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Do Vibrational Excitations of CHD3 Preferentially Promote Reactivity Toward the Chlorine Atom?

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Science  22 Jun 2007:
Vol. 316, Issue 5832, pp. 1723-1726
DOI: 10.1126/science.1142313

Abstract

The influence of vibrational excitation on chemical reaction dynamics is well understood in triatomic reactions, but the multiple modes in larger systems complicate efforts toward the validation of a predictive framework. Although recent experiments support selective vibrational enhancements of reactivities, such studies generally do not properly account for the differing amounts of total energy deposited by the excitation of different modes. By precise tuning of translational energies, we measured the relative efficiencies of vibration and translation in promoting the gas-phase reaction of CHD3 with the Cl atom to form HCl and CD3. Unexpectedly, we observed that C–H stretch excitation is no more effective than an equivalent amount of translational energy in raising the overall reaction efficiency; CD3 bend excitation is only slightly more effective. However, vibrational excitation does have a strong impact on product state and angular distributions, with C–H stretch-excited reactants leading to predominantly forward-scattered, vibrationally excited HCl.

Several decades of experimental and theoretical molecular collision studies culminated in the formulation of Polanyi'srules of reaction dynamics (1). For reactions of an atom with a diatomic molecule, the rules predict the efficiency of reactant vibrational and translational energy in driving reactions over barriers; namely, vibration can be more effective than translation for a barrier located late along the reaction coordinate, and the reverse is true for reactions with early barriers. An extension of the rules to reactions of polyatomic species becomes ambiguous as a result of the higher degrees of freedom associated with multiple types of vibrational motion. Thus, one may ask: Are different vibrational modes equivalent in their capacity to promote a polyatomic reaction?

In recent years, the issue of mode-specific or bond-selective chemistry (25) has been the subject of several pioneering investigations, for which the reaction of the Cl atom with methane is becoming the benchmark (619). For example, Simpson et al. found that one-quantum excitation in the antisymmetric stretch (v3) mode of CH4 increases the reaction rate by a factor of ∼30 (10). On the other hand, Zhou et al. observed a mere threefold reactivity enhancement for one-quantum excitation of bending (v4) or torsional (v2) modes of CH4 and CD4 (18), in contrast to 200-fold and 80-fold enhancements measured earlier (12, 13). Further experiments (17) and a quasiclassical trajectory calculation (20) supported the results of Zhou et al. Moreover, Yoon et al. found that excitation of the v1 + v4 symmetric stretch-bend combination mode of CH4 enhances reactivity toward the Cl atom roughly twice as much as does the nearly isoenergetic excitation of the antisymmetric combination v3 + v4, which itself promotes a 10-fold rate enhancement over ground-state methane (6). In a similar study, Yoon et al. observed a sevenfold reactivity increase of CH3D when the symmetric, rather than antisymmetric, C–H stretching mode was initially excited (8). All these experiments, however, were performed at a fixed translational or collision energy (Ec); thus, the enhanced reactivity refers to a comparison with the ground-state reaction at the same Ec. As elegant as these experiments are, it remains uncertain whether vibrational motion is more effective in driving this reaction than translation.

We report here a series of experiments aimed to resolve this uncertainty for the Cl + CHD3 → HCl + CD3 reaction. We first studied the groundstate reaction over a wide energy range from the threshold to about 20 kcal/mol of excess energy. Experiments were then performed for the reaction with C–H stretch-excited CHD3, again over a range of initial Ec. To refine the comparison, we also present the results for the bend- and/or torsion-excited reactants. We performed all measurements under single-collision conditions, using the rotatable, crossed molecular-beam apparatus described previously (21, 22). The Cl beam was generated by a pulsed high-voltage discharge of ∼4% Cl2 seeded in a pulsed supersonic expansion of either Ne or He at 6 atm. The CHD3 beam was also produced by pulsed supersonic expansion of either pure CHD3 or ∼20% CHD3 seeded in H2 (for acceleration) at 5 atm. Both beams were collimated by double skimmers and crossed in a differential-pumped scattering chamber. Ec was tuned by varying the intersection angle of the two molecular beams. A pulsed ultraviolet laser that was operated near 333 nm probed the ground-state CD3 product via (2 + 1) resonance-enhanced multiphoton ionization, and a time-sliced velocity imaging technique mapped the recoil vector of the CD +3 ion (21). For studies with C–H stretch-excited reactants, an infrared (IR) laser was used to excite CHD3 directly in front of the first skimmer (19). For reactions with bend-excited reactants, a heated pulsed valve for thermal excitation was used instead (18).

Figure 1 shows two typical raw images, with and without the IR-pumping laser, of the probed CD3(v = 0) products at Ec = 8.9 kcal/mol. Superimposed on the images are the scattering directions; the 0° angle refers to the initial CHD3 beam direction in the center-of-mass frame. Thanks to the time-sliced velocity imaging approach, even the raw data can be easily interpreted by inspection. Whereas the IR-off image is dominated by a side-scattered structure, the IR- on image exhibits two distinct ringlike features reflecting the impact of C–H stretch excitation on the reaction dynamics (23). A sharp forward peak now appears in the inner ring, and additional broad-scattered products form the outer ring. The energetics of the reaction are well defined: The reaction endothermicity is 1.73 kcal/mol, and Ec is 8.9 kcal/mol. The initial ro-vibration excitation of CHD3(v1 = 1, j = 2) adds another 8.63 kcal/mol to the total energy for the IR-on image. By conservation of energy and momentum, these ringlike features can readily be assigned as indicated. The angular distributions of product pairs (0, 00)g and (0, 00)s (the notation of which is described in the legend of Fig. 1) from the ground-state and stretch-excited reactions can be obtained directly from the IR-off and IR-on images, respectively. However, the near degeneracy (only 0.39 kcal/mol of energy difference) of the two paired channels, Cl + CHD3(v = 0) → HCl(v′ = 0) + CD3(v = 0) and Cl + CHD3(v1 = 1) → HCl(v′ = 1) + CD3(v = 0), complicates the data analysis of the IR-on inner ring. Using the threshold method (19), we found that ∼20% of CHD3 reactants were stretch-excited. By scaling down the IR-off distribution by 0.2 and subtracting it from the IR-on data set, the genuine distribution for (1, 00)s was then recovered from the overlapped inner ring. The resultant pair-correlated angular distributions are presented in the lower right panel of Fig. 1, showing totally different appearances for the two pairs, which qualitatively corroborate the HCl state-resolved (not pair-correlated) results at 4.1 kcal/mol reported by Simpson et al. (11). Integrating each distribution over all angles, weighted by the sinθ term for the solid-angle factor (21) (where θ is the product-scattering angle), and accounting for about one-fifth of the CHD3 reactants being pumped, we recover the respective normalized pair-correlated integral cross section (19).

Fig. 1.

(Top) Three-dimensional representation of the raw images, with (right panel) and without (left panel) IR-excitation, of the probed CD3(v = 0) products from the Cl + CHD3 reaction at Ec = 8.9 kcal/mol. Based on energy conservation, the ringlike features in each image are assigned to the labeled product pairs. For clarity, the labelings (1, 00)Cl* and (0, 00)b are omitted for the IR-on image. The numbers in the parentheses denote (from left to right) the quanta of vibrational excitation in HCl and the modes in CD3 products, respectively [the inner subscript specifies the quantum of CD3 mode and the outer subscript indicates the reactant state (“g” for groundstate CHD3, “s” for stretch-excited CHD3, and “b” for bend-excited CHD3)]. (Bottom) The left panel shows the product angular distributions of the inner rings for the IR-on and IR-off images, and the right panel shows the deduced pair-correlated distributions from the stretch-excited reaction. dσ/d(cosθ) is the differential cross section at the product-scattering angle θcm in the center-of-mass frame.

Repeating the measurements under different collision energies, normalized as stated previously (5, 19), we obtain the reactive excitation function σ(Ec), which is the dependence of the integral cross section on Ec, for the ground-state and vibrationally excited reactants (Fig. 2, A and B). Although both reactant vibrations promote reactivity, the degrees of enhancement exhibit different energy dependences, which are accentuated when plotted as ratios to the ground-state reaction (Fig. 2, C and D). Whereas the bend-excited reaction displays a nearly constant enhancement factor of ∼2.5 in the post-threshold region followed by a gradual decline starting from Ec ∼15 kcal/mol, the stretch-excited reaction efficiency drops sharply near threshold and levels off around 2 at higher Ec. Compared with previous studies, the bend result reasonably corroborates an energy-independent enhancement found for bend-excited CH4 over an Ec range of 2.7 to 5.9 kcal/mol (17), and the stretch result is not entirely inconsistent with the apparently larger factors reported at single Ec for the other isotopologues (24).

Fig. 2.

Normalized reactive excitation functions for (A) C–H stretch-excited reactant and (B) CD3 bend/torsion-excited CHD3 as compared to the groundstate reaction. The dotted lines are visual guides. Note the characteristic step feature for a reactive resonance in the stretch-excited reaction near the energetic threshold. For the bend-excited reactant, the thermal populations (∼4%) of the three low-frequency modes (v3, v5, and v6) are assumed (18); thus, the results represent the average cross sections of the three modes. The horizontal lines indicate the equivalent amounts of extra translational energy necessary to achieve reactivity observed upon vibrational excitation. Presented in (C) and (D) are the (conventional) vibrational enhancement factors for the stretch- and bend-excited reactants, respectively, where σs, σb, and σg are the integral cross sections for stretch-excited, bend-excited, and ground-state reactions. The preferential promotions in reactivity, based on an equivalent amount of total energy, are shown in (E) and (F), where the vibrational energies Ev are 8.63 and 3.05 kcal/mol, respectively.

The above-described vibrational enhancement factors are based on comparisons at the same Ec, as in all earlier studies; thus, the total available energies for the ground-state and vibrationally excited reactions are not the same. Are these factors then intrinsically mode-specific, or do they arise purely from the consideration of total deposited energy? A closer inspection, highlighted by the horizontal lines in Fig. 2, A and B, quantifies the additional translational energy needed for the ground-state reaction to proceed as efficiently as the vibrationally excited cases. This translational contribution increases from threshold to higher Ec values, suggesting an alternative and more informative view of the mode-specific enhancement factor. On an equivalent energy base, the mode-specific reactivity here refers to the differential reactivity enhancement or inhibition of the excited species relative to ground-state species that are translationally accelerated to afford an equivalent amount of total energy. Depicted in Fig. 2, E and F, are the reactivity ratios based on such a framework. Contrary to the uncalibrated ratios in Fig. 2, C and D, a very different picture emerges. At low Ec, depositing an equivalent amount of additional energy into translation turns out to be more effective in driving the reaction than exciting a stretching vibration. At higher Ec, there is no preference for either degree of freedom in dictating efficiency. This finding is unexpected in that exciting the bond to be broken in a chemical reaction would intuitively seem to be a singularly effective means of acceleration (25). Moreover, from the perspective of Polanyi's rules, ab initio calculations predicted a more product-like structure at the transition state (2628); thus, a propensity for vibration over translation would be expected for this late-barrier reaction.

For the bending excitation, though the collisions at low Ec are also more sensitive to translation, at higher Ec, bending motion preferentially promotes the reactivity. The bending vibration is of lower frequency and involves nonlocalized, concerted motions of three or more atoms. The approach of the Cl atom can steer and distort the shearing motions of the CD3 moiety. The results presented in Fig. 2F imply that a coupling of this mode to the reaction coordinate is not simply a transfer of the bending energy into translation; rather, a synergistic combination of CD3 distortion and translation can facilitate the C–H cleavage in this direct reaction more effectively than pure translation at the same total energy. Clearly, the picture for polyatomic reactions is more complicated than the extension of Polanyi's rules would have suggested.

To shed light onto these findings, we examine the pair-correlated angular distributions I(θ) in the I(θ)-θ-Ec representation (5, 29, 30). Figure 3 summarizes the results for the five product pairs probed in this study: (0, 00)g, (1, 00)g, (0, 00)b, (0, 00)s, and (1, 00)s. A casual inspection of the I(θ)-θ-Ec patterns reveals that the ground-state product pairs from all three reactions (with ground-state, bend-excited, and stretch-excited reactants, respectively) are similar, showing the direct-scattering ridge characteristic of a peripheral collision (29). On the other hand, the excited product pair from either the stretch-excited or the ground-state reactant displays distinct patterns with pronounced forward peaking and somewhat less backward peaking, suggestive of different reaction mechanisms. Also shown in Fig. 3 (bottom right panel) are the vibrational branching fractions of the HCl(v′ = 1) productsfrom the stretch-excited and ground-state reactions. [Only a single product pair (0, 00)b was detected from the bend-excited reactant.] Both branching fractions increase abruptly near the energetic threshold and remain roughly constant with further increases in Ec. Notably, the initial stretching excitation exerts a large effect on vibrational energy disposal: The branching fraction increases 20-fold for the reaction with C–H stretch-excited CHD3. In other words, C–H stretch excitation strongly favors a product distribution with vibrationally excited HCl.

Fig. 3.

Evolution of the state-correlated angular distributions as a function of collision energies, where Ec is in kcal/mol and θ in degrees. Note the difference in energy ranges and the large disparities in the vertical scales, which have been normalized to one another and to the excitation functions (Fig. 2). The energy evolutions of the angular distribution display distinct patterns: in particular, the ridge structures of the ground-state product pairs and the sharp forward-backward peaking for the HCl(v′ = 1) pairs. Also shown are the vibrational branching fractions of the coincidently formed HCl(v′ = 1) products from the stretched-excited and ground-state reactions (see the bottom right panel). The magnitude of the former reaction is nearly 20 times as large as that of the latter reaction. The vertical arrows mark the respective energetic thresholds.

We interpret these results using a model previously proposed for the ground-state reaction of Cl + CH4 (29, 30). Theoretical calculations on the isotopically analogous reactions suggest that the interaction with an approaching Cl atom causes rapid and strong decreases in the C–H stretching and the CD3 umbrella-bending frequencies in the transition-state region (8, 2628). Based on those calculations, the model adiabatically correlates the vibrational energy curves of the reactant and product pairs by assuming that the vibrational modes preserve their character along the reaction path, as depicted in Fig. 4. Theory also predicts that these two modes not only strongly couple to the reaction coordinate through the curvature passage near the transition-state region but also couple to each other via Coriolis interactions (shaded areas in Fig. 4), fostering nonadiabatic transitions. As evidenced from the exceedingly small branching fraction for (1, 00)g indicated in Fig. 3, the reaction with ground-state CHD3 is therefore largely vibrationally adiabatic, presumably because of the inefficiency of translation-to-vibration energy transfer in the entrance valley. Thus, most of the reactive flux proceeds along the ground-state potential curve, producing the (0, 00)g pair (31).

Fig. 4.

Schematic representation of vibrationally adiabatic potential energy curves along the reaction coordinate S. The curves are depicted in keeping with the theoretically predicted vibrational frequencies with approximate isotope corrections. For clarity, only those relevant to this study are shown. Note the shifting and lowering of the barriers for the reaction with stretch-excited reactants, which might partially account for the higher cross sections at low Ec shown in Fig. 2A. The shaded areas denote the strong curvature and Coriolis couplings region, where vibrationally nonadiabatic transitions occur. Also illustrated are reactions at the same initial (total) energy from three different reactant states and the typical branching ratios of the resultant product pairs (from Fig. 3). amu, atomic mass unit.

The reaction with bend-excited CHD3 produces exclusively the ground-state (0, 00)b product pair, in sharp contrast to theoretical predictions of the predominant formation of umbrella bend-excited methyl radicals (2628). However, the observed I(θ)-θ-Ec pattern is very similar to that for the (0, 00)g pair, in accord with the theoretical prediction of a strong curvature coupling of this mode to the reaction coordinate (2628). To reconcile these seemingly conflicting predictions, the experimental results suggest that the low-frequency bending vibrations of CHD3, despite its adiabatic correlation to the (0, 21) product pair, do not preserve their characters onto the analogous motions of the CD3 products but rather behave as transitional modes in this reaction by promptly funneling the vibrational energy into the rotational and translational motions of the departing products.

In the stretch-excited reaction, the correlated angular distributions of the two product pairs exhibit very different patterns but bear strong resemblance to the distributions of corresponding product pairs from the ground-state reaction. By pattern comparison, we assert that the (1, 00)s pair is produced adiabatically with the salient forward peak resulting from a resonance state temporarily trapped by the dynamic well of the stretch-excited (red) curve in Fig. 4 (4, 30, 32). In that regard, the observation of a step-like feature in the reactive excitation function near threshold (Fig. 2A) is particularly noteworthy, because a similar feature has been observed experimentally in F + HD and confirmed theoretically as an unambiguous fingerprint for reactive resonance (3234); this small step also echoes our recent contention for a resonance in the analogous Cl + CH4 reaction (30).

In contrast, the pattern of the (0, 00)s pair suggests the presence of nonadiabatic pathways induced by the curvature coupling of stretching motions to the reaction coordinate (2628). Hence, a bifurcation of reaction paths for stretch-excited reactants must occur, presumably near the entrance valley of the transition state. The vibrational branching fraction for the nonadiabatic pathway is quite substantial, σ 0s/(σ 0s + σ 1s)∼ 0.55 from Fig. 3 (where σ 0s and σ 1s are the integral cross sections for the (0,00)s and (1,00)s product pairs from the stretch-excited reaction, respectively), indicating a facile process. Theory also predicts a strong Coriolis coupling between the stretching and bending modes (20, 27); this facile nonadiabatic transition could then be mediated and facilitated by the transitional nature of the bending motions of the CD3 moiety during the course of the reaction.

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