Experimental tests of reaction rate theory: Mu+H2 and Mu+D2

Copyright @ 1987 American Institute of Physics.Bimolecular rate constants for the thermal chemical reactions of muonium (Mu) with hydrogen and deuterium—Mu+H2→MuH+H and Mu+D2→MuD+D—over the temperature range 473–843 K are reported. The Arrhenius parameters and 1σ uncertainties for the H2 reaction are log A (cm3 molecule-1 s-1)=-9.605±0.074 and Ea =13.29±0.22 kcal mol-1, while for D2 the values are -9.67±0.12 and 14.73±0.40, respectively. These results are significantly more precise than those reported earlier by Garner et al. For the Mu reaction with H2 our results are in excellent agreement with the 3D quantum mechanical calculations of Schatz on the Liu–Siegbahn–Truhlar–Horowitz potential surface, but the data for both reactions compare less favorably with variational transition-state theory, particularly at the lower temperatures.NSERC (Canada) and the Petroleum Research Foundation of the Americal Chemical Society

Reaction kinetics of muonium with the halogen gases (F2, Cl2, and Br2)

Copyright @ 1989 American Institute of PhysicsBimolecular rate constants for the thermal chemical reactions of muonium (Mu) with the halogen gases—Mu+X2→MuX+X—are reported over the temperature ranges from 500 down to 100, 160, and 200 K for X2=F2,Cl2, and Br2, respectively. The Arrhenius plots for both the chlorine and fluorine reactions show positive activation energies Ea over the whole temperature ranges studied, but which decrease to near zero at low temperature, indicative of the dominant role played by quantum tunneling of the ultralight muonium atom. In the case of Mu+F2, the bimolecular rate constant k(T) is essentially independent of temperature below 150 K, likely the first observation of Wigner threshold tunneling in gas phase (H atom) kinetics. A similar trend is seen in the Mu+Cl2 reaction. The Br2 data exhibit an apparent negative activation energy [Ea=(−0.095±0.020) kcal mol−1], constant over the temperature range of ∼200–400 K, but which decreases at higher temperatures, indicative of a highly attractive potential energy surface. This result is consistent with the energy dependence in the reactive cross section found some years ago in the atomic beam data of Hepburn et al. [J. Chem. Phys. 69, 4311 (1978)]. In comparing the present Mu data with the corresponding H atom kinetic data, it is found that Mu invariably reacts considerably faster than H at all temperatures, but particularly so at low temperatures in the cases of F2 and Cl2. The current transition state calculations of Steckler, Garrett, and Truhlar [Hyperfine Interact. 32, 779 (986)] for Mu+X2 account reasonably well for the rate constants for F2 and Cl2 near room temperature, but their calculated value for Mu+Br2 is much too high. Moreover, these calculations seemingly fail to account for the trend in the Mu+F2 and Mu+Cl2 data toward pronounced quantum tunneling at low temperatures. It is noted that the Mu kinetics provide a crucial test of the accuracy of transition state treatments of tunneling on these early barrier HX2 potential energy surfaces.NSERC (Canada), Donors of the Petroleum Research Fund, administered by the American Chemical Society, for their partial support of this research and the Canada Council

Muonium Formation as a Probe of Radiation Chemistry in Sub- and Supercritical Carbon Dioxide

Muonium (Mu = μ+e-), which can be considered a light isotope of the H atom, has been observed for the first time in supercritical CO2 (ScCO2). It is unreactive on a time scale of a few microseconds and over a wide density range from well below to well above the CO2 critical density pc = 0.47 g/cm 3. The fraction of muon polarization in muonium, PMu, does not vary significantly at low densities but changes quickly at the highest densities, approaching zero. This density dependence is reflected in a concomitant increase observed in the lost fraction of polarization, P L, demonstrating that the dynamics of Mu formation and depolarization in ScCO2 is a direct probe of radiolysis effects in the terminal muon radiation track. In marked contrast to previous studies in hydrogen-containing solvents, C2H6 and H2O, over comparable density ranges, the diamagnetic fraction, PD, was found to be almost independent of density in CO2, attributed to the formation of the stable solvated MuCO2+ molecular ion in this hydrogen-free solvent. The differing density dependences of both the Mu and the diamagnetic fraction in CO2, in comparison with the rather similar trends seen for both in C2H2, and H2O, supports previous claims of a significant role played by proton (muon) transfer reactions in the competing processes involved in Mu formation in hydrogen-containing solvents. In addition to this being the first report of radiolysis effects accompanying energetic positive muons stopping in ScCO 2, it is the only report of end of track effects in this solvent, which has many applications in nuclear waste management and green chemistry. With a mass intermediate between that of the electron, which has provided most radiation-chemistry studies in ScCO2 to date, and the proton (or alpha-particle), implanted muons provide a unique data set, characteristic of higher LET radiation, that may be relevant to radiolysis effects induced in ScCO2 by alpha decay from heavy nuclei, for which there are no comparable studies

Hyperfine Interactions and Molecular Motion of the Mu−Ethyl Radical in Faujasites: NaY, HY, and USY

The adsorption and dynamical behavior of the Mu-ethyl radical (MuC 2H 4) in NaY, HY, and USY faujasites was investigated by the muon spin resonance (μSR) technique, at loadings of one to five ethene molecules per supercage and over a temperature range of ca. 5-500 K (for NaY). The temperature dependences of both the muon and proton hyperfine coupling constants (Hfc's) are reported and compared with similar studies of MuC 2H 4 in different environments. Both transverse field (TF) μSR and avoided level crossing resonance (ALC) μSR spectra were recorded, with information on molecular motion mainly provided by the ALC line shapes. The muon Hfc's show only a small sensitivity to different frameworks and loadings but exhibit significant (∼10%) shifts at low temperatures, in comparison with bulk values, due to binding of the ethyl radical to cations at S II sites in NaY and to framework hydroxyls in the case of HY(USY). The Δ 1 resonances are symmetric and quite broad at the lower temperatures studied, but dramatically further broaden near room temperature, seen also in the TF relaxation rates, suggesting that the Mu-ethyl radical either desorbs from or hops between its binding sites at the higher temperatures. An Arrhenius estimate of the activation energy for desorption gives ∼ 20 kJ/mol, consistent with the dipolar interaction energy between the Mu-ethyl radical and an NaY cluster. The observation of such highly broadened Δ 1 ALC lines at the higher temperatures contrasts with the largely static line widths reported previously for the Mu-cyclohexadienyl radical (MuC 6H 6) in NaY. Sharper Δ 0 ALC lines for both the α and β protons of MuC 2H 4 appear near the same temperatures at which the Δ 1 lines overly broaden, and which persist to the highest temperatures (350 K). For NaY, the α proton resonances also broaden further at these temperatures. For both NaY and particularly HY, the temperature dependence of the α proton Hfc's indicates considerable distortion of the Mu-ethyl radical geometry, due to its binding to zeolite sites. Recently published calculations of binding energies and Hfc's for ethyl radicals in NaY and HY suggest a much stronger binding of the MuC 2H 4 radical than seems warranted by the data and pose as well a conundrum in comparison with earlier results for MuC 6H 6 in NaY. On the other hand, the temperature dependence of the isotropic muon Hfc's found from the T-atom model for NaY employed in these calculations is in excellent agreement with experiment. © 2007 American Chemical Society

Isotope Effects and the Temperature Dependences of the Hyperfine Coupling Constants of Muoniated sec-Butyl Radicals in Condensed Phases

Reported here is the first μSR study of the muon (A(μ)) and proton (A(p)) β-hyperfine coupling constants (Hfcc) of muoniated sec-butyl radicals, formed by muonium (Mu) addition to 1-butene and to cis- and trans-2-butene. The data are compared with in vacuo spin-unrestricted MP2 and hybrid DFT/B3YLP calculations reported in the previous paper (I), which played an important part in the interpretation of the data. The T-dependences of both the (reduced) muon, A(μ)′(T), and proton, A(p)(T), Hfcc are surprisingly well explained by a simple model, in which the calculated Hfcc from paper I at energy minima of 0 and near ±120° are thermally averaged, assuming an energy dependence given by a basic 2-fold torsional potential. Fitted torsional barriers to A(μ)′(T) from this model are similar (~3 kJ/mol) for all muoniated butyl radicals, suggesting that these are dominated by ZPE effects arising from the C−Mu bond, but for A(p)(T) exhibit wide variations depending on environment. For the cis- and trans-2-butyl radicals formed from 2-butene, A(μ)′(T) exhibits clear discontinuities at bulk butene melting points, evidence for molecular interactions enhancing these muon Hfcc in the environment of the solid state, similar to that found in earlier reports for muoniated tert-butyl. In contrast, for Mu−sec-butyl formed from 1-butene, there is no such discontinuity. The muon hfcc for the trans-2-butyl radical are seemingly very well predicted by B3LYP calculations in the solid phase, but for sec-butyl from 1-butene, showing the absence of further interactions, much better agreement is found with the MP2 calculations across the whole temperature range. Examples of large proton Hfcc near 0 K are also reported, due to eclipsed C−H bonds, in like manner to C−Mu, which then also exhibit clear discontinuities in A(p)(T) at bulk melting points. The data suggest that the good agreement found between theory and experiment from the B3LYP calculations for eclipsed bonds in the solid phase may be fortuitous. For the staggered protons of the sec-butyl radicals formed, no discontinuities are seen at all in A(p)(T), also demonstrating no further effects of molecular interactions on these particular proton Hfcc

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

A first complete μSR study of the T dependences of the (reduced) muon, Aμ′(T), and proton, Ap(T), β-hyperfine coupling constants (hfcc) of the muoniated t-butyl radical is reported in the faujasitic zeolites NaY and USY, and the results are compared with similar data and with early EPR results in condensed bulk phases. The results are also compared with single-molecule UMP2 and DFT/B3LYP calculations in the bulk and in an NaY zeolite fragment of Si and O atoms with both OH- and H-capping. Muon hfcc are reported for the first time for the Mu-isobutyl radical in the bulk phase and are also compared with theory and with EPR data. The present results for the muon and proton hfcc of Mu-t-butyl in the bulk complement earlier work published elsewhere at higher temperatures but are extended here down to 5 K to facilitate comparisons with in vacuo theory at 0 K. Good fits to the data for both Aμ′(T) and Ap(T) for Mu-t-butyl are found from the calculated hfcc in both the bulk and in NaY, assuming a Boltzmann-weighted energy dependence given by a simple twofold torsional potential, providing an estimate of the barrier to internal rotation. In contrast to the bulk data, there is no clear discontinuity seen in Aμ′(T) for Mu-t-butyl in NaY or USY at the melting point of isobutene, demonstrating the dominance of single-molecule guest-host interactions in the faujasite supercage. In contrast to the Aμ′(T) dependence in the bulk, there is no discontinuity seen for either of the proton hfcc, Ap,CH3(T) or Ap,CH2Mu(T), at the melting point, which also exhibit similar behavior in NaY, suggesting that its observation in the bulk for only the muon hfcc arises from a specific effect of the intermolecular interactions on the vibrational averaging of the muon hfcc. The measured muon hfcc for Mu-t-butyl in NaY fall below those in the bulk at low temperatures, indicating some transfer of electron spin density to the Na cation, which is confirmed by specific additional level-crossing resonances not observed in USY. The Na nuclear hfcc, ANa(T), follow a similar trend with temperature as Aμ′(T), with an estimate of the Na spin density at 0 K that also agrees well with theory. © 2013 American Chemical Society

Hyperfine Coupling Constants of the Mu‑<i>t</i>‑Butyl Radical in NaY and USY Compared with Similar Data in the Bulk and with Ab Initio Theory

A first complete μSR study of the <i>T</i> dependences of the (reduced) muon, <i>A</i>_μ^′(<i>T</i>), and proton, <i>A</i>_p(<i>T</i>), β-hyperfine coupling constants (hfcc) of the muoniated <i>t</i>-butyl radical is reported in the faujasitic zeolites NaY and USY, and the results are compared with similar data and with early EPR results in condensed bulk phases. The results are also compared with single-molecule UMP2 and DFT/B3LYP calculations in the bulk and in an NaY zeolite fragment of Si and O atoms with both OH- and H-capping. Muon hfcc are reported for the first time for the Mu-isobutyl radical in the bulk phase and are also compared with theory and with EPR data. The present results for the muon and proton hfcc of Mu-<i>t</i>-butyl in the bulk complement earlier work published elsewhere at higher temperatures but are extended here down to 5 K to facilitate comparisons with in vacuo theory at 0 K. Good fits to the data for both <i>A</i>_μ^′(<i>T</i>) and <i>A</i>_p(<i>T</i>) for Mu-<i>t</i>-butyl are found from the calculated hfcc in both the bulk and in NaY, assuming a Boltzmann-weighted energy dependence given by a simple twofold torsional potential, providing an estimate of the barrier to internal rotation. In contrast to the bulk data, there is no clear discontinuity seen in <i>A</i>_μ^′(<i>T</i>) for Mu-<i>t</i>-butyl in NaY or USY at the melting point of isobutene, demonstrating the dominance of single-molecule guest–host interactions in the faujasite supercage. In contrast to the <i>A</i>_μ^′(<i>T</i>) dependence in the bulk, there is no discontinuity seen for either of the proton hfcc, <i>A</i>_p,CH₃(<i>T</i>) or <i>A</i>_p,CH₂Mu(<i>T</i>), at the melting point, which also exhibit similar behavior in NaY, suggesting that its observation in the bulk for only the muon hfcc arises from a specific effect of the intermolecular interactions on the vibrational averaging of the muon hfcc. The measured muon hfcc for Mu-<i>t</i>-butyl in NaY fall below those in the bulk at low temperatures, indicating some transfer of electron spin density to the Na cation, which is confirmed by specific additional level-crossing resonances not observed in USY. The Na nuclear hfcc, <i>A</i>_Na(<i>T</i>), follow a similar trend with temperature as <i>A</i>_μ^′(<i>T</i>), with an estimate of the Na spin density at 0 K that also agrees well with theory