Dynamical Resonances Accessible Only by Reagent Vibrational Excitation in the F + HD→HF + D Reaction

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Science  20 Dec 2013:
Vol. 342, Issue 6165, pp. 1499-1502
DOI: 10.1126/science.1246546

Access via Vibration

Molecular beam studies over the past decade have elucidated many subtle quantum mechanical factors governing the influence of vibrational excitation on the outcome of elementary chemical reactions. However, these studies have generally had to focus on reagents that can be easily made to vibrate by direct absorption in the infrared (IR). Wang et al. (p. 1499) show that a variation on stimulated Raman pumping can efficiently excite the IR-inactive stretch vibration in the diatomic molecule, hydrogen deuteride (HD). As a result, they can probe the influence of that vibration on the outcome of the HD + F reaction. Through a combined spectroscopic and theoretical investigation, they uncover Feshbach resonances along the reaction coordinate that are only accessible through vibrational preexcitation.


Experimental limitations in vibrational excitation efficiency have previously hindered investigation of how vibrational energy might mediate the role of dynamical resonances in bimolecular reactions. Here, we report on a high-resolution crossed-molecular-beam experiment on the vibrationally excited HD(v = 1) + F → HF + D reaction, in which two broad peaks for backward-scattered HF(v′ = 2 and 3) products clearly emerge at collision energies of 0.21 kilocalories per mole (kcal/mol) and 0.62 kcal/mol from differential cross sections measured over a range of energies. We attribute these features to excited Feshbach resonances trapped in the peculiar HF(v′ = 4)–D vibrationally adiabatic potential in the postbarrier region. Quantum dynamics calculations on a highly accurate potential energy surface show that these resonance states correlate to the HD(v′ = 1) state in the entrance channel and therefore can only be accessed by the vibrationally excited HD reagent.

Molecular vibrations have profound effects on chemical reactivity. Early studies on atom-diatom reactions led to the establishment of the Polanyi rules, which state that vibrational energy is more efficient than translational energy in promoting a late-barrier reaction, whereas the reverse is true for an early barrier reaction (1). Crim, Zare, and co-workers later observed great enhancements of reactivity in the late-barrier H + H2O/HOD/D2O reactions by reagent vibrational excitation (25), based on theoretical predictions made by Schatz and co-workers (6). More recently, experimental and theoretical studies have explored the generality and validity of the rules for polyatomic systems involving CH4 and its isotopically substituted analogs (715). Most notably, Liu and co-workers carried out extensive experimental investigations on the dynamics of the F/Cl + CHD3 reactions with preliminary CH stretching excitation, and their unexpected observations presented strong challenges to theory (1015).

Reactive resonances, transiently trapped quantum states along the reaction coordinate in the transition-state region of a chemical reaction, have also occupied a central place in reaction dynamics research over the past few decades (1619), particularly in the context of F + H2/HD reactions (2029). Recent experimental studies, in combination with quantum dynamics calculations on a highly accurate potential energy surface (PES), revealed that the course of the F + HD (v = 0) reaction is dominated by a dynamical resonance trapped in the peculiar HF(v′ = 3)–D vibrationally adiabatic potential (VAP) well at the low–collision energy region, where v and v′ represent the vibrational quantum number for the reactant and product molecule, respectively (2729). As the collision energy increases, the reaction trajectory eventually encounters the HF(v′ = 4)–D VAP at the product side. However, theoretical studies on the highly accurate PES reveal that there is no resonance signal for the reaction channel in higher-energy collision regions, raising the intriguing question of whether there are any reactive resonances in the high-energy region, trapped in the HF(v′ = 4)–D VAP well. If such resonances exist, how can we probe them properly?

We report here on a combined crossed-molecular-beam experimental and theoretical study on the F + HD(v = 1) reaction to probe the possible dynamical resonances in the high-energy region of the reaction using a vibrationally excited reagent. Molecular vibrational states of infrared (IR) active modes can be efficiently populated by direct excitation using strong narrow-bandwidth IR lasers. In the case of nonpolar molecules such as H2 with IR-inactive modes, stimulated Raman pumping (SRP) has been the method of choice for preparing excited vibrational states. Product state distribution has been measured for the D + H2(v = 1) reaction using the SRP pumping scheme (30). However, the lower excitation efficiency of SRP has thus far limited its application for crossed-molecular-beam experiments. Recently, Mukherjee and Zare proposed a scheme of Stark-induced adiabatic Raman passage (SARP) (31), an important extension of adiabatic passage techniques (32) to excite Raman-active vibrations using a virtual intermediate state. Following this idea, highly efficient excitation of H2 and HD from v = 0 to v = 1 has been demonstrated in two laboratories using state-of-the-art high-power nanosecond lasers (33, 34). However, because the SRP scheme required both the high-power pump and Stokes lasers to be tightly focused (~0.2 by 0.2 mm2) to achieve near-unity pumping efficiency, the prepared HD (v = 1) population throughout the crossed-beams region (~3 by 3 mm2) was insufficient for crossed-molecular-beam experiments. We have therefore explored the SRP pumping conditions by using defocused pump and Stokes lasers to cover the whole crossed region and found that overall higher population of HD(v = 1) can be achieved, thereby enabling a high-resolution crossed-beam experiment on the F + HD(v = 1), using the D-atom Rydberg tagging technique. (See more details in the supplementary materials.)

Time-of-flight (TOF) spectra of the D atom products from the F + HD(v = 0 and 1) reaction, with the Raman Stokes laser on and off, were measured at laboratory angles varied in 10° intervals at collision energies Ec of 0.23 and 0.63 kcal/mol (Fig. 1). Thanks to the high resolution of the Rydberg tagging technique, the spectra for the F + HD(v = 1, j = 0) reaction can be reliably obtained by subtracting the spectra with the Stokes laser off from those with the Stokes laser on, where j is the rotational quantum number for the reactant molecule. The main structures in the resulting TOF spectra can be clearly assigned to the HF product rovibrational states from the HD(v = 1) reaction. The obtained 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 section (DCS) values were determined for these two collision energies (Fig. 2, A and B).

Fig. 1 (A to C) TOF spectra of the D atom product from the F + HD → HF + D reaction at a collision energy of 0.23 kcal/mol.

The laboratory angle is 110°, which corresponds to 170° in the center-of-mass frame. The blue and red lines in (A) indicate measurements with the stimulated Raman (SR) laser pulse on and off, respectively. The counts ratio between SR on and off can be determined by the peak marked “a” in (A). Consequently, the TOF spectra produced by the vibrational exited state HD can be accordingly extracted, as shown in (C), in contrast with that for the ground state HD shown in (B).

Fig. 2 Three-dimensional product contour plots as a function of product velocity.

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 [(A) and (C)] 0.23 kcal/mol and [(B) and (D)] 0.63 kcal/mol.

For both collision energies, the HF product was produced mainly in the v′ = 3 state, in strong contrast with the F + HD(v = 0) reaction, which produces HF mainly in v′ = 2. At Ec = 0.23 kcal/mol, the product HF is largely backward-scattered with respect to the F-atom beam direction, with some very small forward-scattering components. At Ec = 0.63 kcal/mol, forward-scattering peaks appear for both the HF v′ = 2 and 3 products, although in much more pronounced form for v′ = 3, implying that there may be reactive resonances for the reaction.

To provide additional clues for the possible reactive resonances, we also carried out a careful measurement of the collision energy dependence of the DCS for the HF(v′ = 2 and 3) product in the backward-scattering direction with the Stokes laser on and off. The detector was fixed in the backward direction at different collision energies, and the measurement was repeated 10 times at different collision energies to reduce experimental error, which was estimated to be about 10%. The Stokes laser-off measurements reproduced the energy dependence of DCS in the backward direction for the F + HD (v = 0) → HF(v′ = 1 and 2) + D reaction that we obtained in previous studies (27), in which a single resonance peak at 0.4 kcal/mol was clearly observed. The data for the F + HD(v = 1) reaction in the collision energy range of 0.2 to 0.8 kcal/mol, however, exhibit two broad peaks for the HF (v′ = 2 and 3) products, at collision energies of 0.21 (peak a) and 0.62 (peak b) kcal/mol, respectively (Fig. 3A).

Fig. 3 Collision energy dependence of the DCS.

(A) Theoretical (solid lines) and experimental (solid circles and squares) DCS for the backward-scattering HF product of F + HD(v = 1, j = 0) (red line and full circle) and the HF product of F + HD (v = 0, j = 0) (blue line and full square), over a range of collision energies Ec. The backward-scattering product signals (DCS) at different collision energies were measured by varying the collision energy back and forward 10 times and then summed over. The error bars shown in this figure were estimated by analyzing the signal fluctuations in these scans and should be taken as ±1 SD of uncertainty. (B) and (C) present the reactive resonance wave functions (204) and (304), which enhance the reaction at collision energies of 0.20 and 0.66 kcal/mol with reactant HD(v = 1, j = 0). The contour lines in red in (B) and (C) are the corresponding 2D PES, and the yellow cross represents the transition-state point.

To interpret the experimental observation, we improved the Fu-Xu-Zhang (FXZ) PES for the reaction system by adding higher-level ab initio data points to more accurately reproduce the features around the transition barrier (see the supplementary materials). Extensive studies showed that the new PES, without any scaling factor to the original ab initio energies, is better than the FXZ PES in describing the various dynamical processes in the system. Theoretical three-dimensional (3D) polar DCSs obtained on the new PES at collision energies of 0.23 and 0.63 kcal/mol reproduce remarkably well the corresponding experimental counterparts (Fig. 2, C and D). The energy dependence of the backward-scattered HF(v′ = 2 and 3) calculated on the new PES also agrees well with the experimental measurement, despite the fact that the relative peak heights and positions are slightly different from the experiment (Fig. 3A). It is found that the backward-scattered resonance peaks are mainly contributed by J = 0 to 10 partial waves, where J is the total angular momentum of the reaction system (fig. S1). The calculations also reveal that the integral cross sections (ICS) for product HF(v′ = 2 and 3) as a function of collision energy show two similar broad peaks around collision energies of 0.25 and 0.75 kcal/mol (fig. S2). The peaks in the backward-scattering signal and ICS as a function of collision energy are found to have the same dynamical origin.

The energy dependence of the total reaction probability for the total angular momentum J = 0 exhibits two distinct peaks, at 0.20 (A state) and 0.66 (B state) kcal/mol, which correspond to two reactive resonance states (fig. S3). Time-dependent wave-packet calculations were performed to extract the exact scattering wave functions at these two collision energies for J = 0. The 3D wave function at the collision energy of 0.20 kcal/mol shows the existence of four nodes along the H-F coordinate (correlating to the HF product) in the HF-D complex and two nodes along the reaction coordinate, with the outgoing wave function mainly in the HF(v′ = 3) state (Fig. 3B). Therefore, the resonance state A is the second excited state trapped in the HF(v′ = 4)–D vibrational adiabatic potential (VAP) well, which decays mostly to produce HF(v′ = 3) product. It can be assigned as (v1 = 2, v2 = 0, v3 = 4) or (204) state for the reaction complex FHD, where v1 is the quantum number for the D-HF stretching mode, v2 for the bending mode, and v3 for the HF stretching mode. The 3D scattering wave function for J = 0 at the collision energy of 0.66 kcal/mol has a similar structure along the H-F coordinate as state A, but with three nodes along the reaction coordinate, hence corresponding to the third excited resonance state in the HF(v′ = 4) VAP well, i.e., the (304) state (Fig. 3C). Using the spectral quantization method (35), we found that there is another resonance state with an energy ~2.26 kcal/mol below the HD(v = 1) asymptote, with four nodes along the H-F coordinate and one node along the reaction coordinate (fig. S4), which can be assigned as the (104) resonance state and is inaccessible by the F + HD(v = 1) reaction channel.

Wave functions presented in Fig. 3, B and C and fig. S4 clearly show that the resonances decay mostly into the HD(v = 1) state in the entrance channel, indicating that these resonance states are trapped in a vibrationally adiabatic well formed by the HF(v′ = 4)–D VAP in the product side correlating to the HD(v = 1) state in the entrance channel (Fig. 4). Reaction trajectories with HD(v = 0) can only explore the right side of the v′ = 4 well. By adding the same amount of energy of one quantum HD vibration to the translational motion of the F + HD(v = 0) reagents, the reaction can only take place on the v = 0 reaction pathway and, therefore, cannot access these resonance states. Indeed, quantum scattering calculations of the same PES with the same total energy (all in translation) as the F + HD(v = 1) reaction do not show any evidence of resonances (see the supplementary materials). This clearly reveals that initial vibrational excitation not only provides energy required for the reaction but also gives rise to a proper adiabatic pathway that accesses the dynamical resonances in the high-energy region, whereas translational energy cannot provide such a pathway. The results presented here show that vibrationally excited molecular reactions provide a unique context for probing dynamical resonances in chemical reactions when the vibrationally adiabatic potential, which correlates to the vibrationally excited state of the reagent in the entrance channel, supports quasibound resonance states.

Fig. 4 Schematic diagram showing the resonance-mediated reaction mechanism for the F + HD → HF + D reaction.

Three resonance states are trapped in the peculiar HF (v′ = 4)–D VAP well. The 1D wave functions of the resonance states are also shown. The (104), (204), and (304) states are the first, second, and third excited resonance state, respectively. Only reactant HD(v = 1) can effectively correlate with the resonance states (204) and (304).

Supplementary Materials

Supplementary Text

Figs. S1 to S6

References (3639)

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 Chinese Academy of Sciences.
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