Communication: Imaging the effects of the antisymmetric-stretching excitation in the O(³P) + CH₄(v₃ = 1) reaction

The ground-state reaction of O(³P) + CH₄ is slightly endothermic by 1.59 kcal mol⁻¹ with a substantial adiabatic barrier to reaction, ∼10 kcal mol⁻¹. It plays an important role in combustion processes¹ and is the simplest of all saturated hydrocarbon oxidation reactions, as such it serves as a benchmark for detailed investigations.^2–23 Its thermal kinetics has been extensively studied both experimentally² and theoretically.^3–12 There are also a few experimental studies of the ground-state reaction dynamics,^13–17 from which the key observations can be summarized as follows. (1) The OH rotational distribution is relatively cold.¹⁴ (2) The vibrational distribution in the umbrella mode of CH₃ products declines monotonically from v = 0 to v₂ = 4.¹³ (3) The product angular distribution is predominantly backward-peaking.¹⁷ In consistence with theoretical calculations,^3–12 all of these findings can be understood as a direct rebound mechanism with a preferentially collinear O–H–CH₃ transition state.

More recently, the attention to this benchmark central-barrier reaction has turned to the effects of vibrational excitations of methane on reactivity.^18–23 Zhang et al. reported on the influences of the bending excitations of CD₄ and CHD₃.¹⁸ They found little rate-promotion and that when a bend-excited CD₄/CHD₃ does react with O(³P), the initial bending energy, instead of flowing into the umbrella mode of methyl radical products as one might expect, is preferentially deposited into OD/OH vibrations. The former finding is now confirmed in a very recent theoretical study.²² In terms of stretching excitation, Wang et al. found a significant increase of the CD₃(0₀) yields in the reaction with CHD₃(v₁ = 1).¹⁹ The product angular distributions also extend to sideways/forward upon reactant stretching excitation. For the D-atom transfer channel, the initial C–H excitation, despite being conserved in the CHD₂ channel (i.e., yielding mainly CHD₂(v₁ = 1) products), unexpectedly hinders the overall reactivity of the unexcited C–D bonds. The results were interpreted as the result of a vibrationally induced steric mechanism^19,24 by opening up the reactive cone of acceptance in abstracting the H-atom at the expense of cone for the D-atom transfer channel. A recent quasiclassical trajectory (QCT) study,²¹ based on a full-dimensional ab initio potential energy surface, showed excellent agreements with experimental results and confirmed the mechanistic origin.

One of the questions left open in the study of the O(³P) + CHD₃(v₁ = 1) reaction is that “… if the enlarged cone of acceptance toward the stretching C–H bond could be evenly balanced by the steric hindrance of abstracting the unexcited D-atoms. In other words, will the total reactivity, when considering both isotopic channels, change upon CH stretching excitation?.”¹⁹ To partially address this question, we report here an analogous study of the O(³P) + CH₄(v₃ = 1) reaction, in which all four H-atoms of CH₄ are collectively excited, in contrast to the local C–H excitation of CHD₃(v₁ = 1), and only one product channel CH₃ + OH is of concern.

The crossed-beam, product-imaging experiment was essentially the same as the O(³P) + CHD₃(v₁ = 1) report.¹⁹ In brief, two doubly skimmed molecular beams, a discharge-generated O-atom beam (a mixture of 5% O₂ in He at 6 atm), and a seeded CH₄ beam (∼30% in H₂), were crossed in a differentially pumped chamber. A tunable infrared (IR) OPO/A (optical parametric oscillator/amplifier) was tuned to the |$3_0^1 $|$301$ R(1) transition to excite a fraction of the CH₄ molecules to a single rovibrational state (v₃ = 1, j = 2) through a multipass ring reflector.²⁵ After the collisions, the ground state CH₃(0₀) products were detected by a (2+1) resonance-enhanced multiphoton ionization (REMPI) method^26,27 and recorded by a time-sliced, velocity-imaging technique.²⁸ Due to the low S/N ratios, the probe laser wavelength was fixed at the peak of the Q-head; thus, mainly the low N-states of CH₃(0₀) were sampled. To interrogate the effects of antisymmetric-stretching excitation, the product images at each E_c were acquired alternatively with IR-on and IR-off. We exploited the IR-induced depletion of the F + CH₄ reaction signals to estimate the IR-excitation efficiency, i.e., n^≠/n₀,^29–31 in data analysis. We note in passing that the discharge-generated O(³P)-atom beam was less intense than the previous photolysis one.^17,18 A trade-off was made in this study for the convenience of changing E_c.

Figure 1 depicts the relevant energetics of this study. Also exemplified in the inset is a CH₃(0₀) raw image at the collisional energy (E_c) of 12.4 kcal mol⁻¹. That is a difference image between the IR-on and IR-off images, for which the fraction of CH₄ reactants being vibrationally excited (n^≠/n₀ ≃ 0.35) has been taken into account. Thus, the image highlights the dynamical features in the O(³P) + CH₄(v₃ = 1) reaction. The two dashed circles superimposed in the image are the calculated energetic limits for the OH(v^′ = 1) and OH(v^′ = 0) coproducts, respectively. Clearly, the image feature is dominated by the formation of OH(v^′ = 1)—a highly inverted vibrational distribution of the OH coproducts. Its angular distribution spans over a broad angular range—in sharp contrast to the backward dominance in the ground-state reaction.¹⁷ 

After the density-to-flux transformation,^28,32 Figure 2 presents the desired product speed (left) and angular (right) distributions. In each panel the distributions of both stretch-excited (in red) and ground-state (in black) reactions are displayed for ready comparisons. The IR-on and IR-off images at a fixed E_c were experimentally normalized to each other. By knowing the n^≠/n₀value in each experiment,³¹ it is straightforward to normalize the resultant distributions of the stretch-excited and ground-state reactions at each E_c.

We report here the results on the dominant CH₃(0₀) products. [The REMPI signals for vibrationally excited CH₃ products were too weak to be quantified.] The product speed distributions (left column) of the ground-state reaction (black) show a single peak corresponding to the OH(v^′ = 0) coproducts, even when OH(v^′ = 1) becomes energetically accessible at E_c = 12.4 kcal mol⁻¹, suggesting a predominantly vibrational-adiabatic pathway.^17,21 On energetic grounds, the recoil energy of the (1, 0₀)_s product pair in the stretch-excited reaction should be 1.5 kcal mol⁻¹ less than that of (0, 0₀)_g pair in the ground-state reaction. Indeed, the product speed distributions clearly show the anticipated shift. A closer inspection of the stretch-excited distributions (red) also reveals a small, albeit noisy, feature at higher speeds, which energetically corresponds to the formation of the (0, 0₀)_s pair. Qualitatively, a correlated vibrational branching ratio of OH(v^′ = 1):OH(v^′ = 0) ≃ 0.85:0.15 was estimated. Similar findings were noted both experimentally¹⁹ and theoretically²¹ in the O + CHD₃(v₁ = 1) → CD₃(0₀) + OH(v^′) reaction. The QCT calculations further indicated significant populations of the bending-excited CD₃ products.²¹ Summing over all the states of CD₃, the fraction of OH(v^′ = 1) drops to 25%–60%, depending on E_c. The mechanistic origin of such a vibrationally hot, correlated OH distribution is not yet totally understood. As detailed previously,¹⁹ two complementary scenarios – a vibrationally adiabatic viewpoint and a kinematic argument – were suggested to be important factors. Yet, neither of them appeared to provide a full picture. Further theoretical investigation is warranted.

As to the pair-correlated angular distributions, the ground-state pair (0, 0₀)_g is backward-peaking and confined entirely in the backward hemisphere, whereas the angular distributions of the (1, 0₀)_s pair protrude significantly into the forward hemisphere. It is worth noting that the broadening of angular distributions occurs even at E_c = 8.7 and 9.7 kcal mol⁻¹, where tunneling dominates the reactivity. An increase in E_c merely widens the angular range without changing the “flat” shapes in the backward hemisphere. These findings corroborate well with the previous reports on the CD₃(0₀) + HCl(v^′ = 1) channel in Cl + CHD₃(v₁ = 1).^19,21 Again, the vibrationally induced steric mechanism^19,24 may be operative here. The driving force behind this mechanism is attributed to long-range anisotropic interactions,¹⁹ which funnel the trajectories toward the transition state. In other words, the long-range interaction induced by stretching excitation of methane effectively acts as a “positive lens” by focusing the larger impact-parameter collisions into the reactive zone, and thereby widens the range of the product scattered angles as well as promotes the reactivity.

We also note that at E_c = 12.4 kcal mol⁻¹, where the reactions proceed over the barriers, the intensity in the backward direction in the stretch-excited reaction is significantly smaller than that in the ground-state reaction, implicating that the additional reactivity upon stretching excitation occurs at the penalty of the backward-scattered fluxes. This behavior has to be contrasted with that in the O + CHD₃(v₁) → CD₃(0₀) + OH(v^′) reaction, where the intensities for reaction with CHD₃(v₁ = 1) are higher than the ground-state one over all angles. However, the angular distribution of the CHD₂ + OD channel remains backward peaking, as the ground-state reaction, and its reactivity is greatly suppressed when CHD₃ is stretch-excited. Considering both isotopic channels, the relative intensities in the backward direction could conceivably be altered.

Since the distributions shown in Fig. 2 have already been normalized, the vibrational enhancement factors σ_s/σ_g at a fixed E_c can readily be derived. In conjunction with the previously reported excitation function for the ground-state reaction,¹⁷ Figure 3 presents the excited one. Two ways to examine the vibrational effects: let us first take a vertical view of the results. Upon CH stretching excitation, the shape of the excitation function changes, approaching a linear dependency from a distinct concave-up one. Based on the modified line-of-centers models discussed previously,^33,34 this variation in shapes can be ascribed to the softening of the transition-state bending potentials upon stretching excitation. At a fixed E_c, σ_s/σ_g ≃ 1.5–3, in good agreement with recent theoretical predictions.^22,23 This enhancement factor is, however, noticeably smaller than σ_s/σ_g ∼ 5 in O(³P) + CHD₃(v₁) → OH + CD₃(0₀), yet larger than the suppression factor <0.2 of the other isotopic channel OD + CHD₂.¹⁹ Nevertheless, the modest vibrational enhancement factor reported here clearly demonstrates that the stretching excitation of methane indeed promotes the total reaction rate with O(³P), at least for CH₄(v₃ = 1), which partially answers the question mentioned early.

Alternatively, one can view the two excitation functions horizontally. As illustrated by the horizontal line in Fig. 3, a shift of ∼1.6 kcal mol⁻¹ in E_c was observed upon CH₄(v₃ = 1) excitation, compared to the shift of ∼4.4 kcal mol⁻¹ for the O(³P) + CHD₃(v₁ = 1) → OH + CD₃(0₀) reaction.¹⁹ In other words, although the stretching excitation enhances the reactivity, only part of the deposited vibrational energy (∼18% for CH₄(v₃ = 1) and ∼50% for CHD₃(v₁ = 1)) can be used to surmount the reaction barrier. It is also significant to note that exciting the stretching vibration of CH₄(v₃ = 1) does not appear to lower the reaction threshold in any appreciable amount—again in sharp contrast to the O + CHD₃(v₁) → CH + CD₃(0₀) case, where a significant vibrational-induced threshold-lowering (from ≥8 kcal mol⁻¹ to ∼4.5 kcal mol⁻¹) was reported.¹⁹ Both observations, the threshold-lowering and the E_c-shift at a fixed reactivity, are entirely consistent with the above smaller vibrational enhancement factor, implicating that the v₃-mode excitation of CH₄ may be less efficient in promoting the reaction rate than the v₁-mode excitation of CHD₃. It remains to be seen when the issue of the uncertainties in the relative detection sensitivities of the CD₃ and CHD₂ products is resolved—perhaps by exploiting the one-photon ionization detection scheme. Works along this line as well as the relative reactivity in O(³P) + CH₄(v₁ = 1), for which theories predict comparable rate-promotion as CH₄(v₃ = 1) in the post-threshold region but higher efficacy at higher E_c,^22,23 are planned.

As a final remark, judging from Fig. 3 and Fig. 4(a) of Ref. 19 and consistent with theory,^22,23 the translational energy appears to be more efficient to activate the O(³P) reactions with CH₄ and CHD₃ than an equivalent amount of vibrational energy. In this regard, the propensity toward translational energy at low collision energies can also be found in many other activated reactions.^{29–31,35–44} On intuitive grounds, a finite momentum of the two reactants seems necessary in order to drive reactions over barriers. If correct, a translational propensity in the post-threshold region of activated reactions may well be a general trait; regardless it is an early-, central-, or late-barrier reaction. One may wonder: Is there any correlation between the extent of the energy range, over which this translational propensity holds, and the barrier locations?

We thank J.-S. Lin for assistance during the measurements. This work is supported by the Ministry of Science and Technology of Taiwan, Academia Sinica, and the Air Force Office of Scientific Research (Grant No. AOARD-134027).