A comparative account of quantum dynamics of the H⁺ + H₂ reaction at low temperature on two different potential energy surfaces

Rotationally resolved reaction probabilities, integral cross sections, and rate constant for the H(+) + H2 (v = 0, j = 0 or 1) → H2 (v' = 0, j') + H(+) reaction are calculated using a time-independent quantum mechanical method and the potential energy surface of Kamisaka et al. [J. Chem. Phys. 116, 654 (2002)] (say KBNN PES). All partial wave contributions of the total angular momentum, J, are included to obtain converged cross sections at low collision energies and rate constants at low temperatures. In order to test the accuracy of the KBNN PES, the results obtained here are compared with those obtained in our earlier work [P. Honvault et al., Phys. Rev. Lett. 107, 023201 (2011)] using the accurate potential energy surface of Velilla et al. [J. Chem. Phys. 129, 084307 (2008)]. Integral cross sections and rate constants obtained on the two potential energy surfaces considered here show remarkable differences in terms of magnitude and dependence on collision energy (or temperature) which can be attributed to the differences observed in the topography of the surfaces near to the entrance channel. This clearly shows the inadequacy of the KBNN PES for calculations at low collision energies.

The D(+) + H2 reaction: differential and integral cross sections at low energy and rate constants at low temperature

The D(+) + H2 reaction is investigated by means of a time independent quantum mechanical (TIQM) and statistical quantum mechanical (SQM) methods. Differential cross sections and product rotational distributions obtained with these two theoretical approaches for collision energies between 1 meV and 0.1 eV are compared to analyze the dynamics of the process. The agreement observed between the TIQM differential cross sections and the SQM predictions as the energy increases revealed the role played by the complex-forming mechanism. The importance of a good description of the asymptotic regions is also investigated by calculating rate constants for the title reaction at low temperature.

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

The D(+) +H2(v = 0, j = 0, 1) → HD+H(+) reaction has been investigated at the low energy regime by means of a statistical quantum mechanical (SQM) method. Reaction probabilities and integral cross sections (ICSs) between a collisional energy of 10(-4) eV and 0.1 eV have been calculated and compared with previously reported results of a time independent quantum mechanical (TIQM) approach. The TIQM results exhibit a dense profile with numerous narrow resonances down to Ec ~ 10(-2) eV and for the case of H2(v = 0, j = 0) a prominent peak is found at ~2.5 × 10(-4) eV. The analysis at the state-to-state level reveals that this feature is originated in those processes which yield the formation of rotationally excited HD(v' = 0, j' > 0). The statistical predictions reproduce reasonably well the overall behaviour of the TIQM ICSs at the larger energy range (Ec ≥ 10(-3) eV). Thermal rate constants are in qualitative agreement for the whole range of temperatures investigated in this work, 10-100 K, although the SQM values remain above the TIQM results for both initial H2 rotational states, j = 0 and 1. The enlargement of the asymptotic region for the statistical approach is crucial for a proper description at low energies. In particular, we find that the SQM method leads to rate coefficients in terms of the energy in perfect agreement with previously reported measurements if the maximum distance at which the calculation is performed increases noticeably with respect to the value employed to reproduce the TIQM results.

State specific stabilization of H+ + H2(j) collision complexes

Stabilization of H3(+) collision complexes has been studied at nominal temperatures between 11 and 33 K using a 22-pole radio frequency (rf) ion trap. Apparent binary rate coefficients, k(*) = kr + k3[H2], have been measured for para- and normal-hydrogen at number densities between some 10(11) and 10(14) cm(-3). The state specific rate coefficients extracted for radiative stabilization, kr(T;j), are all below 2 × 10(-16) cm(3) s(-1). There is a slight tendency to decrease with increasing temperature. In contrast to simple expectations, kr(11 K;j) is for j = 0 a factor of 2 smaller than for j = 1. The ternary rate coefficients for p-H2 show a rather steep T-dependence; however, they are increasing with temperature. The state specific ternary rate coefficients, k3(T;j), measured for j = 0 and derived for j = 1 from measurements with n-H2, differ by an order of magnitude. Most of these surprising observations are in disagreement with predictions from standard association models, which are based on statistical assumptions and the separation of complex formation and competition between stabilization and decay. Most probably, the unexpected collision dynamics are due to the fact that, at the low translational energies of the present experiment, only a small number of partial waves participate. This should make exact quantum mechanical calculations of kr feasible. More complex is three-body stabilization, because it occurs on the H5(+) potential energy surface.

State-to-state quantum mechanical calculations of rate coefficients for the D+ + H2 → HD + H+ reaction at low temperature

The dynamics of the D(+) + H2 → HD + H(+) reaction on a recent ab initio potential energy surface (Velilla, L.; Lepetit, B.; Aguado, A.; Beswick, J. A.; Paniagua, M. J. Chem. Phys. 2008, 129, 084307) has been investigated by means of a time-independent quantum mechanical approach. Cross-sections and rate coefficients are calculated, respectively, for collision energies below 0.1 eV and temperatures up to 100 K for astrophysical application. An excellent accord is found for collision energy above 5 meV, while a disagreement between theory and experiment is observed below this energy. We show that the rate coefficients reveal a slightly temperature-dependent behavior in the upper part of the temperature range considered here. This is in agreement with the experimental data above 80 K, which give a temperature independent value. However, a significant decrease is found at temperatures below 20 K. This decrease can be related to quantum effects and the decay back to the reactant channel, which are not considered by simple statistical approaches, such as the Langevin model. Our results have been fitted to appropriate analytical expressions in order to be used in astrochemical and cosmological models.

Stabilization of H+-H2 collision complexes between 11 and 28 K

Formation of H(3)(+) via association of H(+) with H(2) has been studied at low temperatures using a 22-pole radiofrequency trap. Operating at hydrogen number densities from 10(11) to 10(14) cm(-3), the contributions of radiative, k(r), and ternary, k(3), association have been extracted from the measured apparent binary rate coefficients, k*=k(r)+k(3)[H(2)]. Surprisingly, k(3) is constant between 11 and 22 K, (2.6±0.8)×10(-29) cm(6) s(-1), while radiative association decreases from k(r)(11 K)=(1.6±0.3)×10(-16) cm(3) s(-1) to k(r)(28 K)=(5±2)×10(-17) cm(3) s(-1). These results are in conflict with simple association models in which formation and stabilization of the complex are treated separately. Tentative explanations are based on the fact that, at low temperatures, only few partial waves contribute to the formation of the collision complex and that ternary association with H(2) may be quite inefficient because of the 'shared proton' structure of H(5)(+).

H2, H3+ and the age of molecular clouds and prestellar cores

Measuring the age of molecular clouds and prestellar cores is a difficult task that has not yet been successfully accomplished although the information is of paramount importance to help in understanding and discriminating between different formation scenarios. Most chemical clocks suffer from unknown initial conditions and are therefore difficult to use. We propose a new approach based on a subset of deuterium chemistry that takes place in the gas phase and for which initial conditions are relatively well known. It relies primarily on the conversion of H(3)(+) into H(2)D(+) to initiate deuterium enrichment of the molecular gas. This conversion is controlled by the ortho/para ratio of H(2) that is thought to be produced with the statistical ratio of 3 and subsequently slowly decays to an almost pure para-H(2) phase. This slow decay takes approximately 1 Myr and allows us to set an upper limit on the age of molecular clouds. The deuterium enrichment of the core takes longer to reach equilibrium and allows us to estimate the time necessary to form a dense prestellar core, i.e. the last step before the collapse of the core into a protostar. We find that the observed abundance and distribution of DCO(+) and N(2)D(+) argue against quasi-static core formation and favour dynamical formation on time scales of less than 1 Myr. Another consequence is that ortho-H(2) remains comparable to para-H(2) in abundance outside the dense cores.