Statistical quantum studies on insertion atom–diatom reactions

Full-dimensional coupled-channel statistical approach to atom-triatom systems and applications to H/D + O3 reaction

The statistical quantum model (SQM), which assumes that the reactivity is controlled by entrance/exit channel quantum capture probabilities, is well suited for chemical reactions with a long-lived intermediate complex. In this work, a time-independent coupled-channel implementation of the SQM approach is developed for atom-triatom systems in full dimensionality. As SQM treats the capture dynamics quantum mechanically, it is capable of handling quantum effects such as tunneling. A detailed study of the H/D + O3 capture dynamics was performed by applying the newly developed SQM method on an accurate global potential energy surface. Agreement with previous ring polymer molecular dynamics (RPMD) results on the same potential energy surface is excellent except for very low temperatures. The SQM results are also in reasonably good agreement with available experimental rate coefficients. The strong H/D kinetic isotope effect underscores the dominant role of quantum tunneling under an entrance channel barrier at low temperatures.

Low temperature dynamics of H + HeH+→ H2+ + He reaction: On the importance of long-range interaction

While the growing realization of the importance of long-range interactions is being demonstrated in cold and ultracold bimolecular collision experiments, their influence on one of the most critical ion-neutral reactions has been overlooked. Here, we address the non-Langevin abrupt decrease observed earlier in the low-energy integral cross-sections and rate coefficients of the astrochemically important H + HeH+→ H2+ + He reaction. We attribute this to the presence of artificial barriers on existing potential energy surfaces (PESs). By incorporating precise long-range interaction terms, we introduce a new refined barrierless PES for the electronic ground state of HeH2+ reactive system, aligning closely with high-level ab initio electronic energies. Our findings, supported by various classical, quantum, and statistical methods, underscore the significance of long-range terms in accurately modeling reactive PESs. The low-temperature rate coefficient on this new PES shows a substantial enhancement as compared to the previous results and aligns with the Langevin behavior. This enhancement could noticeably affect the prediction of HeH+ abundance in early Universe condition.

Quantum and statistical state-to-state studies of cold Ar + H2+ collisions

In this work we present new state-to-state integral scattering cross sections and initial-state selected rate coefficients for the 36Ar (1S) + H2+ (X2Σg+,v = 0,j) reactive system for collision energies up to 0.1 eV (with respect to the 36Ar (1S) + H2+ (X2Σg+,v = 0,j = 0) channel). To the best of our knowledge, these cross sections are the first fully state resolved ones that were obtained by performing time-independent quantum mechanical and quantum statistical calculations. For this purpose a new full-dimensional ground state 2A' adiabatic electronic potential energy surface was calculated at the MRCI+Q/aug-cc-pVQZ level of theory, which was fitted by means of machine learning methods. We find that a statistical quantum method and a statistical adiabatic channel model reproduce quantum mechanical initial-state selected cross sections fairly well, thus suggesting that complex-forming mechanisms seem to be playing an important role in the reaction dynamics of the reaction that was studied.

Quantum Dynamics Studies of the Li + Na2 (V = 0, j = 0) → Na + NaLi Reaction on a New Neural Network Potential Energy Surface

The ultracold reaction offers a unique opportunity to elucidate the intricate microscopic mechanism of chemical reactions, and the Na2Li system serves as a pivotal reaction system in the investigation of ultracold reactions. In this work, a high-precision potential energy surface (PES) of the Na2Li system is constructed based on high-level ab initio energy points and the neural network (NN) method, and a proper asymptotic functional form is adopted for the long-range interaction, which is suitable for the study of cold or ultracold collisions. Based on the new NN PES, the dynamics of the Li + Na2 (v = 0, j = 0) → Na + NaLi reaction are studied in the collision energy range of 10-7 to 80 cm-1. In the high collision energy range of 8 to 80 cm-1, the dynamics of the reaction is studied using the time-dependent wave packet method and the statistical quantum mechanical (SQM) method. Comparing the results of the two methods, it is found that the SQM method provides a rough description of the product ro-vibrational state distribution but overestimates the integral cross-section values. With the decrease of collision energy, the reaction differential cross section gradually changes from forward-backward symmetric scattering to predominant forward scattering. In the low collision energy range from 10-7 to 8 cm-1, the SQM method is used to study the reaction dynamics, and the rate constant in the Wigner threshold region is estimated to be 2.87 × 10-10 cm3/s.

Quantum stereodynamics of cold molecular collisions

Advances in quantum state preparations combined with molecular cooling and trapping technologies have enabled unprecedented control of molecular collision dynamics. This progress, achieved over the last two decades, has dramatically improved our understanding of molecular phenomena in the extreme quantum regime characterized by translational temperatures well below a kelvin. In this regime, collision outcomes are dominated by isolated partial waves, quantum threshold and quantum statistics effects, tiny energy splitting at the spin and hyperfine levels, and long-range forces. Collision outcomes are influenced not only by the quantum state preparation of the initial molecular states but also by the polarization of their rotational angular momentum, i.e., stereodynamics of molecular collisions. The Stark-induced adiabatic Raman passage technique developed in the last several years has become a versatile tool to study the stereodynamics of light molecular collisions in which alignment of the molecular bond axis relative to initial collision velocity can be fully controlled. Landmark experiments reported by Zare and coworkers have motivated new theoretical developments, including formalisms to describe four-vector correlations in molecular collisions that are revealed by the experiments. In this Feature article, we provide an overview of recent theoretical developments for the description of stereodynamics of cold molecular collisions and their implications to cold controlled chemistry.

Ar+ ArH+ Reactive Collisions of Astrophysical Interest: The Case of 36 Ar

The reactive collision between 36 Ar and the 36 ArH+ species has been investigated by means of quantum mechanical (QM), quasiclassical trajectories (QCT) and statistical quantum mechanical (SQM) approaches. Reaction probabilities, cross sections as a function of the energy and rate constants in terms of the temperature have been obtained. Cumulative distributions as a function of the collision time and the inspection of selected QCT corresponding to specific dynamical mechanisms have been analysed. Predictions by means of the SQM method are in good agreement with the QM results, thus supporting the complex-forming nature of the process.

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.

Universal behavior in complex-mediated reactions: Dynamics of S(1D) + o-D2 → D + SD at low collision energies

Reactive and elastic cross sections and rate coefficients have been calculated for the S(1D) + D2(v = 0, j = 0) reaction using a modified hyperspherical quantum reactive scattering method. The considered collision energy ranges from the ultracold regime, where only one partial wave is open, up to the Langevin regime, where many of them contribute. This work presents the extension of the quantum calculations, which in a previous study were compared with the experimental results, down to energies in the cold and ultracold domains. Results are analyzed and compared with the universal case of the quantum defect theory by Jachymski et al. [Phys. Rev. Lett. 110, 213202 (2013)]. State-to-state integral and differential cross sections are also shown covering the ranges of low-thermal, cold, and ultracold collision energy regimes. It is found that at E/kB < 1 K, there are substantial departures from the expected statistical behavior and that dynamical features become increasingly important with decreasing collision energy, leading to vibrational excitation.

ABC+D: A time-independent coupled-channel quantum dynamics program for elastic and ro-vibrational inelastic scattering between atoms and triatomic molecules in full dimensionality

We discuss the details of a time-independent quantum mechanical method and its implementation for full-dimensional non-reactive scattering between a closed-shell triatomic molecule and a closed-shell atom. By solving the time-independent Schrödinger equation within the coupled-channel framework using a log-derivative method, the state-to-state scattering matrix (S-matrix) can be determined for inelastic scattering involving both the rotational and vibrational modes of the molecule. Various approximations are also implemented. The ABC+D code provides an important platform for understanding an array of physical phenomena involving collisions between atoms and molecules.

Recent advances in quantum theory on ro-vibrationally inelastic scattering

Molecular collisions are of fundamental importance in understanding intermolecular interaction and dynamics. Its importance is accentuated in cold and ultra-cold collisions because of the dominant quantum mechanical nature of the scattering. We review recent advances in the time-independent approach to quantum mechanical characterization of non-reactive scattering in tetratomic systems, which is ideally suited for large collisional de Broglie wavelengths characteristic in cold and ultracold conditions. We discuss quantum scattering algorithms between two diatoms and between a triatom and an atom and their implementation, as well as various approximate schemes. They not only enable the characterization of collision dynamics in realistic systems but also serve as benchmarks for developing more approximate methods.

Theoretical Investigation of Rotationally Inelastic Collisions of OH(X2Π) with Hydrogen Atoms

State-to-state cross sections and rate coefficients for transitions between rotational/fine- structure levels of OH(X2Π) induced by collisions with atomic hydrogen are reported in this work. The scattering calculations take into account the full open-shell character of the OH + H system and include the four potential energy surfaces (1A′, 1A′′, 3A′, 3A′′) that correlate with the OH(X2Π) + H(2S) asymptote. Three of these surfaces are repulsive, while the deep H2O well is present on one surface (1A′). The OH + H potential energy curves calculated by Alexander et al. [J. Chem. Phys. 121, 5221 (2004)] are employed in this work. Time independent quantum scattering calculations were performed using the quantum statistical method of Manolopoulos and co-workers [Chem. Phys. Lett. 343, 356 (2001)] because of the presence of the deep H2O well. The computed cross sections include contributions from direct scattering, as well formation and decay of a transient collision complex since the transient HO-H complex is expected to decay nonreactively. Rate coefficients for OH-H inelastic collisions are of interest for astrophysical applications.

Spin-orbit transitions in the N+(3PJA) + H2 → NH+(X2 Π, 4Σ-)+ H(2S) reaction, using adiabatic and mixed quantum-adiabatic statistical approaches

The cross section and rate constants for the title reaction are calculated for all the spin-orbit states of N+(3PJA) using two statistical approaches, one purely adiabatic and the other one mixing quantum capture for the entrance channel and adiabatic treatment for the products channel. This is made by using a symmetry adapted basis set combining electronic (spin and orbital) and nuclear angular momenta in the reactants channel. To this aim, accurate ab initio calculations are performed separately for reactants and products. In the reactants channel, the three lowest electronic states (without spin-orbit couplings) have been diabatized, and the spin-orbit couplings have been introduced through a model localizing the spin-orbit interactions in the N+ atom, which yields accurate results as compared to ab initio calculations including spin-orbit couplings. For the products, eleven purely adiabatic spin-orbit states have been determined with ab initio calculations. The reactive rate constants thus obtained are in very good agreement with the available experimental data for several ortho-H2 fractions, assuming a thermal initial distribution of spin-orbit states. The rate constants for selected spin-orbit JA states are obtained, to provide a proper validation of the spin-orbit effects to obtain the experimental rate constants.

Quantum interference in the mechanism of H + LiH+ → H2 + Li+ reaction dynamics

In this work, the detailed reaction mechanism of the astrochemically relevant exoergic and barrierless H + LiH⁺ → H₂ + Li⁺ reaction is investigated by both time-dependent wave packet and quasi-classical trajectory (QCT) methods on the ab initio electronic ground state potential energy surface reported by Martinazzo et al. [Martinazzo et al., J. Chem. Phys., 2003, 119, 11241]. The interference terms due to the coherence between the partial waves are quantified. When plotted along the scattering angle they reveal interference of constructive or destructive nature. Significant interference was found in the differential cross-section (DCS) which is a symbolic of the non-statistical nature of the reaction. This is further complemented by calculating the lifetime of the collision complex by the QCT method. It is found that the reaction follows a direct stripping mechanism at higher collision energies and yields forward scattered products from collisions involving high total angular momentum. At low collision energies, the reaction follows a mixed direct/indirect mechanism but with a dominant indirect contribution. The product state-resolved DCSs reveal that two opposite mechanisms co-exist, both at low and high collision energies. The microscopic scattering mechanism of the reaction is found to be unaffected by the ro-vibrational excitation of the reagent diatom.

Benchmarking an improved statistical adiabatic channel model for competing inelastic and reactive processes

Inelastic collisions and elementary chemical reactions proceeding through the formation and subsequent decay of an intermediate collision complex, with an associated deep well on the potential energy surface, pose a challenge for accurate fully quantum mechanical approaches, such as the close-coupling method. In this study, we report on the theoretical prediction of temperature-dependent state-to-state rate coefficients for these complex-mode processes, using a statistical quantum method. This statistical adiabatic channel model is benchmarked by a direct comparison using accurate rate coefficients from the literature for a number of systems (H₂ + H⁺, HD + H⁺, SH⁺ + H, and CH⁺ + H) of interest in astrochemistry and astrophysics. For all of the systems considered, an error of less than factor 2 was found, at least for the dominant transitions and at low temperatures, which is sufficiently accurate for applications in the above mentioned disciplines.

Full-Dimensional Global Potential Energy Surface for the KRb + KRb → K2Rb2* → K2 + Rb2 Reaction with Accurate Long-Range Interactions and Quantum Statistical Calculation of the Product State Distribution under Ultracold Conditions

A full-dimensional global potential energy surface (PES) for the KRb + KRb → K₂Rb₂* → K₂ + Rb₂ reaction is reported based on high-level ab initio calculations. The short-range part of the PES is fit with the permutationally invariant polynomial-neural network method, while the long-range parts of the PES in both the reactant and product asymptotes are represented by an asymptotically correct form. The long- and short-range parts are connected with intermediate-range parts to make them smooth. Within a statistical quantum model, this PES reproduces both the measured loss rates of ultracold KRb molecules and the K₂ and Rb₂ product state distributions, underscoring the important role of tunneling in ultracold chemistry. The PES also correctly predicts the lifetime of the K₂Rb₂* intermediate complex within the Rice-Ramsperger-Kassel-Marcus limit. It thus provides a reliable platform for future dynamical studies of the prototypical reaction.

Atom-Diatom Reactive Scattering Collisions in Protonated Rare Gas Systems

The study of the dynamics of atom-diatom reactions involving two rare gas (Rg) atoms and protons is of crucial importance given the astrophysical relevance of these processes. In a series of previous studies, we have been investigating a number of such Rg(1)+ Rg(2)H+→ Rg(2)+ Rg(1)H+ reactions by means of different numerical approaches. These investigations comprised the construction of accurate potential energy surfaces by means of ab initio calculations. In this work, we review the state-of-art of the study of these protonated Rg systems making special emphasis on the most relevant features regarding the dynamical mechanisms which govern these reactive collisions. The aim of this work therefore is to provide an as complete as possible description of the existing information regarding these processes.

Signature of shape resonances on the differential cross sections of the S(1D)+H2 reaction

Shape resonances appear when the system is trapped in an internuclear potential well after tunneling through a barrier. They manifest as peaks in the collision energy dependence of the cross section (excitation function), and in many cases, their presence can be observed experimentally. High-resolution crossed-beam experiments on the S(¹D) + H₂(j = 0) reaction in the 0.81-8.5 meV collision energy range reaction revealed non-monotonic behavior and the presence of oscillations in the reaction cross section as a function of the collision energy, as predicted by quantum mechanical (QM) calculations. In this work, we have analyzed the effect of shape resonances on the differential cross sections for this insertion reaction by performing additional QM calculations. We have found that, in some cases, the resonance gives rise to a large enhancement of extreme backward scattering for specific final states. Our results also show that, in order to yield a significant change in the state-resolved differential cross section, the resonance has to be associated with constructive interference between groups of partial waves, which requires not getting blurred by the participation of many product helicity states.

Dynamics and kinetics of the Si(1D) + H2/D2 reactions on a new global ab initio potential energy surface

Recent studies on the exothermic complex-forming reactions have improved our understanding of complex-forming reactions greatly, however, so far a similar level of study on endothermic ones has been rather limited. In this work, the endothermic complex-forming reaction Si(1D) + H2 → SiH + H and its deuterated isotopic variant are investigated by quantum dynamics (QD) and ring polymer molecular dynamics (RPMD) calculations on a new global ab initio potential energy surface (PES) for the ground electronic state, which is constructed based on 8996 symmetry unique points computed at the icMRCI+Q/aug-cc-pVQZ level. The PES reproduces our ab initio data very well in the dynamically important regions, on which the ro-vibrational energy levels of SiH2 are calculated and general good agreement with experiment is obtained. The integral cross sections and product angular and state distributions are computed in a wide range of collision energies, and interesting dynamics behaviors are revealed. The rate coefficients are also investigated, which display an exponential rise from 2.09 × 10-20 to 6.00 × 10-12 cm3 s-1 for the Si(1D) + H2 reaction as the temperature increases from 300 to 1500 K, in contrast to the nearly temperature-independent behavior of exothermic complex-forming reactions. In addition, the applicability of the RPMD approach is demonstrated, and the kinetic isotope effect is investigated, the ratio of which decreases from 7.89 (300 K) to 1.70 (1500 K). The effects of tunneling and initial rotational excitation are also discussed.

Rate constants for the H+ + H2 reaction from 5 K to 3000 K with a statistical quantum method

An exhaustive investigation of state-to-state H⁺ + H₂(v, j) → H⁺ + H₂(v', j') transitions for rovibrational levels of molecular hydrogen below 1.3 eV from the bottom of the H₂ well is carried out by means of a statistical quantum method, which assumes the complex-forming nature of the process. Integral cross sections for transitions involving states H₂(v = 0, j = 0-12), H₂(v = 1, j = 0-8), and H₂(v = 2, j = 0-3) are obtained for collision energies within a range of E_min = 10^-5 eV and E_max = 2 eV. Rate constants are then calculated between T = 5 K and 3000 K, and they are compared, when possible, with previous values reported in the literature. As a first application, the cooling rate coefficient of H₂ excited by protons is determined and compared with a recent estimate.

Experimental and theoretical studies of the N(2D) + H2 and D2 reactions

This study reports the first kinetic measurements of the N(²D) + H₂, D₂ reactions below 200 K.

Dynamics of H + HeH+(v = 0, j = 0) → H2+ + He: Insight on the Possible Complex-Forming Behavior of the Reaction

The H + HeH⁺→ He + H₂⁺ reaction has been studied by means of a combination of theoretical approaches: a statistical quantum method (SQM), ring polymer molecular dynamics (RPMD), and the quasiclassical trajectory (QCT) method. Cross sections and rate constants have been calculated in an attempt to investigate the dynamics of the process. The comparison with previous calculations and experimental results reveals that despite the fact that statistical predictions seem to reproduce some of the overall observed features, the analysis at a more detailed state-to-state level shows noticeable deviations from a complex-forming dynamics. We find some differences in cross sections and rate constants obtained in the QCT calculation with a Gaussian binning procedure with respect to previous works in which the standard histogram binning was employed.

Experimental and Theoretical Study of the O(1D) + HD Reaction

This work addresses the kinetics and dynamics of the gas-phase reaction between O(¹D) and HD molecules down to low temperature. Here, measurements were performed by using a supersonic flow (Laval nozzle) reactor coupled with pulsed laser photolysis for O(¹D) production and pulsed-laser-induced fluorescence for O(¹D) detection to obtain rate constants over the 50-300 K range. Additionally, temperature-dependent branching ratios (OD + H/OH + D) were obtained experimentally by comparison of the H/D atom atom yields with those of a reference reaction. In parallel, theoretical rate constants and branching ratios were calculated by using three different techniques; mean potential phase space theory (MPPST), the statistical quantum mechanical method (SQM), and ring polymer molecular dynamics (RPMD). Although the agreement between experimental and theoretical rate constants is reasonably good, with differences not exceeding 30% over the entire temperature range, the theoretical branching ratios derived by the MPPST and SQM methods are as much as 50% larger than the experimental ones. These results are presented in the context of earlier work, while the possible origins of the discrepancies between experiment and theory are discussed.

The effect of nonadiabaticity on the C+ + HF reaction

The chemistry of fluorine in the interstellar medium is particularly simple, with only a few key species and important reactions. Of the latter, the rate of the reaction of C⁺ ions with HF is not well established but is one of the key reactions that sets the relative abundance of HF and the CF⁺ ion, the two fluorine-bearing species that have been observed in interstellar clouds. The C⁺ + HF → CF⁺ + H reaction proceeds through a deeply bound HCF⁺ well. In this work, statistical methods, namely, the statistical adiabatic channel method originally developed by Quack and Troe and the quantum statistical method of Manolopoulos and co-workers, are applied to compute the total cross section as a function of energy for this reaction. This reaction proceeds on the ground 1² A' potential energy surface (PES), and there are also two non-reactive PES's, 1² A″ and 2² A', correlating with the C⁺(² P _1/2,3/2) + HF reactants. Two sets of scattering calculations were carried out, namely, a single-surface calculation on the 1² A' PES and the one in which all three PES's and the spin-orbit splitting of C⁺ are included in the description of the entrance channel. In the latter, reactivity of the spin-orbit excited ² P _3/2 level can be computed, and not just assumed to be zero, as in the single-state adiabatic approximation.

Communication: Adiabatic quantum trajectory capture for cold and ultra-cold chemical reactions

The Langevin capture model is often used to describe barrierless reactive collisions. At very low temperatures, quantum effects may alter this simple capture image and dramatically affect the reaction probability. In this paper, we use the trajectory-ensemble reformulation of quantum mechanics, as recently proposed by one of the authors (Poirier) to compute adiabatic-channel capture probabilities and cross-sections for the highly exothermic reaction Li + CaH(v = 0, j = 0) → LiH + Ca, at low and ultra-low temperatures. Each captured quantum trajectory takes full account of tunneling and quantum reflection along the radial collision coordinate. Our approach is found to be very fast and accurate, down to extremely low temperatures. Moreover, it provides an intuitive and practical procedure for determining the capture distance (i.e., where the capture probability is evaluated), which would otherwise be arbitrary.

A combined theoretical and experimental investigation of the kinetics and dynamics of the O(1D) + D2 reaction at low temperature

The O(¹D) + H₂ reaction is a prototype for simple atom-diatom insertion type mechanisms considered to involve deep potential wells. While exact quantum mechanical methods can be applied to describe the dynamics, such calculations are challenging given the numerous bound quantum states involved. Consequently, efforts have been made to develop alternative theoretical strategies to portray accurately the reactive process. Here we report an experimental and theoretical investigation of the O(¹D) + D₂ reaction over the 50-296 K range. The calculations employ three conceptually different approaches - mean potential phase space theory, the statistical quantum mechanical method and ring polymer molecular dynamics. The calculated rate constants are in excellent agreement over the entire temperature range, exhibiting only weak temperature dependence. The agreement between experiment and theory is also very good, with discrepancies smaller than 26%. Taken together, the present and previous theoretical results validate the hypothesis that long-lived complex formation dominates the reaction dynamics at low temperature.

Theoretical investigation of rotationally inelastic collisions of CH(X2Π) with hydrogen atoms

We report calculations of state-to-state cross sections for collision-induced rotational transitions of CH(X²Π) with atomic hydrogen. These calculations employed the four adiabatic potential energy surfaces correlating CH(X²Π) + H(²S), computed in this work through the multi-reference configuration interaction method [MRCISD + Q(Davidson)]. Because of the presence of deep wells on three of the potential energy surfaces, the scattering calculations were carried out using the quantum statistical method of Manolopoulos and co-workers [Chem. Phys. Lett. 343, 356 (2001)]. The computed cross sections included contributions from only direct scattering since the CH₂ collision complex is expected to decay predominantly to C + H₂. Rotationally energy transfer rate constants were computed for this system since these are required for astrophysical modeling.

Dynamical importance of van der Waals saddle and excited potential surface in C(1D)+D2 complex-forming reaction

Encouraged by recent advances in revealing significant effects of van der Waals wells on reaction dynamics, many people assume that van der Waals wells are inevitable in chemical reactions. Here we find that the weak long-range forces cause van der Waals saddles in the prototypical C(¹D)+D₂ complex-forming reaction that have very different dynamical effects from van der Waals wells at low collision energies. Accurate quantum dynamics calculations on our highly accurate ab initio potential energy surfaces with van der Waals saddles yield cross-sections in close agreement with crossed-beam experiments, whereas the same calculations on an earlier surface with van der Waals wells produce much smaller cross-sections at low energies. Further trajectory calculations reveal that the van der Waals saddle leads to a torsion then sideways insertion reaction mechanism, whereas the well suppresses reactivity. Quantum diffraction oscillations and sharp resonances are also predicted based on our ground- and excited-state potential energy surfaces.

It is commonly held that van der Waals wells are inevitable in chemical reactions. Here, the authors show that weak van der Waals forces in the entrance channel of a prototypical complex-forming reaction cause a van der Waals saddle instead, with different dynamical effects from a well at low collision energies.

Molecular collisions and reactive scattering in external fields: Are field-induced couplings important at short range?

We use accurate quantum scattering calculations to elucidate the role of short-range molecule-field interactions in atom-molecule inelastic collisions and abstraction chemical reactions at low temperatures. We consider two examples: elastic and inelastic scattering of NH(Σ3) molecules with Mg(S1) atoms in a magnetic field; reactive scattering LiF + H → Li + HF in an electric field. Our calculations suggest that, for non-reactive collision systems and abstraction chemical reactions, the molecule-field interactions cannot generally be neglected at short range because the atom-molecule potential passes through zero at short range. An important exception occurs for Zeeman transitions in atom-molecule collisions at magnetic fields ≲1000 G, for which the molecule-field couplings need only be included at large ρ outside the range of the atom-molecule interaction. Our results highlight the importance of an accurate description of ρ-dependent molecule-field interactions in quantum scattering calculations on molecular collisions and chemical reactions at low temperatures.

Quasiclassical trajectory study of the C(1D) + HD reaction

Isotopic branching ratios are investigated by detailed quasiclassical trajectory calculations on our recent singlet ground and excited potential energy surfaces.

Theoretical investigation of rotationally inelastic collisions of CH(X2Π) with molecular hydrogen

We report calculations of state-to-state cross sections for collision-induced rotational transitions of CH(X²Π) with molecular hydrogen. These calculations employed the diabatic matrix elements of the interaction potential determined by Dagdigian [J. Chem. Phys. 145, 114301 (2016)], which employed the multi-reference configuration-interaction method [MRCISD+Q(Davidson)]. Because of the presence of a deep well on the lower potential energy surface, the scattering calculations were carried out using the quantum statistical method of Manolopoulos and co-workers [Chem. Phys. Lett. 343, 356 (2001)]. The computed cross sections included contributions from direct scattering, as well as from the formation and decay of a collision complex. The magnitude of latter contribution was found to decrease significantly with increasing collision energy. Rotationally energy transfer rate constants were computed for this system since these are required for astrochemical modeling.

Scattering study of the Ne + NeH(+)(v0 = 0, j0 = 0) → NeH(+) + Ne reaction on an ab initio based analytical potential energy surface

Initial state selected dynamics of the Ne + NeH(+)(v0 = 0, j0 = 0) → NeH(+) + Ne reaction is investigated by quantum and statistical quantum mechanical (SQM) methods on the ground electronic state. The three-body ab initio energies on a set of suitably chosen grid points have been computed at CCSD(T)/aug-cc-PVQZ level and analytically fitted. The fitting of the diatomic potentials, computed at the same level of theory, is performed by spline interpolation. A collinear [NeHNe](+) structure lying 0.72 eV below the Ne + NeH(+) asymptote is found to be the most stable geometry for this system. Energies of low lying vibrational states have been computed for this stable complex. Reaction probabilities obtained from quantum calculations exhibit dense oscillatory structures, particularly in the low energy region and these get partially washed out in the integral cross section results. SQM predictions are devoid of oscillatory structures and remain close to 0.5 after the rise at the threshold thus giving a crude average description of the quantum probabilities. Statistical cross sections and rate constants are nevertheless in sufficiently good agreement with the quantum results to suggest an important role of a complex-forming dynamics for the title reaction.

State-to-State Dynamics of the Ne + HeH(+) (v = 0, j = 0) → NeH(+)(v', j') + He Reaction

The dynamics of the Ne + HeH(+)(v = 0, j = 0) → NeH(+)(v', j') + He reaction was analyzed in detail at the state-to-state level. A time-independent quantum mechanical (TIQM) method was applied to calculate rovibrational distributions and differential cross sections (DCSs), in comparison with quasi-classical trajectory and statistical quantum predictions. Possible changes in the dynamical mechanisms that define the process were also investigated as a function of the collision energy. At the lowest energy regime, the TIQM results produce a noticeably different cross section in comparison with previously reported time-dependent wave packet results. Although the statistical methods reproduce some dynamical features, especially as the energy increases, the marked preference for the forward scattering direction on the DCSs suggests that the reaction mainly follows a direct mechanism.

Complementarity between Quantum and Classical Mechanics in Chemical Modeling. The H + HeH+ → H2 + + He Reaction: A Rigourous Test for Reaction Dynamics Methods

In this work we present a dynamical study of the H + HeH+ → H2+ + He reaction in a collision energy range from 0.1 meV to 10 eV, suitable to be used in applicative models. The paper extends and complements a recent work [ Phys. Chem. Chem. Phys. 2014, 16, 11662] devoted to the characterization of the reactivity from the ultracold regime up to the three-body dissociation breakup. In particular, the accuracy of the quasi-classical trajectory method below the three-body dissociation threshold has been assessed by a detailed comparison with previous calculations performed with different reaction dynamics methods, whereas the reliability of the results in the high energy range has been checked by a direct comparison with the available experimental data. Integral cross sections for several HeH+ roto-vibrational states have been analyzed and used to understand the extent of quantum effects in the reaction dynamics. By using the quasi-classical trajectory method and quantum mechanical close coupling data, respectively, in the high and low collision energy ranges, we obtain highly accurate thermal rate costants until 15 000 K including all (178) the roto-vibrational bound and quasi-bound states of HeH+. The role of the collision-induced dissociation is also discussed and explicitly calculated for the ground roto-vibrational state of HeH+.

Quantum, Statistical, and Quasiclassical Trajectory Studies For the Ne + HeH(+) → NeH(+) + He Reaction on the Ground Electronic State

Real wave packet, statistical quantum, and quasiclassical trajectory methods were employed to study the dynamics of Ne + HeH(+)(v0,j0) → He + NeH(+) reaction on an ab initio potential energy surface [J. Phys. Chem. A 2013, 117, 13070-13078]. Quantum and statistical quantum calculations were performed within the centrifugal sudden (CS) approximation as well as including the Coriolis coupling (CC). Dense oscillatory structures of the quantum reaction probabilities and fair agreement between quantum and statistical cross sections suggest a complex forming mechanism for the reaction. No significant differences between cross sections obtained within the CS and CC approaches are observed. Quasiclassical trajectory results give an excellent average description of the quantum CC results. At low collision energies, there is a substantial decrease in reactivity for the reaction upon rovibrational excitation. Initial state selected rate constants for the title reaction are calculated between 20 and 1000 K, and the calculated value at 300 K agrees quite well with the available experimental result. Reaction cross sections and rate constants are also compared with those calculated via the Langevin capture model for exothermic reactions.

Collision time of a triatomic chemical reaction A + BC

The collision time is an important quantity of an elementary chemical reaction and describes the speed of the collision process in a collision reaction. In this study, we present a generalized method to calculate the collision time of a triatomic reaction in which the collision time is defined by the sum of the incoming time, the intermediate complex time, and the outgoing time. Two variables including the total distance Rtotal and Ravg, the average value of Rtotal over time, are used to compute the three components of the collision time. We compute three triatomic reactions including Ca + HCl → CaCl + H, O + HCl → OH + Cl/OCl + H, and O + HF → OH + F at different collision energies and initial diatomic vibrational levels using the quasi-classical trajectory method to confirm that the method could be reliable and reasonable. The time evolutions of Rtotal could efficiently classify the direct and indirect reactive mechanisms and reveal a distinct discrepancy of the two mechanisms. As the collision energy and initial diatomic vibrational level increase, the percentage of direct reaction trajectories increases. At the same time, the average and maximal values of collision time decrease. Comparing the maximal collision time and the reactive probability distributions of the products, it could be found that most reactive trajectories’ collision time is less than 2 ps. Moreover, the present calculations indicate that the method could be applicable to estimate the lifetime of the intermediate complex for the reaction systems with deep potential wells and the collision time of the reactions with a direct abstraction mechanism.

Wave packet and statistical quantum calculations for the He + NeH⁺ → HeH⁺ + Ne reaction on the ground electronic state

A real wave packet based time-dependent method and a statistical quantum method have been used to study the He + NeH(+) (v, j) reaction with the reactant in various ro-vibrational states, on a recently calculated ab initio ground state potential energy surface. Both the wave packet and statistical quantum calculations were carried out within the centrifugal sudden approximation as well as using the exact Hamiltonian. Quantum reaction probabilities exhibit dense oscillatory pattern for smaller total angular momentum values, which is a signature of resonances in a complex forming mechanism for the title reaction. Significant differences, found between exact and approximate quantum reaction cross sections, highlight the importance of inclusion of Coriolis coupling in the calculations. Statistical results are in fairly good agreement with the exact quantum results, for ground ro-vibrational states of the reactant. Vibrational excitation greatly enhances the reaction cross sections, whereas rotational excitation has relatively small effect on the reaction. The nature of the reaction cross section curves is dependent on the initial vibrational state of the reactant and is typical of a late barrier type potential energy profile.