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

Determination of differential elastic and vibrational excitation cross sections for e-H sub 2 scattering

Elastic scattering of electrons by hydroge

Electron scattering by H2 with and without vibrational excitation. III. Experimental and theoretical study of inelastic scattering

The ratios of the differential cross sections (DCS's) for excitation of the first, second, and third vibrational states of H2 in its ground electronic state to the elastic DCS have been measured as a function of scattering angle in the 10°–80° range and impact energy in the 7–81.6-eV range. From these ratios the DCS's corresponding to transitions from the ground to the first two vibrationally excited levels (fundamental and first overtone bands) were obtained by utilizing the elastic cross sections determined in the previous paper (II). In addition, the DCS for excitation of the second overtone band was determined for an impact energy of 10 eV. By angular extrapolation and integration of the DCS's the integral cross sections for the vibrational excitations were also determined. In addition, all these cross sections have been calculated using a quantum-mechanical method based on potential scattering in a plane wave scattering approximation which is described in Part I of this series. The present experimental and theoretical cross sections and previous measurements and calculations are compared. The calculated DCS ratios and the DCS's themselves for the fundamental excitation are in good agreement with experiment at 7 and 10 eV; however, at higher energies the calculated DCS's are generally larger than the experimental ones, at some angles by as much as a factor of 10. The calculated ratio of the DCS for the fundamental excitation to the elastic DCS shows a minimum as a function of angle, in qualitative agreement with the experimental results in the 13.6–81.6-eV energy range. The experimental DCS's for vibrational excitation also show a deep minimum. For excitation of the first overtone vibration, the experimental ratios are an order of magnitude larger than the calculated ones at low energy but in better agreement for the magnitude at higher energy. This discrepancy at low energies is explained in terms of resonance scattering. Our experiments are in good agreement with those of others in the few (low energy) cases where comparison is possible

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

A Computational Procedure to Detect a New Type of High Dimensional Chaotic Saddle and its Application to the 3-D Hill's Problem

A computational procedure that allows the detection of a new type of high-dimensional chaotic saddle in Hamiltonian systems with three degrees of freedom is presented. The chaotic saddle is associated with a so-called normally hyperbolic invariant manifold (NHIM). The procedure allows to compute appropriate homoclinic orbits to the NHIM from which we can infer the existence a chaotic saddle. NHIMs control the phase space transport across an equilibrium point of saddle-centre-...-centre stability type, which is a fundamental mechanism for chemical reactions, capture and escape, scattering, and, more generally, ``transformation'' in many different areas of physics. Consequently, the presented methods and results are of broad interest. The procedure is illustrated for the spatial Hill's problem which is a well known model in celestial mechanics and which gained much interest e.g. in the study of the formation of binaries in the Kuiper belt.Comment: 12 pages, 6 figures, pdflatex, submitted to JPhys

Differential and integral cross sections for excitation of the 2(1)P state of helium by electron impact

Differential scattering cross sections for excitation of helium by electron impact from its ground state to its 21P excited state have been measured at four incident electron energies in the range 26-55.5 eV for scattering angles between 10° and 70°, and at 81.6 eV for scattering angles between 10° and 80°. These differential cross sections have been placed on an absolute scale by normalizing them to the experimental absolute integral cross sections of Jobe and St. John. These experimental differential and integral cross sections have been compared with the results predicted by the Born approximation, and by several other first-order approximations in which direct excitation is calculated in the Born approximation and exchange scattering by various Ochkurlike approximations. The calculations provide reliable tests of these scattering theories since they are made using the accurate generalized oscillator strengths of Kim and Inokuti. As expected, these first-order theories are poor near threshold and exchange is important at high scattering angles for all energies. Further, the absolute magnitude of the calculated integral and small-angle differential cross sections is too large and is within 50% of experiment only at energies greater than 80 eV. These first-order models are in qualitative agreement with the experimental angular dependence at 34-81.6 eV for scattering angles between 10° and 40°. At higher scattering angles (corresponding to momentum transfers greater than about 1.6 a.u.), the calculated differential cross sections fall well below the experimental ones. The phase between the direct and exchange scattering amplitudes was found to be important at all energies, and is apparently not predicted correctly by any of the first-order models examined here. Some approximations for the exchange (e.g., Ochkur approximation and the post interaction form of the Ochkur-Rudge approximation) were found to be better for integral cross sections and some (e.g., prior Ochkur-Rudge approximation) were better for differential cross sections. The use of good analytic self-consistent-field (SCF) wave functions for both the ground and excited states was tested by computing generalized oscillator strengths from them and comparing these results with the calculations using the accurate generalized oscillator strengths. The SCF functions yield differential cross sections in quantitative disagreement (20%) with the accurate results, although the energy and angle dependence of the cross sections is predicted qualitatively correctly

Ehrenfest Statistical Dynamics in Chemistry: Study of Decoherence Effects

In previous works, we introduced a geometric route to define our Ehrenfest statistical dynamics (ESD) and we proved that, for a simple toy model, the resulting ESD does not preserve purity. We now take a step further: we investigate decoherence and pointer basis in the ESD model by considering some uncertainty in the degrees of freedom of a simple but realistic molecular model, consisting of two classical cores and one quantum electron. The Ehrenfest model is sometimes discarded as a valid approximation to nonadiabatic coupled quantum-classical dynamics because it does not describe the decoherence in the quantum subsystem. However, any rigorous statistical analysis of the Ehrenfest dynamics, such as the described ESD formalism, proves that decoherence exists. In this article, decoherence in ESD is studied by measuring the change in the quantum subsystem purity and by analyzing the appearance of the pointer basis to which the system decoheres, which for our example is composed of the eigenstates of the electronic Hamiltonian.We have received support by Research Grants E24/1 and E24/3 (DGA, Spain), MINECO MTM2015-64166-C2-1-P and FIS2017-82426-P, and MICINN FIS2013-46159-C3-2-P and FIS2014-55867-P. Support from Scholarships B100/13 (DGA) and FPU13/01587 (MECD) for J.A.J.-G. is also acknowledged