Vibrational Enhancement Factor of the Cl + CHD3(v1 = 1) Reaction

Letter pubs.acs.org/JPCL

Vibrational Enhancement Factor of the Cl + CHD3(v1 = 1) Reaction: Rotational-Probe Effects Fengyan Wang,† Jui-San Lin,† Yuan Cheng,† and Kopin Liu*,†,‡,§ †

Institute of Atomic and Molecular Sciences (IAMS), Academia Sinica, P.O. Box 23-166, Taipei, Taiwan 10617 Department of Chemistry, National Tsing Hua University, Hsinchu 300, Taiwan § Department of Physics, National Taiwan University, Taipei, Taiwan 10617 ‡

ABSTRACT: The vibrational enhancement factor in the Cl + CHD3(v1 = 1) reaction is revisited over the collisional energy range of 2−5.9 kcal mol−1. Contrary to the previous results obtained by probing the low-|N, K⟩ states of CD3(v = 0) products, CH stretching excitation becomes more efficacious than the same amount of translational energy in promoting the HCl(v) + CD3(v = 0) product pairs when all-|N, K⟩ states are probed. Whereas the new vibrational enhancement factors, which are three to four times larger than the previous report, agree reasonably well with a recent reduced-dimensionality quantum dynamics calculation, a cautious note is made on the different initial |J,K⟩ rotational selections of the CHD3 reactants in the present theory−experiment comparison. SECTION: Kinetics and Dynamics

E

reaction of polyatomic species involves multiple types of vibrational motion. It is unclear, a priori, if different vibrational modes are equivalent in their capacity to promote the reactivity. An extension of the Polanyi’s rules to polyatomic reactions becomes ambiguous. In the course of studying mode-specific or bond-selective chemistry, we encountered such conceptual issues, and a number of reactions of methane (of different isotopomers) with F(2P),9−12 Cl(2P),13−17 and O(3P)18,19 were examined for establishing general trends. In one of these studies,13 we reported the vibrational enhancement factors (σv/ σg) with respect to the ground-state reaction in Cl + CHD3(v = 1) → HCl + CD3(v = 0) for both CH stretch-excited CHD3(v1 = 1) and bend-excited CHD3(vb = 1) reactants. Two different methods were exploited to prepare the vibrationally excited CHD3.13 A narrow-band OPO/OPA was used for preparing CHD3(v1 = 1) via the R(1) transition of the v1 = 1 ← 0 bands; thus, the stretch-excited reactant has well-defined rotational states of J = 2 and K = 0, ± 1. For the bend-excited reaction, a thermal method was used. As a result, the CHD3(vb = 1) reactants comprise three low-lying vibrational motions (v3, v5, and v6 = 1) with a vibrational temperature about 50 K lower than the pulsed valve temperature11,12 and an estimated rotational temperature of ∼5−10 K. In both cases, vibrational enhancements in reactivity were observed at a fixed initial translational energy (Ec), in accord with the results found in other isotopically analogous Cl + methanes reactions.20−24 The pictures changed, however, when the efficacies of reactant’s vibration versus translation were compared on the basis of the equivalent amount of total energy.13 At low Ec (≲ 4 kcal

nergy disposal and energy requirement are key concepts in chemical reaction dynamics. In the early 1970s, based on extensive quasi-classical trajectory (QCT) calculations on systematically varied London−Eying−Polanyi−Sato (LEPS) surfaces and argument by concurrent infrared (IR) chemiluminescence experiments, Polanyi formulated a set of rules that elucidate how the barrier location influences the energy requirement and energy disposal in a direct atom + diatom chemical reaction.1,2 For an exothermic A + BC reaction, the reaction barrier will be located in the entry valley of the reaction (an early barrier) with a reactant-like transition-state structure, according to the Hammond’s postulate.3 “Polanyi’s rules” then predict that reactant translational energy (Ec) is more effective than vibration (Ev) to surmount the barrier to reaction, thus accelerating the reaction rate. The reverse is true for an endothermic late-barrier reaction. By detailed balance,3 the total available energy will then be deposited mostly into product vibration for an early barrier reaction, whereas translationally hot products will be yielded from a late-barrier reaction. Over the past decades, numerous experimental findings, mostly on the energy disposal in atom + diatom reactions, corroborated well with this simple, appealing rule.3 However, the experimental validations of the energy requirement are sparse, even for the A + BC reactions,3−7 due to the experimental difficulties. With the advances in both the IR lasers (for vibrational up-pumping of the reagents) and the molecular beam technologies (for better control of the initial translational energy over a wide range), only recently have the relative reactivity−efficacy of vibration versus translation been properly addressed, namely, on the basis of an equivalent amount of total energy.8−17 Unlike the A + BC → AB + C reaction, where only one vibration is invoked in the reactant or the product side, the © 2013 American Chemical Society

Received: December 6, 2012 Accepted: January 2, 2013 Published: January 2, 2013 323

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mol−1), translation is more effective in promoting the reaction than either stretch- or bend-excited vibration motion. At higher Ec, the enhancement factor by CH stretching excitation is about the same as the translational energy, whereas the bending excitation yields a moderately higher enhancement factor than translation by a factor of ∼1.8. The former result is unexpected because Cl + CHD3 is a late-barrier reaction and, intuitively, the CH stretching excitation to yield the HCl + CD3 products could be approximately regarded as a pseudo-three-atom reaction, with the spectator of CD3-moiety as a pseudoatom. Hence, by Polanyi’s rule, investing energy into the CH stretching vibration should be a favored way to enhance the reactivity than into translation. This surprising result has been under theoretical scrutiny during the past 2 years.25,26 Using QCT calculations on a highly accurate ab initio potential energy surface (PES)27 a reasonable, nearly quantitative agreement with experiment was found on the preferential vibrational enhancement factor (on the equivalent amount of total energy or σs(Ec)/σg(Ec + Ev)) for the CH stretch-excited reaction.25 More recently a reduceddimensionality (seven dimensions) quantum dynamics on the same PES was performed.26 The reported preferential vibrational enhancement factors for CH stretching excitation are, however, larger than the experimental results almost uniformly by a factor of ∼4 over the Ec range from threshold to ∼10 kcal mol−1. Despite the reduced-dimensionality nature and the centrifugal-sudden approximation employed, the quantum result is thought to be more reliable because the quantum effects, such as tunneling and the zero-point energy, are properly accounted for. Thus, the discrepancy of a factor of ∼4 between the quantum and the experiment is significant and beyond our expectation. To reconcile this discrepancy, we noted that theory and experiment may not refer to the same physical quantities. Experimentally, to achieve a better image resolution for deciphering the weak features of the bend-excited reactions from the adjacent intense signals of the ground and stretchexcited reactions, the probe laser wavelength was fixed at the peak of the Q-head of CD3 (000) REMPI band. As a result, the 2007 experimental results represent the vibrational enhancement factor for the HCl(v′) + CD3(v = 0, low-|N, K⟩) product pair.13,14 The theoretical results correspond to the HCl(v′) + CD3(v = 0, all |N, K⟩) pair. The question then is: Will the two representations, low-|N, K⟩ versus all-|N, K⟩, matter? The issue of this “rotational-probe effect” has been previously investigated in the F + CD4 reaction28 and explored for the present reaction in a preliminary report.29 It was found that the observed image appearances indeed depend sensitively on the precise frequency of the probe laser. For the title reaction, as the red-side of the Q-head peak (higher rotational N-states) was probed, the deduced vibrational enhancement factor appears somewhat larger than that at the peak or at the blue side (low N-states), which clearly hints on one possible source for the aforementioned discrepancy, and a negative correlation between the CD3 rotational excitation and the vibrational excitation of the coincidently formed HCl products was also demonstrated in the stretch-excited reaction. For signal strength considerations, unfortunately, only three probe laser frequencies in the vicinity of the Q-head peak were used at the time. The sampled |N, K⟩ states were quite limited and would not be wide enough to recover the all-|N, K⟩ case. Reported here is our attempt to eliminate the rotationalprobe effects for a fair and quantitative comparison with the

theoretical results. The experiment is essentially the same as the previous reports,13 except for a few aspects. In brief, the Cl beam was generated by pulsed-discharging a mixture of 5% Cl2 in Ne at a pulsed-valve pressure of 5 atm. A seeded beam of 30% CHD3 in He (5 atm) was then crossed with Cl-atom beam in a source-rotatable vacuum chamber. The vibrational ground state of CD3 products was detected by a (2 + 1) REMPI process of the CD3 (000) band and measured by a time-sliced velocity imaging technique.30 Unlike the previous low-|N, K⟩ probe,13,14 the full rotational state distribution of CD3(v = 0) was sampled by scanning the laser frequency back and forth over the Q-head spectral profile while the image was acquired. The product images were recorded in an alternating IR-on and IR-off manner. Each recorded image comprised three spectral scans, and the pair of on/off image was repeated 25−30 times for statistics. As previously alluded to, this wavelength-scan operation trades off the image resolution. Thus, the measurements were limited to Ec < 6 kcal mol−1 to unambiguously remove the signals from the bend-excited reactions. The stretch-excited CHD3(v1 = 1) reactants were prepared in the source chamber by an OPO/OPA operated at 3005.56 cm−1 via the R(1) branch of the CHD3(v1 = 1 ← 0) band.31 To quantitatively evaluate the vibrational enhancement factor at a fixed Ec, one needs to know precisely the fraction of CHD3 in the beam being IR-excited and contributing to the observed product signals, n‡/n0. To this end, two methods, the threshold method32 and the depletion method,9,15,17,19 have been developed. It has also been demonstrated that both approaches yield essentially identical results.15,17 For convenience, the depletion method was used in the present study instead of the previously employed threshold method.13 In this approach, the signal depletions of the CHD2(v = 0) + DF(v = 3, 4) product pairs upon IR irradiation in the F + CHD3(v1 = 0) reactions were determined and taken as n‡/n0. In addition, to increase the IR up-pumping efficiency for higher n‡/n0, we used a multipass ring-reflector33 in this study. (Only a single passage was used in the 2007 works.13,14) These measurements were performed before and after each experiment to ensure consistency. Typical values of n‡/n0 ≈ 0.27 to 0.28 (with one standard deviation of ±0.015) were found over the Ec range of this study (2.0−5.9 kcal mol−1). Figure 1 shows the REMPI spectra over the CD3 (000) band with IR-on (red) and IR-off (black) at three Ec values. Obviously, significant enhancements in the Cl + CHD3 reactivity are induced by IR laser. More importantly, the IRon spectra are more red-shaded than IR-off, indicating that the stretch-excited reaction yields a substantially warmer rotational distribution of the CD3(v = 0) products than the ground-state reaction. The immediate implication is that the experimental vibrational enhancement factor could then depend on how one samples the REMPI band in product imaging measurements. Whereas the REMPI spectra shown in Figure 1 are quite informative, the intensities recorded represent the densities of reaction products and thus by themselves cannot yield the relative reactivity, σs(Ec)/σg(Ec). To this purpose, the CD3(v = 0, all-|N, K⟩ states) product images were acquired and presented in Figure 2. By energy conservation, the ring-like features are readily identified to the labeled product pairs, (νHCl,νCD3), with the subscript g, b, and s denoting the ground-state, bend-excited, and stretch-excited reactions, respectively. Compared with the images previously reported at a fixed-wavelength probe,13,14,32 the present images 324

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Figure 1. (2 + 1) REMPI spectra, IR-off (black) and IR-on (red), of the CD3(v = 0) products from the Cl + CHD3 reaction at three collisional energies. Note that the IR-on spectra are more red-shaded than the IR-off spectra. Integrating the spectral areas and accounting for the IR-excitation efficiencies (n‡/n0) for the IR-on spectra will yield the [(IR-on) − (1−n‡/n0)(IR-off)]/(IR-off) ratios of 73.7, 17.1, and 6.9 for Ec = 2.6, 3.6, and 5.9 kcal mol−1, respectively. These ratios, however, do not represent the desired σs(Ec)/σg(Ec) because of the density-to-flux corrections.

Figure 3. Product speed distributions P(u) and the state-resolved angular distributions of the stretch-excited reaction of Cl + CHD3(v1 = 1) → HCl(v′) + CD3(v = 0) are illustrated at two Ec values. For comparisons, each curve is normalized by the peak. The angular distributions are in good agreements with the previous low-|N, K⟩ results.13 The vibrational branching fraction for HCl(v′=1) products at Ec = 5.9 kcal mol−1 appears smaller than the lower Ec case as well as the previous results at similar Ec values (Table 1).

distributions are in broad agreement. The correlated HCl vibrational distribution (P(u)), however, shows significant rotational-probe effects at Ec ≈ 5.9 kcal mol−1 but not at lower Ec values. (See Table 1.) These findings corroborate well with our previous report at three probe wavelengths.29 Table 1 summarizes the key integral cross section results of this study, along with the previous experiments13 and the QM calculations.26 Clearly the rotational-probe effects exert significant influences on the measured dynamics attributes. Contrasting with the previous low-|N, K⟩ probe,13 the present sampling of all-|N, K⟩ states not only shows a decline in HCl(v = 1) branching fraction at Ec = 5.9 kcal mol−1 but also shows an increase in the preferential vibrational enhancement factors σs(Ec)/σg(Ec + Ev) by a significant factor of three to four, in line with QM prediction (which is also for all-|N, K⟩ states of CD3(v = 0) products). Whereas the previous results for a limited |N, K⟩-probe remain valid by themselves, in terms of Polanyi’s rules, which primarily concern the vibrational and translational motions of the reactants and the products, the question raised as the title of our previous report13 was apparently misled by the rotational-probe effects, and the present enhancement factor should supersede the previous one for the CH stretchexcited reaction. It is significant that recent theoretical advances triggered this reinvestigation. The results not only remove a source of potential confusion and lead to a consistent physical picture but also serve as a cautious note for future experimental investigations. However, along the same line, a remark should also be made about the current experiment-theory agreement on the vibrational enhancement factor. Theoretically, both QCT25

Figure 2. Three pairs of raw images, IR-on and IR-off, at different Ec values are exemplified. The image features are labeled as the product pairs, (νHCl, νCD3), with the subscripts g, b, and s denoting the groundstate, bend-excited, and stretch-excited reactions, respectively. The CD3 product scattering angles are indicated.

appear blurred from sampling all-|N, K⟩ states of CD3(v = 0). Nevertheless, the image resolution is still sufficient to decipher the vibrational distributions of the correlated HCl products without much contamination from the bend-excited reactions. After accounting for the density-to-flux correction,30,34 the product speed P(u) and angular distributions dσ/d(cos θ) of the (“corrected”) IR-on and IR-off images can be obtained. Knowing the IR-excitation efficiency (n‡/n0) from the depletion measurements, the desired distributions for the stretch-excited reaction can then be deduced by [(IR-on) − (1 − n‡/n0)(IRoff)].32 Figure 3 illustrates the distributions thus deduced for the CH stretch-excited reaction at two Ec values. Compared with those with low-|N, K⟩ sampling at similar Ec values from the previous study,13 the product state-resolved angular 325

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Table 1. Comparisons of the Preferential Vibrational Enhancement Factor (σs(Ec)/σg(Ec + Ev)) and the Correlated HCl (v′=1) Branching Fraction σsv′=1/σs by Two Ways of Probe and the QM Calculationa all-|NK>b Ec (kcal/mol) 2.0 2.6 3.6 5.9

σs(Ec)/σg(Ec + Ev) 1.7 2.7 2.5 3.0

± ± ± ±

0.2 0.3 0.2 0.3

low-|NK>c σs ′ /σs

σs(Ec)/σg(Ec + Ev)

± ± ± ±

0.40 ± 0.05 0.61 ± 0.08 0.92 ± 0.10 1.0 ± 0.12

v =1

0.34 0.40 0.39 0.32

0.02 0.03 0.02 0.02

QMd σs ′ /σs

σs(Ec)/σg(Ec + Ev)

± ± ± ±

1.7 2.4 3.1 3.8

v =1

0.40 0.43 0.43 0.43

0.04 0.03 0.03 0.04

a All error bars are ± one standard derivation from repeated measurements and error propagations. bThis work. cPrevious report.13 dQM calculation.26

and QM26 calculations refer to a single rotational state |J,K⟩ = | 0,0⟩ for both the ground CHD3(v = 0) and the stretch-excited CHD3(v1 = 1) reactants (private communications). The R(1) branch of the CHD3(v1 = 1 ← 0) transition was exploited in this and previous studies.13,14,29 Experimentally, the stretchexcited reaction corresponds to the reaction of Cl(2P2/3) + CHD3(v1 = 1, |J,K⟩ = |2,0⟩ and |2, ± 1⟩), whereas the groundstate reaction corresponds to Cl(2P2/3) + CHD3 (v = 0, Trot ≈ 5−10 K). The open question then becomes how the initial rotational selection influences the ground and the vibrationalexcited reactivity − an issue currently under investigation in this laboratory. In any event, because the original Polanyi’s rule1,2 is not formulated for a reaction with rotational-state selected reactants (rather for a thermal distribution of reactants), it remains uncertain, at least subtle, how to fold the effect of initial rotational-selectivity into the context of this venerable rule.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by National Science Council of Taiwan, Academia Sinica, and the Air Force Office of Scientific Research (grant no. AOARD-12-4020.)

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