Muonium Addition Reactions and Kinetic Isotope Effects in the Gas

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Muonium Addition Reactions and Kinetic Isotope E#ects in the Gas Phase: k Rate Constants for Mu+CH #

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Donald J. Arseneau, David M. Garner, Ivan D. Reid, and Donald George Fleming J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp511604q • Publication Date (Web): 09 Feb 2015 Downloaded from http://pubs.acs.org on February 18, 2015

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The Journal of Physical Chemistry

Muonium Addition Reactions and Kinetic Isotope Effects in the Gas Phase: k∞ Rate Constants for Mu+C2H2 Donald J. Arseneau, David M. Garner∗, Ivan D. Reid† and Donald G. Fleming‡ TRIUMF and Department of Chemistry, University of British Columbia, Vancouver, BC, Canada February 5, 2015 Abstract The kinetics of the addition reaction of muonium (Mu) to acetylene have been studied in the gas phase at N2 moderator pressures mainly from ∼ 800 to 1000 Torr and over the temperature range 168 K to 446 K, but also down to 200 Torr at 168 K and over a much higher range of pressures, from 10 bar to 44 bar at 295 K, demonstrating pressure-independent rate constants, kMu (T). Even at 200 Torr moderator pressure, the kinetics for Mu + C2 H2 addition behave as if effectively in the high-pressure limit, giving k∞ = kMu due to depolarization of the muon spin in the MuC2 H2 radical formed in the addition step. The rate constants kMu (T) exhibit clear Arrhenius curvature over the range of measured temperatures. Comparisons with data and with calculations for the corresponding H(D) + C2 H2 addition reactions reveal a much faster rate for the Mu reaction at the lowest temperatures, by two orders of magnitude, in accord with the propensity of Mu to undergo quantum tunneling. Moreover, isotopic atom exchange, which contributes in a major way to the analagous D-atom reaction, forming C2 HD + H, is expected to be unimportant in the case of Mu addition, a consequence of the much higher zero-point energy and hence weaker C–Mu bond that would form, meaning that the present report of the Mu + C2 H2 reaction is effectively the only experimental study of kinetic isotope effects in the high-pressure limit for H atom addition to acetylene. ∗

Present address: B.C. Cancer Agency, Vancouver, Canada Present address: Brunel University, London, UK ‡ Corresponding Author: [email protected], Tel: 604-222-1047, xtn. 6296 †

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Introductory Background

Hydrogen addition and dissociation reactions in alkynes and alkenes are of considerable importance to both theoretical and combustion chemistry,1–14 the prototypical reactions being H + C2 H2 ,1, 4, 8–11 ˙ ∗ free-radical intermediate, and H + C2 H4 ,1–3, 12–14 forming the H3 C-CH ˙ ∗2 forming the HHC=CH intermediate. Both of these reaction systems have been reported on in the 2004 theoretical study of Miller and Klippenstein,1 where the experimental work to that time was also reviewed. The underlying mechanism for such reactions has been known since the LindemannHinshelwood energy-transfer theory of the 1920s, and has the basic form2, 15–20 ka ks H + A (HA)∗ → HA, M kd (∗ )

(1)

where ‘A’ stands for alkene or alkyne (acetylene here), and ka , kd (∗ ) and ks are the rate constants for addition, dissociation and stabilization of the intermediate complex HA∗ by collisions with moderator ‘M’, respectively, and where kd (∗ ) denotes the energy-dependent unimolecular dissociation rate constant at excitation energy ∗ in the complex. Conventionally, within the strong-collision assumption of stabilization in a single collision, the apparent rate constant, kapp , for the recombination reaction (1), is given by the well-known (steady-state) expression kapp =

ka ks [M] , kd + ks [M]

(2)

where ‘kd ’ is meant to represent an appropriate averaged value over excitation energy ∗ and [M] is the total gas density, in concentration units. The present experiment is concerned with the high-pressure regime of Eqn. (2), kapp = k∞ = ka , independent of pressure. There are relatively few studies of primary D-atom isotopic effects in addition reactions: those of Sugawara et al. for D + C2 H4 13 and Michael et al.4 and Keil et al.9 for D + C2 H2 being relevant here. In the latter case, due to the difference in zero-point-energy (ZPE) between the C−H and C−D bonds, the atom exchange reaction (forming C2 HD + H) is exoergic and highly competitive with addition at the temperatures of interest;4, 9 it follows then that the high-pressure limit for the D + C2 H2 addition reaction has not been experimentally established. Atom exchange may also play a role in the D + C2 H4 reaction,1, 5 suggesting that the D-atom results of Ref. 13 may also not have fully attained the high-pressure limit over the range of temperatures studied. The muonium atom (Mu=µ+ e− ), consisting of a positive muon “nucleus”, with a mass 1/9th that of the proton, constitutes the lightest isotope of the H atom (atomic mass 0.114 amu) and, as 2


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such, studies of its chemical reactivity21 have provided unusually sensitive tests of quantum mass effects in reaction rate theory; seen in abstraction reactions like Mu + H2 21–28 and Mu + CH4 ,29–34 where ZPE effects dominate, and in Mu + F2 21, 35, 36 and Mu + N2 O,37 where quantum tunneling dominates, and most recently in the first study of Mu reactivity from state-selected reactants, the Mu + H2 (v=1) reaction.25, 27, 28, 38, 39 Both of these quantum mass effects are also seen for Mu reactivity in addition/recombination reactions, to diatomics, forming the triatomic systems MuO2 ,40 MuNO,41 and MuCO,42 where pressures & 300 bar are needed to approach the high-pressure regime near room temperature (RT), and with unsaturated organic molecules,43, 44 where, with their many more degrees of freedom, this regime is established at much lower pressures, near 1 bar at RT. Of particular interest here is earlier work on Mu addition to C2 H4 ,2, 21, 43, 45 which complements the present study of the Mu + C2 H2 reaction, where the experimental rate constant, kMu (T), was shown to be independent of N2 moderator pressure even down to ∼ 200 Torr, near 170 K. Tunneling tends to dominate over ZPE effects since this addition reaction occurs on an early-barrier surface, as seen in the calculations of kMu (T) in Ref. 2 for Mu + C2 H4 addition. The experimental study of Mu + C2 H2 addition reported herein has been carried out over a range of N2 moderator pressures from 200 Torr at 167 K to as high as 44 bar at 295 K, a much more extensive range than in our earlier study of Mu + C2 H4 .43 In like manner to that study though, kMu (T) for Mu + C2 H2 is also found to be independent of moderator pressure, behaving effectively as if in its high-pressure limit also at the lowest pressure of 200 Torr, a consequence of muon spin relaxation effects in the intermediate MuC2 H∗2 radical formed.

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Muonium reactivity and k∞ in Mu addition kinetics µSR basics and the muonium precession signal

The basics of the µSR technique and its particular application in gas-phase Mu chemistry has been extensively described.21, 22, 40–43, 45, 46 Briefly, positive muons (µ+ ) are produced with 100% spin polarization (|αµ i) from a nuclear accelerator (TRIUMF in the present study). The stable Mu atom is formed by charge exchange in a moderator gas like N2 on a time scale of order 10 ns at 1 atm pressure.46–48 In its decay (µ+ → e+ νe ν µ , τµ = 2.2 µs), the e+ is emitted preferentially along the instantaneous µ+ spin direction, so its detection (by separate “counter telescopes” of plastic scintillators) provides a sensitive measure of the spatial orientation and time evolution of the muon

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spin polarization in muonium.24, 46, 47, 49, 50 It is noteworthy that the technique admits only one Mu atom in the system at a time. As in most previous studies of Mu chemical reactivity,21, 24, 41–43, 46, 50 the present (timedifferential) experiments were also carried out in weak transverse magnetic fields (TFs) giving the measured “asymmetry”, A(t), X A(t) = Ai e−λi t cos(ωi t + φi ), (3) i

which has features in common with free induction decay in NMR.49 The index i labels the possible magnetic environments that the muon may be found in at observation times: as the ˙ muonium atom (i = Mu), a paramagnetic Mu-containing free radical (i = R ,45, 49–53 both MuHCCH ˙ 2 being relevant here, though not actually observed in the experiment), or in a and MuCH2 CH diamagnetic molecule or molecular ion (i = D, mainly N2 µ+ ,43, 46, 54 though C2 H2 µ+ and C2 H4 µ+ are also possible, in analogy with protonated ethylene,55 as well as MuH formed from “hot atom” abstraction reactions by epithermal Mu48 ). The parameters Ai , λi , ωi and φi are, respectively, the initial asymmetry, the relaxation rate, the Larmor precession frequency (ωi = 2πνi , where νi = γi B, with γi the appropriate gyromagnetic ratio, and B the magnetic field strength), and the initial phase of the spin polarization of muons in the ith environment. In the weak TFs of the present experiments (∼8 G), only two environments contribute to A(t), which is dominated by the precession of “triplet” S=1 muonium (|αµ αe i),21, 46, 47, 54, 56 with initial asymmetry (amplitude) AMu , of the simple form A(t) = AMu e−λMu t cos(ωMu t + φMu ) + AD e−λD t cos(ωD t + φD ) ,

(4)

the spin relaxation rate λMu , a pseudo first-order rate constant, being of principal interest here. The amplitude of the diamagnetic fraction is AD but its relaxation rate, λD , is too slow to measure in these weak TF experiments. A typical example of an “asymmetry plot” is shown in Fig. 1. The oscillation shows the dominant precession of S=1 Mu in the presence of 19.7 Torr of acetylene added to N2 in a TF of 7.6 G. The solid line is a least-squares fit of Eqn. (4) to the data. The initial amplitude of this Mu precession signal corresponds to about 80% of incident µ+ thermalizing as the Mu atom.43, 46, 54 The relaxation rate (λMu = 1.47 µs−1 ) arises from the formation of the MuC2 H∗2 adduct in the Mu + C2 H2 addition reaction, causing dephasing or depolarization of the muon spin, due to the change in magnetic environment from Mu to Mu-radical.43, 45 There is a small “background” relaxation rate that is part of λMu (λ0 = 0.11 µs−1 ), mainly due to magnetic field inhomogeneity. 4


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Figure 1: Measured µSR asymmetry plot for Mu precession in the presence of 19.7 Torr of added acetylene at 200 K and at 1000 Torr N2 pressure. The solid line is a fit of Eqn. (4) to the data. The initial amplitude of the signal is AMu = 0.14 ± 0.01, with the fitted relaxation rate λMu = 1.47 ± 0.05 µs−1 , due to formation of the MuC2 H∗2 addition complex, and which includes a small “background” relaxation λ0 = 0.11 ± 0.01 µs−1 .

2.2

The conventional high-pressure limit in H-atom addition kinetics

The high-pressure limit is established in conventional addition/recombination reactions, as in reaction (1), by measurements of kapp with increasing [M] such that, from Eqn. (2), when ks [M] becomes much greater than kd , kapp → k∞ = ka , a pressure-independent value. However, this approach can be fraught with experimental uncertainty because kapp → k∞ asymptotically and most H atom addition reactions are not carried out to sufficiently high pressure to be sure of a pressure-independent result, as discussed by Miller and Klippenstein in their comparisons of theory and experiment for both the H + C2 H2 and H + C2 H4 reactions1 and by Michael et al. for the H + C2 H2 reaction.4 The studies reported in both Refs. 1 and 4 show that the oft-cited experimental results of Payne and Stief for the H + C2 H2 + M reaction,8 with similar results obtained in a later study by Ellul et al.,11 are probably not in the high-pressure limit at any temperature and particularly at the higher temperatures where He moderator pressures & 2000 Torr are required,1 well beyond 5



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the maximum pressure of 700 Torr utilized in Ref. 8. Reservations have also been expressed in Ref. 1 that the H + C2 H4 results of Lightfoot and Pilling12 at the higher temperatures, and by extension also to the earlier results of Sugawara et al.13 (and of Lee et al.14 ), may not be fully in the high-pressure limit, discussed as well by Michael et al.5 In our previous experimental work on the Mu + C2 H4 + M reaction,43 pressure-independent rate constants, kMu (T), were seen over a variation in total N2 pressure from 200 Torr near 170 K to 1500 Torr near 480 K. A similar pressure and temperature range has been explored in the present study of the Mu +C2 H2 +M reaction, also in N2 moderator, with data taken down to 200 Torr and up to 900 Torr near 170 K, again exhibiting pressure-independent rate constants at this temperature, with most of the data taken though over a range of temperatures at pressures between ∼800 and 1000 Torr (Table 1). In a separate and later series of experiments, additional data were taken up to much higher pressures, to 44 bar N2 at 295 K (Table 1), and in Ar moderator at 3 bar and 20 bar. We would expect to approach the conventional high-pressure regime at much higher pressures in Mu addition reactions compared to their H-atom counterparts, due to the weaker C-Mu bond that arises from the increased ZPE of the light muon mass.2, 40–43, 45 In like manner, a higher total pressure to approach this regime would be expected for Mu + C2 H2 + M than for Mu + C2 H4 + M,43 since the dissociation rate constant, kd , in Eqn. (2) should be larger for MuC2 H∗2 ,1, 4 in accord with the trend seen in the calculations of Ref. 1 and in comparisons with earlier studies of H and Mu addition to diatomics.40–42 However, since both Mu reactions with C2 H2 and C2 H4 behave so similarly over the range in moderator pressures studied (seen in Fig. 3 below) and since pressures as low as 200 Torr are found to give pressure-independent rate constants kMu (T), which in fact is well below those expected to guarantee the high-pressure limits in the corresponding H-atom studies,1 the µSR data indicate that the relaxation rates for Mu addition to both C2 H4 and C2 H2 effectively reflect the high pressure limit of the kinetics at almost any pressure, a consequence of change in the muon spin polarization in the new magnetic environment of the Mu-radical formed. Two other remarks are noteworthy here. First, as commented earlier, the high-pressure limit has not been established in kinetics studies for the D + C2 H2 reaction, due to the importance of the D-exchange reaction.4, 9 This kind of atom exchange process is very unlikely for Mu + C2 H2 since, again due to its higher zero-point energy (ZPE), the C–Mu bond is considerably weaker than C–H and hence H atom displacement by Mu is highly endoergic. Secondly, non-stoichiometric effects that can contribute to H + C2 H2 kinetics at high H atom concentrations,10 are impossible in the one-atom-at-a-time Mu depletion µSR technique21, 43, 45, 46 employed here.

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2.3


The µSR technique: kapp = k∞ = kMu at almost any pressure

In µSR studies of Mu reactivity, it is the disappearance of the spin-polarized Mu atom with time that is measured, given by the relaxation rate λMu in Eqn. (4), arising from the dephasing or depolarization of Mu in its environment. There are generally three possible ways this can occur: (i) the formation of a diamagnetic chemical bond like MuH in which the muon precesses a 100-fold more slowly and in the opposite direction to free triplet Mu, thereby dephasing the muon spin in the product; (ii) an inter-molecular “spin exchange” (SE) reaction,56, 57 in which the initial triplet Mu state interacts with a paramagnetic molecule like NO41 or O2 ,40, 56 causing an electron spin-flip |αµ αe i → |αµ βe i, which in turn depolarizes the muon spin via hyperfine mixing on a time scale of ∼ 0.1 ns;56, 57 or (iii) the formation of a muoniated free radical, MuA∗ in reaction (1), and specifically MuC2 H∗2 here, which can undergo muon spin depolarization due to several contributing mechanisms.42, 45, 58, 59 Of these three possibilities, only the third is important here. For case (iii), there is a sudden change in the µ+ - e− hyperfine interaction when the Mu atom adds to an unsaturated bond to form the muoniated radical, MuA∗ , giving rise to the spin relaxation of the precessing Mu atom (λMu ) that is evident in Fig. 1. Generally, there are two sources of this relaxation. First, for the Mu-radical formed (MuC2 H2 or MuC2 H4 here), both with proton nuclear moments, the hyperfine couplings between muon, proton and electron spins can generate a multitude of eigenstates between which a large number of muon precession frequencies are allowed in a weak TF (as many as 792 for MuC2 H4 45, 50, 51 ), essentially none of which are coherent with the initial Mu precession frequency, ωMu . As an approximation, these many possible muon frequencies can be thought of as being replaced by a single average value,45 ωR , such that, when Mu adds to form the muoniated radical, the muon will precess for some time at this frequency in the radical prior to dissociating back to Mu, a process that can be repeated many times, depending on the lifetime, τc = 1/kd , of the intermediate MuA∗ radical complex formed. This process gives rise to spin relaxation due to a dephasing of the muon spin in dissociated Mu with respect to its initial spin precession, albeit with a complicated relationship between a number of parameters contributing to the measured relaxation rate.45 Simplistically, one could expect the contribution of this spin dephasing mechanism to λMu to be ∝ ∆ω 2 , where ∆ω = ωR - ωMu .51, 52, 60 In the weak TFs here, ωMu > 1 at the lowest temperatures. With its fewer degrees of freedom, the nature of the tunneling path may be more amenable to a more rigorous calculation for Mu + C2 H2 than for Mu + C2 H4 .

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Concluding Remarks

The present paper has presented detailed results for the addition reaction of the light H-atom isotope muonium to C2 H2 , a prototypical study of Mu reactivity with this lowest mass alkyne. Though measured up to 44 bar N2 at 295 K, the kinetics data are effectively in the high-pressure limit at essentially any pressure, due to the combined effects of muon spin dephasing and depolarization that contribute to the measured µSR relaxation rate, λMu , in agreement with the measurements of pressure-independent addition rate constants, kMu (Table 1). The higher pressure data at 295 K may also guarantee the conventional high-pressure limit for Mu + C2 H2 addition, but a full theoretical calculation along the lines of that reported in Ref. 1 will be necessary to confirm this. Moreover, in contrast to the D + C2 H2 reaction,4, 9 where atom exchange plays an important, even dominant role, this is expected to be of little or no consequence in the present Mu + C2 H2 study. The weaker C-Mu bond, due to its higher ZPE arising from the muon mass, renders such atom exchange highly endoergic and hence practically guarantees that it is only the addition step

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that is being measured by the µSR experiment. These data arguably represent then the only clear isotopic study of H atom addition to acetylene in the high-pressure limit. Comparisons with earlier work for the Mu + C2 H4 reaction show that Mu + C2 H2 is noticeably slower over the same temperature range, with an apparent reduced propensity for Mu tunneling, as reflected in a comparison of activation energies (Fig. 3), and which is at least qualitatively consistent with the difference in total barrier heights calculated by Miller and Klippenstein1 for the parent H atom addition reactions. Comparisons of the present data with the calculated KIEs for H, D and Mu addition to ethene by Villà et al.2 indicate that an appreciable enhancement in the Mu rate due to quantum tunneling could also be expected for addition to acetylene, but confirmation of this must also await the necessary theoretical calculations of the Mu + C2 H2 addition rate.

Acknowledgments We would like to thank Drs. Randy Mikula and our long-time colleague, Dr. Masayoshi Senba (now deceased) for their help and participation in the early part of these experiments. Helpful remarks from Drs. Joe Michael and Stephen Klippenstein of Argonne National Laboratory were also greatly appreciated. The Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged for their financial support.

References (1) Miller, J. A.; Klippenstein, S. J. The H+ C2H2 (+ M) C2H3 (+ M) and H+ C2H4 (+ M) C2H5 (+ M) Reactions: Electronic Structure, Variational Transition-State Theory, and Solutions to a Two-Dimensional Master Equation. Phys. Chem. Chem. Phys. 2004, 6, 11921202. (2) Villà, J.; Corchado, J.C.; Gonza0 lez-Lafont, A.; Lluch, J.M.; Truhlar, D. G. Variational Transition-State Theory with Optimized Orientation of the Dividing Surface and Semiclassical Tunneling Calculations for Deuterium and Muonium Kinetic Isotope Effects in the Free Radical Association Reaction H+ C2H4 → C2H5. J. Phys. Chem. A 1999, 103, 5061-5074.

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(3) Villà, J.; Corchado, J.C.; Gonz0 lez-Lafont, A.; Lluch, J.M.; Truhlar, D.G. Explanation of Deuterium and Muonium Kinetic Isotope Effects for Hydrogen Atom Addition to an Olefin. J. Am. Chem. Soc. 1998, 120, 12141-12142. (4) Michael, J.V.; Su, M.-C; Sutherland, J.W.; Harding, L.B.; Wagner, A.J. Rate Constants for D+ C2H2→ C2HD+ H at High Temperature: Implications to the High Pressure Rate Constant for H+ C2H2→ C2H3. J. Phys. Chem. A 2003, 107, 10533-10543. (5) Michael, J. V.; Su, M.-C.; Sutherland, J. W.; Harding, L. B.; Wagner, A. F. Rate Constants for D+ C2H4→C2H3D+ H at High Temperature: Implications to the High Pressure Rate Constant for H+ C2H4→C2H5. Proc. Combust. Inst. 2005, 30, 965-973. (6) Narendrapurapu, B.S; Simmonett, A.C.; Schaefer, III, H.F.; Miller, J.A.; Klippenstein, S.J. Combustion Chemistry: Important Features of the C3H5 Potential Energy Surface, Including Allyl Radical, Propargyl + H2, Allene + H, and Eight Transition States. J. Phys. Chem. A 2011, 115, 14209-14214. (7) Rosado-Reyes, C. M.; Manion, J.A.; Tsang, W. Kinetics of the Thermal Reaction of H Atoms with Propyne. J. Phys. Chem A 2010, 114, 5710-5717. (8) Payne, W.A.; Stief, L.J., Absolute Rate Constant for the Reaction of Atomic Hydrogen with Acetylene Over an Extended Pressure and Temperature Range. J. Chem. Phys. 1976, 64, 1150-1155. (9) Keil, D.G.; Lynch, K.P.; Cowfer, J.A.; Michael, J.V. An Investigation of Nonequilibrium Kinetic Isotope Effects in Chemically Activated Vinyl Radicals. Int. J. Chem. Kinet. 1976, 8, 825-857. (10) Harding, L.B.; Wagner, A.F.; Bowman, J.M.; Schatz, G.C.; Christoffel, K. Ab Initio Calculation of the Transition-State Properties and Addition Rate Constants for Atomic Hydrogen+ Acetylene and Selected Isotopic Analogs. J. Phys. Chem. 1982 86, 4312-4327. (11) Ellul, R.; Potzinger, P.O.; Reiman, R.; Camilleri, P. Arrhenius Parameters for the System (CH3)3Si+ D2 (CH3)3SiD+ D; the (CH3)3Si-D Bond Dissociation Energy. Ber. BunsenGes. Phys. Chem 1981, 85, 407-412. (12) Lightfoot, P.D.; Pilling, M.J. Temperature and Pressure Dependence of the Rate Constant for the Addition of Hydrogen Atoms to Ethylene. J. Phys. Chem. 1987, 91, 3373-3379.

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(13) Sugawara, K; Okazaki, K; Sato, S. Kinetic Isotope Effects in the Reaction H+ C2H4→ C2H5. Chem. Phys. Lett. 1981, 78, 259-263. (14) Lee, J.H.; Michael, J.V.; Payne, W.A.; Stief, L.J. Absolute Rate of the Reaction of Atomic Hydrogen with Ethylene from 198 to 320 K at High Pressure. J. Chem. Phys. 1978, 68, 1817-1820. (15) Steinfeld, J.I.; Fransisco J.S.; Hase, W.L.“Chemical Kinetics and Dynamics”, 2nd Edn.; Prentice Hall:Upper Saddle River, NJ. , 1998. (16) Villà, J; Corchado, J.C.; Gonza0 lez-Lafont, A; Lluch, J.M; Truhlar, D.G. Entropic Effects on the Dynamical Bottleneck Location and Tunneling Contributions for C2H4+ H→C2H5: Variable Scaling of External Correlation Energy for Association Reactions. J. Am. Chem. Soc., 1998 120, 5559-5567. (17) Troe, J. Atom and Radical Recombination Reactions. Ann. Rev. Phys. Chem. 1978, 29, 223250. (18) Troe, J. Predictive Possibilities of Unimolecular Rate Theory. J. Phys. Chem. 1979, 83, 114126. (19) Nordholm, S.; Bäck, A. On the Role of Nonergodicity and Slow IVR in Unimolecular Reaction Rate Theory- a Review and a View. Phys. Chem. Chem. Phys. 2001, 3, 2289-2295. (20) Hippler, H.; Krasteva, N.; Striebel, F. The Thermal Unimolecular Decomposition of HCO: Effects of State Specific Rate Constants on the Thermal Rate Constant. Phys. Chem. Chem. Phys. 2004, 6, 3383-3388. (21) Baer, S.; Fleming, D.; Arseneau, D.; Senba, M.; Gonzalez, A. Kinetic Isotope Effects in GasPhase Muonium Reactions. In Isotope Effects in Gas-Phase Chemistry; Kaye, J. A., Ed.; ACS Symposium Series; American Chemical Society: Washington, DC, 1992; Vol. 502, pp. 111-137. (22) 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. (23) 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.

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(24) 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, 184310-18. (25) Mielke, S.L.; Garrett, B.C.; Fleming, D.G.; Truhlar, D.G. Zero-Point Energy, Tunnelling, and Vibrational Adiabaticity in the Mu+ H2 Reaction. Mol. Phys. 2015, 113, 160-175. (26) Garrett, B.C.; Steckler, R.; Truhlar, D.G. Dynamics of Gas-Phase Reactions of Muonium. Hyper. Interact. 1986, 32 779-794. (27) Jambrina, P.G.; Garcia, E.; Herrero, V.J.; Sa0 ez-Ra0 banos, V.; Aoiz, F.J. Dynamics of the Reactions of Muonium and Deuterium Atoms with Vibrationally Excited Hydrogen Molecules: Tunneling and Vibrational Adiabaticity. Phys. Chem. Chem. Phys. 2012, 14, 14596-14604. (28) Aldegunde, J; Jambrina, P.G.; Garcia, E.; Herrero, V.J.; Sa0 ez-Ra0 banos, V.; Aoiz, F.J. Understanding the Reaction Between Muonium Atoms and Hydrogen Molecules: Zero Point Energy, Tunnelling, and Vibrational Adiabaticity. Mol. Phys. 2013, 111, 3169-3181. (29) Snooks, R.; Arseneau, D.J.; Fleming, D.G.; Pan, J.J; Shelley, M.; Baer, S. The Thermal Reaction Rate of Muonium with Methane (and Ethane) in the Gas Phase. J. Chem. Phys. 1995, 102, 4860-4869. (30) Pu, J.; Truhlar, D.G. Validation of Variational Transition State Theory with Multidimensional Tunneling Contributions Against Accurate Quantum Mechanical Dynamics for H+ CH4→ H2+ CH3 in an Extended Temperature Interval. J. Chem. Phys. 2002, 117, 1479-1481. (31) Pu, J.; Truhlar, D.G. Parametrized Direct Dynamics Study of Rate Constants of H with CH4 From 250 to 2400 K. J. Chem. Phys., 2002, 116, 1468-1478. (32) Banks, S.T.; Tautermann, C.S.; Remmert, S.M.; Clary, D.C. An Improved Treatment of Spectator Mode Vibrations in Reduced Dimensional Quantum Dynamics: Application to the Hydrogen Abstraction Reactions Mu +CH4, H+CH4, D+CH4, and CH3+CH4. J. Chem. Phys. 2009, 131, 044111-23. (33) Banks, S.T.; Clary, D.C. Chemical Reaction Surface Vibrational Frequencies Evaluated in Curvilinear Internal Coordinates: Application to H+CH4 H2 +CH3. J. Chem. Phys. 2009, 130, 024106-12 26


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(34) Li, Y.; Suleimanov, Y.V.; Li, J.; Green, W.H.; Guo, H. Rate Coefficients and Kinetic Isotope Effects of the X + CH4 → CH3 + HX (X = H, D, Mu) Reactions From Ring Polymer Molecular Dynamics. J. Chem. Phys. 2013, 138, 094307-16. (35) 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. (36) 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, 7098-7194. (37) Pan, J.J.; Arseneau, D.J.; Senba, M.; Shelley, M.; Fleming, D.G. Reaction Kinetics of Muonium with N2O in the Gas Phase. J. Phys. Chem. A, 1997, 101, 8470-8479. (38) Bakule, P.; Fleming, D.G.; Sukhorukov, O.; Ishida, K.; Pratt, F.; Momose, T.; Torikai, E.; Mielke, S.L.; Garrett, B.C.; Peterson, K.A.; et al. State-Selected Reaction of Muonium with Vibrationally Excited H2. J. Phys. Chem. Lett. 2012, 3, 2755-2760. (39) Bakule, P.; Sukhorukov, O.; Ishida, K.; Pratt, F.; Fleming, D.; Momose, T.; Matsuda, Y.; Torikai, E. First Accurate Experimental Study of Mu Reactivity From a State-Selected Reactant in the Gas Phase: the Mu+H2{1} Reaction Rate at 300K. J. Phys. B: At. Mol. Opt. Phys. 2015, 48, 045204-22. (40) Himmer, U.; Dilger, H.; Roduner, E.; Pan, J.J; Arseneau, D.J.; Fleming, D.G; Senba, M. Kinetic Isotope Effect in the Gas-Phase Reaction of Muonium with Molecular Oxygen. J. Phys. Chem. A 1999, 103, 2076-2087. (41) Pan, J.J; Arseneau, D.J.; Senba, M; Fleming, D.G.; Himmer, U; Suzuki, Y., Measurements of Mu+ NO Termolecular Kinetics Up to 520 Bar: Isotope Effects and the Troe Theory. Phys. Chem. Chem. Phys. 2000, 2, 621-629. (42) Pan, J.J; Arseneau, D.J; Senba, M; Garner, D.M.; Fleming, D.G.; Xie, T.; Bowman, J.M. Termolecular Kinetics for the Mu + CO + M Recombination Reaction: a Unique Test of Quantum Rate Theory. J. Chem. Phys. 2006, 125, 014307-20. (43) Garner, D.M.; Fleming, D.G.; Arseneau, D.J.; Senba, M.; Reid, I.D.; Mikula, R.J. Muonium Addition Reactions in the Gas Phase: Quantum Tunneling in Mu + C2H4 and Mu+ C2D4. J. Chem. Phys. 1990, 93, 1732-1740. 27



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(44) Roduner, E.; Louwier, P.W.F.; Brinkman, G.A.; Garner, D.M.; Reid, I.D.; Arseneau, D.J.; Senba, M; Fleming, D.G. Quantum Phenomena and Solvent Effects on Addition of Hydrogen Isotopes to Benzene and to Dimethylbutadiene. Ber. Bunsen-Ges. Phys. Chem. 1990 94, 1224-1230. (45) Duchovic, R.J.; Wagner, A.F.; Turner, R.E.; Garner, D.M.; Fleming, D.G. The Analysis of Muonium Hyperfine Interaction Measurements of Thermal Rate Constants for Addition Reactions. J. Chem. Phys. 1991, 94, 2794-2806. (46) Fleming, D.; Senba, M. Recent Results in Gas Phase µSR and Muonium Chemistry (at TRIUMF). In Perspectives of Meson Science; Yamazaki, T.; Nakai, K.; Nagamine, K., Eds.; North Holland: Amsterdam, 1992, pp. 219–264. (47) Senba, M.; Arseneau, D.J.; Pan,J.J.; Fleming, D.G. Slowing-Down Times and Stopping Powers for ∼ 2-MeV µ+ in Low-Pressure Gases. Phys. Rev. A. 2006, 74, 042708-17. (48) Senba, M.; Fleming, D.G.; Arseneau, D.J.; Mayne, H.R. Hot Atom Reaction Yields in Mu*+ H2 and T*+ H2 From Quasiclassical Trajectory Cross Sections on the Liu-Siegbahn-TruhlarHorowitz Surface. J. Chem. Phys., 2000, 112, 9390-9403. (49) Roduner, E. Muon Spin Resonance–a Variant of Magnetic Resonance. Appl. Magn. Reson. 1997, 13, 1-14. (50) Roduner, E. Polarized Positive Muons Probing Free Radicals: a Variant of Magnetic Resonance. Chem. Soc. Rev. 1993, 22, 337-346. (51) Roduner, E.; Fischer, H., Muonium Substituted Organic Free Radicals in Liquids. Theory and Analysis of µSR Spectra. Chem. Phys.1981, 54, 261-276. (52) Roduner, E. Free Radicals in Muonium Chemistry. In Exotic Atoms ‘79, Fundamental Interactions and Structure of Matter, Crowe, K.; Duclos, J.; Fiorentini, G.; Torelli, G., Eds.; Springer US: Boston, MA, 1980; Vol. 4, pp. 379-397. (53) Turner, R.E.; Snider, R.F. Theory of Muon Spin Relaxation of Mu+ CO. Phys. Rev. A 1998, 58, 4431-4446. (54) Johnson, C.; Cottrell, S.P.; Ghandi, K.; Fleming, D.G. Muon Implantation in Inert Gases Studied by Radio Frequency Spectroscopy. J. Phys. B: At. Mol. Opt. Phys. 2005, 38, 119-134.

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(55) Ricks, A.M.; Douberly, G.E.; Schleyer, von R. P.; Duncan, M.D. Infrared Spectroscopy of Protonated Ethylene: the Nature of Proton Binding in the Non-Classical Structure. Chem. Phys. Letts. 2009, 480, 17-20. (56) Senba, M.; Fleming, D.G.; Arseneau, D.J.; Garner, D.M.; Reid, I.D. Muonium Depolarization by Electron Spin Exchange with O2 Gas in the Temperature Range 90-500 K. Phys. Rev. A1989, 39, 3871-3883. (57) Turner, R.E.; Snider.R.F.; Fleming, D.G. Spin Relaxation of Hydrogen-Atom Isotopes via Electron Spin Exchange with Paramagnetic Gases. Phys. Rev. A 1990, 41, 1505-1516. (58) Fleming, D.G.; Pan, J.J.; Senba, M.; Arseneau, D.J.; Kiefl, R.; Shelley, M.; Cox, S.F.J.; Percival, P.W.; Brodovitch, J.-C. Spin Relaxation of Muonium-Substituted Ethyl Radicals (MuCH2H2) in the Gas Phase. J. Chem. Phys. 1996, 105, 7517-7535. (59) Pan, J.J.; Fleming, D.G.; Senba, M.; Arseneau, D.J.; Snooks, R.; Baer, S.; Shelley, M.; Percival, P.W.; Brodovitch, J.-C.; Addison-Jones, B.; et al. Spin Relaxation of Muonated Radicals in the Gas Phase. Hyper. Inter. 1994, 87, 865-870. (60) Percival, P.W.; Brodovitch, J.-C.; Arseneau, D.J.; Senba, M.; Fleming, D.G. Formation of the Muoniated Ethyl Radical in the Gas Phase. Physica B 2003, 326 72-75. (61) Gordon, E.B.; Ivanov, B.I.; Perminov, A.P.; Balalaev, V.E. A Measurement of Formation Rates and Lifetimes of Intermediate Complexes in Reversible Chemical Reactions Involving Hydrogen Atoms. Chem. Phys. 1978, 35, 79-89 . (62) Gordon, E.B.; Ivanov, B.I.; Perminov, A.P.; Ponomarev, A.N.; Tal’roze, V.L.; Khidirov, S.G. Measurement of Cross Sections of Spin H Atom Exchange (F= 1, MF =0 ) on Paramagnetic O2, NO and NO2 Molecules in the Temperature Range 310 - 390K. JETP Lett. 1973, 17, 395-397. (63) Percival, P.W.; Brodovitch, J.-C.; Leung, S.K; Yu, D.; Kiefl, R.F.; Garner, D.M.; Arseneau, D.J.; Fleming, D.G.; Gonzalez, A.; Kempton, J.R.; et al. Hyperfine Constants for the Ethyl Radical in the Gas Phase. Chem. Phys. Letts. 1989, 163, 241-245. (64) Fleming, D.G.; Arseneau, D.J.; Bridges, M.D.; Chen, Y.K.; Wang, Y.A. Hyperfine Coupling Constants of the Mu-T-Butyl Radical in NaY and USY Compared with Similar Data in the Bulk and with Ab Initio Theory. J. Phys. Chem. C 2013, 117, 16523-16539. (65) Hase, W.L.; Schlegel, H.B. Resolution of a Paradox Concerning the Forward and Reverse Rate Constants for Ethyl Atomic Hydrogen+ Ethylene. J. Phys. Chem. 1982, 86, 3901-3904. 29



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(66) Cox, S.F.J.; Eaton, G. H.; Magraw, J. E. Longitudinal Muon Spin Relaxation in Organic Radicals in the Vapour Phase. Hyper. Interact. 1991, 65, 773-777. (67) Geeson, D.A.; Symons, M.C.R.; Roduner, E.; Fischer, H; Cox, S.F.J. Evidence for a TripleBond Muonium Adduct. Chem. Phys. Lett. 1985, 116, 186-191. (68) Cochran, E.L.; Adrain, F.J.; Bowers, V.A. ESR Study of Ethynyl and Vinyl Free Radicals. J. Chem. Phys. 1964, 40, 213-220. (69) Rhodes, C.J. Muonium–the Second Radioisotope of Hydrogen–and Its Contribution to Free Radical Chemistry. J. Chem. Soc., Perkin Trans. 2 2002, 1379-1396. (70) Zheng, J.; Truhlar, D.G. Multi-Path Variational Transition State Theory for Chemical Reaction Rates of Complex Polyatomic Species: Ethanol+ OH Reactions. Faraday Discuss. 2012, 157, 59-88. (71) Zheng, J; Truhlar, D.G. Kinetics of Hydrogen-Transfer Isomerizations of Butoxyl Radicals. Phys. Chem. Chem. Phys. 2010 12, 7782-7793. (72) 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, 063201-5.

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TOC Graphic: Arrhenius plots comparing the present kMu (T) data for the Mu + C2 H2 reaction (solid red squares and fitted line) with the k∞ (T) calculations for kH (T) for the H + C2 H2 reaction from the calculations of Miller & Klippenstein (dark green line, from Ref. 1) and with the early experimental data of Payne & Stief for kH (T) for this reaction (lighter green data points and fitted line, from Ref. 8).

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Muonium Addition Reactions and Kinetic Isotope Effects in the Gas

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