Rate constants and kinetic isotope effects for H-atom abstraction reactions by muonium in the Mu + propane and Mu + n-butane reactions from 300 K to 435 K: challenges for theory.

This paper reports measurements of the temperature dependence of the rate constants for H-atom abstraction reactions from propane and n-butane by the light isotopic H-atom muonium (Mu), kMu(T), over temperatures in the range 300 K to 435 K. Simple Arrhenius fits to these data yield activation energies, E, that are some 2-4 times lower than E found from corresponding fits for the H + propane and H + n-butane reactions studied elsewhere, both experimentally and theoretically, and fit over a similar temperature range. These activation energies E are also much lower than estimated from zero-point-energy corrected vibrationally adiabatic potential barriers, both results suggesting that quantum tunneling plays an important role in determining kMu(T) and for the Mu + propane reaction in particular. The results are expected to pose a considerable challenge to reaction rate theory for isotopic H-atom reactions in alkane systems.

Rate Coefficient for the (4)Heµ + CH4 Reaction at 500 K: Comparison between Theory and Experiment.

The rate constant for the H atom abstraction reaction from methane by the muonic helium atom, Heµ + CH4 → HeµH + CH3, is reported at 500 K and compared with theory, providing an important test of both the potential energy surface (PES) and reaction rate theory for the prototypical polyatomic CH5 reaction system. The theory used to characterize this reaction includes both variational transition-state (CVT/µOMT) theory (VTST) and ring polymer molecular dynamics (RPMD) calculations on a recently developed PES, which are compared as well with earlier calculations on different PESs for the H, D, and Mu + CH4 reactions, the latter, in particular, providing for a variation in atomic mass by a factor of 36. Though rigorous quantum calculations have been carried out for the H + CH4 reaction, these have not yet been extended to the isotopologues of this reaction (in contrast to H3), so it is important to provide tests of less rigorous theories in comparison with kinetic isotope effects measured by experiment. In this regard, the agreement between the VTST and RPMD calculations and experiment for the rate constant of the Heµ + CH4 reaction at 500 K is excellent, within 10% in both cases, which overlaps with experimental error.

Muonium Addition Reactions and Kinetic Isotope Effects in the Gas Phase: k∞ Rate Constants for Mu + C2H2.

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 from 168 to 446 K, but also down to 200 Torr at 168 K and over a much higher range of pressures, from 10 to 44 bar at 295 K, demonstrating pressure-independent rate constants, kMu(T). Even at 200 Torr moderator pressure, the kinetics for Mu + C2H2 addition behave as if effectively in the high-pressure limit, giving k∞ = kMu due to depolarization of the muon spin in the MuC2H2 radical formed in the addition step. The rate constants kMu(T) exhibit modest Arrhenius curvature over the range of measured temperatures. Comparisons with data and with calculations for the corresponding H(D) + C2H2 addition reactions reveal a much faster rate for the Mu reaction at the lowest temperatures, by 2 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 analogous D atom reaction, forming C2HD + 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 + C2H2 reaction is effectively the only experimental study of kinetic isotope effects in the high-pressure limit for H-atom addition to acetylene.

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.

The neutral muonic helium atom (4)Heµ, in which one of the electrons of He is replaced by a negative muon, may be effectively regarded as the heaviest isotope of the hydrogen atom, with a mass of 4.115 amu. We report details of the first muon spin rotation (µSR) measurements of the chemical reaction rate constant of (4)Heµ with molecular hydrogen, (4)Heµ + H(2) → (4)HeµH + H, at temperatures of 295.5, 405, and 500 K, as well as a µSR measurement of the hyperfine coupling constant of muonic He at high pressures. The experimental rate constants, k(Heµ), are compared with the predictions of accurate quantum mechanical (QM) dynamics calculations carried out on a well converged Born-Huang (BH) potential energy surface, based on complete configuration interaction calculations and including a Born-Oppenheimer diagonal correction. At the two highest measured temperatures the agreement between the quantum theory and experiment is good to excellent, well within experimental uncertainties that include an estimate of possible systematic error, but at 295.5 K the quantum calculations for k(Heµ) are below the experimental value by 2.1 times the experimental uncertainty estimates. Possible reasons for this discrepancy are discussed. Variational transition state theory calculations with multidimensional tunneling have also been carried out for k(Heµ) on the BH surface, and they agree with the accurate QM rate constants to within 30% over a wider temperature range of 200-1000 K. Comparisons between theory and experiment are also presented for the rate constants for both the D + H(2) and Mu + H(2) reactions in a novel study of kinetic isotope effects for the H + H(2) reactions over a factor of 36.1 in isotopic mass of the atomic reactant.

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)) ß-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.

Kinetic isotope effects for the reactions of muonic helium and muonium with H2.

The neutral muonic helium atom may be regarded as the heaviest isotope of the hydrogen atom, with a mass of ~4.1 atomic mass units ((4.1)H), because the negative muon almost perfectly screens one proton charge. We report the reaction rate of (4.1)H with (1)H(2) to produce (4.1)H(1)H + (1)H at 295 to 500 kelvin. The experimental rate constants are compared with the predictions of accurate quantum-mechanical dynamics calculations carried out on an accurate Born-Huang potential energy surface and with previously measured rate constants of (0.11)H (where (0.11)H is shorthand for muonium). Kinetic isotope effects can be compared for the unprecedentedly large mass ratio of 36. The agreement with accurate quantum dynamics is quantitative at 500 kelvin, and variational transition-state theory is used to interpret the extremely low (large inverse) kinetic isotope effects in the 10(-4) to 10(-2) range.

Termolecular kinetics for the Mu + CO + M recombination reaction: A unique test of quantum rate theory.

The room-temperature termolecular rate constants, k0, for the Mu + CO + M<==>MuCO + M (M = He, N2, Ar) recombination reaction have been measured by the muSR technique, and are reported for moderator gas pressures of up to approximately 200 bar (densities less, similar 0.4 x 10(22) molec cm(-3)). The experimental relaxation rates reveal an unusual signature, in being dominated by the electron spin-rotation interaction in the MuCO radical that is formed in the addition step. In N2 moderator, k0 = 1.2+/-0.1 x 10(-34) cm(6) s(-1), only about 30% higher than found in Ar or He. The experimental results are compared with theoretical calculations carried out on the Werner-Keller-Schinke (WKS) surface [Keller et al., J. Chem. Phys. 105, 4983 (1996)], within the framework of the isolated resonance model (IRM). The positions and lifetimes of resonance states are obtained by solving the complex Hamiltonian for the nonrotating MuCO system, using an L2 method, with an absorbing potential in the asymptotic region. Accurate values of the vibrational bound and resonance states of MuCO reveal unprecedented isotope effects in comparisons with HCO, due to the remarkable effect of replacing H by the very light Mu atom (m(Mu) approximately (1/9)m(H)). Due to its pronounced zero-point energy shift, there are only two (J = 0) bound states in MuCO. Contributions from nonzero J states to the termolecular rate constants are evaluated through the J-shifting approximation, with rotational constants evaluated at the potential minimum. The value of the important A constant (181 cm(-1)) used in this approximation was supported by accurate J = K = 1 calculations, from which A = 180 cm(-1) was obtained by numerical evaluation. The calculations presented here, with a "weak collision factor" beta c = 0.001, indicative of the very sparse density of MuCO states, give a very good account of both the magnitude and pressure dependence of the experimental rates, but only when the fact that the two initially bound (J = 0) states become resonances for J > 0 is taken into account. This is the first time in IRM calculations of atom-molecule recombination reactions where J not equal to 0 states have proven to be so important, thus providing a truly unique test of quantum rate theory.