Theoretical Insights into the Dynamics of Gas-Phase Bimolecular Reactions with Submerged Barriers

Much attention has been paid to the dynamics of both activated gas-phase bimolecular reactions, which feature monotonically increasing integral cross sections and Arrhenius kinetics, and their barrierless capture counterparts, which manifest monotonically decreasing integral cross sections and negative temperature dependence of the rate coefficients. In this Perspective, we focus on the dynamics of gas-phase bimolecular reactions with submerged barriers, which often involve radicals or ions and are prevalent in combustion, atmospheric chemistry, astrochemistry, and plasma chemistry. The temperature dependence of the rate coefficients for such reactions is often non-Arrhenius and complex, and the corresponding dynamics may also be quite different from those with significant barriers or those completely dominated by capture. Recent experimental and theoretical studies of such reactions, particularly at relatively low temperatures or collision energies, have revealed interesting dynamical behaviors, which are discussed here. The new knowledge enriches our understanding of the dynamics of these unusual reactions.

Theoretical studies on the kinetics and dynamics of the BeH+ + H2O reaction: comparison with the experiment

The reaction of BeH+ with background gaseous H2O may play a role in qubit loss for quantum information processing with Be+ as trapped ions, and yet its reaction mechanism has not been well understood until now. In this work, a globally accurate, full-dimensional ground-state potential energy surface (PES) for the BeH+ + H2O reaction was constructed by fitting a total of 170 438 ab initio energy points at the level of RCCSD(T)-F12/aug-cc-pVTZ using the fundamental invariant-neural network method. The total root-mean-square error of the final PES was 0.178 kcal mol-1. For comparison, quasi-classical trajectory calculations were carried out on the PES at an experimental temperature of 150 K. The obtained thermal rate constant and product branching ratio of the BeD+ + H2O reaction agreed quite well with experimental results. In addition, the vibrational state distributions and energy disposals of the products were calculated and rationalized using the sudden vector projection model.

Validating experiments for the reaction H2 + NH2- by dynamical calculations on an accurate full-dimensional potential energy surface

Ion-molecule reactions play key roles in the field of ion related chemistry. As a prototypical multi-channel ion-molecule reaction, the reaction H₂ + NH₂^- → NH₃ + H^- has been studied for decades. In this work, we develop a new globally accurate potential energy surface (PES) for the title system based on hundreds of thousands of sampled points over a wide dynamically relevant region that covers long-range interacting configuration space. The permutational invariant polynomial-neural network (PIP-NN) method is used for fitting and the resulting total root mean squared error (RMSE) is extremely small, 0.026 kcal mol^-1. Extensive dynamical and kinetic calculations are carried out on this PIP-NN PES. Impressively, a unique phenomenon of significant reactivity suppression by exciting the rotational mode of H₂ is reported, supported by both the quasi-classical trajectory (QCT) and quantum dynamics (QD) calculations. Further analysis uncovers that exciting the H₂ rotational mode would prevent the formation of the reactant complex and thus suppress the reactivity. The calculated rate coefficients for H₂/D₂ + NH₂^- agree well with the experimental results, which show an inverse temperature dependence from 50 to 300 K, consistent with the capture nature of this barrierless reaction. The significant kinetic isotope effect observed by experiments is well reproduced by the QCT computations as well.

Kinetic and dynamic studies of the NH2+ + H2 reaction on a high-level ab initio potential energy surface

The dynamics and kinetics of the NH2+ + H2 reaction are investigated on a newly developed ab initio potential energy surface using the quasi-classical trajectory method.

Study on the kinetics and dynamics of the H2 + NH2- reaction on a high-level ab initio potential energy surface

Gas-phase ion-molecule reactions play major roles in many fields of chemistry and physics. The reaction of an amino radical anion with a hydrogen molecule is one of the simplest proton transfer reactions involving anions. A globally accurate full-dimensional potential energy surface (PES) for the NH₂^- + H₂ reaction is developed by the fundamental invariant-neural network method, resulting in a root mean square error of 0.116 kcal mol^-1. Quasi-classical trajectory calculations are then carried out on the newly developed PES to give integral cross sections, differential cross sections and thermal rate coefficients. This reaction has two reaction channels, proton transfer and hydrogen exchange. The reactivity of the proton transfer channel is about one or two orders of magnitude stronger than that of the hydrogen exchange channel in the energy range studied. Vibrational excitation of H₂ promotes the proton transfer reaction, while fundamental excitation of each vibrational mode of NH₂^- has a negligible effect. In addition, the theoretical rate coefficients of the proton transfer reaction on the PES show inverse temperature dependence from 150 to 750 K, in accordance with the available experimental results.

Effects of bending excitation on the reaction dynamics of fluorine atoms with ammonia

Vibrational excitation has been established as an efficient way to control the chemical reaction outcome. Stretching vibration of polyatomic molecules is believed to be efficient to promote abstraction reactions since energy is placed directly into the breaking bond. In this work, we report on a counterexample showing that exciting the low-frequency umbrella bending mode of ammonia enhances its reaction with fluorine atoms much more than exciting the high-frequency symmetric or asymmetric stretching mode over a wide range of collision energy, validated using both quasiclassical trajectory simulations and full-dimensional quantum dynamics calculations under the centrifugal-sudden approximation. This interesting mode-specific reaction dynamic originates from the increased chance of capturing the fluorine atom by ammonia due to the enlarged attractive interaction between them and the enhancement of the direct stripping reaction mediated by two submerged barriers.

Experimental study of the proton-transfer reaction C + H2+ → CH+ + H and its isotopic variant (D2+)

We report absolute integral cross section (ICS) measurements using a dual-source merged-fast-beams apparatus to study the titular reactions over the relative translational energy range of Er ∼ 0.01-10 eV. We used photodetachment of C- to produce a pure beam of atomic C in the ground electronic 3P term, with statistically populated fine-structure levels. The H2+ and D2+ were formed in an electron impact ionization source, with well known vibrational and rotational distributions. The experimental work is complemented by a theoretical study of the CH2+ electronic system in the reactant and product channels, which helps to clarify the possible reaction mechanisms underlying the ICS measurements. Our measurements provide evidence that the reactions are barrierless and exoergic. They also indicate the apparent absence of an intermolecular isotope effect, to within the total experimental uncertainties. Capture models, taking into account either the charge-induced dipole interaction potential or the combined charge-quadrupole and charge-induced dipole interaction potentials, produce reaction cross sections that lie a factor of ∼4 above the experimental results. Based on our theoretical study, we hypothesize that the reaction is most likely to proceed adiabatically through the 14A' and 14A'' states of CH2+via the reaction C(3P) + H2+(2Σ+g) → CH+(3Π) + H(2S). We also hypothesize that at low collision energies only H2+(v ≤ 2) and D2+(v ≤ 3) contribute to the titular reactions, due to the onset of dissociative charge transfer for higher vibrational v levels. Incorporating these assumptions into the capture models brings them into better agreement with the experimental results. Still, for energies ⪅0.1 eV where capture models are most relevant, the modified charge-induced dipole model yields reaction cross sections with an incorrect energy dependence and lying ∼10% below the experimental results. The capture cross section obtained from the combined charge-quadrupole and charge-induced dipole model better matches the measured energy dependence but lies ∼30-50% above the experimental results. These findings provide important guidance for future quasiclassical trajectory and quantum mechanical treatments of this reaction.

Final-State-Resolved Dynamics of the H3+ + CO → H2 +HCO+/HOC+ Reaction: A Quasi-Classical Trajectory Study

The ion-molecule reaction H₃⁺ + CO → H₂ + HCO⁺/HOC⁺, which initiates the formation of crucial organic molecules, plays a key role in interstellar and circumstellar environments. In this work, the quasi-classical trajectory method is employed to study the reaction dynamics on a recently developed full-dimensional global potential energy surface (PES). The calculated product internal energy distributions and relative internal excited fractions agree reasonably well with the experimental measurements. For the two reaction channels, most of the available energy flows into the vibrational modes of HCO⁺ or HOC⁺ at low collision energies, followed by the translational mode and the rotational modes of HCO⁺ or HOC⁺. As the collision energy increases, the proportion of the product translational energy increases while the proportion of the product vibrational energy decreases. Furthermore, the CH and CO stretching modes and their combination bands are effectively excited for the product HCO⁺ while the bending mode is remarkably excited for the product HOC⁺.

Theoretical study of the F(2P) + NH3→ HF + NH2 reaction on an accurate potential energy surface: dynamics and kinetics

The highly exothermic hydrogen abstraction reaction of the F atom with NH₃ is investigated using the quasi-classical trajectory method on a newly developed potential energy surface (PES) for the ground electronic state. The full-dimensional PES is constructed by fitting 41 282 ab initio energy points at the level of UCCSD(T)-F12/aug-cc-pVTZ. The flexible fundamental invariant-neural network method is applied in the fitting, resulting in a total root mean square error of 0.13 kcal mol^-1. On one hand, the calculated differential cross sections agree reasonably well with the experimental results and indicate that the reaction is dominated by the direct abstraction and stripping mechanisms while a considerable amount of reaction takes place by the indirect "yo-yo" mechanism. The product energy partition also reproduces well the experimental result, which can be understood according to the geometry change along the minimum energy path. On the other hand, the obtained vibrational state distribution of the product HF follows P_νHF=2≈P_νHF=1 > P_νHF=0 > P_νHF=3, less consistent with the scattered experimental results. In addition, the calculated thermal rate coefficients have practically no temperature dependence within the statistical errors.

Mode-specific quantum dynamics and kinetics of the hydrogen abstraction reaction OH + H2O → H2O + OH

The synergistic effect between the reactant stretching and bending modes on promoting the reaction.

Low temperature rates for key steps of interstellar gas-phase water formation

The gas-phase formation of water molecules in the diffuse interstellar medium (ISM) proceeds mainly via a series of reactions involving the molecular ions OH⁺, H₂O⁺, and H₃O⁺ and molecular hydrogen. These reactions form the backbone for the chemistry leading to the formation of several complex molecular species in space. A comprehensive understanding of the mechanisms involved in these reactions in the ISM necessitates an accurate knowledge of the rate coefficients at the relevant temperatures (10 to 100 K). We present measurements of the rate coefficients for two key reactions below 100 K, which, in both cases, are significantly higher than the values used in astronomical models thus far. The experimental rate coefficients show excellent agreement with dedicated theoretical calculations using a novel ring-polymer molecular dynamics approach that offers a first-principles treatment of low-temperature barrierless gas-phase reactions, which are prevalent in interstellar chemical networks.

The Selective Role of Long-Range Forces in the Stereodynamics of Ion-Molecule Reactions: The He+ +Methyl Formate Case From Guided-Ion-Beam Experiments

Long-range intermolecular forces play a crucial role in controlling the outcome of ion-molecule chemical reactions, such as those determining the disappearance of organic or inorganic "complex" molecules recently detected in various regions of the interstellar medium due to collisions with abundant interstellar atomic ions (e.g. H⁺ and He⁺ ). Theoretical treatments, for example, based on simple capture models, are nowadays often adopted to evaluate the collision-energy dependence of reactive cross sections and the temperature dependent rate coefficients of many ion-molecule reactions. The obtained results are widely used for the modelling of phenomena occurring in different natural environments or technological applications such as astrophysical and laboratory plasmas. Herein it is demonstrated, through a combined experimental and theoretical investigation on a prototype ion-molecule reaction (He⁺ +methyl formate), that the dynamics, investigated in detail, shows some intriguing features that can lead to rate coefficients at odds with the expectations (e.g. Arrhenius versus anti-Arrhenius behaviour). Therefore, this study casts light on some new and general guidelines to be properly taken into account for a suitable evaluation of rate coefficients of ion-molecule reactions.

A quantum-rovibrational-state-selected study of the proton-transfer reaction H2+(X2Σ: v+ = 1-3; N+ = 0-3) + Ne → NeH+ + H using the pulsed field ionization-photoion method: observation of the rotational effect near the reaction threshold

Using the sequential electric field pulsing scheme for vacuum ultraviolet (VUV) laser pulsed field ionization-photoion (PFI-PI) detection, we have successfully prepared H₂⁺(X²Σ: v⁺ = 1-3; N⁺ = 0-5) ions in the form of an ion beam in single quantum-rovibrational-states with high purity, high intensity, and narrow laboratory kinetic energy spread (ΔE_lab ≈ 0.05 eV). This VUV-PFI-PI ion source, when coupled with the double-quadrupole double-octupole ion-molecule reaction apparatus, has made possible a systematic examination of the vibrational- as well as rotational-state effects on the proton transfer reaction of H₂⁺(X²Σ: v⁺; N⁺) + Ne. Here, we present the integral cross sections [σ(v⁺; N⁺)'s] for the H₂⁺(v⁺ = 1-3; N⁺ = 0-3) + Ne → NeH⁺ + H reaction observed in the center-of-mass kinetic energy (E_cm) range of 0.05-2.00 eV. The σ(v⁺ = 1, N⁺ = 1) exhibits a distinct E_cm onset, which is found to agree with the endothermicity of 0.27 eV for the proton transfer process after taking into account of experimental uncertainties. Strong v⁺-vibrational enhancements are observed for σ(v⁺ = 1-3, N⁺) in the E_cm range of 0.05-2.00 eV. While rotational excitations appear to have little effect on σ(v⁺ = 3, N⁺), a careful search leads to the observation of moderate N⁺-rotational enhancements at v⁺ = 2: σ(v⁺ = 2; N⁺ = 0) < σ(v⁺ = 2; N⁺ = 1) < σ(v⁺ = 2; N⁺ = 2) < σ(v⁺ = 2; N⁺ = 3), where the formation of NeH⁺ is near thermal-neutral. The σ(v⁺ = 1-3, N⁺ = 0-3) values obtained here are compared with previous experimental results and the most recent state-of-the-art quantum dynamics predictions. We hope that these new experimental results would further motivate more rigorous theoretical calculations on the dynamics of this prototypical ion-molecule reaction.

Competition between the H- and D-atom transfer channels in the H2O+ + HD reaction: reduced-dimensional quantum and quasi-classical studies

The ion-molecule reaction between a water cation and a hydrogen molecule has recently attracted considerable interest due to its importance in astrochemistry. In this work, the intramolecular isotope effect of the H₂O⁺ + HD reaction is investigated using a seven-dimensional initial state-selected time-dependent wave packet approach as well as a full-dimensional quasi-classical trajectory method on a full-dimensional ab initio global potential energy surface. The calculated branching ratios for the formation of H₃O⁺ and H₂DO⁺via H- and D-transfer agree reasonably well with the experimental values. The preference to the formation of the H₃O⁺ product observed using the experiment at low collision energies is reproduced by theoretical calculations and explained by a one-dimensional effective potential model.

A quantum-rovibrational-state-selected study of the reaction in the collision energy range of 0.05-10.00 eV: translational, rotational, and vibrational energy effects

We report detailed absolute integral cross sections (σ's) for the quantum-rovibrational-state-selected ion-molecule reaction in the center-of-mass collision energy (E_cm) range of 0.05-10.00 eV, where (vvv) = (000), (100), and (020), and . Three product channels, HCO⁺ + OH, HOCO⁺ + H, and CO⁺ + H₂O, are identified. The measured σ(HCO⁺) curve [σ(HCO⁺) versus E_cm plot] supports the hypothesis that the formation of the HCO⁺ + OH channel follows an exothermic pathway with no potential energy barriers. Although the HOCO⁺ + H channel is the most exothermic, the σ(HOCO⁺) is found to be significantly lower than the σ(HCO⁺). The σ(HOCO⁺) curve is bimodal, indicating two distinct mechanisms for the formation of HOCO⁺. The σ(HOCO⁺) is strongly inhibited at E_cm < 0.4 eV, but is enhanced at E_cm > 0.4 eV by (100) vibrational excitation. The E_cm onsets of σ(CO⁺) determined for the (000) and (100) vibrational states are in excellent agreement with the known thermochemical thresholds. This observation, along with the comparison of the σ(CO⁺) curves for the (100) and (000) states, shows that kinetic and vibrational energies are equally effective in promoting the CO⁺ channel. We have also performed high-level ab initio quantum calculations on the potential energy surface, intermediates, and transition state structures for the titled reaction. The calculations reveal potential barriers of ≈0.5-0.6 eV for the formation of HOCO⁺, and thus account for the low σ(HOCO⁺) and its bimodal profile observed. The E_cm enhancement for σ(HOCO⁺) at E_cm ≈ 0.5-5.0 eV can be attributed to the direct collision mechanism, whereas the formation of HOCO⁺ at low E_cm < 0.4 eV may involve a complex mechanism, which is mediated by the formation of a loosely sticking complex between HCO⁺ and OH. The direct collision and complex mechanisms proposed also allow the rationalization of the vibrational inhibition at low E_cm and the vibrational enhancement at high E_cm observed for the σ(HOCO⁺).

Isotopic and quantum-rovibrational-state effects for the ion-molecule reaction in the collision energy range of 0.03-10.00 eV

We report detailed quantum-rovibrational-state-selected integral cross sections for the formation of H₃O⁺via H-transfer (σ_HT) and H₂DO⁺via D-transfer (σ_DT) from the reaction in the center-of-mass collision energy (E_cm) range of 0.03-10.00 eV, where (vvv) = (000), (100), and (020) and . The E_cm inhibition and rotational enhancement observed for these reactions at E_cm < 0.5 eV are generally consistent with those reported previously for H₂O⁺ + H₂(D₂) reactions. However, in contrast to the vibrational inhibition observed for the latter reactions at low E_cm < 0.5 eV, both the σ_HT and σ_DT for the H₂O⁺ + HD reaction are found to be enhanced by (100) vibrational excitation, which is not predicted by the current state-of-the-art theoretical dynamics calculations. Furthermore, the (100) vibrational enhancement for the H₂O⁺ + HD reaction is observed in the full E_cm range of 0.03-10.00 eV. The fact that vibrational enhancement is only observed for the reaction of H₂O⁺ + HD, and not for H₂O⁺ + H₂(D₂) reactions suggests that the asymmetry of HD may play a role in the reaction dynamics. In addition to the strong isotopic effect favoring the σ_HT channel of the H₂O⁺ + HD reaction at low E_cm < 0.5 eV, competition between the σ_HT and σ_DT of the H₂O⁺ + HD reaction is also observed at E_cm = 0.3-10.0 eV. The present state-selected study of the H₂O⁺ + HD reaction, along with the previous studies of the H₂O⁺ + H₂(D₂) reactions, clearly shows that the chemical reactivity of H₂O⁺ toward H₂ (HD, D₂) depends not only on E_cm, but also on the rotational and vibrational states of H₂O⁺(X²B₁). The detailed σ_HT and σ_DT values obtained here with single rovibrational-state selections of the reactant H₂O⁺ are expected to be valuable benchmarks for state-of-the-art theoretical calculations on the chemical dynamics of the title reaction.

Quantum-state-selected integral cross sections for the charge transfer collision of O2+(a4Πu5/2,3/2,1/2,−1/2: v+= 1–2; J+) [O2+(X2Πg3/2,1/2: v+= 22–23; J+)] + Ar at center-of-mass collision energies of 0.05–10.00 eV

Study of spin–orbit and rovibronically selected ion-molecule reactions between O₂⁺(a⁴Π_u,ν⁺= 1–2; X²Π_g,ν⁺= 22–23) and Ar.

Mode-Specific SN2 Reaction Dynamics

Despite its importance in chemistry, the microscopic dynamics of bimolecular nucleophilic substitution (SN2) reactions is still not completely elucidated. In this publication, the dynamics of a prototypical SN2 reaction (F(-) + CH3Cl → CH3F + Cl(-)) is investigated using a high-dimensional quantum mechanical model on an accurate potential energy surface (PES) and further analyzed by quasi-classical trajectories on the same PES. While the indirect mechanism dominates at low collision energies, the direct mechanism makes a significant contribution. The reactivity is found to depend on the specific reactant vibrational mode excitation. The mode specificity, which is more prevalent in the direct reaction, is rationalized by a transition-state-based model.

Mode specific dynamics in the H2 + SH → H + H2S reaction

Full-dimensional quantum dynamics and quasi-classical trajectory studies indicate strong mode selectivity in the H₂ + SH reaction.