Imaging the Effects of Bend-Excitation in the F + CD4(vb=0,1) → DF(v

Article pubs.acs.org/JPCA

Imaging the Effects of Bend-Excitation in the F + CD4(vb=0,1) → DF(v) + CD3(v2=1,2) Reactions Fengyan Wang†,‡ and Kopin Liu*,†,§ †

Institute of Atomic and Molecular Sciences (IAMS), Academia Sinica, P.O. Box 23-166, Taipei, Taiwan 10617 Department of Chemistry, Fudan University, Shanghai 200433, China § Department of Physics, National Taiwan University, Taipei, Taiwan 10617 ‡

ABSTRACT: The title reaction was studied over the collisional energy range 0.9−4.0 kcal mol−1, using a time-sliced velocity-imaging technique in a crossed-beam experiment. Both the integral and differential cross sections were measured in a product paircorrelation manner. Experimental evidence for the dual reaction mechanisms, a direct abstraction and a resonance-mediated pathway, were presented and await future theoretical confirmation.

1. INTRODUCTION We recently reported an experimental investigation on the effects of reactant’s bending excitations in the F + CD4 → DF + CD3 reaction.1 The reaction of F + CD4 is highly exothermic (ΔHrx = −31.13 kcal mol−1) and very fast (k = 6.7 × 10−11 cm3 molecule−1 s−1 at 298 K)2,3 with an early barrier.4−17 To scrutinize the bendexcited reactivity, the experiment was performed under the crossed-beam conditions, using a time-sliced velocity-imaging technique18 to probe the predominant ground-state methyl radical products, CD3(00,low N-states).1 Two major findings were reported. (1) In terms of the integral cross sections (ICS) in forming the CD3(00) products, the relative excitation function of the bend-excited CD4(vb=1) reactants to that of the ground-state CD4(v=0), σb/σg, is greater than one for Ec ≲ 1.3 kcal mol−1. With the increase of Ec, this ratio gradually declines and levels to about 0.6 for Ec ≳ 2 kcal mol−1. And (2) in terms of the product angular distributions, the three-dimensional (3D) plots of dσ/ d(cos θ) − θ − Ec for the product pairs of (vDF, vCD3) = (4, 00)g, (4, 00)b, and (3, 00)g show vastly different patterns, where the subscripts “g” and “b” denote respectively the ground-state and bend-excited reagents. The (3, 00)g pair shows a pattern characteristic of a direct rebound mechanism, but both the (4, 00)g and (4, 00)b pairs display distinct features, suggestive of a reaction mediated by reaction resonances. Although the resonance implication for the (4, 00)g pair in the F + CD4(v=0) reaction may not be too surprising, in view of the evidence presented previously for the isotopically analogous reactions of F + CH4(v=0) and F + CHD3(v=0),19−24 the experimental observation of the signatures for a resonancemediated pathway in a bend-excited reaction is unprecedented and significant, which might provide an additional clue as to the © 2013 American Chemical Society

nature of the intermediate resonance states. Within the framework of reaction path Hamiltonian,25 we previously conjectured that the reactant bending excitations could act either as a transitional mode,26,27 which will transform into the rotational and translational motions of recoiled products, or as an adiabatic mode that retains its vibrational character and evolves into the bending excitations of the products. Hence, interrogating the bending excitation of CD3 products in a reaction with bend-excited reactants could be regarded as a direct probe of the vibrational adiabaticity and would shed further light onto the microscopic pathway. Here we report the investigations of the umbrella mode (v2) excited CD3 product channels. We will focus on the two reactions: F + CD4 (v b=0,1) → DF(v) + CD3(v2=1,low N )

(1)

and F + CD4 (v b=0,1) → DF(v) + CD3(v2=2,low N )

(2)

For clarity, Figure 1 depicts the relevant energies of the reactant states and product pairs probed in this work.

2. EXPERIMENTAL METHODS The experiment was carried out using a rotating-source, crossedbeam apparatus as detailed in previous reports.1,4−6 In short, a double-skimmed F-atom beam was generated by pulsedischarging a mixture of 5% F2 seeded in Ne at 6 atm. A neat Special Issue: Structure and Dynamics: ESDMC, IACS-2013 Received: February 11, 2013 Revised: February 25, 2013 Published: March 12, 2013 8536

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products, respectively. To clearly separate the contributions of the bend-excited reaction from that of the ground-state reaction in the recorded product images, the laser frequencies were fixed at the peak of Q-heads. That is, the UV photon wavelengths were 330.563 nm for the 211 band and 339.364 nm for the 202 band.4 [Scanning the probe laser wavelengths over the Q-head blurred the image resolution, rendering quantitative image analysis ambiguous.] As a result, only the low rotational N-states, ⟨N⟩ ∼ 3, were sampled.32,33 Nonetheless, REMPI spectra indicated that low-N product states dominate the reactivity.4,34 Because the signals from both bend-excited and ground-state reactions were simultaneously measured, the bias caused by the low-N probe might be partially canceled. We believe that the reactivity comparisons reported here should at least be semiquantitatively correct, and the general conclusions would remain valid.

Figure 1. Energetics of the relevant CD4 reactant states and product pairs, labeled as (vDF, 2i).

CD4 beam was released from a heated, pulsed valve at the stagnation pressure of 6 atm. Two source temperatures (Ts) (292 and 479 K measured by a thermocouple) were used to vary the initial populations of the bend-excited CD4 reactants. A fast ionization gauge located at two positions separated by 261 mm were employed to characterize the beam speed distributions.1,28 Through careful analysis of the speed distribution of the supersonic beam and by virtue of energy balance as detailed in the Appendix, the vibrational energy content of CD4 in the beam and thus the corresponding vibration temperature (Tv) can be deduced. We found that over the temperature range of this study, Tv was approximately 45−60 K lower than Ts, from which the relative populations of bend-excited CD4 reactant (v4 (f) = 996 cm−1 and v2 (e) = 1092 cm−1) were estimated. To isolate the effects of bending excitation, the intersection angles of the two molecular beams were adjusted so that the experiments under different source temperatures yield essentially the same collision (translation) energy Ec.1,28−30 The CD3 products were detected by a (2 + 1) resonanceenhanced multiphoton ionization (REMPI) process through the intermediate 3Pz2A″ Rydberg state.4,31 We exploited the 211 band and 202 band as the probe of the CD3(v2=1) and CD3(v2=2)

3. RESULTS AND DISCUSSION A. Sliced Images and Product States Identification. Figure 2 illustrates the effects of heating the CD4 pulsed valve on the CD3(v2=1) product images in the F + CD4 reaction at two representative collision energies. For both cases the image at Ts = 292 K is dominated by a small-radius feature around the center and a larger ring with sharp forward-peak. At Ts = 479 K an additional full-circle ring lying between becomes apparent. After the density-to-flux transformation,18,35 which accounts for the nonuniformity of the detection sensitivity, these image features can readily be identified from the product speed distributions P(u), as presented in the right (Figure 2). By normalizing the two distributions with the same intensities of the fastest peak (3, 21)g and subtracting from each other, the resultant distribution then represents the differential contributions of the bend-excited reactants at the two temperatures.1,28−30,36 Similarly, two pairs of images recorded for the CD3(v2=2) products are presented in Figure 3. Again, on energetic grounds all image features can be readily assigned, and the differential

Figure 2. Pairs of CD3(v2=1) product raw images at two Ec’s. The two images on the left (middle) were recorded at the source temperature Ts = 497 K (292 K). The right panels show the corresponding product speed distributions P(u). On energetic grounds, the structural features are assigned as the labeled product pairs. The enhancement of the bend-excited reaction signals, (4, 21)b, upon heating the reactant CD4 beam is vividly displayed. 8537

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Figure 3. As Figure 2, but for the CD3(v2=2) products.

contributions from the bend-excited reactants can also be extracted from the analysis of the product speed distributions. B. Pair-Correlated Excitation Functions. It is clear from Figures 2 and 3 that heating the pulsed valve can result in significant thermal populations of the two low-lying bend-excited states (v2 and v4 modes). Unfortunately, the small vibration energy difference (∼100 cm−1) and the accompanied DF product rotational excitations prevented us from resolving their individual contributions to the product image. Hence, a Boltzmann average vibration distribution at a given Tv was assumed, and the sum of both low-lying modes was taken to be the concentration of the bend-excited CD4 reactant nb(Tv). By analyzing the respective product speed distribution P(u), the relative cross section of σb/σg can then be obtained.1,28−30 The relative σb thus deduced is therefore best viewed as the average cross section of the two (v2 and v4 modes) bending states. Despite the approximation, a recent state-selected (by direct IR laser excitation) study of the Cl + CH4(v4=1) → HCl + CH3 reaction37 yielded a vibration enhancement factor of nearly the same as that using the thermal approach.29 The same conclusion that excitation of the methane torsional (v2) or the umbrella (v4) mode yield similar increases in reactivity was also drawn in a QCT study.38 Following the procedures described previously,39 Figure 4 shows the excitation functions (the Ec dependence of the ICS) of the CD3(v2=1) product channels. For the ground-state reaction (middle panel) the excitation function displays a relatively flat behavior at lower Ec and then increases rather abruptly near Ec ∼ 2 kcal mol−1, where the (4, 21)g pair becomes energetically open. On the other hand, the excitation function for the bend-excited reaction (top panel) does not indicate obvious dependence on Ec, except minor oscillations at Ec ∼ 1.5 and 3.5 kcal mol−1, which are barely outside the experimental error bars. As to the relative reactivity σb/σg (bottom panel), the bend-excited CD4 clearly promotes reactivity at low Ec (≲2.5 kcal mol−1) but suppresses the reaction rates at higher Ec’s. These behaviors: an activated excitation function for the ground-state reaction and a relatively flat one with minor oscillations for the bend-excited reaction, as

Figure 4. Pair-correlated excitation functions for the bend-excited reaction of F + CD4(vb=1) (top) and for the ground-state reaction (middle) when the CD3(v2=1,low N) products were probed. At each Ec the two reactions were simultaneously probed from the recorded product image, and the relative populations of the two reagents (the bend-excited and the vibrationally ground state of CD4) were accounted for by the Tv of our CD4 beam (see the Appendix). Thus, the relative cross sections shown in the top and the middle panels are normalized to one another. The dependence of the relative reactivity, σb/σg, on the initial collision energy Ec is presented in the bottom panel. The error bars are one standard deviation of several repeated measurements.

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increase of σ with Ec. And their relative magnitudes are such that σb/σg displays an Ec-independent behavior with the bend-excited reactivity being about half of the ground-state reaction. C. Pair-Correlated Differential Cross Section (DCS). The pair-correlated DCSs of the CD3(v2=1) product channels, (4, 21)g, (4, 21)b, and (3, 21)g, are presented in Figure 6 at four different Ec’s. As illustrated, all (4, 21)g pairs (the top panel) are predominantly forward-scattered, whereas the (3, 21)g pairs (the bottom panel) are mainly backward/sideways scattered with a noticeable forward peak at lower Ec’s. [No image feature can be assigned to the (4, 21)g pair at Ec = 0.8 kcal mol−1, in accord with its energetic threshold of 1.85 kcal mol−1, Figure 1.] The DCSs of the (4, 21)b pair from the bend-excited reactants (the middle panel) display more striking dependences on Ec. It shows a preferential forward-scattering at Ec = 3.7 kcal mol−1 (as the (4, 21)g pairs), then evolves into a sideways dominant distribution at Ec = 3.0 kcal mol−1, further into a distribution with a sharp forward peak at Ec = 2.0 kcal mol−1, and finally becomes backward dominant at Ec = 0.8 kcal mol−1. Qualitatively, the three pair-correlated angular distributions of the CD3(v2=1) channels shown here behave similarly as the corresponding pairs reported previously for the ground-state CD3(v=0) channels.1 Figure 7 shows a few representative DCSs when the CD3(v2=2) products were probed, specifically for the (4, 22)b, (3, 22)g, and (2, 22)g pairs. [The energetic threshold for the (4, 22)g pair occurs at Ec = 3.3 kcal mol−1. Its DCSs observed at higher Ec are essentially the same as those for the (4, 22)b pair at the same Ec, thus not presented here.] Unlike the (4, 21)b pair shown in Figure 6, the shapes of the DCSs for the (4, 22)b pair (top) appear less sensitive to the Ec values, all showing strong forward preference. As for the ground-state reaction, whereas the (2, 22)g pairs (bottom) are mainly backward-scattered, the (3, 22)g pairs (middle) feature a sideways-scattered component, which evolves into a broad backward component and a sharp forward peak at low Ec. The Ec-dependent behaviors of the (3, 22)g pair resemble what observed in Figure 6 for the (3, 21)g pair.

well as the relative cross sections σb/σg, are reminiscent of the previous findings for the F + CD4(vb=0,1) → CD3(v=0) + DF reaction.1 Similarly, the excitation functions for the CD3(v2=2) product channels are presented in Figure 5. In contrast to the above

Figure 5. As Figure 4, but for the CD3(v2=2,low N) products.

CD3(v2=1) products, both the ground-state (middle panel) and the bend-excited (top panel) reactions show a monotonic

Figure 6. Pair-correlated DCSs of the CD3(v2=1) product channels, (4, 21)g, (4, 21)b, and (3, 21)g, are exemplified at four different Ec’s. At each Ec two images under different source temperatures were acquired and analyzed to yield the resultant angular distributions. 8539

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Figure 7. As Figure 6, but for the (4, 22)b, (3, 22)g, and (2, 22)g product pairs.

D. Comparisons with the CD3(v=0) Product Channel. It is instructive to take a closer look at the vibrational enhancement factors, σb/σg, of the two product channels, CD3(v2=1) and CD3(v2=2), and the previously reported major channel CD3(v=0).1 Figure 8 summarizes the results. A few remarks are

vibrational enhancement factors for the CD3(v=0) and CD3(v2=1) channels at low Ec appear to approach to ∼2.5. The shift-over from rate-promotion to rate-suppression occurs at Ec ∼ 1.3 kcal mol−1 for CD3(v=0) and at ∼2.6 kcal mol−1 for CD3(v2=1). It is interesting that the difference of the shift-over Ec’s is roughly the same as the vibrational energy spacing (458 cm−1)6,40,41 between the v2 = 1 and v = 0 states of CD3 products. Because the excitation functions for both CD3(v2=1) (Figure 4) and CD3(v=0) products1 in the bend-excited reaction are nearly Ec-independent, such distinct dependences of σb/σg on Ec must reflect the shapes of the excitation functions of the ground-state reactions. As can be seen from Figure 4 and ref 1 (Figure 3), the collisional energies at which σb/σg change from rate-enhancement to rate-suppression for CD3(v2=1) and CD3(v=0) indeed coincide energetically with the activated behavior in forming the predominant (4, 21)g and (4, 00)g pairs. In that regard, a roughly constant σb/σg for CD3(v2=2) could be attributed to the fact that the (4, 22)g pair is barely open at the highest Ec of this study (Figure 5). It is worth noting that a similar shift of σb/σg from ratepromotion to rate-suppression was previously observed in the F + CHD3(vb=0,1) → CD3(v2=0,1) + HF reactions,28 where the shift-over occurs at at Ec ∼ 1.8 kcal mol−1 for CD3(v=0) and at ∼3.2 kcal mol−1 for CD3(v2=1). Again, these values coincide respectively with the activated excitation functions of the dominated (3, 00)g and (3, 21)g pairs (ref 28, Figure 2). Remarkably, the shift-over energies in the four cases (of the CD3(v2=1) and CD3(v=0) products in both the F + CD4(vb=0,1) and CHD3(vb=0,1) reactions) all appear around 0.7−0.75 kcal mol−1 above the energetic onsets of forming the least exothermic product pairs, respectively, in the ground-state reactions. As mentioned in the Experimental Methods, the probe laser frequencies were fixed at the peak the Q-heads of the respective REMPI bands so that the signals of the bend-excited reaction can be reliably extracted from the adjacent, more intense groundstate reaction signals. Consequently, the results reported here are biased toward the (presumably dominant) low-N-states of

Figure 8. Comparison of the vibrational enhancement factors of the two umbrella-mode excited CD3 products with that of the ground-state CD3(v=0).1 Only low N-states were probed for all three vibrational states. Both CD3(v=0) and CD3(v2=1) show rate promotion at lower Ec values and become rate suppression at higher Ec with the suppression factors nearly the same as the CD3(v2=2) products.

worth noting. (1) For all three product channels the ratios of σb/ σg converge to about 0.6 for Ec ≳3 kcal mol−1. That is, one quantum excitation of the bending modes (v2 and v4) of the CD4 reactants quenches the reactivity to about the same extent for the three dominant product channels at higher Ec. (2) Although the ratios of σb/σg for CD3(v2=2) remain roughly constant, those for CD3(v=0) and CD3(v2=1) display distinct Ec-dependencies and become rate-promoting at lower Ec’s. And (3) the bend8540

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Figure 9. Three dimensional plots of dσ/d(cos θ) − θ − Ec of the nine product pairs (the three pairs on the left are taken from ref 1), which summarize the evolution of the normalized angular distributions against both the product scattering angle θ and the initial collision energy Ec. Each plot was constructed by combining the pair-correlated angular distribution at eight different Ec values (Figures 6 and 7) with the state-specific excitation functions (Figures 4 and 5).

22)g pairs, on the other hand, display a vastly different pattern. Their angular distributions are mainly backward over the Ec range of this study, forming a pronounced backward swath indicative of a direct abstraction reaction mechanism.1,45,48,49,54 [A tiny bit of resonance contribution in the forward direction can also be noted.] As to the remaining (3, 21)g and (3, 22)g pairs, clearly both resonance and direct scatterings contribute. Stated from an alternative perspective, for all three probed CD3(v2=0,1,2) states the formation of the correlated DF(v=4) products, which are the least exothermic channels, appear to be predominantly mediated by reactive resonances. This holds true for both the ground-state and bend-excited reactions. As to the most exothermic pair (2, 22)g, the direct scattering clearly dominates. For the correlated DF(v=3) products, (3, 22)g and (3, 21)g, and (3, 00)g, both resonance and direct scattering pathways contribute. Judging from the appearances of 3D-patterns, the extent of resonance contributions descends in the order (3, 22)g ≳ (3, 21)g ≫ (3, 00)g which seems in line with energetic order (Figure 1). Nonetheless, it is worth noting that the extent of resonance contribution to the (3, 21)g pair appears similar to (3, 22)g yet significantly more than (3, 00)g (which is closer to the (2, 22)g pair), which might suggest that other factors, besides energetics, are also at play. We conjecture that the resonance states in the F + CD4 reaction could also involve the combination bands of the stretching-bending nature. As such, the partial widths of the resonance decay yield higher probabilities in forming the bend-excited CD3(v2=1,2) products than the ground-state CD3(v=0) product. Referring to the possible dual role of the transitional and adiabatic mode characters of the bend-excitation in a reaction, as alluded to in Introduction, this conjecture will imply that the vibrational adiabaticity partakes more (than the transitional character) in the resonance decay

products. Although this applies to both bend-excited and ground-state reactions (i.e., the reactivity comparisons refer to the same subset of CD3 rotational states of a given vibrational state of the two reactions), the quantitative comparisons of σb/σg may alter somewhat when all N-states are considered, as clearly demonstrated in our recent report on the Cl + CHD3(v1=1) reaction.42 That study showed a significant product rotational probe effect in the Cl + CHD3(v1=1) reaction, and the inclusion of all N-states of the probed CD3(v=0) products improved the agreement with a 7-dimensionality quantum dynamics result that concerned only vibrational states.43 This serves as a cautious note for future theoretical and/or experimental comparisons. For the pair-correlated angular distributions, a more taletelling presentation will be to plot the normalized DCS of dσ/ d(cos θ) against θ and Ec, as first suggested in a quantum dynamics study of the D + H2 reaction44 and later experimentally demonstrated in the F + HD reaction,45−47 as well as advocated for a number of polyatomic reactions in several reviews.48−51 Inspections of such 3D plots often afford new insights into the underlying reaction mechanisms.24,48−54 Figure 9 summarizes the results for the three product channels CD3(v2=0,1,2). Because of the signal-to-noise ratio, only three dominant product pairs of each channel are presented. Shown on the top panels are the three CD3 states correlated to DF(v=4) from the bendexcited reaction. As is seen, their patterns are alike, dominated by a pronounced forward-scattering feature at high Ec’s and a ridgelike feature near 2 kcal mol−1. On the basis of pattern comparison, we then infer that all three pairs (4, 00)b, (4, 21)b, and (4, 22)b proceed predominantly via a resonance reaction pathway.1,19−24,44−53 For the ground-state reaction (the middle and bottom panels), the (4, 00)g and (4, 21)g product pairs show similar patterns as the bend-excited reaction pairs and thus are also likely mediated by reaction resonances. The (3, 00)g and (2, 8541

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We employed a fast ionization gauge (FIG) mounted on a Lshaped support, which can be swung to two positions separated by 261 mm, to characterize the skimmed molecular beam speed distribution. The observed time-of-flight profiles can be fitted to Gaussian, from which the speed ratio S was determined by the ratio of the flight time of the peak (tpk) to the fwhm of the distribution,56−59 t pk S = 2 ln 2 (A.3) FWHM

pathway. Further theoretical works will be needed for deeper understandings. It is significant to note that several previous reduceddimensionality quantum dynamics studies on the F + CH4/ CHD3 reactions also found imprints for reactive resonances.20−22,55 The nature or the quantum-number assignment of the resonance state is yet to be elucidated because of the approximation of the reduced-dimensionality treatments. Our assertion of the combination bands of the stretching-bending nature does not exclude the participation of a pure stretchexcited resonance state, and thus is not inconsistent with the theoretical findings.20−22,55 However, we do wish to reiterate here the possible and important role of the bending motions partaken in the resonance-mediated pathway of the F + methane reactions, as was previously surmised in the F + CHD3(v=0) case.24

Thus, the translational temperature Tt of the skimmed beam can be obtained from either

Figure A1. Supersonic beam speed analysis of a He beam at 10 atm, measured by a FIG located at two positions. The peak speeds (solid points) agree well with an anticipated dependence on the source temperatures for a fully expanded beam (solid line). The half-widths of the speed distributions (open points taken at the height of the leading part of the peak, along with the best-fitted dashline) yield the translational temperature (Tt ∼ 0.9 K) of the He atoms in the beam.

and the open points from the leading part of the Gaussian profile at the half height. [The trailing part of the distribution is susceptible to the skimmer interferences, showing a slightly broader distortion from the Gaussian profile.] As is seen, both display a linear dependence on Ts, from which Tt ∼ 0.9 K can be deduced over this source temperature range (or the speed ratio S increases from about 30 at 290 K to about 40 at 470 K). Having established the method for the He beam expansion, Figure A2 presents the data for a CD4 beam at 6 atm. Again, at a given Ts, the solid data points are the mean speeds, υpk, and Tt obtained from the difference between the solid and open points. The Tt was found to vary slightly from 10 K at Ts = 290 to 20 K at Ts = 470 K (and the S changes from ∼11 at 290 K to ∼9.5 at 470 K), which can be compared with the direct IR absorption spectroscopic determination of Tr = 5−7 K for a free jet expansion of a mixture of 10% CH4 in Ar at room temperature.60 Once vpk and Tt are determined, eq A.2 yields the vibrational energy of the CD4 molecules, ∫ TvTsCv dT, relaxed in the

(A.1)

where the heat capacity (C) for each degree of freedom (t for translation, r for rotation, and v for vibration of the molecules) is explicitly written, and k denotes the Boltzmann constant. The terminal speed of a supersonic expansion beam (vpk) from a source temperature Ts can then be written as Ts

Cr dT +

r

≈ (k + C t + Cr)(Ts − Tt) +

∫T

Ts

C v dT

v

∫T

Ts

C v dT

v

= 4k(Ts − Tt) +

∫T

Ts

v

C v dT

(A.5)

where γ = Cp/Cv. Figure A1 shows the results for a He beam at the stagnation pressure of 10 atm. The solid points are from the peak

APPENDIX. DETERMINATION OF THE VIBRATIONAL TEMPERATURE OF A SUPERSONICALLY EXPANDED CD4 BEAM For an isentropic expansion of a gas into vacuum, the enthalpy is conserved, namely, 1/2mv2 + CpT = constant.56 Expressing it in the differential form, one has

∫T

2kTt /m

Δυ =

■

1 mυpk 2 = (k + C t)(Ts − Tt) + 2

(A.4)

or

4. CONCLUDING REMARKS We report here an extensive crossed-beam study of the F + CD4(vb=0,1) → DF(v) + CD3(v2=1,2) reactions. Both the integral and differential cross sections, in the product paircorrelated manner,5,34 were measured for Ec = 0.9 − 4.0 kcal mol−1. In conjunction with the recently reported DF(v) + CD3(v=0) product channel,1 a rather complete set of data is presented and the underlying reaction mechanism elucidated. The results suggest the dual reaction mechanisms, resonance and direct scatterings, contribute to the F + CD4 reaction. Thanks to the product pair correlation measurements,49,50 the relative contributions of the two pathways can be qualitatively deciphered for each individual product pair. However, due to the limitation of the image resolution, these experiments were restricted to sampling the low-N rotational states of the probed CD3(v2=0−2) vibrational states, which prevents us from examining more quantitatively the effects of reactant bendexcitation on chemical reactivity in a purely vibrational state-tostate manner (i.e., integrating the rotational levels of both reactants and products).

−mv dv = (k + C t + Cr + Cv) dT

⎛ γ − 1 2⎞ S⎟ Tt = Ts/⎜1 + γ ⎠ ⎝

(A.2)

where Tr ∼ Tt is assumed (vide infra) and Ct = Cr = 3k/2 for CD4 are used. 8542

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Taiwan, Academia Sinica, and the Air Force Office of Scientific Research (grant No. AOARD-13-4027).

■

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Figure A2. As Figure A1, but for a CD4 beam at 6 atm. Again, the peak speeds show an anticipated source temperature dependence. The widths of the speed distributions result in a Tt varying slightly from 10 K at Ts = 290 to 20 K at Ts = 470 K. The dashline is to guide the eyes, showing slight deviations from the linear dependence at higher temperatures.

supersonic expansion. To determine the vibrational temperature Tv, recall that61 Cv / k =

∑ [(θi/T )2 exp(θi/T )/[exp(θi/T ) − 1]2 ] i

(A.6)

Then

∫T

Ts

C v dT =

v

∑ kθi[1/(eθ /T i

s

− 1) − 1/(e θi / Tv − 1)]

i

(A.7)

where θi = hvi/k. Hence, from the relaxed vibrational energy and eq A.7, the vibrational temperature Tv of the supersonic expansion beam could be determined, from which the relative populations of v2 = 1 and v4 = 1 states were obtained. The results at the three representative source temperatures are presented in Table A1. Roughly speaking, Tv ∼ Ts − 55 K. Table A1. Deduced Vibrational Temperatures Tv and the Relative Populations of the Bend-Excited CD4 in a Supersonic-Expanded Beam

■

Ts (K)

Tv (K)

∑n(v2/v4=1)

292 376 479

230 ± 20 330 ± 15 420 ± 15

0.008 0.057 0.15

REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We are grateful to J.-S. Lin for assisting with the experiment and to Dr. H. Kawamata for helping with the beam characterizations. F.W. thanks the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning. This work was supported by the National Science Council of 8543

dx.doi.org/10.1021/jp4014866 | J. Phys. Chem. A 2013, 117, 8536−8544

The Journal of Physical Chemistry A

Article

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