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

Abstract

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.

New results for the formation of a muoniated radical in the Mu + Br2 system: a van der Waals complex or evidence for vibrational bonding in Br–Mu–Br?

“…The muon hfcc found for this radical is unusually high, even allowing for considerable latitude due to systematic effects on the (8.5%) statistical error found, a much higher hfcc in fact than for any other muoniated radical reported in the literature to date, including for MuQ _ CO, an a-radical with a muon hfcc of B1400 MHz. 47 Though such a high value is qualitatively consistent with the results of rudimentary (classical) molecular dynamics simulations (MDS) reported on in ref. 19 for the Br-Mu-Br radical, our own ab initio calculations of hfcc discussed below suggest that the muon-electron coupling constant of vibrationally-bound Br-Mu-Br would be much smaller than this.…”

“…In the former case, only a single undisturbed Mu component is seen, with an intercept at 0.5 and an inflection point at B1600 G, as expected, while at the fastest formation rates only the MuC 6 H 6 radical is seen, formed essentially instantaneously, with an inflection point at the radical hyperfine field of 185 G. The Quantum simulations for the solution data, exhibiting two components, show, as X -0, an intercept that falls below that for the pure radical, arising from the sequential formation of the radical from Mu, the muon having lost half its polarization due to charge exchange in forming Mu, 22,30,36,42 and then expected to lose half again in the radical, due to fast electron spin exchange, which again leads to depolarization of the muon spin. 40,47,48 That the solution data (dashed green line) is above the simulated curve at low fields, while that for the pure benzene (dashed blue line) falls below, reflects the difficulty of analyzing these data sets. In particular, a reliable calibration of the asymmetry response of the spectrometer over the full LF range of the measurement is difficult to obtain, which impacts in turn on the accuracy with which the diamagnetic component can be removed, a problem that is exacerbated at low fields due to nuclear dipolar couplings.…”

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

“…We would expect to approach the conventional high-pressure limit 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][41][42][43]45 In a like manner, a higher total pressure to approach this regime would be expected for Mu + C 2 H 2 + M than for Mu + C 2 H 4 + M, 43 since the dissociation rate constant, k d , in eq 2 should be larger for MuC 2 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 C 2 H 2 and C 2 H 4 behave so similarly over the range in moderator pressures studied (seen in Figure 3 below) and since pressures as low as 200 Torr are found to give pressure-independent rate constants k Mu (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 C 2 H 4 and C 2 H 2 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.…”

“…As in most previous studies of Mu chemical reactivity, 21,24,[41][42][43]46,50 the present (time-differential) experiments were also carried out in weak transverse magnetic fields (TFs), giving the measured "asymmetry", A(t),…”

Understanding the reaction between muonium atoms and hydrogen molecules: zero point energy, tunnelling, and vibrational adiabaticity

“…Due to its small mass (0.11398 u), collisions involving Mu atoms have constituted a sensitive probe for the importance of ZPE and tunnelling in chemical reactions [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. In turn, C Heμ [11,12,32], whose mass amounts to 4.11548 u, is formed when one of the He electrons is substituted by a negative muon μ − , 206.77 times heavier than the electron.…”