The dynamics of the H⁺+ D₂reaction: a comparison of quantum mechanical wavepacket, quasi-classical and statistical-quasi-classical results

Abstract

A detailed study of the proton exchange reaction H(+) + D(2)(v = 0, j = 0) --> HD + D(+) on its ground 1(1)A' potential energy surface has been carried out using 'exact' close-coupled quantum mechanical wavepacket (WP-EQM), quasi-classical trajectory (QCT), and statistical quasi-classical trajectory (SQCT) calculations for a range of collision energies starting from the reaction threshold to 1.3 eV. The WP-EQM calculations include all total angular momenta up to J(max) = 50, and therefore the various dynamical observables are converged up to 0.6 eV. It has been found that it is necessary to include all Coriolis couplings to obtain reliable converged results. Reaction probabilities obtained using the different methods are thoroughly compared as a function of the total energy for a series of J values. Comparisons are also made of total reaction cross sections as function of the collision energy, and rate constants. In addition, opacity functions, integral cross sections (ICS) and differential cross sections (DCS) are presented at 102 meV, 201.3 meV and 524.6 meV collision energy. The agreement between the three sets of results is only qualitative. The QCT calculations fail to describe the overall reactivity and most of the dynamical observables correctly. At low collision energies, the QCT method is plagued by the lack of conservation of zero point energy, whilst at higher collision energies and/or total angular momenta, the appearance of an effective repulsive potential associated with the centrifugal motion "over" the well causes a substantial decrease of the reactivity. In turn, the statistical models overestimate the reactivity over the whole range of collision energies as compared with the WP-EQM method. Specifically, at sufficiently high collision energies the reaction cannot be deemed to be statistical and important dynamical effects seem to be present. In general the WP-EQM results lie in between those obtained using the QCT and SQCT methods. One of the main, unexpected, conclusions of this work is that an accurate description of the reaction and of its various dynamical features requires a computationally expensive, accurate quantum mechanical treatment.

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

“…Below 0.3 eV the rate coefficients calculated with the different methods are similar in magnitude except for those of the GB procedure for j = 0, and to a lesser extent for j = 1, which are smaller than the rest due to the low weight attributed by the method to trajectories whose internal energies lie below the ZPE of the HD molecule (see ref. 54 and 55 for more details). The specific rate coefficients from the three theoretical methods grow weakly with increasing E T for all the j levels considered (j = 0-3).…”

“…The best overall agreement between theory and measurements is obtained with the QCT-GB results and the worst simulations correspond to the SQCT method; the QM calculations are somewhere in-between. The QCT-HB rotational distributions are not too different from those of QCT-GB at the comparatively high relative translational energies of these experiments 54 and the corresponding simulations have not been included in Fig. 7.…”

Dynamics of the D+ + H2 → HD + H+ reaction at the low energy regime by means of a statistical quantum method

“…32,33 Different alternative approaches based on the assumption of the formation of an intermediate complex with a long enough lifetime before its fragmentation proved adequate to describe the dynamics of the process. [34][35][36][37][38][39] Changes of the mechanisms governing the reaction as a function on the collision energy regime have been, however, reported since the pioneering investigations on the H + 3 system. It is generally understood that as the energy increases the process evolves from a complex-forming pathway to a direct reaction.…”

Cold and ultracold dynamics of the barrierless D+ + H2 reaction: Quantum reactive calculations for ∼R−4 long range interaction potentials

“…In parallel to the electronic structure developments, a selection of theoretical methods of varying accuracy has been applied to the study of the H + + H 2 reaction dynamics. [62][63][64][65][66][67][68][69][70][71][72][73][74][75][76] Of all the possible isotopic variants of the H + + H 2 reaction that of the deuteron with H 2 is exothermic due to the different zero-point energies (ZPEs) of reactants and products and hence is appropriate for its study at the cold and ultra-cold energy regimes. 77 The isotopic substitution makes possible to readily identify reactants and products by mass spectrometry or spectroscopic techniques.…”