V. Sáez-Rábanos

Spatial distributions of angular momenta in quantum and quasiclassical stereodynamics

We have recently reported a derivation of the relationship between the quantum and classical descriptions of angular momentum polarization [M. P. de Miranda and F. Javier Aoiz, Phys. Rev. Lett. 93, 083201 (2004)]. This paper presents a detailed account of the derivation outlined in that paper, and discusses the implications of the new results. These include (i) a new expression of the role of the uncertainty principle in the broadening of angular momentum distributions, (ii) the attribution of azimuthal fluctuations of angular momentum distributions to spatial quantum beats, (iii) the definition of a new Fourier transform of the density matrix, distinct from those suggested in the past, that provides an alternative view of how the quantum description of angular momentum polarization approaches the classical one in the correspondence principle limit, (iv) a prescription for the determination of a quasiclassical angular momentum distribution function that does not suffer from problems encountered with its purely classical counterpart, and (v) a description of how angular momentum distributions commonly visualized with recourse to the classical vector model can be depicted with exact and well-defined quantum mechanics.

Dynamics of the D+ + H2 and H+ + D2 reactions: a detailed comparison between theory and experiment

An extensive set of experimental measurements on the dynamics of the H(+) + D(2) and D(+) + H(2) ion-molecule reactions is compared with the results of quantum mechanical (QM), quasiclassical trajectory (QCT), and statistical quasiclassical trajectory (SQCT) calculations. The dynamical observables considered include specific rate coefficients as a function of the translational energy, E(T), thermal rate coefficients in the 100-500 K temperature range. In addition, kinetic energy spectra (KES) of the D(+) ions reactively scattered in H(+) + D(2) collisions are also presented for translational energies between 0.4 eV and 2.0 eV. For the two reactions, the best global agreement between experiment and theory over the whole energy range corresponds to the QCT calculations using a gaussian binning (GB) procedure, which gives more weight to trajectories whose product vibrational action is closer to the actual integer QM values. The QM calculations also perform well, although somewhat worse over the more limited range of translational energies where they are available (E(T) < 0.6 eV and E(T) < 0.2 eV for the H(+) + D(2) and D(+) + H(2) reactions, respectively). The worst agreement is obtained with the SQCT method, which is only adequate for low translational energies. The comparison between theory and experiment also suggests that the most reliable rate coefficient measurements are those obtained with the merged beams technique. It is worth noting that none of the theoretical approaches can account satisfactorily for the experimental specific rate coefficients of H(+) + D(2) for E(T)≤ 0.2 eV although there is a considerable scatter in the existing measurements. On the whole, the best agreement with the experimental laboratory KES is obtained with the simulations carried out using the state resolved differential cross sections (DCSs) calculated with the QCT-GB method, which seems to account for most of the observed features. In contrast, the simulations with the SQCT data predict kinetic energy spectra (KES) considerably cooler than those experimentally determined.

Can quasiclassical trajectory calculations reproduce the extreme kinetic isotope effect observed in the muonic isotopologues of the H + H2 reaction?

Rate coefficients for the mass extreme isotopologues of the H + H(2) reaction, namely, Mu + H(2), where Mu is muonium, and Heμ + H(2), where Heμ is a He atom in which one of the electrons has been replaced by a negative muon, have been calculated in the 200-1000 K temperature range by means of accurate quantum mechanical (QM) and quasiclassical trajectory (QCT) calculations and compared with the experimental and theoretical results recently reported by Fleming et al. [Science 331, 448 (2011)]. The QCT calculations can reproduce the experimental and QM rate coefficients and kinetic isotope effect (KIE), k(Mu)(T)/k(Heμ)(T), if the Gaussian binning procedure (QCT-GB)--weighting the trajectories according to their proximity to the right quantal vibrational action--is applied. The analysis of the results shows that the large zero point energy of the MuH product is the key factor for the large KIE observed.

Dynamics of the reactions of muonium and deuterium atoms with vibrationally excited hydrogen molecules: tunneling and vibrational adiabaticity

Quantum mechanical (QM) and quasiclassical trajectory (QCT) calculations have been carried out for the exchange reactions of D and Mu (Mu = muonium) with hydrogen molecules in their ground and first vibrational states. In all the cases considered, the QM rate coefficients, k(T), are in very good agreement with the available experimental results. In particular, QM calculations on the most accurate potential energy surfaces (PESs) predict a rate coefficient for the Mu + H(2) (ν = 1) reaction which is very close to the preliminary estimate of its experimental value at 300 K. In contrast to the D + H(2) (ν = 0,1) and the Mu + H(2) (ν = 0) reactions, the QCT calculations for Mu + H(2) (ν = 1) predict a much smaller k(T) than that obtained with the accurate QM method. This behaviour is indicative of tunneling. The QM reaction probabilities and total reactive cross sections show that the total energy thresholds for the reactions of Mu with H(2) in ν = 0 and ν = 1 are very similar, whereas for the corresponding reaction with D the ν = 0 total energy threshold is about 0.3 eV lower than that for ν = 1. The results just mentioned can be explained by considering the vibrational adiabatic potentials along the minimum energy path. The threshold for the reaction of Mu with H(2) in both ν = 0 and ν = 1 states is the same and is given by the height of the ground vibrational adiabatic collinear potential, whereas for the D + H(2) reaction the adiabaticity is preserved and the threshold for the reaction in ν = 1 is very close to the height of the ν = 1 adiabatic collinear barrier. For Mu + H(2) (ν = 1) the reaction takes place by crossing from the ν = 1 to the ν = 0 adiabat, since the exit channel leading to MuH (ν = 1) is not energetically accessible. At the lowest possible energies, the non-adiabatic vibrational crossing implies a strong tunneling effect through the ν = 1 adiabatic barrier. Absence of tunneling in the classical calculations results in a threshold that coincides with the height of the ν = 1 adiabatic barrier. Most interestingly, the expected tunneling effect in the reaction of Mu with hydrogen molecules occurs for H(2) (ν = 1) but not for H(2) (ν = 0) where zero-point-energy effects clearly dominate.

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

The advent of very precise measurements of rate coefficients in reactions of muonium (Mu), the lightest hydrogen isotope, with H2 in its ground and first vibrational state and of kinetic isotope effects with respect to heavier isotopes has triggered a renewed interests in the field of muonic chemistry. The aim of the present article is to review the most recent results about the dynamics and mechanism of the reaction Mu+H2 to shed light on the importance of quantum effects such as tunnelling, the preservation of the zero point energy, and the vibrational adiabaticity. In addition to accurate quantum mechanical (QM) calculations, quasiclassical trajectories (QCT) have been run in order to check the reliability of this method for this isotopic variant. It has been found that the reaction with H2(v=0) is dominated by the high zero point energy (ZPE) of the products and that tunnelling is largely irrelevant. Accordingly, both QCT calculations that preserve the products’ ZPE as well as those based on the Ring Polymer Molecular Dynamics methodology can reproduce the QM rate coefficients. However, when the hydrogen molecule is vibrationally excited, QCT calculations fail completely in the prediction of the huge vibrational enhancement of the reactivity. This failure is attributed to tunnelling, which plays a decisive role breaking the vibrational adiabaticity when v=1. By means of the analysis of the results, it can be concluded that the tunnelling takes place through the ν1=1 collinear barrier. Somehow, the tunnelling that is missing in the Mu+H2(v=0) reaction is found in Mu+H2(v=1).