State-Specific Correlation of Coincident Product Pairs in the F + CD4 Reaction

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Science  09 May 2003:
Vol. 300, Issue 5621, pp. 966-969
DOI: 10.1126/science.1083672


When a chemical reaction forms two molecular products, even if the state-resolved differential cross section (DCS) for each product is obtained individually, the coincident attributes of the coproducts are still lacking. We exploit a method that provides coincidence information by measuring the state-resolved, pair-correlated DCS. Exemplified by the reaction F + CD4 → DF + CD3, a time-sliced ion velocity imaging technique was used to measure the velocity distribution of a state-selected CD3 product and to reveal the information of the coincident DF in a state-correlated manner. The correlation of different product state pairs shows a striking difference, which opens up a new way to unravel the complexity of a polyatomic reaction.

Much of our current understanding about chemical reactivity stems from experimental and theoretical studies of reactions that involve only three atoms (1), traditionally symbolized as A + BC → AB + C. The most detailed quantity that experimentalists can measure is the state-to-state differential cross section (DCS) or angular distribution. Only quite recently has this “Holy Grail” been achieved for a few benchmark systems such as H + D2 (25), F + HD (6, 7), and O(1D) + H2 (8). Comparisons with theoretical studies from the first-principle calculations have not only generated tremendous excitement in the field but also have profoundly advanced our basic understanding of the nature of chemical reactions (9).

The vast majority of elementary chemical reactions, however, involve more than three atoms. The added degree of complexity that results from extra atoms presents a formidable challenge to both experimentalists and theoreticians. At the same time, the complex reaction system offers opportunities to address dynamical questions other than those already encountered in A + BC reactions. The concept of mode- or bond-specific reactivity is one of the most celebrated examples (10). The premise underlying this concept is that the “action” in a reactive collision is concentrated in a few degrees of freedom coupled strongly to the motion that carries the system across the reaction barrier. For example, in the reaction of H + HOD(ν) → H2 + OD or HD + OH, both the rate of reaction and the [OD]/[OH] product channel branching depend sensitively on the type of mode or bond excitation of the HOD reactant (11, 12). Similar behaviors were also found for several other atom + triatomics reactions (10), as well as for Cl + CH4(ν) → HCl + CH3 (13, 14). Those pioneering investigations revealed how different vibrational modes or chemical bonds of the molecular reactant couple to the reaction coordinate and how they intimately correlate to the vibration excitation of the product.

For a complex reaction, there is another type of correlation. For example, in the reaction F + CD4 → DF(ν′) + CD3i), for which the methyl radical (CD3) has four vibrational modes, what is the correlation between the vibrational modes of two product molecules? And for a given mode of CD3, what is the quantum-state correlation between DF and CD3? We believe that such pair-correlated information about the two products will provide a powerful way to elucidate the detailed dynamics of chemical events of a complex system.

What makes the present correlation measurement possible is the implementation of a newly developed three-dimensional (3D) ion-velocity imaging technique (15). The experimental apparatus consists of two rotatable, pulsed molecular beams and a fixed detector assembly housed in a large vacuum chamber (16, 17). The F-atom beam was generated by a pulsed high-voltage discharge of F2 seeded 5% in a pulsed supersonic expansion of He at 6 atm. The CD4 beam was produced by pulsed supersonic expansion of pure CD4 at 5 atm. Both beams were collimated by double skimmers and crossed in a differentially pumped scattering chamber. The intersection angle of the two pulsed molecular beams was set such that the collision energy was 5.37 kcal/mol. A pulsed laser operating near 333 nm was used to interrogate the nascent distribution of CD3 radicals at the intersection region by (2 + 1) resonance-enhanced multiphoton ionization.

A specially designed ion-optics assembly (15) was used to map the 3D velocity components of the CD3+ ion onto an imaging detector, which was situated 75 cm from the scattering center. This “mapping” takes full advantage of the conventional 2D velocity mapping (18), while retaining information about the speed of products along the third direction such that the 3D velocity distribution at the collision region can be transported, in one-to-one correspondence, onto an imaging detector. The imager consists of two microchannel plates, a fast-decaying phosphor, and a gatable intensified charge-coupled device (CCD) camera. As the ion packet strikes the detector, a short pulsed voltage is applied to the intensifier to slice out the central portion of the ion-packet signal. The spatial distribution of ions thus sliced is then captured by the CCD camera and transferred to a computer on every laser shot for image accumulation.

Four raw images acquired in this manner are shown in Fig. 1. The laser frequencies were set at the peak of the Q branch of the respective bands. From the spectroscopic analyses, the ranges of rotational levels being sampled are <N> = 4 ± 3, 4 ± 2, 3 ± 2, and 7 ± 2 for the vibrational states starting from CD3 (0000) to (0300) in successive order. Superimposed on the images are the velocity vector diagrams (Newton diagrams) of the collision system. The energetics of this reaction are well defined: The reaction exo-thermicity is 31.04 kcal/mol, and the collision energy is 5.37 kcal/mol. The CD3 products were state-selectively detected. By conservation of energy and momentum, the maximum velocities of the coproduct DF, recoiling from the selected state of CD3, in different vibration states were calculated and are represented as dashed lines in Fig. 1. The successive rings on each image can be unambiguously assigned to the vibrational states of the DF coproduct (19), and their clear separation indicates unequivocally the low rotational excitation of the DF product. The intensity around each ring then gives an immediate impression about the preferred scattering direction of the coincidently formed DF states—the state pair-correlated angular distribution or correlated differential cross section (CDCS).

Fig. 1.

Raw images of the state-selected CD3 products from the F + CD4 → DF + CD3 reaction at Ec = 5.37 kcal/mol. The successive rings on each image correspond to the labeled vibrational states of the coincident DF product. A background spot seen along the CD4 beam velocity vector in the image for the band Embedded Image was discounted in the data analysis. In addition to the density-to-flux correction, the image displays a desired physical quantity d2σ/μ2dμd(cosθ).

The 3D-sliced imaging approach can yield quantitative information about the CDCS through density-to-flux transformation (15). The transformation accounts for the detection sensitivity of a laser spectroscopic probe of CD3 products depending on their velocity and spatial distributions in the laboratory frame. The resultant CDCSs are shown on the CD3 product flux-velocity contour map (Fig. 2) (1). More precisely, the contour map represents the doubly differential cross section [d2σ/dμd(cosθ)] in the center-of-mass polar coordinate (μ, θ).

Fig. 2.

CD3 product state-resolved flux-velocity contour maps derived from the four raw images shown in Fig. 1. The intensities of the four contours are not normalized to one another. The density-to-flux corrections have been made, and the intensity of each contour has been weighted by μ2 in accordance with conventional representation of the doubly differential cross section [d2σ/dμd(cosθ)].

Although there are some similarities among the four contours, their differences are striking. For all CD3 states, the coincidently formed DF in ν′= 2 is confined within the backward hemisphere. The gradual protrusion of its angular distribution in the sideways direction with higher excited CD32) coproduct state is reminiscent of the usual trend observed for a typical A + BC direct reaction proceeding through a rebound mechanism. The angular distributions for DF(ν′= 3) are spread over all angles, but its dominant feature shifts progressively from sideways to forward as increasingly more energy is deposited into the umbrella mode of the CD3 coproduct. In particular, a narrow-peaked forward feature is quite pronounced for CD3 (0200) and (0300) but is entirely absent for (0000) and (0100). For the DF product in ν′ = 4, the most prominent feature is a very sharp forward-scattered peak, except for CD3 (0300), in which the concomitant formation of DF (ν′= 4) is barely open energetically. In addition, a rainbowlike structure adjacent to the sharp forward peak, similar to that for the DF(ν′= 3) + CD3(0300) pair, is quite distinct for CD3 (0000) but becomes vanishingly small for the other CD3 states.

The observation of a sharp state-specific forward peak deserves special attention. A similar feature was noted previously for the least exothermic channel in several three-atom reactions such as H + D2 (35), F + H2 (20), and F + HD → HF + D (6, 7). However, counterexamples also exist, such as F + D2 (21) and OH + D2 (22). This sharp forward feature has often been regarded as experimental evidence for reactive resonance (3, 4, 20). In our opinion, although a reactive resonance can indeed yield a sharp forward feature in product angular distribution, the converse does not necessarily hold true (9, 23). Hence, the mere observation of a sharp state-specific forward peak for the present reaction is not sufficient to establish the existence of a reactive resonance.

Summing up all CDCSs for a given CD3 product state yields the CD3 state-resolved angular distribution as depicted by the black line in Fig. 3. Integrating all angles for each individual CDCS, however, gives the pair-correlated population—a quantity that has recently received much attention in several photofragmentation studies (2426). The pair-correlated population represents the joint probability matrix P(ν′,ν2) for finding a DF vibrator coincidently formed in state ν′ when a CD3 oscillator is in state ν2 in the same reactive event. The traditional product state distribution P(ν′) and P2) are simply averages of P(ν′,ν2) according to Embedded Image, and likewise for P2). If the two products are completely uncorrelated, that is, if the vibrational distribution of DF is independent of the CD3 state, one has P(ν′,ν2) =P(ν′)P2). If, on the other extreme, the two vibrators are strictly correlated, for example, ν2 = ν′+ n, with n an integer, the probability matrix can be written as P(ν′,ν2) =δν′+n, ν2 P2). In both extreme cases it suffices to merely measure the averaged probabilities P2) and P(ν′). More often, the situation lies between the two limiting cases, and P(ν′,ν2) will be more telling.

Fig. 3.

Summary of the state-resolved, pair-correlated angular distributions (CDCS). The scales of the four panels are normalized according to the CD3 product state distribution (17). The black lines represent the vibration-resolved angular distributions of the indicated CD3 states.

Figure 4 depicts the normalized, correlated population or the correlated integral cross section (CICS) obtained from Fig. 3 in conjunction with the CD3 vibration state distribution measurement (17). An anticorrelation between the vibration excitations of the paired products is apparent. Viewing this anticorrelation in a different way provides further insights. The averaged vibration energy of the DF subensembles <Eν>DF, which correlates with a specific CD3 vibration state, can be calculated from the correlated branching. As seen in Table 1, < Eν>DF decreases as the vibration energy of the coincident CD3 increases. More notable, perhaps, is the observation that, except for CD32 = 3), the sums of <Eν>DF and ECD3(ν2) are nearly the same, 28.6 ± 0.3 kcal/mol, which accounts for ∼80% of the total available energy. Two possibilities can account for the abnormal behavior of CD3 (0300): the energetic quantum effect for the near-threshold formation of the coproduct DF in ν′= 4 or, as mentioned previously, the effect of rotational sampling for the (0300) state, which is significantly different from the other vibration states. Resolving these possibilities will require extending the measurement to rotationally resolved spectral features.

Fig. 4.

A 3D representation of CICS or the correlated population of product pairs. The data have been scaled according to the CD3 product-state distribution. Summing up the pair-correlated populations for each fixed vibration state of CD3 (or DF) yields the traditional product DF (or CD3) vibration distributions, which are displayed as open circles (the solid lines are to guide the eye) on the respective background.

Table 1.

Correlated vibrational branching ratios and energy disposal into DF(v′) + CD3(v2) products.

CD3(v1v2v3v4) (0000) (0100) (0200) (0300)
DF v′ = 1 - - - 0.088
DF v′ = 2 0.02 0.06 0.09 0.59
DF v′ = 3 0.33 0.50 0.57 0.32
DF v′ = 4 0.65 0.44 0.34 0.005
Σv 1.0 1.0 1.0 1.0
PCD3 (v2)View inline 1.00 1.45 0.95 0.44
<Ev>DFView inline 28.8 27.0 25.9 18.2
ECD3 (v2)View inline 0 1.31 2.76 4.31
  • View inline* CD3 vibrational state distribution is from (17).

  • View inline All energies are in kcal/mol, and the total available energy is 36.41 kcal/mol.

  • The reaction of F + CD4 is believed to be direct, and the geometry of the transition state is likely of a linear F-D-C configuration with a stretched F-D bond length (27). The geometry of the reactant CD4 is of tetrahedral structure, whereas that of the product CD3 is planar. Hence the umbrella motion of the CD3 moiety, like the DF stretch oscillation, is anticipated to couple favorably to reaction coordinates. The chattering of the light, transferred D atom between the two heavy “particles” (the F atom and the CD3 moiety) in the transition-state region may serve to mediate the energy flow between the vibration of DF and the umbrella motion of CD3, resulting in the vibrational anticorrelation of the two receding products. The result presented in Table 1 suggests that the intramolecular energy transfer induced by the chattering motion of D atoms in the transition-state region occurs as a way of conserving the combined energy of the two vibrators. This notable aspect can be regarded as an extension of the dynamics trait of conservation of vibration action found previously for a typical heavy-light-heavy, three-atom reaction (28).

    Whereas the CICS seems to reflect mostly the concerted motions of D atoms at and beyond the transition-state region, the CDCS, for which the scattering angle should be governed mainly by the trajectories of two heavy atoms, must also carry the imprint of the initial impact parameter and orientation information. We speculate that for a direct reaction the CDCS might provide a vehicle, at least as a first-order approximation, to unfold the “unfoldable”—the impact parameter and the angle-of-attack averaging of a full collision process.

    Because ν2 is the only mode that is excited for CD3 from this reaction (17), the present work concerns only the quantum-state correlation of the two product vibrators. The mode correlation offers another exciting frontier for exploration. The correlated information holds great promise to unravel the “extra-atom” complexity of a polyatomic reaction.

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