Spectroscopic observation of resonances in the F + H2 reaction

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Science  31 Jul 2015:
Vol. 349, Issue 6247, pp. 510-513
DOI: 10.1126/science.aac6939

Glimpsing resonances as F and H2 react

The reaction of fluorine atoms with hydrogen molecules has long provided a window into the subtle effects of quantum mechanics on chemical dynamics. Kim et al. now show that the system still has some secrets left to reveal. The authors applied photodetachment to FH2 anions and their deuterated analogs. This allowed them to intercept the reaction trajectory in the middle and thereby uncover unanticipated weakly bound resonances. Theoretical calculations explain these observations and predict additional similar features that have yet to be seen.

Science, this issue p. 510


Photodetachment spectroscopy of the FH2 and FD2 anions allows for the direct observation of reactive resonances in the benchmark reaction F + H2 → HF + H. Using cooled anion precursors and a high-resolution electron spectrometer, we observe several narrow peaks not seen in previous experiments. Theoretical calculations, based on a highly accurate F + H2 potential energy surface, convincingly assign these peaks to resonances associated with quasibound states in the HF + H and DF + D product arrangements and with a quasibound state in the transition state region of the F + H2 reaction. The calculations also reveal quasibound states in the reactant arrangement, which have yet to be resolved experimentally.

Much of our understanding of the structures of stable molecules has come from spectroscopy. The analysis of bound-bound transitions yields molecular geometries and frequencies, fingerprints of the molecular potential energy surface (PES). The observation of similar sharp structures during a chemical reaction would give comparable insight into the reactive PES, in particular in the all-important transition state region (1). The fleeting nature of the transition state makes this task much more challenging, however. Here, we report the spectroscopic observation of sharp resonance structures associated with the transition state and product valley regions of the F + H2 → HF + H reaction, a benchmark reaction in the field of chemical reaction dynamics (2).

The rapid variation of a scattering cross section with energy or angle has long guided physicists in the investigation of nuclear and subnuclear structure. These so-called resonances are signs of metastable excited states or previously unknown particles. In chemistry, the experimental and theoretical search for these quantum features in reactive scattering experiments has been intense (37). Although tentative experimental evidence for resonances in the F + H2 reaction was first reported in the 1980s (8), it took until 2000 for a resonance to be unambiguously identified in a crossed molecular beam experiment, as a steplike feature in the energy dependence of the integral cross section of F + HD → HF + D (9, 10). The same resonance—a quasibound state in the FHD transition state region with three quanta of excitation in the H–F stretch and none in either the H–D stretch or the bend—has since been found under higher resolution to give rise to undulations in individual state-to-state differential cross sections of the reaction as a function of the collision energy (11). More recent molecular beam experiments combined with theoretical simulations have also provided some evidence for a resonance (12) [or perhaps two resonances (13)] in F + H2.

Anion photoelectron spectroscopy provides an alternative experimental approach to the study of chemical reactions (14). Because the geometry of the FH2 anion is close to that of the neutral F + H2 transition state, photodetachment of the electron from the anion provides a direct spectroscopic probe of the transition state dynamics (15), as illustrated in Fig. 1. If the precursor anion is rotationally cold, this probe avoids the averaging over angular momentum that tends to obscure resonances in a crossed molecular beam experiment. Previous spectra of FH2 have revealed broad peaks associated with the bending levels of the FH2 transition state complex, which correspond to the “quantized bottlenecks” of the reaction rather than reactive scattering resonances (16). Calculations based on the best potential energy surface then available reproduced the positions and intensities of these broad peaks, as well as predicting a number of narrower peaks, which were assigned to resonances (17). Unfortunately, the experimental resolution available at the time (∼20 meV) was not high enough to permit the detection of these features.

Fig. 1 Schematic of the energetics of the photodetachment process.

Arrows show the relationship between the experimental electron binding energy (Ebe) and the scattering energy (E).

The development of slow-electron velocity-map imaging (SEVI) with cryogenic ion cooling has enabled the acquisition of photoelectron spectra of complex species with sub–millielectron volt (sub-meV) resolution (18). Much improved signal-to-noise ratio compared to that of a previous SEVI report (19) has allowed the detection of sharp peaks in the spectra of both FH2 and FD2, which we report here.

The experimental apparatus has been described in detail previously (18, 20), with relevant features highlighted in the supplementary materials (21). The FH2 and FD2 ions are created by introducing F anions into a cryogenically cooled ion trap containing H2 or D2 buffer gas at low pressure; the resulting ion yield is substantially higher than in previous work, where FH2 was generated in a molecular beam ion source. The ions are extracted from the trap, mass-selected, and photodetached at various photon energies. The photoelectron kinetic energy (Eke) distribution is obtained with SEVI, in which a velocity-map imaging electron spectrometer (22) operated at comparatively low extraction voltages produces high-resolution (sub-meV) photoelectron spectra at low Eke. The electron binding energy (Ebe) gives the energy difference between the anion and neutral states and is obtained by subtracting the measured Eke from the photon energy. As previous simulations suggested more obvious signatures of resonances with para-H2 than ortho-H2 (17), the FH2 ions were enriched in p-H2. However, the FD2 ions were formed by trapping F in a buffer gas of normal deuterium (n-D2).

Several earlier publications outline the calculation of the photodetachment spectrum of the FH2 anion (17, 23). Photodetachment projects the vibrational wave function of the anion onto the F + H2 potential energy surface, where it evolves under the influence of the neutral FH2 Hamiltonian. In the Condon approximation, the photodetachment spectrum P(E) is the Fourier transform of the overlap between this evolving wave function and the initial anion vibrational wave function (17). We use here the very high quality LWAL F + H2 potential energy surface (24), which is based on multireference, configuration-interaction calculations. The relation between the experimentally measured binding energy of the electron (Ebe) and the energy E in the theoretical simulation, which refers to the bottom of the F + H2 reactant valley with the F atom in its ground (2P3/2) spin-orbit state, isEbe = EZPE(H2) + EA(F) + D0(FH2) (1)where ZPE is the zero-point energy of H2, EA is the electron affinity of F, and D0 is the dissociation energy of the FH2 anion. These energetics are illustrated schematically in Fig. 1. In the theoretical simulations, we use the experimental EA of F [3.4012 eV (25)] and the ZPEs for H2 and D2 as predicted by the LWAL PES (0.2705 and 0.1918 eV, respectively). To determine D0, we have performed new ab initio and vibrational bound state calculations described in the supplementary materials, obtaining D0 = 0.2005 eV for FH2 and 0.2219 eV for FD2.

The experimental and simulated SEVI spectra of p-FH2 and n-FD2 are presented in Figs. 2 and 3, respectively. Spectra at additional photon energies are shown in figs. S1 and S2. Figures S3 and S4 show a comparison of the p-FH2 photodetachment spectra obtained with two different anion wave functions (fig. S3) and two different potential energy surfaces (fig. S4).

Fig. 2 Photodetachment spectra of p-FH2‾.

Green: experimental overview spectrum (~10 meV resolution). Purple: highest-resolution experimental spectrum (2 to 3 meV) over a narrower energy window. Blue: theoretical simulation at 1 meV energy resolution. Red: convolution of the theoretical simulation over a Gaussian function with full width at half maximum (FWHM) of 3 meV. The calculated spectra have not been shifted to match experiment. The relation between the experimental electron binding energy Ebe and the energy E relative to F(2P3/2) + H2(re) is given by Eq. 1 as Ebe = E + 3.3312 eV.

Fig. 3 Photodetachment spectra of n-FD2‾.

Green: experimental overview spectrum (~10 meV resolution). Purple: highest-resolution experimental spectrum (2 to 3 meV) over a narrower energy window. Blue: theoretical simulation at 1 meV energy resolution. Red: convolution of the theoretical simulation over a Gaussian function with FWHM of 3 meV. The calculated spectra have not been shifted to match experiment. The relation between the experimental electron binding energy Ebe and the energy E relative to F(2P3/2) + H2(re) is given by Eq. 1 as Ebe = E + 3.4313 eV.

The overview p-FH2 photodetachment spectrum is dominated by three broad peaks, labeled A, B, and C in Fig. 2. These had been previously assigned to hindered H2 rotor (or bending) states of the transient FH2 complex (16, 26). The equilibrium geometry of the linear FH2 anion is just on the reactant side of the neutral transition state. Because the minimum F + H2 barrier on the neutral potential energy surface has a bent geometry, photodetachment of the electron excites a bending progression in the neutral FH2 complex. We also observe a smaller peak in the high-resolution p-FH2 spectrum (purple), labeled a, just above the first broad peak A. This peak has not been resolved in any previous experiment. It also occurs in the simulated spectra, along with two smaller peaks (labeled β and γ) at higher energy, and a pronounced peak (labeled α, seen experimentally as a slight shoulder) on the low-energy side of peak A.

The situation for n-FD2 is similar. The experimental overview spectrum in Fig. 3 is dominated by two broad peaks, labeled D and E. The high-resolution spectrum shows two smaller peaks at lower energy, labeled b and c. These smaller peaks are also seen in the theoretical spectra, along with an additional small peak labeled δ, which is not resolved in the experimental spectrum. In both cases (p-FH2 and n-FD2), the agreement between the positions of the calculated and the observed high-resolution peaks (peak a in Fig. 2 and peaks b and c in Fig. 3) is excellent, suggesting that an analysis of the theoretical calculations will provide a reliable guide to the origin of these experimental peaks. What makes this comparison especially compelling is that no arbitrary shift was introduced to align the experimental and theoretical spectra in Figs. 2 and 3; use of the ab initio values of D0 for FH2 and FD2 in the relationship between E and Ebe in Eq. 1 locates the theoretical spectra.

Calculating the scattering wave function ψ(E) at the energy E of each peak allows us to characterize the peaks in the theoretical spectra in Figs. 2 and 3. This is the same procedure used previously by Russell and Manolopoulos (17). The details of the present, more accurate calculations of the wave functions ψ(E) are given in the supplementary materials (21).

Figure 4 shows plots of the wave functions corresponding to the low-energy resonance peaks α, A, and a in Fig. 2 and peaks b, c, and δ in Fig. 3, in collinear F–H–H (F–D–D) geometry. This figure unambiguously reveals the nature of the peaks in the photodetachment spectra: Peaks α and δ are reactant resonances, peak A is a transition state resonance, and peaks a, b, and c are product resonances. The quasibound states that give rise to these resonances are localized in the reactant F + H2 (F + D2) van der Waals well, the FH2 transition state, and the product HF + H (DF + D) van der Waals well, respectively. The green contours in Fig. 4 depict the anion wave functions.

Fig. 4 Resonance wave functions.

The wave functions ψ(E) at the energies E of the first three peaks in the p-FH2‾ spectrum in Fig. 2 (α, A, and a; left), and the first three peaks in the n-FD2‾ spectrum in Fig. 3 (b, c, and δ; right), plotted in collinear geometry, as red [ψ(E) > 0] and blue [ψ(E) < 0] contours, as a function of the distance R between F and the center-of-mass of H2 (D2) and the bond length r of H2 (D2). Superimposed in gray are contours of the LWAL potential energy surface (24). Contours of the FH2‾ and FD2‾ anion wave functions are shown in green for comparison. The contoured regions of all wave functions encompass probability density values greater than 10% of their maxima; the apparent lack of overlap between the anion wave functions and some of the resonance wave functions arises because the overlap is in the tail (<10%) of the probability distribution.

It is possible to assign quantum numbers to the resonance wave functions on the basis of their nodal structure. The reactant resonances have quantum numbers v, j, and t, where v enumerates the number of quanta in the H–H stretch; j, in the hindered H2 rotation; and t, in the F–H2 stretch of the F + H2 van der Waals complex. For the product resonances, v′, j′, and t′ refer, similarly, to the H–F stretch, the hindered HF rotation, and the H–HF van der Waals stretch. The quantum numbers of the reactant resonances in Fig. 4 are (v,j,t) = (0,0,0) for both α (p-FH2) and δ (n-FD2), whereas the quantum numbers of the product resonances are (v′,j′,t′) = (3,0,0) for a and (v′,j′,t′) = (4,0,0) and (4,0,1) for b and c, respectively. Finally, the transition state resonance that gives rise to peak A in the p-FH2 spectrum has three quanta in the H–F stretch (ν1) and none in either the F–H–H bend (ν2) or the H–H stretch (ν3).

The resonances a, b, and c that have been detected as narrow peaks in the present high-resolution SEVI spectra of p-FH2 and n-FD2 are thus all product resonances: quasibound states localized in the van der Waals well region in the product valley. For additional clarification, fig. S5 shows how well the positions of the FH–H and FD–D product state resonances are captured by an adiabatic-bender model (2729). Because the energies of these resonances are below the thresholds for production of HF(v′ = 3) + H and DF(v′ = 4) + D, they cannot decay into these channels and must decay instead into HF(v′ = 2) + H and DF(v′ = 3) + D by vibrational predissociation (the hallmark of a Feshbach resonance). The reason why there are two resonances for FD2 and only one for FH2 can be traced to the larger mass of D, which leads to two quasibound states in the D–DF(v′ = 4, j′ = 0) van der Waals stretching coordinate rather than just one (see the supplementary materials for a more detailed analysis). The emergence of peak a at high resolution was predicted by Russell and Manolopoulos in their earlier theoretical study of the p-FH2 spectrum (17), but peaks b and c in the n-FD2 spectrum have been neither predicted nor measured until now.

The broader low-energy peak A in the p-FH2 spectrum was previously assigned to a “direct scattering” or “quantized bottleneck” state associated with the opening of the F + H2(v = 0, j = 0) channel at the transition state (17). However, it is clear from the present calculations that the wave function ψ(E) at the energy of this peak is localized in the transition state region rather than delocalized along the reaction coordinate. This localization is the characteristic feature of a resonance wave function (30). This resonance has precisely the same form and quantum numbers as the transition state resonance found by Skodje et al. in the F + HD reaction (9, 10). It is thus simply an analytic continuation of this resonance in the mass of one of the two hydrogen atoms. It is the broad peaks B and C in Fig. 2 and D and E in Fig. 3 that are due to quantized bottlenecks, with wave functions that are delocalized along the reaction coordinate (30); the associated wave functions are shown in fig. S6.

All of the other peaks in Figs. 2 and 3 can be assigned in the same way by examining the scattering wave functions at the peak energies. The results of these assignments are summarized in Table 1. The narrow peaks β and γ in Fig. 2 are reactant resonances with quantum numbers (v,j,t) = (0,2,0) and (0,4,0), respectively. Like peak δ in Fig. 3, the theoretical calculations predict only low intensity for these peaks. They have yet to be resolved experimentally. As shown in fig. S4, the agreement between the experimental and theoretical resonance positions is noticeably poorer with the use of another recently developed F + H2 surface (31), illustrating that the resonances are indeed a sensitive and experimentally accessible probe of the neutral reactive surface.

Table 1 Assignment of the peaks in the p-FH2‾ and n-FD2‾ photodetachment spectra in Figs. 2 and 3.

The quantum numbers given for the quantized bottlenecks (see fig. S6) are those of the reactant channel that becomes energetically accessible as a hindered rotor (bending) state at the transition state at the energy of the peak in the photodetachment spectrum.

View this table:

We have shown that high-resolution SEVI photodetachment spectra of p-FH2 and n-FD2 anions reveal previously unresolved peaks in the low-energy region that can unambiguously be attributed to reactive scattering resonances. The signatures of these resonances in the SEVI spectra are far clearer than they would be in a crossed molecular beam experiment, where angular momentum averaging washes out resonance features in both integral and differential cross sections. Thanks to recent experimental developments (including SEVI and, crucially for the present study, the use of a cryogenically cooled ion trap to produce large amounts of p-FH2 and n-FD2), high-resolution anion photodetachment spectroscopy does indeed provide an effective way to observe the elusive resonances in F + H2 reactive scattering, as was predicted by Russell and Manolopoulos almost 20 years ago (17).

Supplementary Materials

Materials and Methods

Supplementary Text

Figs. S1 to S7

Tables S1 and S2

References (3259)

References and Notes

  1. Methods are detailed in the supplementary materials at Science Online.
  2. Acknowledgments: The experimental part of this work was funded by the Air Force Office of Scientific Research (AFOSR) under grant no. FA9550-12-1-0160 and the Defense University Research Instrumentation Program (DURIP) under grant no. FA9550-11-1-0330. M.L.W. thanks the National Science Foundation for a graduate research fellowship. The experimental data are available upon request from M.H.A. is grateful for partial support by the U.S. National Science Foundation under grant CHE-1213332. D.E.M. is funded by the Wolfson Foundation and the Royal Society.
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