Nuclear spin dependence of the reaction of H3+ with H2. II. Experimental measurements

Dynamics of the isotope exchange reaction of D with H3 +, H2D+, and D2H. J Chem Phys 2021;154:084307. [PMID: 33639774 DOI: 10.1063/5.0038434]

We have measured the merged-beams rate coefficient for the titular isotope exchange reactions as a function of the relative collision energy in the range of ∼3 meV-10 eV. The results appear to scale with the number of available sites for deuteration. We have performed extensive theoretical calculations to characterize the zero-point energy corrected reaction path. Vibrationally adiabatic minimum energy paths were obtained using a combination of unrestricted quadratic configuration interaction of single and double excitations and internally contracted multireference configuration interaction calculations. The resulting barrier height, ranging from 68 meV to 89 meV, together with the various asymptotes that may be reached in the collision, was used in a classical over-the-barrier model. All competing endoergic reaction channels were taken into account using a flux reduction factor. This model reproduces all three experimental sets quite satisfactorily. In order to generate thermal rate coefficients down to 10 K, the internal excitation energy distribution of each H₃ ⁺ isotopologue is evaluated level by level using available line lists and accurate spectroscopic parameters. Tunneling is accounted for by a direct inclusion of the exact quantum tunneling probability in the evaluation of the cross section. We derive a thermal rate coefficient of <1×10^-12 cm³ s^-1 for temperatures below 44 K, 86 K, and 139 K for the reaction of D with H₃ ⁺, H₂D⁺, and D₂H⁺, respectively, with tunneling effects included. The derived thermal rate coefficients exceed the ring polymer molecular dynamics prediction of Bulut et al. [J. Phys. Chem. A 123, 8766 (2019)] at all temperatures.

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.

Towards state selective recombination of H3+ under astrophysically relevant conditions

We present studies on the thermalisation of H3+ ions in a cold He/Ar/H2 plasma at temperatures 30-70 K. We show that we are able to generate a rotationally thermalised H3+ ensemble with a population of rotational and nuclear spin states corresponding to a particular ion translational temperature. By varying the para-H2 fraction used in the experiment we are able to produce para-H3+ ions with fractional populations higher than those corresponding to thermodynamic values. At 35 K, only the lowest rotational states of para and ortho H3+ are populated. This is the first step towards experimental studies of electron-molecular ion recombination processes with precisely specified quantum states at astrophysically relevant temperatures.

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.

Mid-infrared concentration-modulated noise-immune cavity-enhanced optical heterodyne molecular spectroscopy of a continuous supersonic expansion discharge source

Concentration-modulated noise-immune cavity-enhanced optical heterodyne molecular spectroscopy (NICE-OHMS) is implemented for the first time on a continuous gas-flow pinhole supersonic expansion discharge source for the study of cooled molecular ions. The instrument utilizes a continuous-wave optical parametric oscillator easily tunable from 2.5 to 3.9 μm and demonstrates a noise equivalent absorption of ∼1 × 10(-9) cm(-1). The effectiveness of concentration-modulated NICE-OHMS is tested through the acquisition of transitions in the ν1 fundamental band of HN2 (+) centered near 3234 cm(-1), with a signal-to-noise of ∼40 obtained for the strongest transitions. The technique is used to characterize the cooling abilities of the supersonic expansion discharge source itself, and a Boltzmann analysis determines a rotational temperature of ∼29 K for low rotational states of HN2 (+). Further improvements are discussed that will enable concentration-modulated NICE-OHMS to reach its full potential for the detection of molecular ions formed in supersonic expansion discharges.

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.

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.

Non-Born-Oppenheimer potential energy curve: Hydrogen molecular ion with highly accurate free complement method

Although the concept of a potential energy curve (PEC) originates from the outgrowth of the Born-Oppenheimer (BO) approximation, we propose the application of analysis methods for the physical PEC with non-Born-Oppenheimer (non-BO) wave functions. A numerical examination was performed with the highly accurate non-BO vibronic wave functions of hydrogen molecular ion, which were obtained in our previous studies with the free complement method. The reduced density function integrated over the electron coordinates plays an important role in understanding nuclear motion dynamics, since it corresponds to the wave function density of the vibrational and rotational motions. The maximum positions of this density indicate the high existence probability of nuclei and can be considered as a discrete representation of the PEC. Whereas an ordinary PEC with the BO approximation is obtained as a numeric curve after multiple electronic state calculations at fixed nuclear coordinates, we propose a new analytical expression of the PEC from a non-BO wave function.

Transfer of a proton between H2 and O2

The proton affinities of hydrogen and oxygen are very similar. Therefore, it has been discussed that the proton transfer from the omnipresent H(3)(+) to molecular oxygen in the near thermoneutral reaction H(3)(+) + O(2) <--> O(2)H(+) + H(2) effectively binds the interstellar oxygen in O(2)H(+). In this work, the proton transfer reaction has been investigated in a low-temperature 22-pole ion trap from almost room temperature (280 K) down to the lowest possible temperature limited by freeze out of oxygen gas (about 40 K at a low pressure). The Arrhenius behaviour of the rate coefficient for the forward reaction shows that it is subject to an activation energy of E(A)/k=113 K. Thus, the forward reaction can proceed only in higher temperature molecular clouds. Applying laser-induced reactions to the given reaction (in the backward direction), a preliminary search for spectroscopic signatures of O(2)H(+) in the infrared was unsuccessful, whereas the forward reaction has been successfully used to probe the population of the lowest ortho and para levels of H(3)(+).

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.

Chemistry, astronomy and physics of H3+

The great developments in the chemistry, astronomy and physics of H(3)(+) since 2006, which have led to this Royal Society Theo Murphy Meeting, are reviewed.

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.