Enhanced reactivity of fluorine with para-hydrogen in cold interstellar clouds by resonance-induced quantum tunnelling

Higher-Order Split Operator Schemes for Solving Tetratomic Reactions Using the Time-Dependent Wave Packet Method

In this work, using the time-dependent quantum wave packet method, quite a few typical higher-order split operators (HOSOs) were for the first time applied to calculate the tetratomic reactive scattering processes in the hyperspherical coordinate. It was found that the HOSOs were hardly efficient for a tetratomic reaction calculation, unlike those for a triatomic reactive scattering calculation. We proposed an efficient HOSO with a force gradient (denoted as 2G1 in the main text) for efficiently and accurately calculating a tetratomic reaction using the quantum wave packet method. Several typical tetratomic reactions, such as H2 + OH, HF + OH, and H2 + OH+, are calculated for demonstrating the effectiveness of the proposed 2G1 in terms of (product state-resolved) reaction probability and inelastic probability, by comparing with the performance of the previously reported various HOSOs. We suggest that the 2G1 propagator could be applied to efficiently calculate a general tetratomic reaction.

Spiers Memorial Lecture: New directions in molecular scattering

The field of molecular scattering is reviewed as it pertains to gas-gas as well as gas-surface chemical reaction dynamics. We emphasize the importance of collaboration of experiment and theory, from which new directions of research are being pursued on increasingly complex problems. We review both experimental and theoretical advances that provide the modern toolbox available to molecular-scattering studies. We distinguish between two classes of work. The first involves simple systems and uses experiment to validate theory so that from the validated theory, one may learn far more than could ever be measured in the laboratory. The second class involves problems of great complexity that would be difficult or impossible to understand without a partnership of experiment and theory. Key topics covered in this review include crossed-beams reactive scattering and scattering at extremely low energies, where quantum effects dominate. They also include scattering from surfaces, reactive scattering and kinetics at surfaces, and scattering work done at liquid surfaces. The review closes with thoughts on future promising directions of research.

Development of the Time-Independent Methods for the Cl + H2/F + HD Reaction Using Hyper-Spherical Coordinates Including (Full) Spin-Orbit Characteristics

Recently, a combined study of high-resolution molecular crossed beam experiment and accurate full-dimensional time-dependent theory, including full spin-orbit characteristics on the effect of electronic spin and orbital angular momenta in the F + HD reaction, was reported by some of us, focusing on the partial wave resonance phenomenon (Science 2021, 371, 936-940). It revealed that the time-dependent theory could explain all of the details observed in the high-resolution experiment. Here, we develop two time-independent close-coupling methods using hyperspherical coordinates, including the two-state model, where only a part of the spin-orbit characteristics is considered, and the six-state model, where the full spin-orbit characteristics is considered. With these two newly developed theoretical models and the adiabatic theoretical model, the detailed reaction dynamics of the F + HD (v = 0, j = 0) reaction and the Cl + H2 (v = 0, j = 0) reaction are investigated and compared. Some of the results are compared with the time-dependent quantum wave packet theory and the experimental observations, and good agreements have been obtained, which suggests the validity of the pure-procession approximation in the six-state model using different theoretical methods. This work demonstrates the ability of the reactive scattering theory including full spin-orbit characteristics for describing the reactions of a halogen atom plus hydrogen molecule and its isotopologues.

Reactant-Product Decoupling Technique Using the Intermediate Coordinate Method

Although the reactant-product decoupling (RPD) technique was proposed over two decades ago, it remains an efficient approach for calculating product state-resolved information on some simple direct reactions using the quantum wave packet method. In the past, usually the RPD technique employed the collocation method to transform the wave function between reactant and product arrangements, which requires quite large computational efforts. In this work, the intermediate coordinate (IC) method is employed to realize the RPD technique. Numerical examples demonstrate that this new IC RPD (IRPD) technique has superior computational efficiency compared with the original method employing the collocation method. Especially, the new IRPD technique significantly saves disk space and computer memory. To illustrate the features of our new method, the total reaction probabilities of the H + H2, H + Br2, and F + H2 reactions with J = 0 and the differential cross sections of the H + H2 and F + H2 reactions at a series of collision energy are calculated and presented. With this efficient and effective new RPD technique, the Li + HF reaction, which involves sharp resonances with long-range wave functions in the van der Waals wells in both the reactant and product arrangements, is also calculated with several J at the product state-resolved level to reveal the ability of the RPD technique for describing resonance wave functions. With these numerical examples, it is found that, for the reaction with resonances, the RPD approach should be applied carefully. Otherwise, it is very possible that the resonances could disappear with the application of the RPD technique.

Significant Isotope Effects from the Nonadiabatic Couplings in the Cl(2P) + HD(v = 0, j = 0) Reaction

The impact of non-Born-Oppenheimer couplings on the isotopic effects in the reaction of the Cl(2P) atom with the HD (v = 0, j = 0) molecule is investigated with our recently developed nonadiabatic time-independent quantum scattering methods, where the full open-shell characteristics are included in the six-state model, and also with the recently developed two-state model solving by time-independent methods, where part of the open-shell characteristic is included. The same reaction is also calculated with the simple adiabatic model using the lowest adiabatic potential energy surface. Compared with the results from different models, it is found that the reactivity of the Cl + HD → HCl + D channel is significantly overestimated in the adiabatic model. In contrast, the reactivity of the other channel agrees well with the nonadiabatic models. This is due to the van der Waals well in the reactant channel being changed a lot by including the nonadiabatic couplings. These quantum dynamics calculations suggest that sometimes the adiabatic model should be used with caution; otherwise, it may result in significant deviations for some reactions.

Sequential flipping: the donor-acceptor exchange mechanism in water trimers

The donor-acceptor exchange (DAE) is a significant hydrogen bond network rearrangement (HBNR) mechanism because it can lead to the change of the hydrogen bond direction. In this work, we report a new DAE mechanism found in water trimers that is realized by sequential flipping (SF) of all molecules rather than the well-known proton transfer (PT) process. Meanwhile, the SF process has a much smaller potential barrier (0.262 eV) than the previously predicted collective rotation process (about 1.7 eV), implying that the SF process is the main flipping process that can lead to DAE. Importantly, high-precision ab initio calculations show that SF-DAE can make the water ring to show a clear chiral difference from PT-DAE, which brings the prospect of distinguishing the two confusing processes based on circular dichroism spectra. The reaction rate analysis including quantum tunneling indicates an obvious temperature-dependent competitive relationship between the SF and PT processes; specifically, the SF process dominates above 65 K, while the PT process dominates below 65 K. Therefore, in most cases, the contribution for DAE mainly comes from the flipping process, rather than the PT process as previously thought. Our work enriches the understanding of the DAE mechanism in water trimers and provides a piece of the jigsaw that has been sought for the HBNR mechanism.

H2 formation via non-Born-Oppenheimer hydrogen migration in photoionized ethane

Neutral H2 formation via intramolecular hydrogen migration in hydrocarbon molecules plays a vital role in many chemical and biological processes. Here, employing cold target recoil ion momentum spectroscopy (COLTRIMS) and pump-probe technique, we find that the non-adiabatic coupling between the ground and excited ionic states of ethane through conical intersection leads to a significantly high yield of neutral H2 fragment. Based on the analysis of fingerprints that are sensitive to orbital symmetry and electronic state energies in the photoelectron momentum distributions, we tag the initial electronic population of both the ground and excited ionic states and determine the branching ratios of H2 formation channel from those two states. Incorporating theoretical simulation, we established the timescale of the H2 formation to be ~1300 fs. We provide a comprehensive characterization of H2 formation in ionic states of ethane mediated by conical intersection and reveals the significance of non-adiabatic coupling dynamics in the intramolecular hydrogen migration.

Feshbach resonances in the F + CHD3 → HF + CD3 reaction

The signature of dynamics resonances was observed in the benchmark polyatomic F + CH₄/CHD₃ reactions more than a decade ago; however, the dynamical origin of the resonances is still not clear due to the lack of reliable quantum dynamics studies on accurate potential energy surfaces. Here, we report a six-dimensional state-to-state quantum dynamics study on the F + CHD₃ → HF + CD₃ reaction on a highly accurate potential energy surface. Pronounced oscillatory structures are observed in the total and product rovibrational-state-resolved reaction probabilities. Detailed analysis reveals that these oscillating features originate from the Feshbach resonance states trapped in the peculiar well on the HF(v' = 3)-CD₃ vibrationally adiabatic potential caused by HF chemical bond softening. Most of the resonance structures on the reaction probabilities are washed out in the well converged integral cross sections (ICS), leaving only one distinct peak at low collision energy. The calculated HF vibrational state-resolved ICS for CD₃(v = 0) agrees quantitatively with the experimental results, especially the branching ratio, but the theoretical CD₃ umbrella vibration state distribution is found to be much hotter than the experiment.

Enhancing reactivity of SiO+ ions by controlled excitation to extreme rotational states

Optical pumping of molecules provides unique opportunities for control of chemical reactions at a wide range of rotational energies. This work reports a chemical reaction with extreme rotational excitation of a reactant and its kinetic characterization. We investigate the chemical reactivity for the hydrogen abstraction reaction SiO⁺ + H₂ → SiOH⁺ + H in an ion trap. The SiO⁺ cations are prepared in a narrow rotational state distribution, including super-rotor states with rotational quantum number (j) as high as 170, using a broad-band optical pumping method. We show that the super-rotor states of SiO⁺ substantially enhance the reaction rate, a trend reproduced by complementary theoretical studies. We reveal the mechanism for the rotational enhancement of the reactivity to be a strong coupling of the SiO⁺ rotational mode with the reaction coordinate at the transition state on the dominant dynamical pathway.

Tunnelling measured in a very slow ion-molecule reaction

Quantum tunnelling reactions play an important role in chemistry when classical pathways are energetically forbidden¹, be it in gas-phase reactions, surface diffusion or liquid-phase chemistry. In general, such tunnelling reactions are challenging to calculate theoretically, given the high dimensionality of the quantum dynamics, and also very difficult to identify experimentally^2-4. Hydrogenic systems, however, allow for accurate first-principles calculations. In this way the rate of the gas-phase proton-transfer tunnelling reaction of hydrogen molecules with deuterium anions, H₂ + D^- → H^- + HD, has been calculated⁵, but has so far lacked experimental verification. Here we present high-sensitivity measurements of the reaction rate carried out in a cryogenic 22-pole ion trap. We observe an extremely low rate constant of (5.2 ± 1.6) × 10^-20 cm³ s^-1. This measured value agrees with quantum tunnelling calculations, serving as a benchmark for molecular theory and advancing the understanding of fundamental collision processes. A deviation of the reaction rate from linear scaling, which is observed at high H₂ densities, can be traced back to previously unobserved heating dynamics in radiofrequency ion traps.

Real-time hydrogen molecular dynamics satisfying the nuclear spin statistics of a quantum rotor

Apparent presence of the nuclear-spin species of a hydrogen molecule, para-hydrogen and ortho-hydrogen, associated with the quantum rotation is a manifestation of the nuclear quantum nature of hydrogen, governing not only molecular structures but also physical and chemical properties of hydrogen molecules. It has been a great challenge to observe and calculate real-time dynamics of such molecularized fermions. Here, we developed the non-empirical quantum molecular dynamics method that enables real-time molecular dynamics simulations of hydrogen molecules satisfying the nuclear spin statistics of the quantum rotor. While reproducing the species-dependent quantum rotational energy, population ratio, specific heat, and H-H bond length and frequency, we found that their translational, orientational and vibrational dynamics becomes accelerated with the higher rotational excitation, concluding that the nuclear quantum rotation stemmed from the nuclear spin statistics can induce various kinds of dynamics and reactions intrinsic to each hydrogen species.

Time-dependent wave packet dynamics study of the resonances in the H + LiH+(v = 0, j = 0) → Li+ + H2 reaction at low collision energies

The depletion process of LiH⁺ by H collision plays an important role in the evolution of the early universe and astrophysical processes, including the eventual charge-states, abundances of atomic and molecular species and ensuing astrochemistry. Here, a quantum dynamics study on the H + LiH⁺(v = 0, j = 0) → Li⁺ + H₂ reaction is performed at the low collision energy range from 0.1 meV to 10 meV using the time-dependent wave packet method. A Feshbach resonance peak is observed near 0.8 meV collision energy on the total reaction probability curves. This resonance originates from the coupling with the v = 0, j = 1 energy level of the reactant LiH⁺, and it is dominated by the contributions of J = 0-4 partial waves. Another partial wave resonance is also found on the total integral cross section at 1.2 meV, which is closely connected to the opening of the J = 7 partial wave. The opening of the J = 7 partial wave generates a notable forward scattering peak, and the Feshbach resonance can promote both the forward and backward scatterings. Moreover, the total and product vibrational state-resolved rate coefficients for the temperature range of 1-100 K are also reported.

Low-temperature reaction dynamics of paramagnetic species in the gas phase

Radicals are abundant in a range of important gas-phase environments. They are prevalent in the atmosphere, in interstellar space, and in combustion processes. As such, understanding how radicals react is essential for the development of accurate models of the complex chemistry occurring in these gas-phase environments. By controlling the properties of the colliding reactants, we can also gain insights into how radical reactions occur on a fundamental level. Recent years have seen remarkable advances in the breadth of experimental methods successfully applied to the study of reaction dynamics involving paramagnetic species-from improvements to the well-known crossed molecular beams approach to newer techniques involving magnetically guided and decelerated beams. Coupled with ever-improving theoretical methods, quantum features are being observed and interesting insights into reaction dynamics are being uncovered in an increasingly diverse range of systems. In this highlight article, we explore some of the exciting recent developments in the study of chemical dynamics involving paramagnetic species. We focus on low-energy reactive collisions involving neutral radical species, where the reaction parameters are controlled. We conclude by identifying some of the limitations of current methods and exploring possible new directions for the field.

Strong non-Arrhenius behavior at low temperatures in the OH + HCl → H2O + Cl reaction due to resonance induced quantum tunneling

The OH + HCl reaction possesses many Feshbach resonances trapped in the hydrogen bond well in the entrance channel, which substantially enhance the reaction rates at low temperatures.

Atomistic dynamics of elimination and nucleophilic substitution disentangled for the F- + CH3CH2Cl reaction

Chemical reaction dynamics are studied to monitor and understand the concerted motion of several atoms while they rearrange from reactants to products. When the number of atoms involved increases, the number of pathways, transition states and product channels also increases and rapidly presents a challenge to experiment and theory. Here we disentangle the dynamics of the competition between bimolecular nucleophilic substitution (S_N2) and base-induced elimination (E2) in the polyatomic reaction F^- + CH₃CH₂Cl. We find quantitative agreement for the energy- and angle-differential reactive scattering cross-sections between ion-imaging experiments and quasi-classical trajectory simulations on a 21-dimensional potential energy hypersurface. The anti-E2 pathway is most important, but the S_N2 pathway becomes more relevant as the collision energy is increased. In both cases the reaction is dominated by direct dynamics. Our study presents atomic-level dynamics of a major benchmark reaction in physical organic chemistry, thereby pushing the number of atoms for detailed reaction dynamics studies to a size that allows applications in many areas of complex chemical networks and environments.

Development and characterization of high-repetition-rate sources for supersonic beams of fluorine radicals

We present and compare two high-pressure, high-repetition-rate electric-discharge sources for the generation of supersonic beams of fluorine radicals. The sources are based on dielectric-barrier-discharge (DBD) and plate-discharge units attached to a pulsed solenoid valve. The corrosion-resistant discharge sources were operated with fluorine gas seeded in helium up to backing pressures as high as 30 bars. We employed a (3 + 1) resonance-enhanced multiphoton ionization combined with velocity-map imaging for the optimization, characterization, and comparison of the fluorine beams. Additionally, universal femtosecond-laser-ionization detection was used for the characterization of the discharge sources at experimental repetition rates up to 200 Hz. Our results show that the plate discharge is more efficient in F₂ dissociation than the DBD by a factor between 8 and 9, whereas the DBD produces internally colder fluorine radicals.

Feshbach Resonances in the Vibrationally Excited F + HOD(vOH/vOD = 1) Reaction Due to Chemical Bond Softening

Experiments and theories showed the ground-state reaction F + H₂O → HF + OH possesses Feshbach resonances trapped in the hydrogen bond well in the product region. However, it is not clear whether F + H₂O and its isotopic analogues have the same Feshbach resonances caused by chemical bond softening as those in the F + H₂/HD. Here, we reported state-to-state quantum dynamics studies of the F + HOD(v_OH = 1) → HF + OD and F + HOD(v_OD = 1) → DF + OH reactions on an accurate neural network potential energy surface. Detailed analysis reveals that the course of the title reactions is dominated by the Feshbach resonance states trapped in the peculiar HF(v'=3)-OD/DF(v'=4)-OH vibrationally adiabatic potential well created by the HF/DF bond softening, which can only be accessed via the HOD(v_OH = 1)/HOD(v_OD = 1) reaction pathway. Therefore, we confirm the wide existence of chemical bond softening resonances in reactions involving vibrationally excited molecules.

Quantum interference between spin-orbit split partial waves in the F + HD → HF + D reaction

The effect of electron spin-orbit interactions on chemical reaction dynamics has been a topic of much research interest. Here we report a combined experimental and theoretical study on the effect of electron spin and orbital angular momentum in the F + HD → HF + D reaction. Using a high-resolution imaging technique, we observed a peculiar horseshoe-shaped pattern in the product rotational-state-resolved differential cross sections around the forward-scattering direction. The unusual dynamics pattern could only be explained properly by highly accurate quantum dynamics theory when full spin-orbit characteristics were considered. Theoretical analysis revealed that the horseshoe pattern was largely the result of quantum interference between spin-orbit split-partial-wave resonances with positive and negative parities, providing a distinctive example of how spin-orbit interaction can effectively influence reaction dynamics.

Interaction-Asymptotic Region Decomposition Method for an Insertion Reaction: Application to the S(1D) + H2 Reaction

With adjusting principal axes hyperspherical (APH) coordinate in the interaction region, and the Jacobi coordinates in the asymptotic regions, an efficient multidomain interaction-asymptotic region decomposition (IARD) method has been developed to solve the "coordinate problem" in a product-state-resolved reactive scattering calculation using the quantum wave packet method. Although the APH coordinate treats with all three channels equally, and is efficient for describing the interaction region for some direct reactions, it is inefficient for describing the insertion-type reaction due to the singularity problem, such as the S(¹D) + H₂ reaction. To deal with this issue, in this work, the channel-dependent Delves hyperspherical (DH) coordinate is proposed to describe the interaction region using the IARD method. The proposed DH-IARD method was applied to calculate the product-state-resolved reaction probabilities of the H + HD reaction, and the differential and integral cross sections of the typical insertion reaction S(¹D) + H₂. It is found that the new DH-IARD method is much more efficient than the previous APH-IARD method for dealing with insertion reactions. The partial wave resonance structures were observed in the integral cross section. It is found that at a low collision energy, the position of the initial wave packet has to be put far away. Otherwise, the partial wave resonance structures could not be correctly reproduced due to the reef well arising with a large total angular momentum J.

Unveiling shape resonances in H + HF collisions at cold energies

Scattering resonances are pure quantum effects that appear whenever the collision energy matches the energy of a quasi-bound state of the intermolecular complex. Here we show that rotational quenching of HF(j = 1, 2) with H is strongly influenced by the presence of two resonance peaks, leading to up to a two-fold increase in the thermal rate coefficients at the low temperatures characteristic of the interstellar medium. Our results show that each resonance peak is formed by a cluster of shape resonances, each of them characterized by the same value of the orbital angular momentum but different values of the total angular momentum. The relative intensity of these resonances depends on the relative geometry of the incoming reactants, and our results predict that by changing the alignment of the HF rotational angular momentum it is possible to decompose the resonance peaks, disentangling the underlying resonance pattern and the contribution of different total angular momenta to the resonance.

Advances and New Challenges to Bimolecular Reaction Dynamics Theory

Dynamics of bimolecular reactions in the gas phase are of foundational importance in combustion, atmospheric chemistry, interstellar chemistry, and plasma chemistry. These collision-induced chemical transformations are a sensitive probe of the underlying potential energy surface(s). Despite tremendous progress in past decades, our understanding is still not complete. In this Perspective, we survey the recent advances in theoretical characterization of bimolecular reaction dynamics, stimulated by new experimental observations, and identify key new challenges.

Prediction of a Feshbach Resonance in the Below-the-Barrier Reactive Scattering of Vibrationally Excited HD with H

Quantum reactive scattering calculations on the vibrational quenching of HD due to collisions with H were carried out employing an accurate potential energy surface. The state-to-state cross sections for the chemical reaction HD(v = 1, j = 0) + H → D + H₂(v' = 0, j') at collision energies between 1 and 10 000 cm^-1 are presented, and a Feshbach resonance in the low-energy regime, below the reaction barrier, is observed for the first time. The resonance is attributed to coupling with the vibrationally adiabatic potential correlating to the v = 1, j = 1 level of the HD molecule, and it is dominated by the contribution from a single partial wave. The properties of the resonance, such as its dynamic behavior, phase behavior, and lifetime, are discussed.

A crossed molecular beam apparatus with multi-channel Rydberg tagging time-of-flight detection

We report a new crossed molecular beam apparatus with the H atom Rydberg tagging detection technique. The multi-channel detection scheme with 15 microchannel plate (MCP) detectors enables simultaneously accumulating time-of-flight spectra over a wide range of scattering angles (112°). The efficiency of data acquisition has been enhanced by an order of magnitude. The angular distribution of H atoms from photodissociation of CH₄ at 121.6 nm was used for calibrating the detection efficiency of different MCP detectors. The differential cross section of the reaction F + H₂ → HF + H at the collision of 6.9 meV was measured, demonstrating the feasibility and accuracy of this multi-channel detection method. This apparatus could be a powerful tool for investigating the dynamics of reactions at very low collision energy.

Quantum interference in H + HD → H2 + D between direct abstraction and roaming insertion pathways

Understanding quantum interferences is essential to the study of chemical reaction dynamics. Here, we provide an interesting case of quantum interference between two topologically distinct pathways in the H + HD → H2 + D reaction in the collision energy range between 1.94 and 2.21 eV, manifested as oscillations in the energy dependence of the differential cross section for the H2 (v′ = 2, j′ = 3) product (where v′ is the vibrational quantum number and j′ is the rotational quantum number) in the backward scattering direction. The notable oscillation patterns observed are attributed to the strong quantum interference between the direct abstraction pathway and an unusual roaming insertion pathway. More interestingly, the observed interference pattern also provides a sensitive probe of the geometric phase effect at an energy far below the conical intersection in this reaction, which resembles the Aharonov–Bohm effect in physics, clearly demonstrating the quantum nature of chemical reactivity.

Quantum resonances near absolute zero

Ultralow-energy atom-molecule collisions reveal quasi-bound state quantum resonances

Feshbach resonances in the F + H2O → HF + OH reaction

Transiently trapped quantum states along the reaction coordinate in the transition-state region of a chemical reaction are normally called Feshbach resonances or dynamical resonances. Feshbach resonances trapped in the HF-OH interaction well have been discovered in an earlier photodetchment study of FH₂O^-; however, it is not clear whether these resonances are accessible by the F + H₂O reaction. Here we report an accurate state-to-state quantum dynamics study of the F + H₂O → HF + OH reaction on an accurate newly constructed potential energy surface. Pronounced oscillatory structures are observed in the total reaction probabilities, in particular at collision energies below 0.2 eV. Detailed analysis reveals that these oscillating structures originate from the Feshbach resonance states trapped in the hydrogen bond well on the HF(v' = 2)-OH vibrationally adiabatic potentials, producing mainly HF(v' = 1) product. Therefore, the resonances observed in the photodetchment study of FH₂O^- are accessible to the reaction.

Competing Dynamical Mechanisms in Inelastic Collisions of H + HF

The dynamics of inelastic collisions between HF and H has been investigated in detail by means of time-independent quantum mechanical calculations on the LWA-78 potential energy surface ( Li , G. ; et al. J. Chem. Phys. 2007 , 127 , 174302 ). Reaction probabilities, differential cross sections, and three-vector correlations have been calculated and analyzed. Our results show that there are two competing collision mechanisms that correlate with low and high impact parameters and show very different stereodynamical preferences. The mechanism promoted by high impact parameters is the only one present at low collision energies. We also observe the presence of an apparent threshold in the inelastic cross section for relatively high initial HF rotational quantum numbers, which is associated with the larger energy difference between adjacent rotational quantum states with increasing rotation.