State-Selected Reaction of Muonium with Vibrationally Excited H2

Letter pubs.acs.org/JPCL

State-Selected Reaction of Muonium with Vibrationally Excited H2 Pavel Bakule,†,⊗ Donald G. Fleming,*,‡,§ Oleksandr Sukhorukov,⊥ Katsuhiko Ishida,# Francis Pratt,† Takamasa Momose,§ Eiko Torikai,∥ Steven L. Mielke,∇ Bruce C. Garrett,× Kirk A. Peterson,∞ George C. Schatz,¶ and Donald G. Truhlar∇ †

ISIS & RIKEN/RAL Muon Facility, Rutherford Appleton Laboratory, United Kingdom TRIUMF, 4004 Wesbrook Mall, Vancouver BC V6T 2A3, Canada § Department of Chemistry, University of British Columbia, Vancouver V6T 1Z1, Canada, ⊥ Department of Chemistry, University of Alberta, Edmonton, T6G 2G2, Canada # RIKEN Nishina Center for Accelerator Based Science, RIKEN, Wako, Saitama 351-0198, Japan ∥ Faculty of Engineering, Yamanashi University, Kofu, Yamanashi 4008511, Japan ∇ Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States × Pacific Northwest National Laboratory, Richland, Washington 99352-4630, United States ∞ Department of Chemistry, Washington State University, Pullman, Washington 99164-4630, United States ¶ Department of Chemistry, Northwestern University, Evanston, Illinois 60208-3113, United States ‡

S Supporting Information *

ABSTRACT: We report a new advance in the study of muonium (Mu) reactivity; specifically, we report the rate constant for the Mu + H2(vibrational quantum number n = 1) reaction determined by measurements at 300 K and by converged quantum mechanical calculations. Comparisons are made with earlier results for D + H2 (n = 1) and with the corresponding thermal reaction rates. The measurements are a sensitive probe of the high-curvature region in the entrance valley of the potential energy surface (PES) and thus provide a qualitatively different probe of the PES than that provided by any previous experiment.

SECTION: Kinetics and Dynamics

M

uonium (Mu), composed of a positive muon (μ+) and an electron, can be regarded as the lightest isotope (0.113 amu) of the H atom;1−3 hence, its study has proven uniquely effective in elucidating the nature of quantum mass effects in chemical reaction rates.1,3−8 Here, we report a Mu reaction rate with vibrationally state-selected reactants, specifically, the rate of the Mu + H2{1} reaction, where {1} denotes vibrational quantum number n = 1, in which stimulated Raman pumping (SRP)9−11 has been used to populate H2{1}. The motion of Mu is much less classical than that of any other atom; therefore, comparison of theory to experiment for Mu dynamics provides a critical test both of the potential energy surface (PES) and of our ability to use quantum mechanical (QM) calculations to predict reaction dynamics from first principles. We use the Born−Huang (BH) definition of a PES,12 which consists of the isotope-independent Born−Oppenheimer PES plus an isotope-dependent adiabatic nuclear kinetic energy © 2012 American Chemical Society

term. Using BH PESs, excellent agreement between theory and experiment has been obtained for thermal rate constants of D, Mu, and Heμ reacting with H2,1,8,13 where Heμ is effectively the heaviest H isotope, consisting of a single electron orbiting a pseudonucleus composed of a negative muon and an α particle.1,8 Measuring state-selected reaction rates with H2 has proven particularly challenging;14 the result presented here is the most accurate state-selected rate constant measurement for any H isotope reacting with vibrationally excited H2. A vibrationally adiabatic potential energy profile defined by Va = VMEP(s) + ε(n , m, s)

(1)

can be used to illustrate the energetic requirements for a stateselected reaction; here, s is the signed distance from the saddle Received: August 8, 2012 Accepted: September 10, 2012 Published: September 10, 2012 2755

dx.doi.org/10.1021/jz3011496 | J. Phys. Chem. Lett. 2012, 3, 2755−2760

The Journal of Physical Chemistry Letters

Letter

Although the population of different rotational states of the n = 1 vibrational level also occurs in the SRP process, at 50 bar of pressure, relaxation of rotational states is rapid compared to vibrational relaxation;27 therefore, a thermal rotational distribution is expected (at 300 K for n = 1, this is about 12% j = 0, 64% j = 1, 12% j = 2, and 10% j = 3). Rotational alignment can also be induced by SRP but requires much higher laser powers than were used in the experiment (by several orders of magnitude). The SRP process employed the 532 nm pulse in a double-pass arrangement, where high-reflectivity mirrors were used to retroreflect the incident 532 nm and Raman-generated 683 nm beams. Although higher pumping efficiencies are achievable by a cavity arrangement,28,29 the two-mirror arrangement used allowed us to monitor the number of pumped molecules, Np{1} = (3.65 ± 0.31) × 1017 at 550 mJ/ pulse, determined from measurements of both the Stokes red at 683 nm and depleted green at 532 nm; it also reduced laser damage of the optical components over long run periods. Additional details are presented in the Supporting Information. Muons are produced fully spin polarized, with their decay positrons (μ+ → e+νeνμ̅ ) subsequently emitted preferentially along the muon spin direction and detected by counter arrays in “forward” and “backward” directions, providing a determination of the μSR “asymmetry”.2,30−32 A transverse magnetic field (TF) of 2.1 G causes Mu precession, resulting in each counter array seeing a change in count rate as the muon spin sweeps past, giving rise to oscillations at the Mu Larmor frequency, νMu = 3.00 MHz. The laser was synchronized with every second muon pulse, with the time spectra of decay positrons routed into separate laser-off and laser-on histograms (Figure 2, top). Three separate data sets were collected, two at the maximum laser power of 550 mJ/pulse (one with a different delay) and one at about half of this power, effectively halving [H2{1}]. The temperature was ambient, 300 ± 4 K, for the first two data sets and was 300.6 ± 1.4 K for the third. Although there are only a few hundred muons in the target cell from each beam burst, wherein Mu is produced during the slowing-down of the μ+,30 this process is repeated many times, allowing us to analyze the reaction in terms of an ensemble of spin-polarized Mu atoms of concentration [Mu] that undergo reaction and decay.33 Of several contributing processes, only two are central to the kinetics measurements

point along the minimum-energy path (MEP) in isoinertial coordinates, VMEP is the PES along the MEP, n is the quantum number of the mode that starts as a H2 vibration and adiabatically transforms to a quasi-symmetric stretch at the saddle point and a MuH stretch at the products, m is the collection of other quantum numbers for modes transverse to the reaction coordinate, namely, bending and rotational modes (including the total angular momentum), and ε is the energy in these transverse modes with quantum numbers n and m.15−19 Figure 1 displays Mu + H2 vibrationally adiabatic potential

Figure 1. Vibrationally adiabatic potential curves, Va, (eq 1) (left axis) and the reaction path curvature (right axis) for the Mu + H2 reaction. Asymptotic values of Va are indicated by horizontal dashed lines.

curves for n = 0 and 1 with all other modes in their ground states (m = 0), as calculated using the WKB approximation for stretches and the centrifugal oscillator approximation for the coupled bending motions.20 Because of the large zero-point energy of the product relative to the reactant,1,8,21 for energies that contribute significantly to the rate constant at 300 K, only the n = 0 vibrational level of MuH is energetically accessible. The thermal reaction is wellcharacterized by considering motions in the vicinity of the variational transition state (VTS), which for this isotopic combination is shifted well into the product valley of the PES,22 as shown by the maximum of Va for n = 0 in Figure 1. The vibrationally state-specific n = 1 rate constant, kMu{1}, is expected to be controlled primarily by this VTS region17−19 but is also sensitive to the regions in the reactant valley and saddle point vicinity where the reaction path curvature, κ,23−26 is highest because vibrationally nonadiabatic transitions occur most frequently in these regions.24−26 The new measurements are thus a probe of both of these PES regions. The experiment employs a spin-polarized pulsed muon beam (at the RIKEN/RAL muon facility at ISIS) at 50 Hz, which is stopped in 50 bar of normal H2 to generate Mu atoms. This generation is synchronized with an overlapping Nd:YAG pulsed laser used at 25 Hz, operating at 532 nm. A single aluminum “Raman/reaction” cell was used, with a muon channel of 40 mm × 4 mm profile spark-cut to 55 mm deep, accommodating a window of separate Mylar sheets that were adjusted to optimize the stopping distribution of Mu atoms in the (6 N pure) H2 gas. The laser channel was cut perpendicular to the muon channel with the same cross section and a length of 100 mm. The laser beam was collimated to an elliptical spot size of only ∼0.15 cm2 in order to maximize the overlap of the laser with the stopping profile of Mu atoms, an important aspect of the experiment.

λ1

Mu + H 2{1} → MuH + H λC

H 2{1} + H 2 → 2H 2

(2)

where λ1 is the pseudo-first-order relaxation rate constant for the reaction of Mu with H2{1} and λC is the pseudo-first-order relaxation rate constant for H2{1} colliding with unpumped molecules. The Mu + H2 (n = 0) reaction is too slow to contribute significantly. 7 Wall de-excitation, which was significant in the D + H2{1} study,14 can be neglected because the H2{1} lifetime at 50 bar is too short compared to the time scale for diffusion to the walls. Inelastic collisions also do not contribute to the Mu relaxation rate because they have no effect on the muon polarization. For each spatial point in the reaction cell, r ≡ (x,y,z), where z denotes the muon beam direction, the change of the spinpolarized Mu concentration is 2756



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S(t ) = f

−λC AMu cos(ωMut + ϕMu)e−λbt (e−(λ1/ λC)(1 − e ) − 1) 2

(7)

where AMu, ωMu, and ϕMu are the initial amplitude, frequency, and phase of Mu precession, respectively. These values, along with λb, were determined from a fit to the laser-off data (Figure 2, top) and then fixed in fitting S(t). The collisional relaxation rate λC was fixed at 0.145 μs−1 at 50 bar, from an average of several measurements29,34−37 (uncertainty ±0.015 μs−1). The parameter f accounts for the overlap between the laser profile (region of pumped H2) and the muon stopping distribution and was determined independently by integrating this overlap. At maximum laser power, and for a 500 μm Mylar window, f is 0.13, and for this case, the (red line) fit of eq 7 is shown in Figure 2, bottom, giving λ1 = (0.281 ± 0.047) μs−1. Equation 6 then gives kMu{1} = (9.7 ± 2.6) × 10−13 cm3 molecule−1 s−1 for the assumed uniform concentration of H2{1}, determined from the number of pumped molecules, Np{1}, and the measured laser volume, giving [H2{1}] = (29 ± 6) × 1016 molecules/cm3. In the second, more-accurate, method, kMu{1} was found globally by simultaneously fitting the laser-on and laser-off data, taking into account the spatial variations of both the Mu stopping density and H2{1} concentrations by Monte Carlo simulations38 of the overlap of the laser and muon beams that explicitly include the target design, the laser profile, and the large spread in the muon stopping distribution along the muon direction. Fitted values for kMu{1} were determined from the three data sets, exemplified by that shown for set 2 in Table 1. Table 1. Results of Global Fits Determining kMu{1} (in 10−13 cm3 molecule−1 s−1) at 300 K (Data Set 2) and Its Sensitivity to Parameter Variations with Fixed λC = 0.145 μs−1

Figure 2. Experimental results for data set 2. (a) Mu decay asymmetry signals for laser-on (green) and laser-off (red) measurements, showing a small but noticeable difference in amplitude at later times. The low value of λb = 0.0228 ± 0.0014 μs−1 is a 20 times improvement over a preliminary result.47 (b) Laser difference data fit to eq 7. The fit (red line) is for the overlap f = 0.13 with the collisional rate λC fixed at 0.145 μs−1.

offset, Mu profile center Mu profile width number of H2{1} offset, laser profile center

d[Mu(t , r)] = −(kMu{1}[H 2({1}, t , r)] + λb)[Mu(t , r)] dt

where t is time and λb is a background spin relaxation constant for the muon spin in muonium (due to impurities or inhomogeneity in the TF). Collisional relaxation leads to (4)

Solving eq 3 gives [Mu(t , r)] = [Mu(t = 0, r)] ⎛ −λ (r)(1 − e−λCt ) ⎞ ⎟⎟e−λbt × exp⎜⎜ 1 λC ⎝ ⎠

(5)

where λ1(r) = kMu{1}[H 2({1}, t = 0, r)]

10.4 10.4 10.4 10.4

± ± ± ±

1.1 1.1 1.1 1.1

kmin 9.6 10.2 9.6 9.5

± ± ± ±

kmax 1.0 1.1 1.0 1.0

11.6 10.5 11.4 11.8

± ± ± ±

1.2 1.1 1.2 1.2

The fitted result with its statistical error is in the second column, along with an estimate of further experimental uncertainties obtained by varying the profile parameters and the value of Np{1} by their estimated uncertainties, labeled kmin and kmax in the table. These are combined to determine an error bar for the data set; the weighted average for the three data sets gives kMu{1} = 9.9(−1.2)(+1.4) × 10−13 cm3 molecule−1 s−1. Repeating the fits to include the uncertainty in λC noted above gives the final result kMu{1} = 9.9(−1.4)(+1.7) × 10−13 cm3 molecule−1 s−1. This global-fit value for kMu{1} is compared with QM calculations, earlier measurements for D + H2{1},14 and thermal rate constants in Figure 3. The QM calculations employed the outgoing wave variational principle39,40 to calculate cumulative reaction probabilities (CRPs) and stateselected CRPs that were then integrated with Boltzmann weighting to yield rate constants.1,8 These calculations were performed with a BH PES that was obtained by combining the CCI41 BO PES with an analytical fit42 of the BO diagonal correction.12,43 Additional numerical details are presented in the Supporting Information. In the D + H2{1} reaction, both n′ = 0 and 1 states for the HD product are formed, whereas in Mu + H2, only the n′ = 0 MuH product is appreciably populated. The technique used in

(3)

[H 2({1}, t , r)] = [H 2({1}, t = 0, r)]e−λCt

kMu{1}

parameter

(6)

The data were analyzed by two methods. In the first, simpler, method, a uniform “top-hat” concentration of H2{1} over the volume excited by the laser was assumed, allowing a determination of λ1 and hence of kMu{1} from eq 6 by subtraction of laser-on and laser-off data. The difference in the Mu spin precession for this case is given by 2757



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Figure 3. Arrhenius plots from QM calculations for Mu + H2{1} (solid red line) compared with that for the thermal Mu + H2 reaction (dashed red line), with similar comparisons for the D atom reactions (green lines). Also plotted are kMu7 and kD from thermal measurements48−51 (different symbols correspond to different experimental data sets). Experimental results for kMu{1} and kD{1} are shown by the two upper plotted symbols.

Figure 4. Comparison of the density of states and the state-selected density of states for Mu + H2 and D + H2 for a total angular momentum of J = 0 and para-H2. Results for ortho-H2 are very similar. The zero of energy is at the classical minimum of H2 infinitely separated from the incident atom.

the D-atom studies14 allowed a separate determination of the vibrationally adiabatic kD{1}(n′ = 1) = (1.7 ± 0.5) × 10−13 cm3 molecule−1 s−1, and nonadiabatic, kD{1}(n′ = 0) = (4.3 ± 0.5) × 10−14 cm3 molecule−1 s−1 channels, yielding a total stateselected rate constant of kD{1} = (2.1 ± 0.6) × 10−13 cm3 molecule−1 s−1 at 330 K. The present kMu{1} measurement is both more precise and a factor of 5 larger, even though at lower temperature. The theoretical kMu{1} is 26% above that of the experiment but is only 8% above the upper error bar. For D + H2{1}, theory gives kD{1}(n′ = 1) = 2.71 × 10−13 cm3 molecule−1 s−1 and kD{1}(n′ = 0) = 7.09 × 10−14 cm3 molecule−1 s−1, for a total kD{1} of 3.42 × 10−13 cm3 molecule−1 s−1, 63% above the experimental value. (The calculated branching ratio agrees well with experiment, perhaps because the ratio is less sensitive14 to wall deactivation collisions.) The QM inelastic vibrational de-excitation rate for Mu + H2{1} is 2.50 × 10−11 cm3 molecule−1 s−1 at 300 K, which is a factor of 20 higher than the reaction rate, whereas for D + H2{1}, this rate at 300 K is only 18% of the reaction rate. The large inelastic vibrational de-excitation rate for Mu + H2{1} is due to the late dynamical bottleneck, which causes trajectories to be reflected well after the point at which vibrationally nonadiabatic transitions have occurred. It is important for both fundamental understanding and applications to assess the extent to which vibrationally excited reactants contribute to thermal reaction rates.44,45 The QM calculations show that H2{1} contributes 4.4, 11, and 21% to the kMu thermal rate constant at 300, 500, and 1000 K, respectively. (For kD the comparable contributions are 1.5 × 10−4, 3.9 × 10−2, and 2.3%, respectively.) Understanding the relative magnitudes of the various rates is facilitated by examining their reaction thresholds. Figure 4 displays the densities of reactive states,19 that is, the energy derivatives of the CRPs as functions of energy, with quantized levels of the transition state (TS) labeled as [ν1,ν2K], where ν1, ν2, and K are the numbers of quanta in the quasi-symmetric stretch, the doubly degenerate bend, and the vibrational angular momentum,46 respectively. The QM reaction thresholds correspond closely to the peak energies in Figure 4. For

brevity, herein, we consider only the theoretical rate constants at 300 K. The ratio kD{1}/kD equals 661 and can be understood in terms of two competing effects, vibrational excitation raises the energy available for reaction by 0.516 eV for D + H2{1}, but the first TS level that gates excited-state flux is [100], which is ∼0.34 eV higher than the [000] level that controls the lowtemperature thermal reactivity. The ratio of thermal rates kMu/ kD = 2.04 × 10−4 is governed mainly by the large difference in VTS zero-point energies8,21 that causes the [000] level to be ∼0.30 eV higher in the Mu reaction. The huge kMu{1}/kMu ratio, 1.94 × 107, is controlled predominantly by the 0.516 eV vibrational excitation energy because the two reaction thresholds are very similar. This is because vibrationally nonadiabiatic transitions in Mu + H2{1} are essentially complete by the time the reactive flux reaches the late TS barrier; therefore, in contrast to the D + H2{1} reaction, appreciable excited-state flux is gated by the [000] state. The threshold observed in the Mu + H2{1} state-selected CRP (Figure 4) of ∼0.95 eV agrees well with the ∼1.01 eV energy of Va(n = 1) at the reactantvalley (s ≈ −1) maximum of the reaction path curvature, κ, (Figure 1), further indicating that vibrationally nonadiabatic transitions are correlated with high κ. The good experimental/theoretical agreement presented herein for Mu + H2{1} affirms the high accuracy of the H3 PES in a region that was previously not sensitively tested and also demonstrates the reliability of the experimental technique for studying state-selected Mu reactivity. This technique provides a powerful new tool for gaining information about unexplored regions of PESs for other chemical reactions.

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ASSOCIATED CONTENT

S Supporting Information *

Tables of QM rate constants and additional details of the calculations and the experiment. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: fl[email protected]. 2758



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Present Address

(12) Born, M.; Huang, K. The Dynamical Theory of Crystal Lattices; Oxford University Press: New York, 1954. (13) Mielke, S. L.; Peterson, K. A.; Schwenke, D. W.; Garrett, B. C.; Truhlar, D. G.; Michael, J. V.; Su, M.-C.; Sutherland, J. W. H + H2 Thermal Reaction: A Convergence of Theory and Experiment. Phys. Rev. Lett. 2003, 91, 063201. (14) Buchenau, H.; Toennies, J. P.; Arnold, J.; Wolfrum, J. H + H2: The Current Status. Ber. Bunsen-Ges. Phys. Chem. 1990, 94, 1231− 1248. (15) Marcus, R. A. Analytical Mechanics and Almost VibrationallyAdiabatic Chemical Reactions. Discuss. Faraday Soc. 1967, 44, 7−13. (16) Truhlar, D. G.; Kuppermann, A. Exact Tunneling Calculations. J. Am. Chem. Soc. 1971, 93, 1840−1851. (17) Garrett, B. C.; Truhlar, D. G.; Bowman, J. M.; Wagner, A. F. Evaluation of Dynamical Approximations for Calculating the Effects of Vibrational Excitation on Reaction Rates. O + H2(n = 0,1) ↔ OH(n = 0,1) + H. J. Phys. Chem. 1986, 90, 4305−4311. (18) Haug, K.; Schwenke, D. W.; Shima, Y.; Truhlar, D. G.; Zhang, J.; Kouri, D. J. L2 Solution of the Quantum Mechanical Reactive Scattering Problem. The Threshold Energy for D + H2(v = 1) → HD + H. J. Phys. Chem. 1986, 90, 6757−6759. (19) Chatfield, D. C.; Friedman, R. S.; Schwenke, D. W.; Truhlar, D. G. Control of Chemical Reactivity by Quantized Transition States. J. Phys. Chem. 1992, 96, 2414−2421. (20) Garrett, B. C.; Truhlar, D. G. Critical Tests of Variational Transition State Theory and Semiclassical Tunneling Methods for Hydrogen and Deuterium Atom Transfer Reactions and Use of the Semiclassical Calculations to Interpret the Overbarrier and Tunneling Dynamics. J. Phys. Chem. 1991, 95, 10374−10379. (21) Garrett, B. C.; Steckler, R.; Truhlar, D. G. Dynamics of GasPhase Reactions of Muonium. Hyperfine Interact. 1986, 32, 779−793. (22) Bondi, D. K.; Clary, D. C.; Connor, J. N. L.; Garrett, B. C.; Truhlar, D. G. Kinetic Isotope Effects in the Mu + H2 and Mu + D2 Reactions: Accurate Quantum Calculations for the Collinear Reactions and Variational Transition State Theory Predictions for One and Three Dimensions. J. Chem. Phys. 1982, 76, 4986−4995. (23) Wu, S.-f.; Marcus, R. A. Analytical Mechanics of Chemical Reactions. V. Application to the Linear Reactive H + H2 Systems. J. Chem. Phys. 1970, 53, 4026−4035. (24) Hofacker, G. L.; Levine, R. D. A Non Adiabatic Model for Population Inversion in Molecular Collisions. Chem. Phys. Lett. 1971, 9, 617−620. (25) Hofacker, G. L. Quantentheorie Chemischer Reaktionen. Z. Naturforsch., A: Phys. Sci. 1963, 18, 607−619. (26) Duff, J. W.; Truhlar, D. G. Effect of Curvature of the Reaction Path on Dynamic Effects in Endothermic Reactions and Product Energies in Exothermic Reactions. J. Chem. Phys. 1975, 62, 2477− 2491. (27) Arnold, J.; Dreier, T.; Chandler, D. W. Rotational and Vibrational Energy Transfer of H2(v = 1, J = 1) in Collisions with H2, Ar, HD and D2. Chem. Phys. 1989, 133, 123−136. (28) Sukhorukov, O.; Bakule, P.; Matsuda, Y.; Kamal, S.; Momose, T.; Fleming, D. Application of Stimulated Raman Pumping toward the First Study of Chemical Reaction Dynamics of the Muonium Atom with H2*. Phys. Status Solidi C 2009, 6, S263−S266. (29) Matsui, H.; Resler, J. E. L.; Bauer, S. H. Vibrational Relaxation in H2CO and D2CO Mixtures, Measured Via Stimulated Raman− IR Fluorescence. J. Chem. Phys. 1975, 63, 4171−4176. (30) Senba, M.; Arseneau, D. J.; Pan, J. J.; Fleming, D. G. SlowingDown Times and Stopping Powers for ∼2-MeV μ+ in Low-Pressure Gases. Phys. Rev. A 2006, 74, 042708. (31) Roduner, E. Muon Spin ResonanceA Variant of Magnetic Resonance. Appl. Magn. Reson. 1997, 13, 1−14. (32) Johnson, C.; Cottrell, S. P.; Ghandi, K.; Fleming, D. G. Muon Implantation in Inert Gases Studied by Radio Frequency Spectroscopy. J. Phys. B 2005, 38, 119−134. (33) Duchovic, R. J.; Wagner, A. F.; Turner, R. E.; Garner, D. M.; Fleming, D. G. The Analysis of Muonium Hyperfine Interaction

⊗

Institute of Physics, The Academy of Sciences of the Czech Republic, Na Slovance 2, 18221 Prague 8, Czech Republic.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We would like to acknowledge helpful comments and suggestions made by Profs. I. W. M. Smith, J. Wolfrum, M. Shapiro, and R. N. Zare. We would also like to thank Prof. Yasuyuki Matsuda, now at the University of Tokyo (Komaba), Japan, for his important contributions to the early phase of this study. We are grateful for the financial, technical, and engineering support provided by RIKEN/RAL. One of the authors (E.T.) is grateful to the Japan Society for the Promotion of Science for a Grant-in-Aid for Scientific Research (No. 19340080). Financial support was also provided by NSERC, Canada, the U.S. National Science Foundation under Grant No. CHE09-56776, by the U.S. Air Force Office of Scientific Research under Grant No. FA9550-10-1-0205, and, for the work at Pacific Northwest National Laboratory, by the Chemical Sciences, Geosciences and Biosciences Division of the Office of Basic Energy Science, U.S. Department of Energy.

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REFERENCES

(1) Fleming, D. G.; Arseneau, D. J.; Sukhorukov, O.; Brewer, J. H.; Mielke, S. L.; Schatz, G. C.; Garrett, B. C.; Peterson, K. A.; Truhlar, D. G. Kinetic Isotope Effects for the Reactions of Muonic Helium and Muonium with H2. Science 2011, 331, 448−450. (2) Fleming, D. G.; Senba, M. In Perspectives of Meson Science; Yamazaki, T., Nakai, K., Nagamine, K., Eds.; North-Holland: Amsterdam, The Netherlands, 1992; pp 219−264. (3) Baer, S.; Fleming, D.; Arseneau, D.; Senba, M.; Gonzalez, A. Isotope Effects in Chemical Reactions and Photodissociation Processes; ACS Symposium Series 502; American Chemical Society: Washington, DC, 1992; pp 111−137. (4) Tanaka, T.; Takayanagi, T. Quantum Reactive Scattering Calculations of H + F2 and Mu + F2 Reactions on a New Ab Initio Potential Energy Surface. Chem. Phys. Lett. 2010, 496, 248−253. (5) Takayanagi, T.; Kurosaki, Y. Theoretical Calculations of Potential Energy Surface and Thermal Rate Constants for the H(Mu) + F2 Reaction. J. Phys. Chem. A 1997, 101, 7098−7104. (6) Pan, J. J.; Arseneau, D. J.; Senba, M.; Shelly, M.; Fleming, D. G. Reaction Kinetics of Muonium with N2O in the Gas Phase. J. Phys. Chem. A 1997, 101, 8470−8479. (7) Reid, I. D.; Garner, D. M.; Lee, L. Y.; Senba, M.; Arseneau, D. J.; Fleming, D. G. Experimental Tests of Reaction Rate Theory: Mu + H2 and Mu + D2. J. Chem. Phys. 1987, 86, 5578−5583. (8) Fleming, D. G.; Arseneau, D. J.; Sukhorukov, O.; Brewer, J. H.; Mielke, S. L.; Truhlar, D. G.; Schatz, G. C.; Garrett, B. C.; Peterson, K. A. Kinetics of the Reaction of the Heaviest Hydrogen Atom with H2, the 4Heμ + H2→ 4HeμH + H Reaction: Experiments, Accurate Quantal Calculations, and Variational Transition State Theory, Including Kinetic Isotope Effects for a Factor of 36.1 in Isotopic Mass. J. Chem. Phys. 2011, 135, 184310−184318. (9) Hitchcock, L. M.; Kim, G. S.; Rothe, E. W.; Reck, G. P. Stimulated Raman Pumping to H2 (v″ = 1, J″ = 1) and ResonanceEnhanced Multiphoton Ionization from It Using a Single Laser. Appl. Phys. B: Laser Opt. 1991, 52, 27−31. (10) Bartlett, N. C. M.; Miller, D. J.; Zare, R. N.; Sofikitis, D.; Rakitzis, T. P.; Alexander, A. J. Preparation of Oriented and Aligned H2 and HD by Stimulated Raman Pumping. J. Chem. Phys. 2008, 129, 084312−084316. (11) DeMartini, F.; Ducuing, J. Stimulated Raman Scattering in Hydrogen: A Measurement of the Vibrational Lifetime. Phys. Rev. Lett. 1966, 17, 117−119. 2759



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Measurements of Thermal Rate Constants for Addition Reactions. J. Chem. Phys. 1991, 94, 2794−2806. (34) Audibert, M. M.; Joffrin, C.; Ducuing, J. Vibrational Relaxation of H2 in the Range 500−40 K. Chem. Phys. Lett. 1974, 25, 158−163. (35) Audibert, M.-M.; Vilaseca, R.; Lukasik, J.; Ducuing, J. Vibrational Relaxation of Ortho and Para-H2 in the Range 400−50 K. Chem. Phys. Lett. 1975, 31, 232−236. (36) Kovacs, M. A.; Mack, M. E. Vibrational Relaxation Measurements Using “Transient” Stimulated Raman Scattering. Appl. Phys. Lett. 1972, 20, 487−490. (37) Carraro, T.; Heuveline, R.; Rannacher, R. In Reactive Flows, Diffusion and Transport; Jäger, W., Rannacher, R., Warnatz, J., Eds.; Springer: Heidelberg, Germany, 2005; pp 211−249. (38) Shiroka, T.; Prokscha, T.; Morenzoni, E.; Sedlak, K. GEANT4 as a Simulation Framework in μSR. Physica B 2009, 404, 966−969. (39) Sun, Y.; Kouri, D. J.; Truhlar, D. G. A Comparative Analysis of Variational Methods for Inelastic and Reactive Scattering. Nucl. Phys. A 1990, 508, 41c−62c. (40) Schwenke, D. W.; Mielke, S. L.; Truhlar, D. G. Variational Reactive Scattering Calculations: Computational Optimization Strategies. Theor. Chim. Acta 1991, 79, 241−269. (41) Mielke, S. L.; Garrett, B. C.; Peterson, K. A. A Hierarchical Family of Global Analytic Born−Oppenheimer Potential Energy Surfaces for the H + H2 Reaction Ranging in Quality from Double Zeta to the Complete Basis Set Limit. J. Chem. Phys. 2002, 116, 4142− 4161. (42) Mielke, S. L.; Schwenke, D. W.; Schatz, G. C.; Garrett, B. C.; Peterson, K. A. Functional Representation for the Born−Oppenheimer Diagonal Correction and Born−Huang Adiabatic Potential Energy Surfaces for Isotopomers of H3. J. Phys. Chem. A 2009, 113, 4479− 4488. (43) Mielke, S. L.; Schwenke, D. W.; Peterson, K. A. Benchmark Calculations of the Complete Configuration-Interaction Limit of Born−Oppenheimer Diagonal Corrections to the Saddle Points of Isotopomers of the H + H2 Reaction. J. Chem. Phys. 2005, 122, 224313. (44) Smith, I. W. M.; Williams, M. D. Effects of Isotopic Substitution and Vibrational Excitation on Reaction Rates. Kinetics of OH(v = 0, 1) and OD(v = 0, 1) with HCl and DCl. J. Chem. Soc., Faraday Trans. 2 1986, 82, 1043−1055. (45) Wu, G.-s.; Schatz, G. C.; Lendvay, G.; Fang, D.-C.; Harding, L. B. A New Potential Surface and Quasiclassical Trajectory Study of H + H2O → OH + H2. J. Chem. Phys. 2000, 113, 3150−3161. (46) Bernath, P. F. Spectra of Atoms and Molecules; Oxford University Press: New York, 1995. (47) Bakule, P.; Sukhorukov, O.; Matsuda, Y.; Pratt, F.; Gumplinger, P.; Momose, T.; Torikai, E.; Fleming, D. Toward the First Study of Chemical Reaction Dynamics of Mu with Vibrational-State-Selected Reactants in the Gas Phase: The Reaction by Stimulated Raman Pumping. Physica B 2009, 404, 1013−1016. (48) Ridley, B. A.; Schulz, W. R.; Le Roy, D. J. Kinetics of the Reaction D + H2 = HD + H. J. Chem. Phys. 1966, 44, 3344−3347. (49) Westenberg, A. A.; de Haas, N. Atom-Molecule Kinetics Using ESR Detection. II. Results for D + H2 → HD + H and H + D2 → HD + D. J. Chem. Phys. 1967, 47, 1393−1405. (50) Michael, J. V.; Fisher, J. R. Rate Constants for the Reaction D + H2 → HD + H, over the Temperature Range 655−1979 K, by the Flash Photolysis−Shock Tube Technique. J. Phys. Chem. 1990, 94, 3318−3323. (51) Mitchell, D. N.; Le Roy, D. J. Rate Constants for the Reaction D + H2 = DH + H at Low Temperatures Using ESR Detection. J. Chem. Phys. 1973, 58, 3449−3453.

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