approach,39 ab initio calculations of isotopically analogous reactions mapped out the minimum energy path and the evolution of the vibrational frequencies of various modes along the reaction path. It was found that only two reactant’s modes, the CH3 symmetric stretch and the umbrella mode, couple strongly to the reaction coordinate en route to the barrier,16 rendering significant decreases of the corresponding generalized vibrational frequencies and thus developing the vibrational-adiabatic (or dynamic) wells. As illustrated in Fig. 5, a number of such wells are possible and deep enough for supporting quasibound states. [Not depicted in Fig. 5 are the analogous dynamic wells and quasi-bound states associated with the alternative CH2D + HF product channel, whose wave functions might also extend and mix with those shown in Fig. 5; see ref. 13 for more detailed discussion in the F + CHD3 reaction]. Note that energetically the (00, 4) product pair is exothermic by merely 0.05 kcal mol-1; thus, for collisions with higher partial waves (or impact parameters) the centrifugal-shifted barrier can develop a dynamic well to support quasi-bound states (then the shape-resonances) above the reactant asymptote. Conceivably, those quasi-bound states are congested in energy, yielding a manifold (or cluster) of overlapped resonances or even the overlapping resonance. Those resonance states situate behind the reaction barrier in the transition state region, and are dynamically trapped in the vibrational-adiabatic potential wells. Hence, in analogy to the F + HD case,30-32 the formation of the resonant compound states is mediated 9 ACS Paragon Plus Environment


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and enhanced via a resonant tunneling process. Interestingly, the lack of significant rate-enhancement in forming the CH3(22) products by bend-excited reactants (Fig. S3) will imply that the tunneling path may largely be confined along the D‒F stretching motion, whereas the reactant’s bend-motions play a minor role. The decay of those metastable species to the reaction products must be induced by the coupling to the continuum, i.e., the energy flow into the reaction coordinate. Intuitively, one may envision it as a unimolecular predissociation process.3,11,13,14 Since the characters of the resonances states likely invoke the collective excitations of the (four-quanta) D‒F stretch and the umbrella motions of the CH3 moiety and recalling that the propensity in vibrational predissociation prefers small energy-gap channels,40 the dominances of the resonance decay into the (00, 4) and (22, 3) product pairs are anticipated. The involvement of umbrella motion in resonance decay may not be too surprising in view of the planar methyl radical product. In other words, the underlying decay mechanism is governed by the intramolecular vibrational energy redistribution (IVR) within the resonant compound states. For the present pair (22, 3), because of the small contribution from the direct abstraction pathway, the resonance features prevail, and the energy flow arises predominantly from the de-excitation of four quanta of D‒F stretch and/or its combination modes with bend into the umbrella-mode excited CH3 and the recoil of the two departing products. In summary, the title reaction was investigated in a product-pair manner over the energy range of 0.46 – 4.53 kcalmol-1. The ICS measurement indicated a predominant formation of the (22, 3) pair (Fig. 3), whose DCS behaviors (Fig. 4) strongly resemble that of the well-studied F + HD → HF(v = 3) + D resonance reaction. Extending what we learnt from the latter case enables us to delineate the formation mechanism of the overlapped resonances in this polyatomic reaction and their dominant decay pathways (Fig. 5). At first glance, the analogy to the F + HD reaction seems obvious if the methyl moiety is treated as a pseudo-atom. As it turns out, the methyl moiety is not just an innocent spectator. It instead 10 ACS Paragon Plus Environment

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plays a central role in mediating the resonance decay mechanism, thus, offering an unparalleled opportunity to unravel the IVR energy flow while the activated, transient complex is breaking apart into products. Because of the complexity of the system, the discussion is necessarily qualitative at present. Some subtlety remains: Will a cluster of overlapped resonances or the overlapping resonance be a more appropriate view? This question is related to the mode-specificity of (overlapped) resonance states.7-10,41 A detailed comparison with all other product channels may shed further light on it―a task is currently on-going in this laboratory. More quantitative understanding and deeper insights await future theoretical developments.

ACKNOWLEDGMENTS This work was supported by the Minister of Science and Technology of Taiwan (MOST-105-2113-M001-019-My3) and Academia Sinica.

SUPPORTING INFORMATION AVAILABLE: Energy level diagram, REMPI spectra of the CH3(220) band, Image and the product speed distribution dσ/du analysis for the hot-band reaction, Ec dependence of the signal ratios of S(2241)/S(22).

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Figure 1. Exemplified raw images of the CH3 products with the probe laser frequencies scanned over the CH3( 2 20 ) REMPI band. On energetic grounds, the prominent ring-like features can be assigned to the vibrational states of the coproducts DF(v), as labeled in red. The weak feature adjacent to the DF(v = 3) ring corresponds to the combination-band excited CH3 product, (2241, 2), see text for details. The discharge-generated background along the 0o can readily be identified, and was discarded in the image analysis. The number in the rectangular box gives the collisional energy, in kcal mol-1.



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Figure 2. (a) The product speed distribution dσ/du derived from the images shown in Fig. 1, The peak structures are assigned to the state-pair, (vCH3, vDF). (b) The corresponding pair-correlated angular distributions dσ/d(cosθ). The “total” is the sum of all, corresponding to the state-resolved differential cross section of the CH3(22) + DF(all v) product channel.


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Figure 3. (a) The pair-correlated excitation functions, with the error bar denoting ± one standard deviation. The “total” means the sum. (b) The vibrational branching fraction derived from (a). (c) The product energy disposal as a function of the initial Ec.



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Figure 4. Three-dimensional (3D) representation of the pair-correlation angular distribution dσ/d(cosθ) showing its evolution with the change in Ec. Distinct patterns for different state-pairs are clearly displayed; see text for detailed discussion.


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Figure 5. Vibrationally adiabatic representation of the reaction of F + CH3D → CH3 + DF. The strong couplings of the CH3 symmetric stretch and the umbrella mode to the reaction coordinate give rise to the vibrationally adiabatic (or dynamical) wells, which provide necessary attractive forces to trap numerous quasi-bound states (the reactive resonances) embedded in the continuum. The reaction is envisioned to proceed through a resonant tunneling process to form the resonant compound states with finite lifetime. The products are formed by the decay of reactive resonance―a unimolecular process induced by the intramolecular vibrational redistribution (IVR) of the metastable species.



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Imaging a Resonance-Dominant Polyatomic Reaction: F + CH3D

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