Microcanonical statistical study of ortho-para conversion in the reaction H3++H2→(H5+)*→H3++H2 at very low energies

Quantum Effects on the D + H3+ → H2D+ + H Deuteration Reaction and Isotopic Variants

The title reaction and its isotopic variants are studied using quasi-classical trajectory (QCT) (without taking into account corrections to account for the possible zero point energy breakdown) and ring polymer molecular dynamics (RPMD) methods with a full dimensional and accurate potential energy surface which presents an exchange barrier of approximately 0.144 eV. The QCT rate constant increases when the temperature decreases from 1500 to 10 K. On the contrary, the RPMD rate constant decreases with decreasing temperature, in semiquantitative agreement with recent experimental results. The present RPMD results are in between the thermal and translational experimental rate constants, extracted from the measured data to eliminate the initial vibrational excitation of H₃⁺, obtained in an arc discharge. The difference between the present RPMD results and experimental values is attributed to the possible existence of non thermal vibrational excitation of H₃⁺, not completely removed by the semiempirical model used for the analysis of the experimental results. Also, it is found that, below 200 K, the RPMD trajectories are trapped, forming long-lived collision complexes, with lifetimes longer than 1 ns. These collision complexes can fragment by either redissociating back to reactants or react to products, in the two cases tunneling through the centrifugal and reaction barriers, respectively. The contribution of the formation of the complex to the total deuteration rate should be calculated with more accurate quantum methods, as has been found recently for reactions of larger systems, and the present four atoms system is a good candidate to benchmark the adequacy of RPMD method at temperatures below 100 K.

The smallest proton-bound dimer H5+: theoretical progress

The protonated hydrogen dimer, H5+, is the smallest system including proton transfer, and has been of long-standing interest since its first laboratory observation in 1962. H5+ and its isotopologues are the intermediate complexes in deuterium fractionation reactions, and are of central importance in molecular astrophysics. The recently recorded infrared spectra of both H5+ and D5+ reveal a rich vibrational dynamics of the cations, which presents a challenge for standard theoretical approaches. Although H5+ is a four-electron ion, which makes highly accurate electronic structure calculations tractable, the construction of ab initio-based potential energy and dipole moment surfaces has proved a hard task. In the same vein, the difficulties in treating the nuclear motion could also become cumbersome due to their high dimensionality, floppiness and/or symmetry. These systems are prototypical examples for studying large-amplitude motions, as they are highly delocalized, interconverting between equivalent minima through internal rotation and proton transfer motions requiring state-of-the-art treatments. Recent advances in the computational vibrational spectroscopy of the H5+ cation and its isotopologues are reported from full quantum spectral simulations, providing important information in a rigorous manner, and open perspectives for further future investigations. This article is part of a discussion meeting issue 'Advances in hydrogen molecular ions: H3+, H5+ and beyond'.

A Ring Polymer Molecular Dynamics Approach to Study the Transition between Statistical and Direct Mechanisms in the H2 + H3+ → H3+ + H2 Reaction

Because of its fundamental importance in astrochemistry, the H₂ + H₃⁺ → H₃⁺ + H₂ reaction has been studied experimentally in a wide temperature range. Theoretical studies of the title reaction significantly lag primarily because of the challenges associated with the proper treatment of the zero-point energy (ZPE). As a result, all previous theoretical estimates for the ratio between a direct proton-hop and indirect exchange (via the H₅⁺ complex) channels deviate from the experiment, in particular, at lower temperatures where the quantum effects dominate. In this work, the ring polymer molecular dynamics (RPMD) method is applied to study this reaction, providing very good agreement with the experiment. RPMD is immune to the shortcomings associated with the ZPE leakage and is able to describe the transition from direct to indirect mechanisms below room temperature. We argue that RPMD represents a useful tool for further studies of numerous ZPE-sensitive chemical reactions that are of high interest in astrochemistry.

An Empirical Dynamical Barrier for Statistical Theory of Low-Energy Reactive S(1D) + HD(j = 0), H2(j = 0) Collisions

A simple model potential is proposed to describe the dynamical barrier in the mean interaction potential at small distances between the reactants in S(¹D) + HD(¹Σ, v = 0, j = 0) reaction. The statistical theory of collision complex formation and complex decay is applied to calculate the total reaction cross sections and the cross sections for SH and SD productions in the range of low collision energies E_c = (0.4-60) meV. The results are compared with measured cross sections and results of hyperspherical close coupling calculations. As a check of consistency the same comparisons are presented for the case of S(¹D) + H₂(¹Σ, v = 0, j = 0) reaction.

Non-adiabatic couplings and dynamics in proton transfer reactions of Hn (+) systems: Application to H2+H2 (+)→H+H3 (+) collisions

Analytical derivatives and non-adiabatic coupling matrix elements are derived for Hn (+) systems (n = 3-5). The method uses a generalized Hellmann-Feynman theorem applied to a multi-state description based on diatomics-in-molecules (for H3 (+)) or triatomics-in-molecules (for H4 (+) and H5 (+)) formalisms, corrected with a permutationally invariant many-body term to get high accuracy. The analytical non-adiabatic coupling matrix elements are compared with ab initio calculations performed at multi-reference configuration interaction level. These magnitudes are used to calculate H2(v(')=0,j(')=0)+H2 (+)(v,j=0) collisions, to determine the effect of electronic transitions using a molecular dynamics method with electronic transitions. Cross sections for several initial vibrational states of H2 (+) are calculated and compared with the available experimental data, yielding an excellent agreement. The effect of vibrational excitation of H2 (+) reactant and its relation with non-adiabatic processes are discussed. Also, the behavior at low collisional energies, in the 1 meV-0.1 eV interval, of interest in astrophysical environments, is discussed in terms of the long range behaviour of the interaction potential which is properly described within the triatomics-in-molecules formalism.

Probing the Relationship Between Large-Amplitude Motions in H5(+) and Proton Exchange Between H3(+) and H2

Understanding the spectroscopy and dynamics of H5(+) is central in gaining insights into the H3(+) + H2 → H5(+) → H2 + H3(+) proton transfer reaction. This molecular ion exhibits large-amplitude vibrations, which allow for the transfer of a proton between H3(+) and H2 even in its ground vibrational state. With vibrational excitation, the number of open channels for permutations of protons increase. In this work, the minimized energy path variant of diffusion Monte Carlo is used to investigate how the energetically accessible proton permutations evolve as H5(+) is dissociated into H3(+) + H2. Two mechanisms for proton permutation are investigated. The first is the proton hop, which correlates to large-amplitude vibrations of the central proton in H5(+). The second is the exchange of a pair of hydrogen atoms between H3(+) and H2. This mechanism requires several proton hops along with a 120° rotation of H3(+) within the H5(+) molecular ion. This analysis shows that while there is a narrow region of configuration space over which both isomerization processes are energetically accessible, full permutation of the five protons in H5(+) more likely occurs through a stepwise mechanism. Such full permutation of the protons becomes accessible when the shared proton stretch is excited to the vpt = 2 or 3 excited state. The effects of deuteration and rotational excitation of the H2 and H3(+) products are also investigated. Deuteration inhibits permutation of protons, while rotational excitation has only a small impact on these processes.

Theoretical predictions on the role of the internal H3(+) rotation in the IR spectra of the H5(+) and D5(+) cations

The IR spectra of the H5(+) and D5(+) cations in the mid- and far-IR spectral regions have been recently reported by experimentalists. These spectra show very rich vibrational patterns representing a challenge for state-of-the-art theoretical methods to provide definitive interpretations of them. Using a full-dimensional quantum anharmonic treatment, within the MCTDH approach, together with ab initio potential and dipole moment surfaces, the predominant features in the spectra are assigned, completing an important part in previous theoretical and experimental comparisons. The internal rotation of the H3(+) unit by exciting the H3(+)-H2 stretching mode is found to correspond to the new calculated features at 1182, 1876, and 2139 cm(-1) of the H5(+) spectrum, leading to a consistent assignment with the experimental spectra. In the calculated spectra of both H5(+) and D5(+) clusters, the progressions in the H3(+)-H2 stretch of the shared proton and the in- and out-of- plane H3(+) rotation are demonstrated to be the main features. Such states are expected to play a central role in the low temperature hydrogen/deuterium proton hop/exchange H3(+) + H2 reactions.

Full-dimensional quantum calculations of the vibrational states of H5(+)

Full-dimensional quantum calculations of the vibrational states of H5(+) have been performed on the accurate potential energy surface developed by Xie et al. [J. Chem. Phys. 122, 224307 (2005)]. The zero point energies of H5(+), H4D(+), D4H(+), and D5(+) and their ground-state geometries are presented and compared with earlier theoretical results. The first 10 low-lying excited states of H5(+) are assigned to the fundamental, overtone, and combination of the H2-H3(+) stretch, the shared proton hopping and the out-of-plane torsion. The ground-state torsional tunneling splitting, the fundamental of the photon hopping mode and the first overtone of the torsion mode are 87.3 cm(-1), 354.4 cm(-1), and 444.0 cm(-1), respectively. All of these values agree well with the diffusion Monte Carlo and multi-configuration time-dependent Hartree results where available.

The ortho : para ratio of H3+ in laboratory and astrophysical plasmas

In diffuse molecular clouds, the nuclear spin temperature of H(3)(+) (approx. 30 K) is much lower than the cloud kinetic temperature (approx. 70 K). To understand this temperature discrepancy, we have measured the ratio of the hop to exchange pathways (α) in the H(3)(+) + H(2) --> H(2) + H(3)(+) reaction (which interconverts ortho- and para-H(3)(+)) using high-resolution spectroscopy of the ν(2) fundamental band of H(3)(+) in a hydrogenic plasma. We find that α decreases from 1.6±0.1 at 350 K to its statistical value of 0.5±0.1 at 135 K. We use this result to model the steady-state chemistry of diffuse molecular clouds, finding good agreement with astronomical data provided the dissociative recombination rates of ortho- and para-H(3)(+) are equal and the identity branching fraction for the H(3)(+) + H(2) reaction is large. Our results highlight the need for further studies of the H(3)(+) + H(2) reaction as well as state-selective measurements of H(3)(+) dissociative recombination.

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.

Nuclear spin effect on recombination of H₃⁺ ions with electrons at 77 K

Utilizing different ratios of para to ortho H₂ in normal and para enriched hydrogen, we varied the population of para-H₃⁺ in an H₃⁺ dominated plasma at 77 K. Absorption spectroscopy was used to measure the densities of the two lowest rotational states of H₃⁺. Monitoring plasma decays at different populations of para-H₃⁺ allowed us to determine the rate coefficients for binary recombination of para-H₃⁺ and ortho-H₃⁺ ions: (p)α(bin)(77 K) = (1.9 ± 0.4) × 10⁻⁷ cm³ s⁻¹ and (o)α(bin)(77 K) = (0.2 ± 0.2) × 10⁻⁷ cm³ s⁻¹.

Toward a realistic density functional theory potential energy surface for the H5+ cluster

The potential energy surface of H(5)(+) is characterized using density functional theory. The hypersurface is evaluated at selected configurations employing different functionals, and compared with results obtained from ab initio CCSD(T) calculations. The lowest ten stationary points (minima and saddle-points) on the surface are located, and the features of the short-, intermediate-, and long-range intermolecular interactions are also investigated. A detailed analysis of the surface's topology, and comparisons with extensive CCSD(T) results, as well as a recent ab initio analytical surface, shows that density functional theory calculations using the B3(H) functional represent very well all aspects studied on the H(5)(+) potential. These include the tiny energy difference between the minimum at 1-C(2v) configuration and the 2-D(2d) one corresponding to the transition state for the proton transfer between the two equivalent C(2v) minima, and also the correct asymptotic behavior of the long-range interactions. The calculated binding energy and dissociation enthalpies compare very well with previous benchmark coupled-cluster ab initio data, and with experimental data available. Based on these results the use of such approach to perform first-principles molecular dynamics simulations could provide reliable information regarding the dynamics of protonated hydrogen clusters.