Extremely short-lived reaction resonances in Cl + HD (v = 1) → DCl + H due to chemical bond softening

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Science  02 Jan 2015:
Vol. 347, Issue 6217, pp. 60-63
DOI: 10.1126/science.1260527

A few very brief pauses in the action

Chemical reactions proceed by the cumulative effect of trillions upon trillions of collisions between atoms and molecules. Usually, a given collision bounces the participants right back out again, either in their original form or with the atoms shuffled around into distinct products. In certain cases, the reacting partners experience a brief lull, termed a resonance, before they rearrange. Yang et al. report the discovery of particularly short-lived resonances in certain reactive collisions of chlorine atoms with vibrationally excited hydrogen deuteride (HD). Their results suggest that similar, as yet overlooked, resonances may lurk in other reactions of vibrationally excited molecules.

Science, this issue p. 60


The Cl + H2 reaction is an important benchmark system in the study of chemical reaction dynamics that has always appeared to proceed via a direct abstraction mechanism, with no clear signature of reaction resonances. Here we report a high-resolution crossed–molecular beam study on the Cl + HD (v = 1, j = 0) → DCl + H reaction (where v is the vibrational quantum number and j is the rotational quantum number). Very few forward scattered products were observed. However, two distinctive peaks at collision energies of 2.4 and 4.3 kilocalories per mole for the DCl (v′ = 1) product were detected in the backward scattering direction. Detailed quantum dynamics calculations on a highly accurate potential energy surface suggested that these features originate from two very short-lived dynamical resonances trapped in the peculiar H-DCl (v′ = 2) vibrational adiabatic potential wells that result from chemical bond softening. We anticipate that dynamical resonances trapped in such wells exist in many reactions involving vibrationally excited molecules.

Reaction resonances are quasi-trapped quantum states in the transition state region that profoundly influence both the rate and product distribution of a chemical reaction (13). Since the landmark theoretical predictions of reaction resonances in the H/F + H2 reaction in the early 1970s (4, 5), extensive studies have been carried out to detect the resonances experimentally and to elucidate them theoretically. However, direct observations have proven to be extremely challenging. Through a series of crossed–molecular beam experiments (69), a physical picture of reaction resonances in F + H2(HD) beyond chemical accuracy has been established. In addition, threshold photodetachment spectroscopy has been used to probe resonances in the I + HI reaction (10). Recently, resonance signatures have also been detected in polyatomic reactions (1114). Forward scattering of reaction products in crossed-beam scattering experiments can be caused by long-lived resonances. However, the presence of forward scattering does not necessarily imply that there are resonances in a chemical reaction. An intriguing question then is if and how we can probe reaction resonances in systems that show no or little forward scattering product, in which the reaction intermediate is very short lived.

Here we report a combined high-resolution crossed-beam and accurate quantum reaction dynamics study on the Cl + HD (v = 1, j = 0) → DCl + H reaction (v, vibrational quantum number; j, rotational quantum number). Our study provides very strong evidence for the existence of short-lived quantum dynamical resonances in this reaction. The Cl + H2 system has served as one of the most important benchmark systems in the study of chemical reaction dynamics (15), along with the H + H2 and F + H2 reactions. It has also played a special role in development of the transition state theory and in the verification of kinetic isotope effects (1619). In contrast to the F + H2 reaction, the Cl + H2 (v = 0) reaction was shown to be a direct abstraction with a colinear later reaction barrier (2025). No resonance features have been detected for this ground-state reaction. Kandel et al. investigated the Cl + HD (v = 1, j = 1,2) reaction at averaged collision energy of 1.5 kcal/mol (26). The observed angular distribution of the HCl product showed predominantly backward and sideways scattering, offering no clear evidence of resonances. Skouteris et al. observed a strong effect of the van der Waals interaction on the branching between the two product channels—HCl + D and DCl + H—in the Cl + HD (v = 0) reaction (21). In addition, the Cl/Cl* + H2 (Cl/Cl*, chlorine atom in the ground/excited spin-orbit state) reaction has also served as a benchmark system for spin-orbit nonadiabatic dynamics (2729). These extensive studies have firmly established that the Cl reaction with HD in both ground and vibrational excited states is a direct abstraction reaction, without any clear signature of reaction resonances.

In the present experiment, the Cl atom beam was generated using a home-designed double-stage–discharge molecular beam source (30), whereas the vibrationally excited HD (v = 1) beam was prepared using the stimulated Raman pumping (SRP) method. Because HD is not infrared-active, SRP is the only good approach to prepare a substantial amount of HD in the v = 1 state for a crossed-beam study. A high-power seeded yttrium-aluminum-garnet (YAG) laser was used as the pump beam, and a home-built high-power tunable optical parametric oscillator (OPO) as the Raman Stokes beam (9, 3133). Because of the frequency drift of the high-power YAG laser, a difference frequency (ωYAG – ωOPO) locking scheme was developed to ensure that the Raman pumping process was locked to the HD (v = 0, j = 0)–to–(v = 1, j = 0) transition during the experiment. In the crossed-beams region, ~13% of the HD molecules were pumped to the (v = 1, j = 0) level. In the experiment, the H atom products were sensitively detected using the H atom Rydberg tagging technique (34), and the collision energy was varied by changing the crossing angle between the Cl and HD beams. A detailed description of the experimental apparatus used in this study can be found in (35).

The time-of-flight (TOF) spectra of the H atom from the Cl + HD (v = 0,1) → DCl + H reaction, with the Stokes laser on and off, were measured at laboratory angles scanned in 10° intervals at collision energies of 2.4 and 4.3 kcal/mol. The H atom TOF spectra for the Cl + HD (v = 1, j = 0) reaction were obtained by subtracting the Stokes laser-off TOF spectra from the Stokes laser-on spectra (fig. S1). Figure 1 shows a few typical TOF spectra for the Cl + HD (v = 1, j = 0) → DCl(v′) + H reaction at a collision energy of 4.3 kcal/mol, which exhibit clear structures corresponding to DCl products in v′ = 0,1,2 vibrational states. For v′ = 0,1 products (in particular, for v′ = 1), bimodal features appear, indicating bimodal distribution of the DCl rotational states. In contrast, no bimodal feature was observed in the TOF spectra at collision energy EC = 2.4 kcal/mol. The obtained TOF spectra were then converted to the center-of-mass frame to obtain the product kinetic energy distributions, from which full rovibrational state–resolved differential cross sections (DCSs) were constructed at collision energies of 2.4 and 4.3 kcal/mol (Fig. 2, A and B). The DCl products at both collision energies are predominantly backward scattered with respect to the Cl atom beam direction, but with a sideways component and even a small forward component at EC = 4.3 kcal/mol. Overall, the reaction of Cl + HD (v = 1) seems to proceed mainly via a direct abstraction mechanism, as the Cl + HD (v = 0) reaction does. However, the observation of a small forward scattering component in the DCS at EC = 4.3 kcal/mol merited further investigation of its origin.

Fig. 1 Time-of-flight spectra of the H atom product from the Cl + HD (v = 1, j = 0) → DCl (v′) + H reaction at the collision energy of 4.3 kcal/mol at different laboratory angles.

Fig. 2 Three-dimensional scattering product contour plots as a function of product velocity for the Cl + HD (v = 1) → DCl + H reaction.

Product contour plots versus product velocity are shown in the center-of-mass frame for (A and B) experimental measurements and (C and D) theoretical calculations at collision energies of 2.4 kcal/mol (A and C) and 4.3 kcal/mol (B and D).

Collision-energy dependence of DCSs in the backward scattering direction can provide clues to possible dynamical resonances, as previously demonstrated in the studies of the F + HD system (9). This is because the backward scattering mainly arises from a small number of low–angular momentum partial waves and largely retains the oscillatory structures of these partial waves as a function of collision energy that may be caused by reaction resonances. Here we designate this collision-energy–dependent DCS in the backward scattering direction as the backward scattering spectrum (BSS). To probe possible reactive resonances in this system, we have carried out a careful measurement of the BSS for the Cl + HD (v = 1) reaction, with the Stokes laser on and off. In this measurement, the microchannel plate detector was always fixed at the laboratory angle corresponding to the center-of-mass backward scattering direction at different collision energies (see table S1), and the measurement was repeated 10 times at each collision energy. The experimental DCS for DCl (v′ = 1) shown in Fig. 3A was the averaged result of the 10 repeated measurements. The corresponding error bar (±1 SD of uncertainty) was determined from the scattered data points of the 10 repeated measurements (see more detailed description of error analysis in the supplementary materials). The obtained BSS for the DCl (v′ = 1) product shows two clear peaks at EC = 2.4 (peak “a”) and 4.3 kcal/mol (peak “b”) (Fig. 3A).

Fig. 3 Collision energy–dependent differential cross sections in the backward scattering direction and the J = 0 reaction probability as a function of collision energy.

(A) Theoretical (solid red lines) and experimental (solid circles) DCS for the backward scattering DCl product of Cl + HD (v = 1, j = 0) over a range of collision energies. The theoretical DCS was shifted by 0.15 kcal/mol lower in energy for the comparison. The experimental DCS for DCl(v′ = 1) was obtained by averaging the results of the 10 repeated measurements for each collision energy, and the corresponding error bar is ±1 SD of uncertainty (see detailed description in the supplementary materials). (B) Total and product state-resolved reaction probabilities with J = 0 as a function of collision energy. The resonance peaks, which correspond to peaks a and b in (A), are clearly evident.

To interpret the experimental observations, we constructed a new potential energy surface (PES) for the Cl + HD reaction based on ~13,000 ab initio energies evaluated at the UCCSD(T)/avqz level of theory (36). DCSs were then calculated for the Cl + HD (v = 1, j = 0) on the PES for collision energies up to 8.0 kcal/mol using the time-dependent wave-packet method (37). The computed three-dimensional (3D) DCSs at E = 2.4 and 4.3 kcal/mol (Fig. 2, C and D) reproduce the corresponding experimental results shown in Fig. 2, A and B, indicating that the new PES is highly accurate in describing the dynamics of the reaction at this high total energy. We have also computed the BSS for the DCl (v′ = 1) product and compared with the experimental results (Fig. 3A). Excellent agreement between theory and experiment is achieved by shifting the theoretical results lower in collision energy by 0.15 kcal/mol, most notably with the two observed peaks reproduced almost exactly. Because the estimated uncertainty of the collision energy is ~0.1 kcal/mol in this experiment, the small discrepancy of 0.15 kcal/mol in the collision energy between theory and experiment indicates that the PES is sufficiently accurate to elucidate the physical origin of the observed oscillatory structures.

The calculated total reaction probabilities for the total angular momentum J = 0 (Fig. 3B) and J ≤ 16 (fig. S4) for the reaction exhibit clear peak structures, very similar to those in the reactions of F + H2/HD (7, 8). The peaks at higher-J partial waves clearly originate from the corresponding J = 0 peaks by progressive J shifting (figs. S4 and S5). The calculated peak positions of the total reaction probability for the J = 0 partial wave in Fig. 3B are very close to those on the measured BSS shown in Fig. 3A. These J-shifting peak structures in the total reaction probabilities of different partial waves are clear theoretical evidence of dynamical resonances in the Cl + HD (v = 1) → DCl + H reaction. We label the two resonances as resonance state a and resonance state b, corresponding to the two observed peaks in the BSS. The peaks in the J = 0 total reaction probability shown in Fig. 3B originate from the DCl (v′ = 0,1) vibrational state–resolved probabilities; in contrast, the DCl (v′ = 2) reaction probability shows peaks at the valley positions of the total reaction probability. Thus, the resonances enhance the DCl (v′ = 0,1) probabilities but, to some extent, depress the DCl (v′ = 2) probabilities.

To understand the nature of these resonances, we performed time-dependent quantum wave-packet calculations to obtain the wave functions at collision energies of 2.4 and 4.2 kcal/mol for the J = 0 partial wave. We use the node structure of the scattering wave function to determine the nature of the resonance states. The 2D contour of the scattering wave function at the collision energy of 2.4 kcal/mol (Fig. 4A1, resonance state a) shows the existence of two nodes along the DCl coordinate (correlating to the DCl product) in the H–DCl complex and one node along the reaction coordinate; the wave function for bending and the DCl coordinate (Fig. 4A2) shows no node on the bending coordinate. Note that the number of nodes in the scattering wave function provides important clues of the vibrational character of the resonance state. Here the wave function for resonance state a is the first excited state trapped in the H–DCl (v′ = 2) vibrational adiabatic potential (VAP) well and can be assigned as the (v1 = 1, v2 = 0, v3 = 2) or (102) state for the reaction complex (HDCl)†, where v1 is the quantum number for the H-DCl stretching mode, v2 for the bending mode, and v3 for the DCl stretching mode, and † indicates that HDCl is a metastable reaction complex instead of a stable molecule. The 2D contour of the scattering wave function at the collision energy of 4.2 kcal/mol (Fig. 4A3, resonance state b) has a similar nodal structure to the (102) state for the DCl and the reaction coordinate but has two nodes on the bend mode (Fig. 4A4). This resonance state can therefore be assigned as the (122) state. Clearly, the two observed states (a and b) are quasi-bound resonance states trapped in the transition state region, with all three vibrational quantum numbers assignable. This confirms that the observed peaks in the BSS (Fig. 3A) in the Cl + HD (v = 1) → DCl + H reaction are caused by dynamical resonances.

Lifetimes of the two resonance states can also be obtained from the widths of the peaks in the total reaction probability of the J = 0 partial wave. The widths for DCl (v′ = 0,1) peaks are determined to be 0.53 and 1.1 kcal/mol, corresponding to lifetimes of 28 and 14 fs for states a and b, respectively (fig. S3). This indicates that the two resonance states in the Cl + HD (v = 1) reaction are extremely short-lived in nature, in comparison with the resonance observed in the F + HD reaction, which lives longer than 100 fs. Partial waves analysis of the BSS for DCl (v′ = 1) revealed that the peaks are mainly contributed by partial waves with small total angular momentum as expected, where resonance enhancement is most substantial (fig. S6).

Figure 4B shows a few VAP curves relevant to the Cl + HD (v = 0,1) → DCl + H reactions. On the ground VAP, there is a single barrier located at the product side close to the static barrier of the reaction system as shown in Fig. 4A. The interaction between H and DCl in the transition state region softens the DCl bond, manifesting not only in smaller vibrational frequency but, more importantly, also in larger anharmonicity. Mainly the latter considerably lowers the DCl energy levels for vibrationally excited states (for details, see section IV in the supplementary materials), resulting in a shallow well on the DCl (v2 = 0, v3 = 2)–H VAP around the peak position of the ground VAP, which supports one resonance state as shown in Fig. 4B. The resonance state b has the same origin as the state a, except on the bending excited state.

Fig. 4 Reactive scattering wave functions and schematic of resonance pathways in the Cl + HD (v = 1) → H + DCl reaction.

(A) Reactive scattering wave functions at collision energies of EC = 2.4 kcal/mol (panel 1) and 4.3 kcal/mol (panel 3) in the Jacobi coordinates RH-DCl and rDCl, with the bending angle θ fixed at 0 and the transition barrier denoted as a green cross in panels 1 and 3. Reactive scattering wave functions at collision energies of EC = 2.4 kcal/mol (panel 2) and 4.3 kcal/mol (panel 4) in the Jacobi coordinates for the bending angle θ and rDCl, with the value of RH-DCl along the yellow dashed curves shown in panels 1 and 3, respectively. (B) VAPs along the reaction coordinate. The VAPs of vHD = 1 and vDCl = 2 correlate strongly, channeling the reactant flux and produces resonance states above the well of VAP of vDCl = 2.

Both resonance states a and b are shape resonances on the DCl (v3 = 2) VAP, and they enhance the overall reactivity as shown in Fig. 3B. They decay either through tunneling over the barrier to yield DCl (v′ = 2) product or through coupling with the DCl (v3 = 0,1) VAP to form DCl (v′ = 0,1) products (Fig. 4B). Hence, these two resonance states are also Feshbach resonances. Because the state b is a bending excited (122) state, it produces DCl with a bimodal rotational distribution, in contrast with a Gaussian distribution from the state a (fig. S9). At EC = 4.3 kcal/mol, the low–partial-wave contribution of the state b yields DCl with bimodal rotational distributions in the backward scattering hemisphere, whereas the contribution from high partial waves of resonance a generates broad peaks in the forward scattering hemisphere with a rotationally cold DCl product (fig. S10).

Quantum reactive scattering calculations showed that similar dynamical resonances also exist in the Cl + HD (v = 1) → HCl + D reaction channel (see supplementary materials for details). However, because of the considerably smaller cross sections of this reaction channel as compared with the DCl channel, which are due to the strong effect of the van der Waals interaction in the entrance channel as has been observed for the ground HD reaction (21), it is extremely difficult to perform crossed-beam experiments on this reaction channel.

From the above studies, we have demonstrated that extremely short-lived resonances in the Cl + HD (v = 1) reaction can be clearly probed with the backward scattering spectroscopy method. These resonances are supported by shallow wells on the DCl (v′ = 2) VAP caused by chemical bond softening in the transition state region. Because chemical bond softening in the transition state region always occurs in reactions with energetic barriers and can result in potential wells on highly excited VAPs, we anticipate the existence of similar resonances in many other chemical reactions involving vibrationally excited reagents. Therefore, reaction dynamics studies with vibrationally excited reagents open the door to probe resonances in many direct chemical reactions.

Supplementary Materials

Supplementary Text

Figs. S1 to S13

Tables S1 and S2

References (3845)

References and Notes

  1. Acknowledgments: This work was supported by the National Natural Science Foundation of China, the Ministry of Science and Technology of China, and the Key Research Program of the Chinese Academy of Sciences.
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